diff options
| -rw-r--r-- | src/ChangeLog | 4 | ||||
| -rw-r--r-- | src/algebra/boolean.spad.pamphlet | 20 | ||||
| -rw-r--r-- | src/algebra/strap/BOOLEAN.lsp | 88 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 1132 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 208 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1322 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 7974 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 25635 |
8 files changed, 18195 insertions, 18188 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 249c4ed6..8e415f5f 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,7 @@ +2009-02-03 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/boolean.spad.pamphlet (Boolean): Tidy. + 2009-02-02 Gabriel Dos Reis <gdr@cs.tamu.edu> * algebra/domain.spad.pamphlet (FunctionDescriptor): New. diff --git a/src/algebra/boolean.spad.pamphlet b/src/algebra/boolean.spad.pamphlet index 75b5b325..b4ecb100 100644 --- a/src/algebra/boolean.spad.pamphlet +++ b/src/algebra/boolean.spad.pamphlet @@ -375,20 +375,18 @@ Boolean(): Join(OrderedFinite, Logic, PropositionalLogic, ConvertibleTo InputFor test: % -> % ++ test(b) returns b and is provided for compatibility with the new compiler. == add - nt: % -> % - test a == a - nt b == (b => false; true) + nt(a: %): % == NOT(a)$Lisp true == 'T pretend % false == NIL$Lisp sample() == true - not b == NOT(b)$Lisp + not b == nt b _~ b == (b => false; true) _and(a, b) == AND(a,b)$Lisp - _/_\(a, b) == (a => b; false) + _/_\(a, b) == AND(a,b)$Lisp _or(a, b) == OR(a,b)$Lisp - _\_/(a, b) == (a => true; b) + _\_/(a, b) == OR(a,b)$Lisp xor(a, b) == (a => nt b; b) nor(a, b) == (a => false; nt b) nand(a, b) == (a => nt b; true) @@ -409,12 +407,14 @@ Boolean(): Join(OrderedFinite, Logic, PropositionalLogic, ConvertibleTo InputFor true convert(x:%):InputForm == - x => convert("true"::Symbol) - convert("false"::Symbol) + convert + x => 'true + 'false coerce(x:%):OutputForm == - x => message "true" - message "false" + outputForm + x => 'true + 'false @ diff --git a/src/algebra/strap/BOOLEAN.lsp b/src/algebra/strap/BOOLEAN.lsp index 882c8a74..93546360 100644 --- a/src/algebra/strap/BOOLEAN.lsp +++ b/src/algebra/strap/BOOLEAN.lsp @@ -9,6 +9,8 @@ (DECLAIM (FTYPE (FUNCTION (|%Boolean| |%Shell|) |%Boolean|) |BOOLEAN;nt|)) +(PUT '|BOOLEAN;nt| '|SPADreplace| 'NOT) + (DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Boolean|) |BOOLEAN;true;$;3|)) (PUT '|BOOLEAN;true;$;3| '|SPADreplace| '(XLAM NIL 'T)) @@ -33,6 +35,8 @@ (DECLAIM (FTYPE (FUNCTION (|%Boolean| |%Boolean| |%Shell|) |%Boolean|) |BOOLEAN;/\\;3$;8|)) +(PUT '|BOOLEAN;/\\;3$;8| '|SPADreplace| 'AND) + (DECLAIM (FTYPE (FUNCTION (|%Boolean| |%Boolean| |%Shell|) |%Boolean|) |BOOLEAN;or;3$;9|)) @@ -41,6 +45,8 @@ (DECLAIM (FTYPE (FUNCTION (|%Boolean| |%Boolean| |%Shell|) |%Boolean|) |BOOLEAN;\\/;3$;10|)) +(PUT '|BOOLEAN;\\/;3$;10| '|SPADreplace| 'OR) + (DECLAIM (FTYPE (FUNCTION (|%Boolean| |%Boolean| |%Shell|) |%Boolean|) |BOOLEAN;xor;3$;11|)) @@ -87,7 +93,7 @@ (DEFUN |BOOLEAN;test;2$;1| (|a| $) (DECLARE (IGNORE $)) |a|) -(DEFUN |BOOLEAN;nt| (|b| $) (COND (|b| 'NIL) ('T 'T))) +(DEFUN |BOOLEAN;nt| (|a| $) (DECLARE (IGNORE $)) (NOT |a|)) (DEFUN |BOOLEAN;true;$;3| ($) (DECLARE (IGNORE $)) 'T) @@ -101,22 +107,26 @@ (DECLARE (IGNORE $)) (AND |a| |b|)) -(DEFUN |BOOLEAN;/\\;3$;8| (|a| |b| $) (COND (|a| |b|) ('T 'NIL))) +(DEFUN |BOOLEAN;/\\;3$;8| (|a| |b| $) + (DECLARE (IGNORE $)) + (AND |a| |b|)) (DEFUN |BOOLEAN;or;3$;9| (|a| |b| $) (DECLARE (IGNORE $)) (OR |a| |b|)) -(DEFUN |BOOLEAN;\\/;3$;10| (|a| |b| $) (COND (|a| 'T) ('T |b|))) +(DEFUN |BOOLEAN;\\/;3$;10| (|a| |b| $) + (DECLARE (IGNORE $)) + (OR |a| |b|)) (DEFUN |BOOLEAN;xor;3$;11| (|a| |b| $) - (COND (|a| (|BOOLEAN;nt| |b| $)) ('T |b|))) + (COND (|a| (NOT |b|)) ('T |b|))) (DEFUN |BOOLEAN;nor;3$;12| (|a| |b| $) - (COND (|a| 'NIL) ('T (|BOOLEAN;nt| |b| $)))) + (COND (|a| 'NIL) ('T (NOT |b|)))) (DEFUN |BOOLEAN;nand;3$;13| (|a| |b| $) - (COND (|a| (|BOOLEAN;nt| |b| $)) ('T 'T))) + (COND (|a| (NOT |b|)) ('T 'T))) (DEFUN |BOOLEAN;=;3$;14| (|a| |b| $) (DECLARE (IGNORE $)) @@ -128,8 +138,7 @@ (DECLARE (IGNORE $)) (EQ |a| |b|)) -(DEFUN |BOOLEAN;<;3$;17| (|a| |b| $) - (COND (|b| (|BOOLEAN;nt| |a| $)) ('T 'NIL))) +(DEFUN |BOOLEAN;<;3$;17| (|a| |b| $) (COND (|b| (NOT |a|)) ('T 'NIL))) (DEFUN |BOOLEAN;size;Nni;18| ($) (DECLARE (IGNORE $)) 2) @@ -142,17 +151,10 @@ (COND ((SPADCALL (|random|) (|getShellEntry| $ 26)) 'NIL) ('T 'T))) (DEFUN |BOOLEAN;convert;$If;22| (|x| $) - (COND - (|x| (SPADCALL (SPADCALL "true" (|getShellEntry| $ 33)) - (|getShellEntry| $ 35))) - ('T - (SPADCALL (SPADCALL "false" (|getShellEntry| $ 33)) - (|getShellEntry| $ 35))))) + (SPADCALL (COND (|x| '|true|) ('T '|false|)) (|getShellEntry| $ 33))) (DEFUN |BOOLEAN;coerce;$Of;23| (|x| $) - (COND - (|x| (SPADCALL "true" (|getShellEntry| $ 38))) - ('T (SPADCALL "false" (|getShellEntry| $ 38))))) + (SPADCALL (COND (|x| '|true|) ('T '|false|)) (|getShellEntry| $ 36))) (DEFUN |Boolean| () (PROG () @@ -176,7 +178,7 @@ (RETURN (PROGN (LETT |dv$| '(|Boolean|) . #0=(|Boolean|)) - (LETT $ (|newShell| 41) . #0#) + (LETT $ (|newShell| 40) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -198,16 +200,16 @@ |BOOLEAN;<;3$;17| (|NonNegativeInteger|) |BOOLEAN;size;Nni;18| (|Integer|) (0 . |even?|) (|PositiveInteger|) |BOOLEAN;index;Pi$;19| - |BOOLEAN;lookup;$Pi;20| |BOOLEAN;random;$;21| (|String|) - (|Symbol|) (5 . |coerce|) (|InputForm|) (10 . |convert|) - |BOOLEAN;convert;$If;22| (|OutputForm|) (15 . |message|) - |BOOLEAN;coerce;$Of;23| (|SingleInteger|)) - '#(~= 20 ~ 26 |xor| 31 |true| 37 |test| 41 |size| 46 |random| - 50 |or| 54 |not| 60 |nor| 65 |nand| 71 |min| 77 |max| 87 - |lookup| 97 |latex| 102 |index| 107 |implies| 112 |hash| - 118 |false| 123 |equiv| 127 |convert| 133 |coerce| 138 - |and| 143 |\\/| 149 >= 155 > 161 = 167 <= 173 < 179 |/\\| - 185) + |BOOLEAN;lookup;$Pi;20| |BOOLEAN;random;$;21| (|Symbol|) + (|InputForm|) (5 . |convert|) |BOOLEAN;convert;$If;22| + (|OutputForm|) (10 . |outputForm|) |BOOLEAN;coerce;$Of;23| + (|String|) (|SingleInteger|)) + '#(~= 15 ~ 21 |xor| 26 |true| 32 |test| 36 |size| 41 |random| + 45 |or| 49 |not| 55 |nor| 60 |nand| 66 |min| 72 |max| 82 + |lookup| 92 |latex| 97 |index| 102 |implies| 107 |hash| + 113 |false| 118 |equiv| 122 |convert| 128 |coerce| 133 + |and| 138 |\\/| 144 >= 150 > 156 = 162 <= 168 < 174 |/\\| + 180) 'NIL (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0 0)) (CONS '#(NIL |OrderedSet&| NIL NIL |Logic&| @@ -215,21 +217,21 @@ (CONS '#((|OrderedFinite|) (|OrderedSet|) (|PropositionalLogic|) (|Finite|) (|Logic|) (|SetCategory|) - (|ConvertibleTo| 34) (|BasicType|) - (|CoercibleTo| 37)) - (|makeByteWordVec2| 40 - '(1 25 18 0 26 1 32 0 31 33 1 34 0 32 - 35 1 37 0 31 38 2 0 18 0 0 1 1 0 0 0 - 10 2 0 0 0 0 15 0 0 0 7 1 0 0 0 6 0 0 - 23 24 0 0 0 30 2 0 0 0 0 13 1 0 0 0 9 - 2 0 0 0 0 16 2 0 0 0 0 17 0 0 0 1 2 0 - 0 0 0 1 0 0 0 1 2 0 0 0 0 1 1 0 27 0 - 29 1 0 31 0 1 1 0 0 27 28 2 0 0 0 0 - 20 1 0 40 0 1 0 0 0 8 2 0 0 0 0 21 1 - 0 34 0 36 1 0 37 0 39 2 0 0 0 0 11 2 - 0 0 0 0 14 2 0 18 0 0 1 2 0 18 0 0 1 - 2 0 18 0 0 19 2 0 18 0 0 1 2 0 18 0 0 - 22 2 0 0 0 0 12))))) + (|ConvertibleTo| 32) (|BasicType|) + (|CoercibleTo| 35)) + (|makeByteWordVec2| 39 + '(1 25 18 0 26 1 32 0 31 33 1 35 0 31 + 36 2 0 18 0 0 1 1 0 0 0 10 2 0 0 0 0 + 15 0 0 0 7 1 0 0 0 6 0 0 23 24 0 0 0 + 30 2 0 0 0 0 13 1 0 0 0 9 2 0 0 0 0 + 16 2 0 0 0 0 17 0 0 0 1 2 0 0 0 0 1 0 + 0 0 1 2 0 0 0 0 1 1 0 27 0 29 1 0 38 + 0 1 1 0 0 27 28 2 0 0 0 0 20 1 0 39 0 + 1 0 0 0 8 2 0 0 0 0 21 1 0 32 0 34 1 + 0 35 0 37 2 0 0 0 0 11 2 0 0 0 0 14 2 + 0 18 0 0 1 2 0 18 0 0 1 2 0 18 0 0 19 + 2 0 18 0 0 1 2 0 18 0 0 22 2 0 0 0 0 + 12))))) '|lookupComplete|)) (MAKEPROP '|Boolean| 'NILADIC T) diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index d717bbcd..958715a9 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2281924 . 3442535947) +(2282336 . 3442698064) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL NIL (-19 S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4399 . T) (-4397 . T) (-4396 . T) ((-4404 "*") . T) (-4395 . T) (-4400 . T) (-4394 . T)) +((-4400 . T) (-4398 . T) (-4397 . T) ((-4405 "*") . T) (-4396 . T) (-4401 . T) (-4395 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,14 +56,14 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -3197) +(-32 R -3196) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4402))) +((|HasAttribute| |#1| (QUOTE -4403))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,17 +82,17 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -3197 UP UPUP -3518) +(-40 -3196 UP UPUP -2685) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4395 |has| (-406 |#2|) (-362)) (-4400 |has| (-406 |#2|) (-362)) (-4394 |has| (-406 |#2|) (-362)) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 |has| (-406 |#2|) (-362)) (-4401 |has| (-406 |#2|) (-362)) (-4395 |has| (-406 |#2|) (-362)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-4037 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-4037 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-4037 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -635) (QUOTE (-562)))) (-4037 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) -(-41 R -3197) +(-41 R -3196) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-306)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4399 |has| |#1| (-554)) (-4397 . T) (-4396 . T)) +((-4400 |has| |#1| (-554)) (-4398 . T) (-4397 . T)) ((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) -((-4402 . T) (-4403 . T)) -((-4037 (-12 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-845))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2694) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2694) (|devaluate| |#2|))))))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-845))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-845))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2694) (|devaluate| |#2|))))))) +((-4403 . T) (-4404 . T)) +((-4037 (-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-845))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|))))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-845))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-845))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-362)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| $ (QUOTE (-1044))) (|HasCategory| $ (LIST (QUOTE -1033) (QUOTE (-562))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4399 . T)) +((-4400 . T)) NIL (-51 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3197) +(-54 |Base| R -3196) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -158,7 +158,7 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) NIL (-58 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) @@ -166,65 +166,65 @@ NIL NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) -(-61 -3254) +(-61 -3253) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -3254) +(-62 -3253) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -3254) +(-63 -3253) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -3254) +(-64 -3253) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -3254) +(-65 -3253) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -3254) +(-66 -3253) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -3254) +(-67 -3253) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -3254) +(-68 -3253) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -3254) +(-69 -3253) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -3254) +(-70 -3253) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -3254) +(-71 -3253) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -3254) +(-72 -3253) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -3254) +(-73 -3253) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -3254) +(-74 -3253) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -3254) +(-77 -3253) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -3254) +(-78 -3253) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -3254) +(-79 -3253) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -3254) +(-80 -3253) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -3254) +(-81 -3253) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -3254) +(-82 -3253) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3254) +(-83 -3253) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3254) +(-84 -3253) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3254) +(-85 -3253) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3254) +(-86 -3253) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -3254) +(-87 -3253) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -3254) +(-88 -3253) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -3254) +(-89 -3253) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -294,7 +294,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-362)))) (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) @@ -318,15 +318,15 @@ NIL NIL (-97) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4402 . T)) +((-4403 . T)) NIL (-98) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,{}b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4402 . T) ((-4404 "*") . T) (-4403 . T) (-4399 . T) (-4397 . T) (-4396 . T) (-4395 . T) (-4400 . T) (-4394 . T) (-4393 . T) (-4392 . T) (-4391 . T) (-4390 . T) (-4398 . T) (-4401 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4389 . T)) +((-4403 . T) ((-4405 "*") . T) (-4404 . T) (-4400 . T) (-4398 . T) (-4397 . T) (-4396 . T) (-4401 . T) (-4395 . T) (-4394 . T) (-4393 . T) (-4392 . T) (-4391 . T) (-4399 . T) (-4402 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4390 . T)) NIL (-99 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,{}n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f,{} g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-4399 . T)) +((-4400 . T)) NIL (-100 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a,{} [b1,{}...,{}bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,{}...,{}bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a,{} b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{\\spad{pi}} is balanced with respect to \\spad{b}."))) @@ -342,15 +342,15 @@ NIL NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4404 "*")))) +((|HasAttribute| |#1| (QUOTE (-4405 "*")))) (-105) ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4402 . T)) +((-4403 . T)) NIL (-106 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -358,11 +358,11 @@ NIL NIL (-107 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4403 . T)) +((-4404 . T)) NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| (-562) (QUOTE (-904))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-562) (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-146))) (|HasCategory| (-562) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-562) (QUOTE (-1017))) (|HasCategory| (-562) (QUOTE (-815))) (-4037 (|HasCategory| (-562) (QUOTE (-815))) (|HasCategory| (-562) (QUOTE (-845)))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-1143))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-562) (QUOTE (-232))) (|HasCategory| (-562) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-562) (LIST (QUOTE -513) (QUOTE (-1168)) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -308) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -285) (QUOTE (-562)) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-306))) (|HasCategory| (-562) (QUOTE (-544))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-562) (LIST (QUOTE -635) (QUOTE (-562)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (|HasCategory| (-562) (QUOTE (-144))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) @@ -370,11 +370,11 @@ NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1092))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-112) (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-112) (QUOTE (-1092))) (|HasCategory| (-112) (LIST (QUOTE -609) (QUOTE (-857))))) (-111 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) @@ -388,22 +388,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -3197 UP) +(-115 -3196 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL (-116 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| (-116 |#1|) (QUOTE (-904))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-116 |#1|) (QUOTE (-1017))) (|HasCategory| (-116 |#1|) (QUOTE (-815))) (-4037 (|HasCategory| (-116 |#1|) (QUOTE (-815))) (|HasCategory| (-116 |#1|) (QUOTE (-845)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-116 |#1|) (QUOTE (-1143))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -513) (QUOTE (-1168)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-306))) (|HasCategory| (-116 |#1|) (QUOTE (-544))) (|HasCategory| (-116 |#1|) (QUOTE (-845))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-904)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4403))) +((|HasAttribute| |#1| (QUOTE -4404))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -414,7 +414,7 @@ NIL NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) @@ -422,7 +422,7 @@ NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,19 +430,19 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#buf} returns the number of active elements in the buffer.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| (-129) (QUOTE (-845))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1092))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-4037 (-12 (|HasCategory| (-129) (QUOTE (-1092))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-129) (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| (-129) (QUOTE (-845))) (|HasCategory| (-129) (QUOTE (-1092)))) (|HasCategory| (-129) (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-129) (QUOTE (-1092))) (|HasCategory| (-129) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-129) (QUOTE (-1092))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) @@ -462,13 +462,13 @@ NIL NIL (-133) ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4404 "*") . T)) +(((-4405 "*") . T)) NIL -(-134 |minix| -2241 S T$) +(-134 |minix| -2240 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-135 |minix| -2241 R) +(-135 |minix| -2240 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -490,7 +490,7 @@ NIL NIL (-140) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) -((-4402 . T) (-4392 . T) (-4403 . T)) +((-4403 . T) (-4393 . T) (-4404 . T)) ((-4037 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-141 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) @@ -506,7 +506,7 @@ NIL NIL (-144) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4399 . T)) +((-4400 . T)) NIL (-145 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,{}r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -514,9 +514,9 @@ NIL NIL (-146) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4399 . T)) +((-4400 . T)) NIL -(-147 -3197 UP UPUP) +(-147 -3196 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,{}y),{} p(x,{}y))} returns \\spad{[g(z,{}t),{} q(z,{}t),{} c1(z),{} c2(z),{} n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,{}y) = g(z,{}t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z,{} t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,{}y),{} f(x),{} g(x))} returns \\spad{p(f(x),{} y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p,{} q)} returns an integer a such that a is neither a pole of \\spad{p(x,{}y)} nor a branch point of \\spad{q(x,{}y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g,{} n)} returns \\spad{[m,{} c,{} P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x,{} y))} returns \\spad{[c(x),{} n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,{}y))} returns \\spad{[c(x),{} q(x,{}z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x,{} z) = 0}."))) NIL NIL @@ -527,14 +527,14 @@ NIL (-149 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasAttribute| |#1| (QUOTE -4402))) +((|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasAttribute| |#1| (QUOTE -4403))) (-150 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-151 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,{}[i1,{}i2,{}...,{}iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,{}[i1,{}i2,{}...,{}iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((-4397 . T) (-4396 . T) (-4399 . T)) +((-4398 . T) (-4397 . T) (-4400 . T)) NIL (-152) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,{}xMin,{}xMax,{}yMin,{}yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,{}frac,{}sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,{}frac,{}sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -556,7 +556,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-157 R -3197) +(-157 R -3196) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -587,10 +587,10 @@ NIL (-164 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) NIL -((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-997))) (|HasCategory| |#2| (QUOTE (-1192))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4398)) (|HasAttribute| |#2| (QUOTE -4401)) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-845)))) +((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-997))) (|HasCategory| |#2| (QUOTE (-1192))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4399)) (|HasAttribute| |#2| (QUOTE -4402)) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-845)))) (-165 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) -((-4395 -4037 (|has| |#1| (-554)) (-12 (|has| |#1| (-306)) (|has| |#1| (-904)))) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) (-4398 |has| |#1| (-6 -4398)) (-4401 |has| |#1| (-6 -4401)) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 -4037 (|has| |#1| (-554)) (-12 (|has| |#1| (-306)) (|has| |#1| (-904)))) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4399 |has| |#1| (-6 -4399)) (-4402 |has| |#1| (-6 -4402)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-166 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -602,8 +602,8 @@ NIL NIL (-168 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4395 -4037 (|has| |#1| (-554)) (-12 (|has| |#1| (-306)) (|has| |#1| (-904)))) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) (-4398 |has| |#1| (-6 -4398)) (-4401 |has| |#1| (-6 -4401)) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| 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T) (-4397 . T) (-4398 . T) (-4400 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| 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(|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-904))))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| |#1| (QUOTE (-997))) (|HasCategory| |#1| (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-554)))) (-4037 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1053))) (-12 (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-362)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasAttribute| |#1| (QUOTE -4399)) (|HasAttribute| |#1| (QUOTE -4402)) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168))))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-348))))) (-169 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -614,7 +614,7 @@ NIL NIL (-171) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-172) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -622,7 +622,7 @@ NIL NIL (-173 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialQuotients(x) = [b0,{}b1,{}b2,{}b3,{}...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialDenominators(x) = [b1,{}b2,{}b3,{}...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialNumerators(x) = [a1,{}a2,{}a3,{}...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,{}b)} constructs a continued fraction in the following way: if \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,{}a,{}b)} constructs a continued fraction in the following way: if \\spad{a = [a1,{}a2,{}...]} and \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-4404 "*") . T) (-4395 . T) (-4400 . T) (-4394 . T) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") . T) (-4396 . T) (-4401 . T) (-4395 . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-174) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|Binding|) $) "\\spad{push(c,{}b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -661,11 +661,11 @@ NIL NIL NIL (-183 S) -((|constructor| (NIL "This category declares basic operations on all constructors.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(i+1) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) +((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(i+1) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) NIL NIL (-184) -((|constructor| (NIL "This category declares basic operations on all constructors.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(i+1) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) +((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(i+1) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) NIL NIL (-185) @@ -676,7 +676,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Symbol|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-187 R -3197) +(-187 R -3196) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -784,23 +784,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-214 -3197 UP UPUP R) +(-214 -3196 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f,{} ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-215 -3197 FP) +(-215 -3196 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-216) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| (-562) (QUOTE (-904))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-562) (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-146))) (|HasCategory| (-562) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-562) (QUOTE (-1017))) (|HasCategory| (-562) (QUOTE (-815))) (-4037 (|HasCategory| (-562) (QUOTE (-815))) (|HasCategory| (-562) (QUOTE (-845)))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-1143))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-562) (QUOTE (-232))) (|HasCategory| (-562) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-562) (LIST (QUOTE -513) (QUOTE (-1168)) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -308) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -285) (QUOTE (-562)) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-306))) (|HasCategory| (-562) (QUOTE (-544))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-562) (LIST (QUOTE -635) (QUOTE (-562)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (|HasCategory| (-562) (QUOTE (-144))))) (-217) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-218 R -3197) +(-218 R -3196) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -814,19 +814,19 @@ NIL NIL (-221 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-222 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) -((-4399 . T)) +((-4400 . T)) NIL -(-223 R -3197) +(-223 R -3196) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} x,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-224) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-1406 . T) (-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-1406 . T) (-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-225) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -834,15 +834,15 @@ NIL NIL (-226 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) -((-4402 . T) (-4403 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-554))) (|HasAttribute| |#1| (QUOTE (-4404 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) +((-4403 . T) (-4404 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-554))) (|HasAttribute| |#1| (QUOTE (-4405 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-227 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-228 S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) -((-4403 . T)) +((-4404 . T)) NIL (-229 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -850,7 +850,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232)))) (-230 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4399 . T)) +((-4400 . T)) NIL (-231 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -858,36 +858,36 @@ NIL NIL (-232) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4399 . T)) +((-4400 . T)) NIL (-233 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -4402))) +((|HasAttribute| |#1| (QUOTE -4403))) (-234 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4403 . T)) +((-4404 . T)) NIL (-235) ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-236 S -2241 R) +(-236 S -2240 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-788))) (|HasCategory| |#3| (QUOTE (-843))) (|HasAttribute| |#3| (QUOTE -4399)) (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-721))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1044))) (|HasCategory| |#3| (QUOTE (-1092)))) -(-237 -2241 R) +((|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-788))) (|HasCategory| |#3| (QUOTE (-843))) (|HasAttribute| |#3| (QUOTE -4400)) (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-721))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1044))) (|HasCategory| |#3| (QUOTE (-1092)))) +(-237 -2240 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4396 |has| |#2| (-1044)) (-4397 |has| |#2| (-1044)) (-4399 |has| |#2| (-6 -4399)) ((-4404 "*") |has| |#2| (-171)) (-4402 . T)) +((-4397 |has| |#2| (-1044)) (-4398 |has| |#2| (-1044)) (-4400 |has| |#2| (-6 -4400)) ((-4405 "*") |has| |#2| (-171)) (-4403 . T)) NIL -(-238 -2241 A B) +(-238 -2240 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-239 -2241 R) +(-239 -2240 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) -((-4396 |has| |#2| (-1044)) (-4397 |has| |#2| (-1044)) (-4399 |has| |#2| (-6 -4399)) ((-4404 "*") |has| |#2| (-171)) (-4402 . T)) -((-4037 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-721))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-843))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (LIST 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -898,7 +898,7 @@ NIL NIL (-242) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4395 . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-243 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,{}v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,{}v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) @@ -906,7 +906,7 @@ NIL NIL (-244 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-245 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) @@ -914,8 +914,8 @@ NIL NIL (-246 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE -895) (QUOTE (-1168))))) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1044)))) (-4037 (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1044)))) (|HasCategory| |#3| (QUOTE (-721))) (-12 (|HasCategory| |#3| (QUOTE (-1044))) (|HasCategory| |#3| (LIST (QUOTE -635) (QUOTE (-562))))) (-12 (|HasCategory| |#3| (QUOTE (-1044))) (|HasCategory| |#3| (LIST (QUOTE -895) (QUOTE (-1168)))))) (-12 (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562))))) (-4037 (|HasCategory| |#3| (QUOTE (-1044))) (-12 (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#3| (QUOTE (-1092)))) (-4037 (|HasAttribute| |#3| (QUOTE -4400)) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1044)))) (-12 (|HasCategory| |#3| (QUOTE (-1044))) (|HasCategory| |#3| (LIST (QUOTE -635) (QUOTE (-562))))) (-12 (|HasCategory| |#3| (QUOTE (-1044))) (|HasCategory| |#3| (LIST (QUOTE -895) (QUOTE (-1168)))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (-251 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-232)))) (-252 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) NIL (-253 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) NIL (-254) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -982,8 +982,8 @@ NIL NIL (-263 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#3| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#3| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4400)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#3| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#3| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) (-264 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1028,11 +1028,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-275 R -3197) +(-275 R -3196) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-276 R -3197) +(-276 R -3196) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1054,7 +1054,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092)))) (-281 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4403 . T)) +((-4404 . T)) NIL (-282 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1075,18 +1075,18 @@ NIL (-286 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4403))) +((|HasAttribute| |#1| (QUOTE -4404))) (-287 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-288 S R |Mod| -2925 -1610 |exactQuo|) +(-288 S R |Mod| -3834 -4103 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-289) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4395 . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-290) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1102,21 +1102,21 @@ NIL NIL (-293 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4399 -4037 (|has| |#1| (-1044)) (|has| |#1| (-472))) (-4396 |has| |#1| (-1044)) (-4397 |has| |#1| (-1044))) +((-4400 -4037 (|has| |#1| (-1044)) (|has| |#1| (-472))) (-4397 |has| |#1| (-1044)) (-4398 |has| |#1| (-1044))) ((|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (QUOTE (-721)))) (|HasCategory| |#1| (QUOTE (-472))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-1092)))) (-4037 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1104)))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-301))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-472)))) (-4037 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-721)))) (-4037 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (QUOTE (-1044)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-171)))) (-294 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) -((-4402 . T) (-4403 . T)) -((-12 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2694) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857))))) +((-4403 . T) (-4404 . T)) +((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857))))) (-295) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-296 -3197 S) +(-296 -3196 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-297 E -3197) +(-297 E -3196) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) NIL NIL @@ -1154,7 +1154,7 @@ NIL NIL (-306) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-307 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1164,7 +1164,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-309 -3197) +(-309 -3196) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,{}s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -1178,7 +1178,7 @@ NIL NIL (-312 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-904))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-1017))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-815))) (-4037 (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-815))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-845)))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-1143))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-232))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -513) (QUOTE (-1168)) (LIST (QUOTE -1242) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -308) (LIST (QUOTE -1242) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (LIST (QUOTE -285) (LIST (QUOTE -1242) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1242) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-306))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-544))) (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-845))) (-12 (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-904))) (|HasCategory| $ (QUOTE (-144)))) (-4037 (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (-12 (|HasCategory| (-1242 |#1| |#2| |#3| |#4|) (QUOTE (-904))) (|HasCategory| $ (QUOTE (-144)))))) (-313 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) @@ -1190,9 +1190,9 @@ NIL NIL (-315 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4399 -4037 (-2246 (|has| |#1| (-1044)) (|has| |#1| (-635 (-562)))) (-12 (|has| |#1| (-554)) (-4037 (-2246 (|has| |#1| (-1044)) (|has| |#1| (-635 (-562)))) (|has| |#1| (-1044)) (|has| |#1| (-472)))) (|has| |#1| (-1044)) (|has| |#1| (-472))) (-4397 |has| |#1| (-171)) (-4396 |has| |#1| (-171)) ((-4404 "*") |has| |#1| (-554)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-554)) (-4394 |has| |#1| (-554))) +((-4400 -4037 (-2245 (|has| |#1| (-1044)) (|has| |#1| (-635 (-562)))) (-12 (|has| |#1| (-554)) (-4037 (-2245 (|has| |#1| (-1044)) (|has| |#1| (-635 (-562)))) (|has| |#1| (-1044)) (|has| |#1| (-472)))) (|has| |#1| (-1044)) (|has| |#1| (-472))) (-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) ((-4405 "*") |has| |#1| (-554)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-554)) (-4395 |has| |#1| (-554))) ((-4037 (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (QUOTE (-1104)))) (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-1044)))) (-12 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554)))) (-4037 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-1104)))) (-4037 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))))) (-4037 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-1104)))) (-4037 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))))) (-4037 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1104))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| $ (QUOTE (-1044))) (|HasCategory| $ (LIST (QUOTE -1033) (QUOTE (-562))))) -(-316 R -3197) +(-316 R -3196) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1202,8 +1202,8 @@ NIL NIL (-318 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) (-4396 . T) (-4397 . T) (-4399 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-562)) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasSignature| |#1| (LIST (QUOTE -4054) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -2667) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1402) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|))))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-562)) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasSignature| |#1| (LIST (QUOTE -4053) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -3081) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1401) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|))))))) (-319 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1214,7 +1214,7 @@ NIL NIL (-321 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) ((|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-787)))) (-322 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1230,19 +1230,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171)))) (-325 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-326 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-327 S -3197) +(-327 S -3196) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-367)))) -(-328 -3197) +(-328 -3196) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-329) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,{}contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,{}e,{}f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,{}e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,{}c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,{}c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,{}n,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) @@ -1260,15 +1260,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-333 S -3197 UP UPUP R) +(-333 S -3196 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-334 -3197 UP UPUP R) +(-334 -3196 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-335 -3197 UP UPUP R) +(-335 -3196 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1282,31 +1282,31 @@ NIL NIL (-338 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-378)))) (|HasCategory| $ (QUOTE (-1044))) (|HasCategory| $ (LIST (QUOTE -1033) (QUOTE (-562))))) (-339 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-340 S -3197 UP UPUP) +(-340 S -3196 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-362)))) -(-341 -3197 UP UPUP) +(-341 -3196 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4395 |has| (-406 |#2|) (-362)) (-4400 |has| (-406 |#2|) (-362)) (-4394 |has| (-406 |#2|) (-362)) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 |has| (-406 |#2|) (-362)) (-4401 |has| (-406 |#2|) (-362)) (-4395 |has| (-406 |#2|) (-362)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-342 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((-4037 (|HasCategory| (-905 |#1|) (QUOTE (-144))) (|HasCategory| (-905 |#1|) (QUOTE (-367)))) (|HasCategory| (-905 |#1|) (QUOTE (-146))) (|HasCategory| (-905 |#1|) (QUOTE (-367))) (|HasCategory| (-905 |#1|) (QUOTE (-144)))) (-343 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-344 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-345 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) @@ -1322,33 +1322,33 @@ NIL NIL (-348) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL -(-349 R UP -3197) +(-349 R UP -3196) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-350 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((-4037 (|HasCategory| (-905 |#1|) (QUOTE (-144))) (|HasCategory| (-905 |#1|) (QUOTE (-367)))) (|HasCategory| (-905 |#1|) (QUOTE (-146))) (|HasCategory| (-905 |#1|) (QUOTE (-367))) (|HasCategory| (-905 |#1|) (QUOTE (-144)))) (-351 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-352 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-353 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((-4037 (|HasCategory| (-905 |#1|) (QUOTE (-144))) (|HasCategory| (-905 |#1|) (QUOTE (-367)))) (|HasCategory| (-905 |#1|) (QUOTE (-146))) (|HasCategory| (-905 |#1|) (QUOTE (-367))) (|HasCategory| (-905 |#1|) (QUOTE (-144)))) (-354 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) -(-355 -3197 GF) +(-355 -3196 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1356,13 +1356,13 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-357 -3197 FP FPP) +(-357 -3196 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-358 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-359 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) @@ -1370,7 +1370,7 @@ NIL NIL (-360 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4399 . T)) +((-4400 . T)) NIL (-361 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1378,7 +1378,7 @@ NIL NIL (-362) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-363 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1394,7 +1394,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-554)))) (-366 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4399 |has| |#1| (-554)) (-4397 . T) (-4396 . T)) +((-4400 |has| |#1| (-554)) (-4398 . T) (-4397 . T)) NIL (-367) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1406,7 +1406,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-362)))) (-369 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) NIL (-370 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1415,14 +1415,14 @@ NIL (-371 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4403)) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092)))) +((|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092)))) (-372 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4402 . T)) +((-4403 . T)) NIL (-373 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4397 . T) (-4396 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4398 . T) (-4397 . T)) NIL (-374 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1434,7 +1434,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562))))) (-376 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) -((-4399 . T)) +((-4400 . T)) NIL (-377 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1442,7 +1442,7 @@ NIL NIL (-378) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4385 . T) (-4393 . T) (-1406 . T) (-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4386 . T) (-4394 . T) (-1406 . T) (-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-379 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1450,11 +1450,11 @@ NIL NIL (-380 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) ((|HasCategory| |#1| (QUOTE (-171)))) (-381 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) NIL (-382) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) @@ -1466,7 +1466,7 @@ NIL NIL (-384 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) ((|HasCategory| |#1| (QUOTE (-171)))) (-385 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1474,7 +1474,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-845)))) (-386) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-387) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1486,13 +1486,13 @@ NIL NIL (-389 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) NIL (-390) ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-391 -3197 UP UPUP R) +(-391 -3196 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL @@ -1516,11 +1516,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) NIL NIL -(-397 -3254 |returnType| -3433 |symbols|) +(-397 -3253 |returnType| -3433 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-398 -3197 UP) +(-398 -3196 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1534,15 +1534,15 @@ NIL NIL (-401) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-402 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4385)) (|HasAttribute| |#1| (QUOTE -4393))) +((|HasAttribute| |#1| (QUOTE -4386)) (|HasAttribute| |#1| (QUOTE -4394))) (-403) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-1406 . T) (-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-1406 . T) (-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-404 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1554,15 +1554,15 @@ NIL NIL (-406 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4389 -12 (|has| |#1| (-6 -4400)) (|has| |#1| (-451)) (|has| |#1| (-6 -4389))) (-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-815))) (-4037 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#1| (QUOTE (-845)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823))))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-544))) (-12 (|HasAttribute| |#1| (QUOTE -4400)) (|HasAttribute| |#1| (QUOTE -4389)) (|HasCategory| |#1| (QUOTE (-451)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) +((-4390 -12 (|has| |#1| (-6 -4401)) (|has| |#1| (-451)) (|has| |#1| (-6 -4390))) (-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-815))) (-4037 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#1| (QUOTE (-845)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823))))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-544))) (-12 (|HasAttribute| |#1| (QUOTE -4401)) (|HasAttribute| |#1| (QUOTE -4390)) (|HasCategory| |#1| (QUOTE (-451)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) (-407 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-408 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) NIL (-409 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-412 R -3197 UP A) +(-412 R -3196 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}."))) -((-4399 . T)) +((-4400 . T)) NIL -(-413 R -3197 UP A |ibasis|) +(-413 R -3196 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,{}...,{}fn])} = the module generated by \\spad{(f1,{}...,{}fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1033) (|devaluate| |#2|)))) @@ -1594,11 +1594,11 @@ NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-416 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4399 |has| |#1| (-554)) (-4397 . T) (-4396 . T)) +((-4400 |has| |#1| (-554)) (-4398 . T) (-4397 . T)) NIL (-417 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-1211))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-1211)))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-451)))) (-418 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) @@ -1626,17 +1626,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-367)))) (-424 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4402 . T) (-4392 . T) (-4403 . T)) +((-4403 . T) (-4393 . T) (-4404 . T)) NIL -(-425 R -3197) +(-425 R -3196) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-426 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) -((-4389 -12 (|has| |#1| (-6 -4389)) (|has| |#2| (-6 -4389))) (-4396 . T) (-4397 . T) (-4399 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4389)) (|HasAttribute| |#2| (QUOTE -4389)))) -(-427 R -3197) +((-4390 -12 (|has| |#1| (-6 -4390)) (|has| |#2| (-6 -4390))) (-4397 . T) (-4398 . T) (-4400 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4390)) (|HasAttribute| |#2| (QUOTE -4390)))) +(-427 R -3196) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL @@ -1646,17 +1646,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-472))) (|HasCategory| |#2| (QUOTE (-1104))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535))))) (-429 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4399 -4037 (|has| |#1| (-1044)) (|has| |#1| (-472))) (-4397 |has| |#1| (-171)) (-4396 |has| |#1| (-171)) ((-4404 "*") |has| |#1| (-554)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-554)) (-4394 |has| |#1| (-554))) +((-4400 -4037 (|has| |#1| (-1044)) (|has| |#1| (-472))) (-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) ((-4405 "*") |has| |#1| (-554)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-554)) (-4395 |has| |#1| (-554))) NIL -(-430 R -3197) +(-430 R -3196) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,{}y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,{}y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,{}y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,{}y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,{}y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,{}y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,{}x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-431 R -3197) +(-431 R -3196) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-432 R -3197) +(-432 R -3196) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,{}k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1664,7 +1664,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-434 R -3197 UP) +(-434 R -3196 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-48))))) @@ -1696,7 +1696,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-442 R UP -3197) +(-442 R UP -3196) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1734,16 +1734,16 @@ NIL NIL (-451) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-452 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,{}b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,{}b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,{}ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,{}v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4399 |has| (-406 (-947 |#1|)) (-554)) (-4397 . T) (-4396 . T)) +((-4400 |has| (-406 (-947 |#1|)) (-554)) (-4398 . T) (-4397 . T)) ((|HasCategory| (-406 (-947 |#1|)) (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| (-406 (-947 |#1|)) (QUOTE (-554)))) (-453 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4404 "*") |has| |#2| (-171)) (-4395 |has| |#2| (-554)) (-4400 |has| |#2| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#2| (QUOTE (-904))) (-4037 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171))) (-4037 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-554)))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4400)) (|HasCategory| |#2| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-144))))) +(((-4405 "*") |has| |#2| (-171)) (-4396 |has| |#2| (-554)) (-4401 |has| |#2| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#2| (QUOTE (-904))) (-4037 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171))) (-4037 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-554)))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4401)) (|HasCategory| |#2| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-144))))) (-454 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1770,7 +1770,7 @@ NIL NIL (-460 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,{}e,{}x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,{}i,{}e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,{}x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) NIL (-461 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1778,7 +1778,7 @@ NIL NIL (-462 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-857))))) (-463 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) @@ -1808,7 +1808,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-470 |lv| -3197 R) +(-470 |lv| -3196 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1818,23 +1818,23 @@ NIL NIL (-472) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4399 . T)) +((-4400 . T)) NIL (-473 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) (-4396 . T) (-4397 . T) (-4399 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-562)) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasSignature| |#1| (LIST (QUOTE -4054) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -2667) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1402) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|))))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-562)) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasSignature| |#1| (LIST (QUOTE -4053) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -3081) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1401) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|))))))) (-474 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4403 . T)) -((-12 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2694) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-845))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092)))) +((-4404 . T)) +((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-845))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092)))) (-475 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-857))))) (-476) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-477) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1842,29 +1842,29 @@ NIL NIL (-478 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) -((-4402 . T) (-4403 . T)) -((-12 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2694) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857))))) +((-4403 . T) (-4404 . T)) +((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857))))) (-479) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-480 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4404 "*") |has| |#2| (-171)) (-4395 |has| |#2| (-554)) (-4400 |has| |#2| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . 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(LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-721))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-843))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))))) (|HasCategory| (-562) (QUOTE (-845))) (-12 (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (QUOTE (-1044)))) (-12 (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168))))) (-4037 (|HasCategory| |#2| (QUOTE (-1044))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-1092)))) (|HasAttribute| |#2| (QUOTE -4400)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))))) (-482) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL NIL (-483 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) -(-484 -3197 UP UPUP R) +(-484 -3196 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1874,12 +1874,12 @@ NIL NIL (-486) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| (-562) (QUOTE (-904))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-562) (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-146))) (|HasCategory| (-562) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-562) (QUOTE (-1017))) (|HasCategory| (-562) (QUOTE (-815))) (-4037 (|HasCategory| (-562) (QUOTE (-815))) (|HasCategory| (-562) (QUOTE (-845)))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-1143))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-562) (QUOTE (-232))) (|HasCategory| (-562) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-562) (LIST (QUOTE -513) (QUOTE (-1168)) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -308) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -285) (QUOTE (-562)) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-306))) (|HasCategory| (-562) (QUOTE (-544))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-562) (LIST (QUOTE -635) (QUOTE (-562)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (|HasCategory| (-562) (QUOTE (-144))))) (-487 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4402)) (|HasAttribute| |#1| (QUOTE -4403)) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) +((|HasAttribute| |#1| (QUOTE -4403)) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (-488 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1900,33 +1900,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-493 -3197 UP |AlExt| |AlPol|) +(-493 -3196 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-494) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,{}y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| $ (QUOTE (-1044))) (|HasCategory| $ (LIST (QUOTE -1033) (QUOTE (-562))))) (-495 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-496 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-497 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-498 R UP -3197) +(-498 R UP -3196) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-499 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1092))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-112) (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-112) (QUOTE (-1092))) (|HasCategory| (-112) (LIST (QUOTE -609) (QUOTE (-857))))) (-500 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) @@ -1940,7 +1940,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-503 -3197 |Expon| |VarSet| |DPoly|) +(-503 -3196 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-1168))))) @@ -1990,7 +1990,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-787)))) (-515 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-516) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) @@ -1998,28 +1998,28 @@ NIL NIL (-517 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((-4037 (|HasCategory| (-579 |#1|) (QUOTE (-144))) (|HasCategory| (-579 |#1|) (QUOTE (-367)))) (|HasCategory| (-579 |#1|) (QUOTE (-146))) (|HasCategory| (-579 |#1|) (QUOTE (-367))) (|HasCategory| (-579 |#1|) (QUOTE (-144)))) (-518 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-519 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-520 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4403))) +((|HasAttribute| |#3| (QUOTE -4404))) (-521 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -4403))) +((|HasAttribute| |#7| (QUOTE -4404))) (-522 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) -((-4402 . T) (-4403 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-554))) (|HasAttribute| |#1| (QUOTE (-4404 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) +((-4403 . T) (-4404 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-554))) (|HasAttribute| |#1| (QUOTE (-4405 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-523) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2052,7 +2052,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-531 K -3197 |Par|) +(-531 K -3196 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2076,7 +2076,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-537 K -3197 |Par|) +(-537 K -3196 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,{}lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,{}lden,{}lvar,{}eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,{}eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,{}eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2106,7 +2106,7 @@ NIL NIL (-544) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4400 . T) (-4401 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4401 . T) (-4402 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-545) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2122,13 +2122,13 @@ NIL NIL (-548 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4402 . T) (-4403 . T)) -((-12 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2694) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857))))) -(-549 R -3197) +((-4403 . T) (-4404 . T)) +((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857))))) +(-549 R -3196) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f,{} x,{} y,{} d)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-550 R0 -3197 UP UPUP R) +(-550 R0 -3196 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f,{} d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL @@ -2138,7 +2138,7 @@ NIL NIL (-552 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-1406 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-1406 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-553 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2146,9 +2146,9 @@ NIL NIL (-554) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL -(-555 R -3197) +(-555 R -3196) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2160,7 +2160,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-558 R -3197 L) +(-558 R -3196 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -650) (|devaluate| |#2|)))) @@ -2168,31 +2168,31 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-560 -3197 UP UPUP R) +(-560 -3196 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} ')} returns \\spad{[g,{}h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-561 -3197 UP) +(-561 -3196 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} D)} returns \\spad{[g,{} h,{} s,{} p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL (-562) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4384 . T) (-4390 . T) (-4394 . T) (-4389 . T) (-4400 . T) (-4401 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4385 . T) (-4391 . T) (-4395 . T) (-4390 . T) (-4401 . T) (-4402 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-563) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-564 R -3197 L) +(-564 R -3196 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -650) (|devaluate| |#2|)))) -(-565 R -3197) +(-565 R -3196) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-1131)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-625))))) -(-566 -3197 UP) +(-566 -3196 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2200,27 +2200,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-568 -3197) +(-568 -3196) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-569 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-1406 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-1406 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-570) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-571 R -3197) +(-571 R -3196) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-625))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168))))) (-12 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-283)))) (|HasCategory| |#1| (QUOTE (-554)))) -(-572 -3197 UP) +(-572 -3196 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-573 R -3197) +(-573 R -3196) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f,{} s,{} t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL @@ -2242,27 +2242,27 @@ NIL NIL (-578 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-579 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367)))) (-580) ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-581 R -3197) +(-581 R -3196) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-582 E -3197) +(-582 E -3196) ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented"))) NIL NIL -(-583 -3197) +(-583 -3196) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) ((|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-1168))))) (-584 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) @@ -2290,7 +2290,7 @@ NIL NIL (-590 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-4037 (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-143) (QUOTE (-1092)))) (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-591 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) @@ -2298,11 +2298,11 @@ NIL NIL (-592 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4396 . T) (-4397 . T) (-4399 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-562)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-562)) (|devaluate| |#1|)))) (|HasCategory| (-562) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -4054) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-562)))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-562)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-562)) (|devaluate| |#1|)))) (|HasCategory| (-562) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -4053) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-562)))))) (-593 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -((-4397 |has| |#1| (-554)) (-4396 |has| |#1| (-554)) ((-4404 "*") |has| |#1| (-554)) (-4395 |has| |#1| (-554)) (-4399 . T)) +((-4398 |has| |#1| (-554)) (-4397 |has| |#1| (-554)) ((-4405 "*") |has| |#1| (-554)) (-4396 |has| |#1| (-554)) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-554)))) (-594 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) @@ -2312,7 +2312,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) NIL NIL -(-596 R -3197 FG) +(-596 R -3196 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2322,12 +2322,12 @@ NIL NIL (-598 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1044))) (-12 (|HasCategory| |#1| (QUOTE (-997))) (|HasCategory| |#1| (QUOTE (-1044)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-599 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -4403)) (|HasCategory| |#2| (QUOTE (-845))) (|HasAttribute| |#1| (QUOTE -4402)) (|HasCategory| |#3| (QUOTE (-1092)))) +((|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-845))) (|HasAttribute| |#1| (QUOTE -4403)) (|HasCategory| |#3| (QUOTE (-1092)))) (-600 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2342,19 +2342,19 @@ NIL NIL (-603 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,{}b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4399 -4037 (-2246 (|has| |#2| (-366 |#1|)) (|has| |#1| (-554))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-554)))) (-4397 . T) (-4396 . T)) +((-4400 -4037 (-2245 (|has| |#2| (-366 |#1|)) (|has| |#1| (-554))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-554)))) (-4398 . T) (-4397 . T)) ((-4037 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-604 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) -((-4402 . T) (-4403 . T)) -((-12 (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (QUOTE (-1150))) (LIST (QUOTE |:|) (QUOTE -2694) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| (-1150) (QUOTE (-845))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (LIST (QUOTE -609) (QUOTE (-857))))) +((-4403 . T) (-4404 . T)) +((-12 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (QUOTE (-1150))) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| (-1150) (QUOTE (-845))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (LIST (QUOTE -609) (QUOTE (-857))))) (-605 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL NIL (-606 |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4403 . T)) +((-4404 . T)) NIL (-607 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) @@ -2372,7 +2372,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-611 -3197 UP) +(-611 -3196 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2394,19 +2394,19 @@ NIL NIL (-616 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((-4399 . T)) +((-4400 . T)) NIL (-617 A R S) ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-843)))) -(-618 R -3197) +(-618 R -3196) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f,{} t,{} s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t),{} t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f,{} t,{} s)} if it cannot compute the transform."))) NIL NIL (-619 R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,{}n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,{}n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) -((-4397 . T) (-4396 . T) ((-4404 "*") . T) (-4395 . T) (-4399 . T)) +((-4398 . T) (-4397 . T) ((-4405 "*") . T) (-4396 . T) (-4400 . T)) ((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (-620 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) @@ -2422,7 +2422,7 @@ NIL NIL (-623 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4399 . T)) +((-4400 . T)) NIL (-624 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) @@ -2432,29 +2432,29 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-626 R -3197) +(-626 R -3196) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-627 |lv| -3197) +(-627 |lv| -3196) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-628) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4403 . T)) -((-12 (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (QUOTE (-1150))) (LIST (QUOTE |:|) (QUOTE -2694) (QUOTE (-52))))))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) (QUOTE (-1092))) (|HasCategory| (-52) (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1150) (QUOTE (-845))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) (QUOTE (-1092)))) +((-4404 . T)) +((-12 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (QUOTE (-1150))) (LIST (QUOTE |:|) (QUOTE -2693) (QUOTE (-52))))))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-52) (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1150) (QUOTE (-845))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (QUOTE (-1092)))) (-629 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-630 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4397 . T) (-4396 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4398 . T) (-4397 . T)) NIL (-631 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4399 -4037 (-2246 (|has| |#2| (-366 |#1|)) (|has| |#1| (-554))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-554)))) (-4397 . T) (-4396 . T)) +((-4400 -4037 (-2245 (|has| |#2| (-366 |#1|)) (|has| |#1| (-554))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-554)))) (-4398 . T) (-4397 . T)) ((-4037 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-632 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) @@ -2467,10 +2467,10 @@ NIL (-634 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2236 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) +((-2234 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) (-635 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4399 . T)) +((-4400 . T)) NIL (-636 A B) ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) @@ -2486,7 +2486,7 @@ NIL NIL (-639 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-640 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) @@ -2494,7 +2494,7 @@ NIL NIL (-641 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-642 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) @@ -2507,22 +2507,22 @@ NIL (-644 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4403))) +((|HasAttribute| |#1| (QUOTE -4404))) (-645 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-646 R -3197 L) +(-646 R -3196 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op,{} g,{} x,{} a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{op y = g,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op,{} g,{} x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL (-647 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-362)))) (-648 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-362)))) (-649 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) @@ -2530,15 +2530,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-650 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) NIL -(-651 -3197 UP) +(-651 -3196 UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a,{} zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-652 A -4330) +(-652 A -3679) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-362)))) (-653 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) @@ -2554,7 +2554,7 @@ NIL NIL (-656 M R S) ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) ((|HasCategory| |#1| (QUOTE (-786)))) (-657 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2562,7 +2562,7 @@ NIL NIL (-658 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4397 . T) (-4396 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4398 . T) (-4397 . T)) ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-171)))) (-659 A S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) @@ -2570,13 +2570,13 @@ NIL NIL (-660 S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL -(-661 -3197) +(-661 -3196) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-662 -3197 |Row| |Col| M) +(-662 -3196 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2586,8 +2586,8 @@ NIL NIL (-664 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) -((-4399 . T) (-4402 . T) (-4396 . T) (-4397 . T)) -((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4404 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-554))) (-4037 (|HasAttribute| |#2| (QUOTE (-4404 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +((-4400 . T) (-4403 . T) (-4397 . T) (-4398 . T)) +((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4405 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-554))) (-4037 (|HasAttribute| |#2| (QUOTE (-4405 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) (-665) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2651,10 +2651,10 @@ NIL (-680 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4404 "*"))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-554)))) +((|HasAttribute| |#2| (QUOTE (-4405 "*"))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-554)))) (-681 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) NIL (-682 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) @@ -2662,8 +2662,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-554)))) (-683 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) -((-4402 . T) (-4403 . T)) -((-4037 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-554))) (|HasAttribute| |#1| (QUOTE (-4404 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4403 . T) (-4404 . T)) +((-4037 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-554))) (|HasAttribute| |#1| (QUOTE (-4405 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-684 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2672,7 +2672,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-686 S -3197 FLAF FLAS) +(-686 S -3196 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2682,11 +2682,11 @@ NIL NIL (-688) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4395 . T) (-4400 |has| (-693) (-362)) (-4394 |has| (-693) (-362)) (-4401 |has| (-693) (-6 -4401)) (-4398 |has| (-693) (-6 -4398)) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . 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T)) +((|HasCategory| (-693) (QUOTE (-146))) (|HasCategory| (-693) (QUOTE (-144))) (|HasCategory| (-693) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-693) (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| (-693) (QUOTE (-367))) (|HasCategory| (-693) (QUOTE (-362))) (-4037 (|HasCategory| (-693) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-693) (QUOTE (-362)))) (|HasCategory| (-693) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-693) (QUOTE (-232))) (-4037 (|HasCategory| (-693) (QUOTE (-362))) (|HasCategory| (-693) (QUOTE (-348)))) (|HasCategory| (-693) (QUOTE (-348))) (|HasCategory| (-693) (LIST (QUOTE -285) (QUOTE (-693)) (QUOTE (-693)))) (|HasCategory| (-693) (LIST (QUOTE -308) (QUOTE (-693)))) (|HasCategory| (-693) (LIST (QUOTE -513) (QUOTE (-1168)) (QUOTE (-693)))) (|HasCategory| (-693) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-693) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-693) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-693) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (-4037 (|HasCategory| (-693) (QUOTE (-306))) (|HasCategory| (-693) (QUOTE (-362))) (|HasCategory| (-693) (QUOTE (-348)))) (|HasCategory| (-693) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-693) (QUOTE (-1017))) (|HasCategory| (-693) (QUOTE (-1192))) (-12 (|HasCategory| (-693) (QUOTE (-997))) (|HasCategory| (-693) (QUOTE (-1192)))) (-4037 (-12 (|HasCategory| (-693) (QUOTE (-306))) (|HasCategory| (-693) (QUOTE (-904)))) (|HasCategory| (-693) (QUOTE (-362))) (-12 (|HasCategory| (-693) (QUOTE (-348))) (|HasCategory| (-693) (QUOTE (-904))))) (-4037 (-12 (|HasCategory| (-693) (QUOTE (-306))) (|HasCategory| (-693) (QUOTE (-904)))) (-12 (|HasCategory| (-693) (QUOTE (-362))) (|HasCategory| (-693) (QUOTE (-904)))) (-12 (|HasCategory| (-693) (QUOTE (-348))) (|HasCategory| (-693) (QUOTE (-904))))) (|HasCategory| (-693) (QUOTE (-544))) (-12 (|HasCategory| (-693) (QUOTE (-1053))) (|HasCategory| (-693) (QUOTE (-1192)))) (|HasCategory| (-693) (QUOTE (-1053))) (|HasCategory| (-693) (QUOTE (-306))) (|HasCategory| (-693) (QUOTE (-904))) (-4037 (-12 (|HasCategory| (-693) (QUOTE (-306))) (|HasCategory| (-693) (QUOTE (-904)))) (|HasCategory| (-693) (QUOTE (-362)))) (-4037 (-12 (|HasCategory| (-693) (QUOTE (-306))) (|HasCategory| (-693) (QUOTE (-904)))) (|HasCategory| (-693) (QUOTE (-554)))) (-12 (|HasCategory| (-693) (QUOTE (-232))) (|HasCategory| (-693) (QUOTE (-362)))) (-12 (|HasCategory| (-693) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-693) (QUOTE (-362)))) (|HasCategory| (-693) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-693) (QUOTE (-845))) (|HasCategory| (-693) (QUOTE (-554))) (|HasAttribute| (-693) (QUOTE -4402)) (|HasAttribute| (-693) (QUOTE -4399)) (-12 (|HasCategory| (-693) (QUOTE (-306))) (|HasCategory| (-693) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-693) (QUOTE (-306))) (|HasCategory| (-693) (QUOTE (-904)))) (|HasCategory| (-693) (QUOTE (-144)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-693) (QUOTE (-306))) (|HasCategory| (-693) (QUOTE (-904)))) (|HasCategory| (-693) (QUOTE (-348))))) (-689 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4403 . T)) +((-4404 . T)) NIL (-690 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,{}n,{}g,{}p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl,{} p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,{}p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,{}p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,{}p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,{}f2,{}p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2696,13 +2696,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-692 OV E -3197 PG) +(-692 OV E -3196 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL (-693) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-1406 . T) (-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-1406 . T) (-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-694 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2710,7 +2710,7 @@ NIL NIL (-695) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4401 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4402 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-696 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,{}x,{}y)} returns a function \\spad{f: (D1,{} D2) -> I} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1,{} D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) @@ -2732,7 +2732,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-701 S -3114 I) +(-701 S -3113 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2742,7 +2742,7 @@ NIL NIL (-703 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,{}1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i,{} i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) NIL (-704 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f,{} p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) @@ -2752,25 +2752,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-706 R |Mod| -2925 -1610 |exactQuo|) +(-706 R |Mod| -3834 -4103 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-707 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4398 |has| |#1| (-362)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4400)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4399 |has| |#1| (-362)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) (-708 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-709 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4397 |has| |#1| (-171)) (-4396 |has| |#1| (-171)) (-4399 . T)) +((-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146)))) -(-710 R |Mod| -2925 -1610 |exactQuo|) +(-710 R |Mod| -3834 -4103 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) -((-4399 . T)) +((-4400 . T)) NIL (-711 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2778,11 +2778,11 @@ NIL NIL (-712 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) NIL -(-713 -3197) +(-713 -3196) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,{}1],{}[1,{}0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,{}h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,{}0],{}[0,{}1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,{}h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,{}k],{}[0,{}1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,{}b,{}c,{}d)} returns \\spad{matrix [[a,{}b],{}[c,{}d]]}."))) -((-4399 . T)) +((-4400 . T)) NIL (-714 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) @@ -2806,7 +2806,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-348))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-367)))) (-719 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((-4395 |has| |#1| (-362)) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 |has| |#1| (-362)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-720 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) @@ -2816,7 +2816,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-722 -3197 UP) +(-722 -3196 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f,{} D)} returns \\spad{[p,{}n,{}s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f,{} D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p,{} D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m,{} s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p,{} D)} returns \\spad{[n,{}s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -2834,8 +2834,8 @@ NIL NIL (-726 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) -(((-4404 "*") |has| |#2| (-171)) (-4395 |has| |#2| (-554)) (-4400 |has| |#2| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#2| (QUOTE (-904))) (-4037 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171))) (-4037 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-554)))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4400)) (|HasCategory| |#2| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-144))))) +(((-4405 "*") |has| |#2| (-171)) (-4396 |has| |#2| (-554)) (-4401 |has| |#2| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#2| (QUOTE (-904))) (-4037 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171))) (-4037 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-554)))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4401)) (|HasCategory| |#2| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-144))))) (-727 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2850,15 +2850,15 @@ NIL NIL (-730 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,{}m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-4397 |has| |#1| (-171)) (-4396 |has| |#1| (-171)) (-4399 . T)) +((-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) (-4400 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-845)))) (-731 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4392 . T) (-4403 . T)) +((-4393 . T) (-4404 . T)) NIL (-732 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) -((-4402 . T) (-4392 . T) (-4403 . T)) +((-4403 . T) (-4393 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-733) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) @@ -2870,7 +2870,7 @@ NIL NIL (-735 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,{}x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,{}x,{}n)} returns \\spad{min(n,{}order(f,{}x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,{}x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,{}x,{}n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4397 . T) (-4396 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4398 . T) (-4397 . T) (-4400 . T)) NIL (-736 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) @@ -2886,7 +2886,7 @@ NIL NIL (-739 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,{}n)} is recursively defined to be \\spad{plenaryPower(a,{}n-1)*plenaryPower(a,{}n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) NIL (-740) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,{}n,{}scale,{}ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,{}n,{}scale,{}ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -2968,11 +2968,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-760 -3197) +(-760 -3196) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-761 P -3197) +(-761 P -3196) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -2980,7 +2980,7 @@ NIL NIL NIL NIL -(-763 UP -3197) +(-763 UP -3196) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -2994,9 +2994,9 @@ NIL NIL (-766) ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) -(((-4404 "*") . T)) +(((-4405 "*") . T)) NIL -(-767 R -3197) +(-767 R -3196) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,{}y),{} N(x,{}y),{} y,{} x)} returns \\spad{F(x,{}y)} such that \\spad{F(x,{}y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,{}y) dx + N(x,{}y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -3016,7 +3016,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-772 -3197 |ExtF| |SUEx| |ExtP| |n|) +(-772 -3196 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -3030,23 +3030,23 @@ NIL NIL (-775 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL (-777 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4398 |has| |#1| (-362)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4400)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4399 |has| |#1| (-362)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) (-778 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-779 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL (-780 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) @@ -3098,7 +3098,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-367)))) (-792 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) NIL (-793 -4037 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) @@ -3106,17 +3106,17 @@ NIL NIL (-794 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-4037 (|HasCategory| (-994 |#1|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (-4037 (|HasCategory| (-994 |#1|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-994 |#1|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-994 |#1|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (-795) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-796 R -3197 L) +(-796 R -3196 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-797 R -3197) +(-797 R -3196) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3124,7 +3124,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-799 R -3197) +(-799 R -3196) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f,{} x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f,{} x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3132,11 +3132,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-801 -3197 UP UPUP R) +(-801 -3196 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-802 -3197 UP L LQ) +(-802 -3196 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3144,41 +3144,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-804 -3197 UP L LQ) +(-804 -3196 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-805 -3197 UP) +(-805 -3196 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-806 -3197 L UP A LO) +(-806 -3196 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op,{} g)} returns \\spad{[m,{} v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,{}...,{}z_m) . (b_1,{}...,{}b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-807 -3197 UP) +(-807 -3196 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-808 -3197 LO) +(-808 -3196 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-809 -3197 LODO) +(-809 -3196 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) NIL NIL -(-810 -2241 S |f|) +(-810 -2240 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4396 |has| |#2| (-1044)) (-4397 |has| |#2| (-1044)) (-4399 |has| |#2| (-6 -4399)) ((-4404 "*") |has| |#2| (-171)) (-4402 . 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(LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-721))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-843))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))))) (|HasCategory| (-562) (QUOTE (-845))) (-12 (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (QUOTE (-1044)))) (-12 (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168))))) (-4037 (|HasCategory| |#2| (QUOTE (-1044))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-1092)))) (|HasAttribute| |#2| (QUOTE -4400)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))))) (-811 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4400)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) (-812 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4404 "*") |has| |#2| (-362)) (-4395 |has| |#2| (-362)) (-4400 |has| |#2| (-362)) (-4394 |has| |#2| (-362)) (-4399 . T) (-4397 . T) (-4396 . T)) +(((-4405 "*") |has| |#2| (-362)) (-4396 |has| |#2| (-362)) (-4401 |has| |#2| (-362)) (-4395 |has| |#2| (-362)) (-4400 . T) (-4398 . T) (-4397 . T)) ((|HasCategory| |#2| (QUOTE (-362)))) (-813 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) @@ -3190,7 +3190,7 @@ NIL NIL (-815) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-816) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) @@ -3218,7 +3218,7 @@ NIL NIL (-822 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-232)))) (-823) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3230,7 +3230,7 @@ NIL NIL (-825 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4402 . T) (-4392 . T) (-4403 . T)) +((-4403 . T) (-4393 . T) (-4404 . T)) NIL (-826) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) @@ -3242,7 +3242,7 @@ NIL NIL (-828 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) -((-4399 |has| |#1| (-843))) +((-4400 |has| |#1| (-843))) ((|HasCategory| |#1| (QUOTE (-843))) (-4037 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (-4037 (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-21)))) (-829 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) @@ -3254,7 +3254,7 @@ NIL NIL (-831 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4397 |has| |#1| (-171)) (-4396 |has| |#1| (-171)) (-4399 . T)) +((-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146)))) (-832) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) @@ -3282,13 +3282,13 @@ NIL NIL (-838 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4399 |has| |#1| (-843))) +((-4400 |has| |#1| (-843))) ((|HasCategory| |#1| (QUOTE (-843))) (-4037 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (-4037 (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-21)))) (-839) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-840 -2241 S) +(-840 -2240 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3302,7 +3302,7 @@ NIL NIL (-843) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4399 . T)) +((-4400 . T)) NIL (-844 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3318,7 +3318,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171)))) (-847 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) NIL (-848 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) @@ -3326,11 +3326,11 @@ NIL ((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-849 R |sigma| -3756) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-362)))) (-850 |x| R |sigma| -3756) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-362)))) (-851 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) @@ -3374,7 +3374,7 @@ NIL NIL (-861 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4397 |has| |#1| (-171)) (-4396 |has| |#1| (-171)) (-4399 . T)) +((-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362)))) (-862 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3386,19 +3386,19 @@ NIL NIL (-864 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-865 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-866 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| (-865 |#1|) (QUOTE (-904))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-865 |#1|) (QUOTE (-144))) (|HasCategory| (-865 |#1|) (QUOTE (-146))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-865 |#1|) (QUOTE (-1017))) (|HasCategory| (-865 |#1|) (QUOTE (-815))) (-4037 (|HasCategory| (-865 |#1|) (QUOTE (-815))) (|HasCategory| (-865 |#1|) (QUOTE (-845)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-865 |#1|) (QUOTE (-1143))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| (-865 |#1|) (QUOTE (-232))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -513) (QUOTE (-1168)) (LIST (QUOTE -865) (|devaluate| |#1|)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -865) (|devaluate| |#1|)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -865) (|devaluate| |#1|)) (LIST (QUOTE -865) (|devaluate| |#1|)))) (|HasCategory| (-865 |#1|) (QUOTE (-306))) (|HasCategory| (-865 |#1|) (QUOTE (-544))) (|HasCategory| (-865 |#1|) (QUOTE (-845))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-865 |#1|) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-865 |#1|) (QUOTE (-904)))) (|HasCategory| (-865 |#1|) (QUOTE (-144))))) (-867 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-815))) (-4037 (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-845))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-144))))) (-868 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) @@ -3459,7 +3459,7 @@ NIL (-882 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-2236 (|HasCategory| |#2| (QUOTE (-1044)))) (-2236 (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168)))))) (-12 (|HasCategory| |#2| (QUOTE (-1044))) (-2236 (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168)))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168))))) +((-12 (-2234 (|HasCategory| |#2| (QUOTE (-1044)))) (-2234 (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168)))))) (-12 (|HasCategory| |#2| (QUOTE (-1044))) (-2234 (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168)))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168))))) (-883 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3468,7 +3468,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-885 R -3114) +(-885 R -3113) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3492,7 +3492,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-891 UP -3197) +(-891 UP -3196) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,{}n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,{}q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,{}m,{}n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL @@ -3510,7 +3510,7 @@ NIL NIL (-895 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4399 . T)) +((-4400 . T)) NIL (-896 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) @@ -3522,7 +3522,7 @@ NIL NIL (-898 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4399 . T)) +((-4400 . T)) NIL (-899 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3530,7 +3530,7 @@ NIL NIL (-900 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4399 . T)) +((-4400 . T)) ((-4037 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-845)))) (-901 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) @@ -3546,13 +3546,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-144)))) (-904) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-905 |p|) ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367)))) -(-906 R0 -3197 UP UPUP R) +(-906 R0 -3196 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL @@ -3566,7 +3566,7 @@ NIL NIL (-909 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,{}denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,{}x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,{}n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-910 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num,{} facdenom,{} var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf,{} var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) @@ -3580,7 +3580,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-913 -3197) +(-913 -3196) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3590,17 +3590,17 @@ NIL NIL (-915) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,{}...,{}fn],{}h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-916) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4404 "*") . T)) +(((-4405 "*") . T)) NIL -(-917 -3197 P) +(-917 -3196 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-918 |xx| -3197) +(-918 |xx| -3196) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) NIL NIL @@ -3624,7 +3624,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-924 R -3197) +(-924 R -3196) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3636,7 +3636,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-927 S R -3197) +(-927 S R -3196) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3656,11 +3656,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -881) (|devaluate| |#1|)))) -(-932 R -3197 -3114) +(-932 R -3196 -3113) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-933 -3114) +(-933 -3113) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3682,7 +3682,7 @@ NIL NIL (-938 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1044))) (-12 (|HasCategory| |#1| (QUOTE (-997))) (|HasCategory| |#1| (QUOTE (-1044)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-939 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) @@ -3703,12 +3703,12 @@ NIL (-943 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-904))) (|HasAttribute| |#2| (QUOTE -4400)) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#4| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#4| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#4| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-845)))) +((|HasCategory| |#2| (QUOTE (-904))) (|HasAttribute| |#2| (QUOTE -4401)) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#4| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#4| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#4| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-845)))) (-944 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) NIL -(-945 E V R P -3197) +(-945 E V R P -3196) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3718,9 +3718,9 @@ NIL NIL (-947 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4400)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) -(-948 E V R P -3197) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) +(-948 E V R P -3196) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-451)))) @@ -3742,13 +3742,13 @@ NIL NIL (-953 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-954) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-955 -3197) +(-955 -3196) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3762,11 +3762,11 @@ NIL NIL (-958 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-6 -4400)) (-4396 . T) (-4397 . T) (-4399 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4400))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4397 . T) (-4398 . T) (-4400 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4401))) (-959 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) -((-4399 -12 (|has| |#2| (-472)) (|has| |#1| (-472)))) +((-4400 -12 (|has| |#2| (-472)) (|has| |#1| (-472)))) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788)))) (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-845))))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-12 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#2| (QUOTE (-472)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#2| (QUOTE (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721))))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#2| (QUOTE (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-845))))) (-960) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) @@ -3782,7 +3782,7 @@ NIL NIL (-963 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,{}q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) NIL (-964 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3802,7 +3802,7 @@ NIL NIL (-968 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-969) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3814,7 +3814,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-554)))) (-971 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4402 . T)) +((-4403 . T)) NIL (-972 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) @@ -3830,7 +3830,7 @@ NIL NIL (-975 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL (-976 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3848,7 +3848,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-980 K R UP -3197) +(-980 K R UP -3196) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3878,7 +3878,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-1143)))) (-987 S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-988 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3890,7 +3890,7 @@ NIL NIL (-990 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) NIL (-991 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) @@ -3898,7 +3898,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-289)))) (-992 R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-4395 |has| |#1| (-289)) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 |has| |#1| (-289)) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-993 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) @@ -3906,11 +3906,11 @@ NIL NIL (-994 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) -((-4395 |has| |#1| (-289)) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 |has| |#1| (-289)) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (QUOTE (-544)))) (-995 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-996 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) @@ -3920,13 +3920,13 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-998 -3197 UP UPUP |radicnd| |n|) +(-998 -3196 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4395 |has| (-406 |#2|) (-362)) (-4400 |has| (-406 |#2|) (-362)) (-4394 |has| (-406 |#2|) (-362)) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 |has| (-406 |#2|) (-362)) (-4401 |has| (-406 |#2|) (-362)) (-4395 |has| (-406 |#2|) (-362)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-4037 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-4037 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-4037 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -635) (QUOTE (-562)))) (-4037 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) (-999 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| (-562) (QUOTE (-904))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-562) (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-146))) (|HasCategory| (-562) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-562) (QUOTE (-1017))) (|HasCategory| (-562) (QUOTE (-815))) (-4037 (|HasCategory| (-562) (QUOTE (-815))) (|HasCategory| (-562) (QUOTE (-845)))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-1143))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-562) (QUOTE (-232))) (|HasCategory| (-562) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-562) (LIST (QUOTE -513) (QUOTE (-1168)) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -308) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -285) (QUOTE (-562)) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-306))) (|HasCategory| (-562) (QUOTE (-544))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-562) (LIST (QUOTE -635) (QUOTE (-562)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (|HasCategory| (-562) (QUOTE (-144))))) (-1000) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) @@ -3947,7 +3947,7 @@ NIL (-1004 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4403)) (|HasCategory| |#2| (QUOTE (-1092)))) +((|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-1092)))) (-1005 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL @@ -3958,21 +3958,21 @@ NIL NIL (-1007) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-4395 . T) (-4400 . T) (-4394 . T) (-4397 . T) (-4396 . T) ((-4404 "*") . T) (-4399 . T)) +((-4396 . T) (-4401 . T) (-4395 . T) (-4398 . T) (-4397 . T) ((-4405 "*") . T) (-4400 . T)) NIL -(-1008 R -3197) +(-1008 R -3196) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n,{} f,{} g,{} x,{} lim,{} ext)} returns \\spad{[y,{} h,{} b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-1009 R -3197) +(-1009 R -3196) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n,{} f,{} g_1,{} g_2,{} x,{}lim,{}ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,{}dy2/dx) + ((0,{} - n df/dx),{}(n df/dx,{}0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1010 -3197 UP) +(-1010 -3196 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a,{} B,{} C,{} n,{} D)} returns either: 1. \\spad{[Q,{} b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1,{} C1,{} m,{} \\alpha,{} \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f,{} g)} returns a \\spad{[y,{} b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,{}g,{}D)} returns \\spad{[A,{} B,{} C,{} T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1011 -3197 UP) +(-1011 -3196 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f,{} g1,{} g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,{}g1,{}g2,{}D)} returns \\spad{[A,{} B,{} H,{} C1,{} C2,{} T]} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} has a solution if and only if \\spad{y1 = Q1 / T,{} y2 = Q2 / T},{} where \\spad{B,{}C1,{}C2,{}Q1,{}Q2} have no normal poles and satisfy A \\spad{(Q1',{} Q2') + ((H,{} -B),{} (B,{} H)) (Q1,{}Q2) = (C1,{}C2)} \\spad{D} is the derivation to use."))) NIL NIL @@ -4006,9 +4006,9 @@ NIL NIL (-1019 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) -((-4395 . T) (-4400 . T) (-4394 . T) (-4397 . T) (-4396 . T) ((-4404 "*") . T) (-4399 . T)) +((-4396 . T) (-4401 . T) (-4395 . T) (-4398 . T) (-4397 . T) ((-4405 "*") . T) (-4400 . T)) ((-4037 (|HasCategory| (-406 (-562)) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-406 (-562)) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-406 (-562)) (LIST (QUOTE -1033) (QUOTE (-562))))) -(-1020 -3197 L) +(-1020 -3196 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4018,12 +4018,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1092)))) (-1022 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-857))))) (-1023 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4404 "*")))) +((|HasAttribute| |#1| (QUOTE (-4405 "*")))) (-1024 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL @@ -4044,14 +4044,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1029 -3197 |Expon| |VarSet| |FPol| |LFPol|) +(-1029 -3196 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) -(((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1030) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) -((-4402 . T) (-4403 . T)) -((-12 (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2694) (QUOTE (-52))))))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (QUOTE (-1092))) (|HasCategory| (-52) (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (QUOTE (-1092))) (|HasCategory| (-1168) (QUOTE (-845))) (|HasCategory| (-52) (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (LIST (QUOTE -609) (QUOTE (-857))))) +((-4403 . T) (-4404 . T)) +((-12 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2693) (QUOTE (-52))))))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-52) (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-1168) (QUOTE (-845))) (|HasCategory| (-52) (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857))))) (-1031) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4094,7 +4094,7 @@ NIL NIL (-1041 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-12 (|HasCategory| (-775 |#1| (-859 |#2|)) (QUOTE (-1092))) (|HasCategory| (-775 |#1| (-859 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -775) (|devaluate| |#1|) (LIST (QUOTE -859) (|devaluate| |#2|)))))) (|HasCategory| (-775 |#1| (-859 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-775 |#1| (-859 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| (-859 |#2|) (QUOTE (-367))) (|HasCategory| (-775 |#1| (-859 |#2|)) (LIST (QUOTE -609) (QUOTE (-857))))) (-1042) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) @@ -4106,9 +4106,9 @@ NIL NIL (-1044) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) -((-4399 . T)) +((-4400 . T)) NIL -(-1045 |xx| -3197) +(-1045 |xx| -3196) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4118,11 +4118,11 @@ NIL ((|HasCategory| |#4| (QUOTE (-306))) (|HasCategory| |#4| (QUOTE (-362))) (|HasCategory| |#4| (QUOTE (-554))) (|HasCategory| |#4| (QUOTE (-171)))) (-1047 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4402 . T) (-4397 . T) (-4396 . T)) +((-4403 . T) (-4398 . T) (-4397 . T)) NIL (-1048 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-4402 . T) (-4397 . T) (-4396 . T)) +((-4403 . T) (-4398 . T) (-4397 . T)) ((-4037 (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-554))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-857))))) (-1049 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) @@ -4142,7 +4142,7 @@ NIL NIL (-1053) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1054 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4150,19 +4150,19 @@ NIL NIL (-1055) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4390 . T) (-4394 . T) (-4389 . T) (-4400 . T) (-4401 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4391 . T) (-4395 . T) (-4390 . T) (-4401 . T) (-4402 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1056) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4402 . T) (-4403 . T)) -((-12 (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2694) (QUOTE (-52))))))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (QUOTE (-1092))) (|HasCategory| (-52) (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (QUOTE (-1092))) (|HasCategory| (-1168) (QUOTE (-845))) (|HasCategory| (-52) (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (LIST (QUOTE -609) (QUOTE (-857))))) +((-4403 . T) (-4404 . T)) +((-12 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2693) (QUOTE (-52))))))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-52) (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-1168) (QUOTE (-845))) (|HasCategory| (-52) (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857))))) (-1057 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -987) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-1168))))) (-1058 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) NIL (-1059) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) @@ -4186,7 +4186,7 @@ NIL NIL (-1064 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL (-1065 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -4200,11 +4200,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1068 |Base| R -3197) +(-1068 |Base| R -3196) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1069 |Base| R -3197) +(-1069 |Base| R -3196) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,{}...,{}rn])} creates the rule set \\spad{{r1,{}...,{}rn}}."))) NIL NIL @@ -4218,7 +4218,7 @@ NIL NIL (-1072 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) -((-4395 |has| |#1| (-362)) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 |has| |#1| (-362)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))))) (-1073 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) @@ -4246,8 +4246,8 @@ NIL NIL (-1079 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-1080 (-1168)) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-1080 (-1168)) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-1080 (-1168)) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-1080 (-1168)) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-1080 (-1168)) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4400)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-1080 (-1168)) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-1080 (-1168)) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-1080 (-1168)) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-1080 (-1168)) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-1080 (-1168)) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1080 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4290,7 +4290,7 @@ NIL NIL (-1090 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4392 . T)) +((-4393 . T)) NIL (-1091 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4306,7 +4306,7 @@ NIL NIL (-1094 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) -((-4402 . T) (-4392 . T) (-4403 . T)) +((-4403 . T) (-4393 . T) (-4404 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-1095 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) @@ -4334,7 +4334,7 @@ NIL NIL (-1101 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,{}mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL (-1102) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4350,8 +4350,8 @@ NIL NIL (-1105 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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(LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#3| (QUOTE (-721))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#3| (QUOTE (-788))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#3| (QUOTE (-843))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#3| (QUOTE (-1044))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562)))))) (|HasCategory| (-562) (QUOTE (-845))) (-12 (|HasCategory| |#3| (QUOTE (-1044))) (|HasCategory| |#3| (LIST (QUOTE -635) (QUOTE (-562))))) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1044)))) (-12 (|HasCategory| |#3| (QUOTE (-1044))) (|HasCategory| |#3| (LIST (QUOTE -895) (QUOTE (-1168))))) (-4037 (|HasCategory| |#3| (QUOTE (-1044))) (-12 (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562)))))) (-12 (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#3| (QUOTE (-1092)))) (|HasAttribute| |#3| (QUOTE -4400)) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (-1106 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4360,7 +4360,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1108 R -3197) +(-1108 R -3196) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4378,19 +4378,19 @@ NIL NIL (-1112) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4390 . T) (-4394 . T) (-4389 . T) (-4400 . T) (-4401 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4391 . T) (-4395 . T) (-4390 . T) (-4401 . T) (-4402 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1113 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) NIL (-1114 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-362))) (|HasAttribute| |#3| (QUOTE (-4404 "*"))) (|HasCategory| |#3| (QUOTE (-171)))) +((|HasCategory| |#3| (QUOTE (-362))) (|HasAttribute| |#3| (QUOTE (-4405 "*"))) (|HasCategory| |#3| (QUOTE (-171)))) (-1115 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-4402 . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4403 . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1116 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,{}B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) @@ -4398,17 +4398,17 @@ NIL NIL (-1117 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4400)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1118 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4397 . T) (-4396 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4398 . T) (-4397 . T) (-4400 . T)) ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-362)))) (-1119 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL -(-1120 UP -3197) +(-1120 UP -3196) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,{}g,{}h,{}i,{}k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,{}g,{}h,{}j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,{}g,{}h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,{}g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,{}g,{}h,{}i,{}j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,{}g,{}h,{}i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,{}g,{}h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,{}g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,{}f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4462,19 +4462,19 @@ NIL NIL (-1133 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| (-1132 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1132) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1132 |#1| |#2|) (QUOTE (-1092)))) (|HasCategory| (-1132 |#1| |#2|) (QUOTE (-1092))) (-4037 (|HasCategory| (-1132 |#1| |#2|) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-1132 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1132) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1132 |#1| |#2|) (QUOTE (-1092))))) (|HasCategory| (-1132 |#1| |#2|) (LIST (QUOTE -609) (QUOTE (-857))))) (-1134 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) -((-4399 . T) (-4391 |has| |#2| (-6 (-4404 "*"))) (-4402 . T) (-4396 . T) (-4397 . T)) -((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4404 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-362))) (-4037 (|HasAttribute| |#2| (QUOTE (-4404 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +((-4400 . T) (-4392 |has| |#2| (-6 (-4405 "*"))) (-4403 . T) (-4397 . T) (-4398 . T)) +((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4405 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-362))) (-4037 (|HasAttribute| |#2| (QUOTE (-4405 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) (-1135 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1136) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL (-1137 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4482,11 +4482,11 @@ NIL NIL (-1138 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-857))))) (-1139 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4402 . T) (-4403 . T)) +((-4403 . T) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-1140 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) @@ -4498,8 +4498,8 @@ NIL NIL (-1142 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4403 . T)) -((-12 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2694) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-845))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092)))) +((-4404 . T)) +((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-845))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092)))) (-1143) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4522,20 +4522,20 @@ NIL NIL (-1148 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4403 . T)) +((-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-1149) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL (-1150) NIL -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-1151 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4402 . T) (-4403 . T)) -((-12 (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (QUOTE (-1150))) (LIST (QUOTE |:|) (QUOTE -2694) (|devaluate| |#1|)))))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (QUOTE (-1092))) (|HasCategory| (-1150) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (LIST (QUOTE -609) (QUOTE (-857))))) +((-4403 . T) (-4404 . 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(|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -4566,9 +4566,9 @@ NIL NIL (-1159 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| (-966) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasAttribute| |#1| (QUOTE -4400))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4397 . T) (-4398 . T) (-4400 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| (-966) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasAttribute| |#1| (QUOTE -4401))) (-1171) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4650,8 +4650,8 @@ NIL NIL (-1180 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) -((-4402 . T) (-4403 . T)) -((-12 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2694) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (LIST (QUOTE -609) (QUOTE (-857))))) +((-4403 . T) (-4404 . T)) +((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857))))) (-1181 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4662,7 +4662,7 @@ NIL NIL (-1183 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4403 . T)) +((-4404 . T)) NIL (-1184 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) @@ -4702,7 +4702,7 @@ NIL NIL (-1193 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (-1194 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) @@ -4712,7 +4712,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1196 R -3197) +(-1196 R -3196) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -4720,7 +4720,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1198 R -3197) +(-1198 R -3196) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -881) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -881) (|devaluate| |#1|))))) @@ -4730,11 +4730,11 @@ NIL ((|HasCategory| |#4| (QUOTE (-367)))) (-1200 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL (-1201 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4397 . T) (-4396 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4398 . T) (-4397 . T) (-4400 . T)) ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-362)))) (-1202 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) @@ -4748,7 +4748,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) -(-1205 -3197) +(-1205 -3196) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,{}n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4774,7 +4774,7 @@ NIL NIL (-1211) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1212) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4794,7 +4794,7 @@ NIL NIL (-1216 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,{}k1,{}k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,{}k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = n0..infinity,{}a[n] * x**n)) = sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1217 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) @@ -4802,16 +4802,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-1218 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1219 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. 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the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4846,8 +4846,8 @@ NIL NIL (-1229 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4404 "*") |has| |#2| (-171)) (-4395 |has| |#2| (-554)) (-4398 |has| |#2| (-362)) (-4400 |has| |#2| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . 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T) (-4397 . T) (-4400 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4858,15 +4858,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-1143)))) (-1232 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4398 |has| |#1| (-362)) (-4400 |has| |#1| (-6 -4400)) (-4397 . T) (-4396 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4399 |has| |#1| (-362)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T)) NIL (-1233 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1104))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4054) (LIST (|devaluate| |#2|) (QUOTE (-1168)))))) +((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1104))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4053) (LIST (|devaluate| |#2|) (QUOTE (-1168)))))) (-1234 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1235 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4878,7 +4878,7 @@ NIL NIL (-1237 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,{}r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,{}st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1238 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) @@ -4886,24 +4886,24 @@ NIL NIL (-1239 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1240 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) (-4396 . T) (-4397 . T) (-4399 . T)) -((|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-562)) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasSignature| |#1| (LIST (QUOTE -4054) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -2667) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1402) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T)) +((|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-562)) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasSignature| |#1| (LIST (QUOTE -4053) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -3081) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1401) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-1241 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4400 |has| |#1| (-362)) (-4394 |has| |#1| (-362)) (-4396 . T) (-4397 . T) (-4399 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-562)) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasSignature| |#1| (LIST (QUOTE -4054) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -2667) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1402) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|))))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-562)) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasSignature| |#1| (LIST (QUOTE -4053) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -3081) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1401) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|))))))) (-1242 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) -(((-4404 "*") |has| (-1241 |#2| |#3| |#4|) (-171)) (-4395 |has| (-1241 |#2| |#3| |#4|) (-554)) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") |has| (-1241 |#2| |#3| |#4|) (-171)) (-4396 |has| (-1241 |#2| |#3| |#4|) (-554)) (-4397 . T) (-4398 . T) (-4400 . T)) ((|HasCategory| (-1241 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-1241 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1241 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1241 |#2| |#3| |#4|) (QUOTE (-171))) (-4037 (|HasCategory| (-1241 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-1241 |#2| |#3| |#4|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| (-1241 |#2| |#3| |#4|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-1241 |#2| |#3| |#4|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-1241 |#2| |#3| |#4|) (QUOTE (-362))) (|HasCategory| (-1241 |#2| |#3| |#4|) (QUOTE (-451))) (|HasCategory| (-1241 |#2| |#3| |#4|) (QUOTE (-554)))) (-1243 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4403))) +((|HasAttribute| |#1| (QUOTE -4404))) (-1244 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4915,20 +4915,20 @@ NIL (-1246 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-954))) (|HasCategory| |#2| (QUOTE (-1192))) (|HasSignature| |#2| (LIST (QUOTE -1402) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2667) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1168))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-362)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-954))) (|HasCategory| |#2| (QUOTE (-1192))) (|HasSignature| |#2| (LIST (QUOTE -1401) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3081) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1168))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-362)))) (-1247 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1248 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4404 "*") |has| |#1| (-171)) (-4395 |has| |#1| (-554)) (-4396 . T) (-4397 . T) (-4399 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-766)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-766)) (|devaluate| |#1|)))) (|HasCategory| (-766) (QUOTE (-1104))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-766))))) (|HasSignature| |#1| (LIST (QUOTE -4054) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-766))))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -2667) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1402) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|))))))) +(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-766)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-766)) (|devaluate| |#1|)))) (|HasCategory| (-766) (QUOTE (-1104))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-766))))) (|HasSignature| |#1| (LIST (QUOTE -4053) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-766))))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -3081) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1401) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|))))))) (-1249 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y<n>=f(y,{}y',{}..,{}y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1250 -3197 UP L UTS) +(-1250 -3196 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-554)))) @@ -4946,7 +4946,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-997))) (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1254 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) NIL (-1255 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4954,7 +4954,7 @@ NIL NIL (-1256 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1044))) (-12 (|HasCategory| |#1| (QUOTE (-997))) (|HasCategory| |#1| (QUOTE (-1044)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-1257) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) @@ -4982,13 +4982,13 @@ NIL NIL (-1263 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4397 . T) (-4396 . T)) +((-4398 . T) (-4397 . T)) NIL (-1264 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1265 K R UP -3197) +(-1265 K R UP -3196) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -5002,56 +5002,56 @@ NIL NIL (-1268 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4397 |has| |#1| (-171)) (-4396 |has| |#1| (-171)) (-4399 . T)) +((-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) (-4400 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362)))) (-1269 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) -((-4403 . T) (-4402 . T)) +((-4404 . T) (-4403 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-857))))) (-1270 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})"))) -((-4396 . T) (-4397 . T) (-4399 . T)) +((-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1271 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((-4399 . T) (-4395 |has| |#2| (-6 -4395)) (-4397 . T) (-4396 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4395))) +((-4400 . T) (-4396 |has| |#2| (-6 -4396)) (-4398 . T) (-4397 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4396))) (-1272 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL (-1273 |vl| R) ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4395 |has| |#2| (-6 -4395)) (-4397 . T) (-4396 . T) (-4399 . T)) +((-4396 |has| |#2| (-6 -4396)) (-4398 . T) (-4397 . T) (-4400 . T)) NIL -(-1274 S -3197) +(-1274 S -3196) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146)))) -(-1275 -3197) +(-1275 -3196) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4394 . T) (-4400 . T) (-4395 . T) ((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL (-1276 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4395 |has| |#2| (-6 -4395)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -712) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasAttribute| |#2| (QUOTE -4395))) +((-4396 |has| |#2| (-6 -4396)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -712) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasAttribute| |#2| (QUOTE -4396))) (-1277 |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,{}n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4395 |has| |#2| (-6 -4395)) (-4397 . T) (-4396 . T) (-4399 . T)) +((-4396 |has| |#2| (-6 -4396)) (-4398 . T) (-4397 . T) (-4400 . T)) NIL (-1278 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4395 |has| |#1| (-6 -4395)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasAttribute| |#1| (QUOTE -4395))) +((-4396 |has| |#1| (-6 -4396)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasAttribute| |#1| (QUOTE -4396))) (-1279 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4399 . T) (-4400 |has| |#1| (-6 -4400)) (-4395 |has| |#1| (-6 -4395)) (-4397 . T) (-4396 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4399)) (|HasAttribute| |#1| (QUOTE -4400)) (|HasAttribute| |#1| (QUOTE -4395))) +((-4400 . T) (-4401 |has| |#1| (-6 -4401)) (-4396 |has| |#1| (-6 -4396)) (-4398 . T) (-4397 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4400)) (|HasAttribute| |#1| (QUOTE -4401)) (|HasAttribute| |#1| (QUOTE -4396))) (-1280 |VarSet| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((-4395 |has| |#2| (-6 -4395)) (-4397 . T) (-4396 . T) (-4399 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4395))) +((-4396 |has| |#2| (-6 -4396)) (-4398 . T) (-4397 . T) (-4400 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4396))) (-1281 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,{}n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL @@ -5066,7 +5066,7 @@ NIL NIL (-1284 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4404 "*") . T) (-4396 . T) (-4397 . T) (-4399 . T)) +(((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T)) NIL NIL NIL @@ -5084,4 +5084,4 @@ NIL NIL NIL NIL -((-3 NIL 2281904 2281909 2281914 2281919) (-2 NIL 2281884 2281889 2281894 2281899) (-1 NIL 2281864 2281869 2281874 2281879) (0 NIL 2281844 2281849 2281854 2281859) (-1284 "ZMOD.spad" 2281653 2281666 2281782 2281839) (-1283 "ZLINDEP.spad" 2280697 2280708 2281643 2281648) (-1282 "ZDSOLVE.spad" 2270546 2270568 2280687 2280692) (-1281 "YSTREAM.spad" 2270039 2270050 2270536 2270541) (-1280 "XRPOLY.spad" 2269259 2269279 2269895 2269964) (-1279 "XPR.spad" 2267050 2267063 2268977 2269076) (-1278 "XPOLY.spad" 2266605 2266616 2266906 2266975) (-1277 "XPOLYC.spad" 2265922 2265938 2266531 2266600) (-1276 "XPBWPOLY.spad" 2264359 2264379 2265702 2265771) (-1275 "XF.spad" 2262820 2262835 2264261 2264354) (-1274 "XF.spad" 2261261 2261278 2262704 2262709) (-1273 "XFALG.spad" 2258285 2258301 2261187 2261256) (-1272 "XEXPPKG.spad" 2257536 2257562 2258275 2258280) (-1271 "XDPOLY.spad" 2257150 2257166 2257392 2257461) (-1270 "XALG.spad" 2256810 2256821 2257106 2257145) (-1269 "WUTSET.spad" 2252649 2252666 2256456 2256483) (-1268 "WP.spad" 2251848 2251892 2252507 2252574) (-1267 "WHILEAST.spad" 2251646 2251655 2251838 2251843) (-1266 "WHEREAST.spad" 2251317 2251326 2251636 2251641) (-1265 "WFFINTBS.spad" 2248880 2248902 2251307 2251312) (-1264 "WEIER.spad" 2247094 2247105 2248870 2248875) (-1263 "VSPACE.spad" 2246767 2246778 2247062 2247089) (-1262 "VSPACE.spad" 2246460 2246473 2246757 2246762) (-1261 "VOID.spad" 2246137 2246146 2246450 2246455) (-1260 "VIEW.spad" 2243759 2243768 2246127 2246132) (-1259 "VIEWDEF.spad" 2238956 2238965 2243749 2243754) (-1258 "VIEW3D.spad" 2222791 2222800 2238946 2238951) (-1257 "VIEW2D.spad" 2210528 2210537 2222781 2222786) (-1256 "VECTOR.spad" 2209203 2209214 2209454 2209481) (-1255 "VECTOR2.spad" 2207830 2207843 2209193 2209198) (-1254 "VECTCAT.spad" 2205730 2205741 2207798 2207825) (-1253 "VECTCAT.spad" 2203438 2203451 2205508 2205513) (-1252 "VARIABLE.spad" 2203218 2203233 2203428 2203433) (-1251 "UTYPE.spad" 2202862 2202871 2203208 2203213) (-1250 "UTSODETL.spad" 2202155 2202179 2202818 2202823) (-1249 "UTSODE.spad" 2200343 2200363 2202145 2202150) (-1248 "UTS.spad" 2195132 2195160 2198810 2198907) (-1247 "UTSCAT.spad" 2192583 2192599 2195030 2195127) (-1246 "UTSCAT.spad" 2189678 2189696 2192127 2192132) (-1245 "UTS2.spad" 2189271 2189306 2189668 2189673) (-1244 "URAGG.spad" 2183903 2183914 2189261 2189266) (-1243 "URAGG.spad" 2178499 2178512 2183859 2183864) (-1242 "UPXSSING.spad" 2176142 2176168 2177580 2177713) (-1241 "UPXS.spad" 2173290 2173318 2174274 2174423) (-1240 "UPXSCONS.spad" 2171047 2171067 2171422 2171571) (-1239 "UPXSCCA.spad" 2169612 2169632 2170893 2171042) (-1238 "UPXSCCA.spad" 2168319 2168341 2169602 2169607) (-1237 "UPXSCAT.spad" 2166900 2166916 2168165 2168314) (-1236 "UPXS2.spad" 2166441 2166494 2166890 2166895) (-1235 "UPSQFREE.spad" 2164853 2164867 2166431 2166436) (-1234 "UPSCAT.spad" 2162446 2162470 2164751 2164848) (-1233 "UPSCAT.spad" 2159745 2159771 2162052 2162057) (-1232 "UPOLYC.spad" 2154723 2154734 2159587 2159740) (-1231 "UPOLYC.spad" 2149593 2149606 2154459 2154464) (-1230 "UPOLYC2.spad" 2149062 2149081 2149583 2149588) (-1229 "UP.spad" 2146219 2146234 2146612 2146765) (-1228 "UPMP.spad" 2145109 2145122 2146209 2146214) (-1227 "UPDIVP.spad" 2144672 2144686 2145099 2145104) (-1226 "UPDECOMP.spad" 2142909 2142923 2144662 2144667) (-1225 "UPCDEN.spad" 2142116 2142132 2142899 2142904) (-1224 "UP2.spad" 2141478 2141499 2142106 2142111) (-1223 "UNISEG.spad" 2140831 2140842 2141397 2141402) (-1222 "UNISEG2.spad" 2140324 2140337 2140787 2140792) (-1221 "UNIFACT.spad" 2139425 2139437 2140314 2140319) (-1220 "ULS.spad" 2129977 2130005 2131070 2131499) (-1219 "ULSCONS.spad" 2122371 2122391 2122743 2122892) (-1218 "ULSCCAT.spad" 2120100 2120120 2122217 2122366) (-1217 "ULSCCAT.spad" 2117937 2117959 2120056 2120061) (-1216 "ULSCAT.spad" 2116153 2116169 2117783 2117932) (-1215 "ULS2.spad" 2115665 2115718 2116143 2116148) (-1214 "UINT8.spad" 2115542 2115551 2115655 2115660) (-1213 "UINT32.spad" 2115418 2115427 2115532 2115537) (-1212 "UINT16.spad" 2115294 2115303 2115408 2115413) (-1211 "UFD.spad" 2114359 2114368 2115220 2115289) (-1210 "UFD.spad" 2113486 2113497 2114349 2114354) (-1209 "UDVO.spad" 2112333 2112342 2113476 2113481) (-1208 "UDPO.spad" 2109760 2109771 2112289 2112294) (-1207 "TYPE.spad" 2109692 2109701 2109750 2109755) (-1206 "TYPEAST.spad" 2109611 2109620 2109682 2109687) (-1205 "TWOFACT.spad" 2108261 2108276 2109601 2109606) (-1204 "TUPLE.spad" 2107745 2107756 2108160 2108165) (-1203 "TUBETOOL.spad" 2104582 2104591 2107735 2107740) (-1202 "TUBE.spad" 2103223 2103240 2104572 2104577) (-1201 "TS.spad" 2101812 2101828 2102788 2102885) (-1200 "TSETCAT.spad" 2088939 2088956 2101780 2101807) (-1199 "TSETCAT.spad" 2076052 2076071 2088895 2088900) (-1198 "TRMANIP.spad" 2070418 2070435 2075758 2075763) (-1197 "TRIMAT.spad" 2069377 2069402 2070408 2070413) (-1196 "TRIGMNIP.spad" 2067894 2067911 2069367 2069372) (-1195 "TRIGCAT.spad" 2067406 2067415 2067884 2067889) (-1194 "TRIGCAT.spad" 2066916 2066927 2067396 2067401) (-1193 "TREE.spad" 2065487 2065498 2066523 2066550) (-1192 "TRANFUN.spad" 2065318 2065327 2065477 2065482) (-1191 "TRANFUN.spad" 2065147 2065158 2065308 2065313) (-1190 "TOPSP.spad" 2064821 2064830 2065137 2065142) (-1189 "TOOLSIGN.spad" 2064484 2064495 2064811 2064816) (-1188 "TEXTFILE.spad" 2063041 2063050 2064474 2064479) (-1187 "TEX.spad" 2060173 2060182 2063031 2063036) (-1186 "TEX1.spad" 2059729 2059740 2060163 2060168) (-1185 "TEMUTL.spad" 2059284 2059293 2059719 2059724) (-1184 "TBCMPPK.spad" 2057377 2057400 2059274 2059279) (-1183 "TBAGG.spad" 2056413 2056436 2057357 2057372) (-1182 "TBAGG.spad" 2055457 2055482 2056403 2056408) (-1181 "TANEXP.spad" 2054833 2054844 2055447 2055452) (-1180 "TABLE.spad" 2053244 2053267 2053514 2053541) (-1179 "TABLEAU.spad" 2052725 2052736 2053234 2053239) (-1178 "TABLBUMP.spad" 2049508 2049519 2052715 2052720) (-1177 "SYSTEM.spad" 2048782 2048791 2049498 2049503) (-1176 "SYSSOLP.spad" 2046255 2046266 2048772 2048777) (-1175 "SYSNNI.spad" 2045431 2045442 2046245 2046250) (-1174 "SYSINT.spad" 2044904 2044915 2045421 2045426) (-1173 "SYNTAX.spad" 2041174 2041183 2044894 2044899) (-1172 "SYMTAB.spad" 2039230 2039239 2041164 2041169) (-1171 "SYMS.spad" 2035215 2035224 2039220 2039225) (-1170 "SYMPOLY.spad" 2034222 2034233 2034304 2034431) (-1169 "SYMFUNC.spad" 2033697 2033708 2034212 2034217) (-1168 "SYMBOL.spad" 2031124 2031133 2033687 2033692) (-1167 "SWITCH.spad" 2027881 2027890 2031114 2031119) (-1166 "SUTS.spad" 2024780 2024808 2026348 2026445) (-1165 "SUPXS.spad" 2021915 2021943 2022912 2023061) (-1164 "SUP.spad" 2018684 2018695 2019465 2019618) (-1163 "SUPFRACF.spad" 2017789 2017807 2018674 2018679) (-1162 "SUP2.spad" 2017179 2017192 2017779 2017784) (-1161 "SUMRF.spad" 2016145 2016156 2017169 2017174) (-1160 "SUMFS.spad" 2015778 2015795 2016135 2016140) (-1159 "SULS.spad" 2006317 2006345 2007423 2007852) (-1158 "SUCHTAST.spad" 2006086 2006095 2006307 2006312) (-1157 "SUCH.spad" 2005766 2005781 2006076 2006081) (-1156 "SUBSPACE.spad" 1997773 1997788 2005756 2005761) (-1155 "SUBRESP.spad" 1996933 1996947 1997729 1997734) (-1154 "STTF.spad" 1993032 1993048 1996923 1996928) (-1153 "STTFNC.spad" 1989500 1989516 1993022 1993027) (-1152 "STTAYLOR.spad" 1981898 1981909 1989381 1989386) (-1151 "STRTBL.spad" 1980403 1980420 1980552 1980579) (-1150 "STRING.spad" 1979812 1979821 1979826 1979853) (-1149 "STRICAT.spad" 1979600 1979609 1979780 1979807) (-1148 "STREAM.spad" 1976458 1976469 1979125 1979140) (-1147 "STREAM3.spad" 1976003 1976018 1976448 1976453) (-1146 "STREAM2.spad" 1975071 1975084 1975993 1975998) (-1145 "STREAM1.spad" 1974775 1974786 1975061 1975066) (-1144 "STINPROD.spad" 1973681 1973697 1974765 1974770) (-1143 "STEP.spad" 1972882 1972891 1973671 1973676) (-1142 "STBL.spad" 1971408 1971436 1971575 1971590) (-1141 "STAGG.spad" 1970483 1970494 1971398 1971403) (-1140 "STAGG.spad" 1969556 1969569 1970473 1970478) (-1139 "STACK.spad" 1968907 1968918 1969163 1969190) (-1138 "SREGSET.spad" 1966611 1966628 1968553 1968580) (-1137 "SRDCMPK.spad" 1965156 1965176 1966601 1966606) (-1136 "SRAGG.spad" 1960253 1960262 1965124 1965151) (-1135 "SRAGG.spad" 1955370 1955381 1960243 1960248) (-1134 "SQMATRIX.spad" 1952986 1953004 1953902 1953989) (-1133 "SPLTREE.spad" 1947538 1947551 1952422 1952449) (-1132 "SPLNODE.spad" 1944126 1944139 1947528 1947533) (-1131 "SPFCAT.spad" 1942903 1942912 1944116 1944121) (-1130 "SPECOUT.spad" 1941453 1941462 1942893 1942898) (-1129 "SPADXPT.spad" 1933592 1933601 1941443 1941448) (-1128 "spad-parser.spad" 1933057 1933066 1933582 1933587) (-1127 "SPADAST.spad" 1932758 1932767 1933047 1933052) (-1126 "SPACEC.spad" 1916771 1916782 1932748 1932753) (-1125 "SPACE3.spad" 1916547 1916558 1916761 1916766) (-1124 "SORTPAK.spad" 1916092 1916105 1916503 1916508) (-1123 "SOLVETRA.spad" 1913849 1913860 1916082 1916087) (-1122 "SOLVESER.spad" 1912369 1912380 1913839 1913844) (-1121 "SOLVERAD.spad" 1908379 1908390 1912359 1912364) (-1120 "SOLVEFOR.spad" 1906799 1906817 1908369 1908374) (-1119 "SNTSCAT.spad" 1906399 1906416 1906767 1906794) (-1118 "SMTS.spad" 1904659 1904685 1905964 1906061) (-1117 "SMP.spad" 1902098 1902118 1902488 1902615) (-1116 "SMITH.spad" 1900941 1900966 1902088 1902093) (-1115 "SMATCAT.spad" 1899051 1899081 1900885 1900936) (-1114 "SMATCAT.spad" 1897093 1897125 1898929 1898934) (-1113 "SKAGG.spad" 1896054 1896065 1897061 1897088) (-1112 "SINT.spad" 1894880 1894889 1895920 1896049) (-1111 "SIMPAN.spad" 1894608 1894617 1894870 1894875) (-1110 "SIG.spad" 1893936 1893945 1894598 1894603) (-1109 "SIGNRF.spad" 1893044 1893055 1893926 1893931) (-1108 "SIGNEF.spad" 1892313 1892330 1893034 1893039) (-1107 "SIGAST.spad" 1891694 1891703 1892303 1892308) (-1106 "SHP.spad" 1889612 1889627 1891650 1891655) (-1105 "SHDP.spad" 1879323 1879350 1879832 1879963) (-1104 "SGROUP.spad" 1878931 1878940 1879313 1879318) (-1103 "SGROUP.spad" 1878537 1878548 1878921 1878926) (-1102 "SGCF.spad" 1871418 1871427 1878527 1878532) (-1101 "SFRTCAT.spad" 1870346 1870363 1871386 1871413) (-1100 "SFRGCD.spad" 1869409 1869429 1870336 1870341) (-1099 "SFQCMPK.spad" 1864046 1864066 1869399 1869404) (-1098 "SFORT.spad" 1863481 1863495 1864036 1864041) (-1097 "SEXOF.spad" 1863324 1863364 1863471 1863476) (-1096 "SEX.spad" 1863216 1863225 1863314 1863319) (-1095 "SEXCAT.spad" 1860767 1860807 1863206 1863211) (-1094 "SET.spad" 1859067 1859078 1860188 1860227) (-1093 "SETMN.spad" 1857501 1857518 1859057 1859062) (-1092 "SETCAT.spad" 1856986 1856995 1857491 1857496) (-1091 "SETCAT.spad" 1856469 1856480 1856976 1856981) (-1090 "SETAGG.spad" 1852990 1853001 1856449 1856464) (-1089 "SETAGG.spad" 1849519 1849532 1852980 1852985) (-1088 "SEQAST.spad" 1849222 1849231 1849509 1849514) (-1087 "SEGXCAT.spad" 1848344 1848357 1849212 1849217) (-1086 "SEG.spad" 1848157 1848168 1848263 1848268) (-1085 "SEGCAT.spad" 1847064 1847075 1848147 1848152) (-1084 "SEGBIND.spad" 1846136 1846147 1847019 1847024) (-1083 "SEGBIND2.spad" 1845832 1845845 1846126 1846131) (-1082 "SEGAST.spad" 1845546 1845555 1845822 1845827) (-1081 "SEG2.spad" 1844971 1844984 1845502 1845507) (-1080 "SDVAR.spad" 1844247 1844258 1844961 1844966) (-1079 "SDPOL.spad" 1841637 1841648 1841928 1842055) (-1078 "SCPKG.spad" 1839716 1839727 1841627 1841632) (-1077 "SCOPE.spad" 1838861 1838870 1839706 1839711) (-1076 "SCACHE.spad" 1837543 1837554 1838851 1838856) (-1075 "SASTCAT.spad" 1837452 1837461 1837533 1837538) (-1074 "SAOS.spad" 1837324 1837333 1837442 1837447) (-1073 "SAERFFC.spad" 1837037 1837057 1837314 1837319) (-1072 "SAE.spad" 1835212 1835228 1835823 1835958) (-1071 "SAEFACT.spad" 1834913 1834933 1835202 1835207) (-1070 "RURPK.spad" 1832554 1832570 1834903 1834908) (-1069 "RULESET.spad" 1831995 1832019 1832544 1832549) (-1068 "RULE.spad" 1830199 1830223 1831985 1831990) (-1067 "RULECOLD.spad" 1830051 1830064 1830189 1830194) (-1066 "RSTRCAST.spad" 1829768 1829777 1830041 1830046) (-1065 "RSETGCD.spad" 1826146 1826166 1829758 1829763) (-1064 "RSETCAT.spad" 1815930 1815947 1826114 1826141) (-1063 "RSETCAT.spad" 1805734 1805753 1815920 1815925) (-1062 "RSDCMPK.spad" 1804186 1804206 1805724 1805729) (-1061 "RRCC.spad" 1802570 1802600 1804176 1804181) (-1060 "RRCC.spad" 1800952 1800984 1802560 1802565) (-1059 "RPTAST.spad" 1800654 1800663 1800942 1800947) (-1058 "RPOLCAT.spad" 1780014 1780029 1800522 1800649) (-1057 "RPOLCAT.spad" 1759088 1759105 1779598 1779603) (-1056 "ROUTINE.spad" 1754951 1754960 1757735 1757762) (-1055 "ROMAN.spad" 1754279 1754288 1754817 1754946) (-1054 "ROIRC.spad" 1753359 1753391 1754269 1754274) (-1053 "RNS.spad" 1752262 1752271 1753261 1753354) (-1052 "RNS.spad" 1751251 1751262 1752252 1752257) (-1051 "RNG.spad" 1750986 1750995 1751241 1751246) (-1050 "RMODULE.spad" 1750624 1750635 1750976 1750981) (-1049 "RMCAT2.spad" 1750032 1750089 1750614 1750619) (-1048 "RMATRIX.spad" 1748856 1748875 1749199 1749238) (-1047 "RMATCAT.spad" 1744389 1744420 1748812 1748851) (-1046 "RMATCAT.spad" 1739812 1739845 1744237 1744242) (-1045 "RINTERP.spad" 1739700 1739720 1739802 1739807) (-1044 "RING.spad" 1739170 1739179 1739680 1739695) (-1043 "RING.spad" 1738648 1738659 1739160 1739165) (-1042 "RIDIST.spad" 1738032 1738041 1738638 1738643) (-1041 "RGCHAIN.spad" 1736611 1736627 1737517 1737544) (-1040 "RGBCSPC.spad" 1736392 1736404 1736601 1736606) (-1039 "RGBCMDL.spad" 1735922 1735934 1736382 1736387) (-1038 "RF.spad" 1733536 1733547 1735912 1735917) (-1037 "RFFACTOR.spad" 1732998 1733009 1733526 1733531) (-1036 "RFFACT.spad" 1732733 1732745 1732988 1732993) (-1035 "RFDIST.spad" 1731721 1731730 1732723 1732728) (-1034 "RETSOL.spad" 1731138 1731151 1731711 1731716) (-1033 "RETRACT.spad" 1730566 1730577 1731128 1731133) (-1032 "RETRACT.spad" 1729992 1730005 1730556 1730561) (-1031 "RETAST.spad" 1729804 1729813 1729982 1729987) (-1030 "RESULT.spad" 1727864 1727873 1728451 1728478) (-1029 "RESRING.spad" 1727211 1727258 1727802 1727859) (-1028 "RESLATC.spad" 1726535 1726546 1727201 1727206) (-1027 "REPSQ.spad" 1726264 1726275 1726525 1726530) (-1026 "REP.spad" 1723816 1723825 1726254 1726259) (-1025 "REPDB.spad" 1723521 1723532 1723806 1723811) (-1024 "REP2.spad" 1713093 1713104 1723363 1723368) (-1023 "REP1.spad" 1707083 1707094 1713043 1713048) (-1022 "REGSET.spad" 1704880 1704897 1706729 1706756) (-1021 "REF.spad" 1704209 1704220 1704835 1704840) (-1020 "REDORDER.spad" 1703385 1703402 1704199 1704204) (-1019 "RECLOS.spad" 1702168 1702188 1702872 1702965) (-1018 "REALSOLV.spad" 1701300 1701309 1702158 1702163) (-1017 "REAL.spad" 1701172 1701181 1701290 1701295) (-1016 "REAL0Q.spad" 1698454 1698469 1701162 1701167) (-1015 "REAL0.spad" 1695282 1695297 1698444 1698449) (-1014 "RDUCEAST.spad" 1695003 1695012 1695272 1695277) (-1013 "RDIV.spad" 1694654 1694679 1694993 1694998) (-1012 "RDIST.spad" 1694217 1694228 1694644 1694649) (-1011 "RDETRS.spad" 1693013 1693031 1694207 1694212) (-1010 "RDETR.spad" 1691120 1691138 1693003 1693008) (-1009 "RDEEFS.spad" 1690193 1690210 1691110 1691115) (-1008 "RDEEF.spad" 1689189 1689206 1690183 1690188) (-1007 "RCFIELD.spad" 1686375 1686384 1689091 1689184) (-1006 "RCFIELD.spad" 1683647 1683658 1686365 1686370) (-1005 "RCAGG.spad" 1681559 1681570 1683637 1683642) (-1004 "RCAGG.spad" 1679398 1679411 1681478 1681483) (-1003 "RATRET.spad" 1678758 1678769 1679388 1679393) (-1002 "RATFACT.spad" 1678450 1678462 1678748 1678753) (-1001 "RANDSRC.spad" 1677769 1677778 1678440 1678445) (-1000 "RADUTIL.spad" 1677523 1677532 1677759 1677764) (-999 "RADIX.spad" 1674425 1674438 1675990 1676083) (-998 "RADFF.spad" 1672839 1672875 1672957 1673113) (-997 "RADCAT.spad" 1672433 1672441 1672829 1672834) (-996 "RADCAT.spad" 1672025 1672035 1672423 1672428) (-995 "QUEUE.spad" 1671368 1671378 1671632 1671659) (-994 "QUAT.spad" 1669950 1669960 1670292 1670357) (-993 "QUATCT2.spad" 1669569 1669587 1669940 1669945) (-992 "QUATCAT.spad" 1667734 1667744 1669499 1669564) (-991 "QUATCAT.spad" 1665650 1665662 1667417 1667422) (-990 "QUAGG.spad" 1664476 1664486 1665618 1665645) (-989 "QQUTAST.spad" 1664245 1664253 1664466 1664471) (-988 "QFORM.spad" 1663708 1663722 1664235 1664240) (-987 "QFCAT.spad" 1662411 1662421 1663610 1663703) (-986 "QFCAT.spad" 1660705 1660717 1661906 1661911) (-985 "QFCAT2.spad" 1660396 1660412 1660695 1660700) (-984 "QEQUAT.spad" 1659953 1659961 1660386 1660391) (-983 "QCMPACK.spad" 1654700 1654719 1659943 1659948) (-982 "QALGSET.spad" 1650775 1650807 1654614 1654619) (-981 "QALGSET2.spad" 1648771 1648789 1650765 1650770) (-980 "PWFFINTB.spad" 1646081 1646102 1648761 1648766) (-979 "PUSHVAR.spad" 1645410 1645429 1646071 1646076) (-978 "PTRANFN.spad" 1641536 1641546 1645400 1645405) (-977 "PTPACK.spad" 1638624 1638634 1641526 1641531) (-976 "PTFUNC2.spad" 1638445 1638459 1638614 1638619) (-975 "PTCAT.spad" 1637694 1637704 1638413 1638440) (-974 "PSQFR.spad" 1637001 1637025 1637684 1637689) (-973 "PSEUDLIN.spad" 1635859 1635869 1636991 1636996) (-972 "PSETPK.spad" 1621292 1621308 1635737 1635742) (-971 "PSETCAT.spad" 1615212 1615235 1621272 1621287) (-970 "PSETCAT.spad" 1609106 1609131 1615168 1615173) (-969 "PSCURVE.spad" 1608089 1608097 1609096 1609101) (-968 "PSCAT.spad" 1606856 1606885 1607987 1608084) (-967 "PSCAT.spad" 1605713 1605744 1606846 1606851) (-966 "PRTITION.spad" 1604658 1604666 1605703 1605708) (-965 "PRTDAST.spad" 1604377 1604385 1604648 1604653) (-964 "PRS.spad" 1593939 1593956 1604333 1604338) (-963 "PRQAGG.spad" 1593370 1593380 1593907 1593934) (-962 "PROPLOG.spad" 1592773 1592781 1593360 1593365) (-961 "PROPFRML.spad" 1590691 1590702 1592763 1592768) (-960 "PROPERTY.spad" 1590185 1590193 1590681 1590686) (-959 "PRODUCT.spad" 1587865 1587877 1588151 1588206) (-958 "PR.spad" 1586251 1586263 1586956 1587083) (-957 "PRINT.spad" 1586003 1586011 1586241 1586246) (-956 "PRIMES.spad" 1584254 1584264 1585993 1585998) (-955 "PRIMELT.spad" 1582235 1582249 1584244 1584249) (-954 "PRIMCAT.spad" 1581858 1581866 1582225 1582230) (-953 "PRIMARR.spad" 1580863 1580873 1581041 1581068) (-952 "PRIMARR2.spad" 1579586 1579598 1580853 1580858) (-951 "PREASSOC.spad" 1578958 1578970 1579576 1579581) (-950 "PPCURVE.spad" 1578095 1578103 1578948 1578953) (-949 "PORTNUM.spad" 1577870 1577878 1578085 1578090) (-948 "POLYROOT.spad" 1576699 1576721 1577826 1577831) (-947 "POLY.spad" 1573996 1574006 1574513 1574640) (-946 "POLYLIFT.spad" 1573257 1573280 1573986 1573991) (-945 "POLYCATQ.spad" 1571359 1571381 1573247 1573252) (-944 "POLYCAT.spad" 1564765 1564786 1571227 1571354) (-943 "POLYCAT.spad" 1557473 1557496 1563937 1563942) (-942 "POLY2UP.spad" 1556921 1556935 1557463 1557468) (-941 "POLY2.spad" 1556516 1556528 1556911 1556916) (-940 "POLUTIL.spad" 1555457 1555486 1556472 1556477) (-939 "POLTOPOL.spad" 1554205 1554220 1555447 1555452) (-938 "POINT.spad" 1553044 1553054 1553131 1553158) (-937 "PNTHEORY.spad" 1549710 1549718 1553034 1553039) (-936 "PMTOOLS.spad" 1548467 1548481 1549700 1549705) (-935 "PMSYM.spad" 1548012 1548022 1548457 1548462) (-934 "PMQFCAT.spad" 1547599 1547613 1548002 1548007) (-933 "PMPRED.spad" 1547068 1547082 1547589 1547594) (-932 "PMPREDFS.spad" 1546512 1546534 1547058 1547063) (-931 "PMPLCAT.spad" 1545582 1545600 1546444 1546449) (-930 "PMLSAGG.spad" 1545163 1545177 1545572 1545577) (-929 "PMKERNEL.spad" 1544730 1544742 1545153 1545158) (-928 "PMINS.spad" 1544306 1544316 1544720 1544725) (-927 "PMFS.spad" 1543879 1543897 1544296 1544301) (-926 "PMDOWN.spad" 1543165 1543179 1543869 1543874) (-925 "PMASS.spad" 1542177 1542185 1543155 1543160) (-924 "PMASSFS.spad" 1541146 1541162 1542167 1542172) (-923 "PLOTTOOL.spad" 1540926 1540934 1541136 1541141) (-922 "PLOT.spad" 1535757 1535765 1540916 1540921) (-921 "PLOT3D.spad" 1532177 1532185 1535747 1535752) (-920 "PLOT1.spad" 1531318 1531328 1532167 1532172) (-919 "PLEQN.spad" 1518534 1518561 1531308 1531313) (-918 "PINTERP.spad" 1518150 1518169 1518524 1518529) (-917 "PINTERPA.spad" 1517932 1517948 1518140 1518145) (-916 "PI.spad" 1517539 1517547 1517906 1517927) (-915 "PID.spad" 1516495 1516503 1517465 1517534) (-914 "PICOERCE.spad" 1516152 1516162 1516485 1516490) (-913 "PGROEB.spad" 1514749 1514763 1516142 1516147) (-912 "PGE.spad" 1506002 1506010 1514739 1514744) (-911 "PGCD.spad" 1504884 1504901 1505992 1505997) (-910 "PFRPAC.spad" 1504027 1504037 1504874 1504879) (-909 "PFR.spad" 1500684 1500694 1503929 1504022) (-908 "PFOTOOLS.spad" 1499942 1499958 1500674 1500679) (-907 "PFOQ.spad" 1499312 1499330 1499932 1499937) (-906 "PFO.spad" 1498731 1498758 1499302 1499307) (-905 "PF.spad" 1498305 1498317 1498536 1498629) (-904 "PFECAT.spad" 1495971 1495979 1498231 1498300) (-903 "PFECAT.spad" 1493665 1493675 1495927 1495932) (-902 "PFBRU.spad" 1491535 1491547 1493655 1493660) (-901 "PFBR.spad" 1489073 1489096 1491525 1491530) (-900 "PERM.spad" 1484754 1484764 1488903 1488918) (-899 "PERMGRP.spad" 1479490 1479500 1484744 1484749) (-898 "PERMCAT.spad" 1478042 1478052 1479470 1479485) (-897 "PERMAN.spad" 1476574 1476588 1478032 1478037) (-896 "PENDTREE.spad" 1475913 1475923 1476203 1476208) (-895 "PDRING.spad" 1474404 1474414 1475893 1475908) (-894 "PDRING.spad" 1472903 1472915 1474394 1474399) (-893 "PDEPROB.spad" 1471918 1471926 1472893 1472898) (-892 "PDEPACK.spad" 1465920 1465928 1471908 1471913) (-891 "PDECOMP.spad" 1465382 1465399 1465910 1465915) (-890 "PDECAT.spad" 1463736 1463744 1465372 1465377) (-889 "PCOMP.spad" 1463587 1463600 1463726 1463731) (-888 "PBWLB.spad" 1462169 1462186 1463577 1463582) (-887 "PATTERN.spad" 1456600 1456610 1462159 1462164) (-886 "PATTERN2.spad" 1456336 1456348 1456590 1456595) (-885 "PATTERN1.spad" 1454638 1454654 1456326 1456331) (-884 "PATRES.spad" 1452185 1452197 1454628 1454633) (-883 "PATRES2.spad" 1451847 1451861 1452175 1452180) (-882 "PATMATCH.spad" 1450004 1450035 1451555 1451560) (-881 "PATMAB.spad" 1449429 1449439 1449994 1449999) (-880 "PATLRES.spad" 1448513 1448527 1449419 1449424) (-879 "PATAB.spad" 1448277 1448287 1448503 1448508) (-878 "PARTPERM.spad" 1445639 1445647 1448267 1448272) (-877 "PARSURF.spad" 1445067 1445095 1445629 1445634) (-876 "PARSU2.spad" 1444862 1444878 1445057 1445062) (-875 "script-parser.spad" 1444382 1444390 1444852 1444857) (-874 "PARSCURV.spad" 1443810 1443838 1444372 1444377) (-873 "PARSC2.spad" 1443599 1443615 1443800 1443805) (-872 "PARPCURV.spad" 1443057 1443085 1443589 1443594) (-871 "PARPC2.spad" 1442846 1442862 1443047 1443052) (-870 "PAN2EXPR.spad" 1442258 1442266 1442836 1442841) (-869 "PALETTE.spad" 1441228 1441236 1442248 1442253) (-868 "PAIR.spad" 1440211 1440224 1440816 1440821) (-867 "PADICRC.spad" 1437541 1437559 1438716 1438809) (-866 "PADICRAT.spad" 1435556 1435568 1435777 1435870) (-865 "PADIC.spad" 1435251 1435263 1435482 1435551) (-864 "PADICCT.spad" 1433792 1433804 1435177 1435246) (-863 "PADEPAC.spad" 1432471 1432490 1433782 1433787) (-862 "PADE.spad" 1431211 1431227 1432461 1432466) (-861 "OWP.spad" 1430451 1430481 1431069 1431136) (-860 "OVERSET.spad" 1430024 1430032 1430441 1430446) (-859 "OVAR.spad" 1429805 1429828 1430014 1430019) (-858 "OUT.spad" 1428889 1428897 1429795 1429800) (-857 "OUTFORM.spad" 1418185 1418193 1428879 1428884) (-856 "OUTBFILE.spad" 1417603 1417611 1418175 1418180) (-855 "OUTBCON.spad" 1416601 1416609 1417593 1417598) (-854 "OUTBCON.spad" 1415597 1415607 1416591 1416596) (-853 "OSI.spad" 1415072 1415080 1415587 1415592) (-852 "OSGROUP.spad" 1414990 1414998 1415062 1415067) (-851 "ORTHPOL.spad" 1413451 1413461 1414907 1414912) (-850 "OREUP.spad" 1412904 1412932 1413131 1413170) (-849 "ORESUP.spad" 1412203 1412227 1412584 1412623) (-848 "OREPCTO.spad" 1410022 1410034 1412123 1412128) (-847 "OREPCAT.spad" 1404079 1404089 1409978 1410017) (-846 "OREPCAT.spad" 1398026 1398038 1403927 1403932) (-845 "ORDSET.spad" 1397192 1397200 1398016 1398021) (-844 "ORDSET.spad" 1396356 1396366 1397182 1397187) (-843 "ORDRING.spad" 1395746 1395754 1396336 1396351) (-842 "ORDRING.spad" 1395144 1395154 1395736 1395741) (-841 "ORDMON.spad" 1394999 1395007 1395134 1395139) (-840 "ORDFUNS.spad" 1394125 1394141 1394989 1394994) (-839 "ORDFIN.spad" 1393945 1393953 1394115 1394120) (-838 "ORDCOMP.spad" 1392410 1392420 1393492 1393521) (-837 "ORDCOMP2.spad" 1391695 1391707 1392400 1392405) (-836 "OPTPROB.spad" 1390333 1390341 1391685 1391690) (-835 "OPTPACK.spad" 1382718 1382726 1390323 1390328) (-834 "OPTCAT.spad" 1380393 1380401 1382708 1382713) (-833 "OPSIG.spad" 1380045 1380053 1380383 1380388) (-832 "OPQUERY.spad" 1379594 1379602 1380035 1380040) (-831 "OP.spad" 1379336 1379346 1379416 1379483) (-830 "OPERCAT.spad" 1378924 1378934 1379326 1379331) (-829 "OPERCAT.spad" 1378510 1378522 1378914 1378919) (-828 "ONECOMP.spad" 1377255 1377265 1378057 1378086) (-827 "ONECOMP2.spad" 1376673 1376685 1377245 1377250) (-826 "OMSERVER.spad" 1375675 1375683 1376663 1376668) (-825 "OMSAGG.spad" 1375463 1375473 1375631 1375670) (-824 "OMPKG.spad" 1374075 1374083 1375453 1375458) (-823 "OM.spad" 1373040 1373048 1374065 1374070) (-822 "OMLO.spad" 1372465 1372477 1372926 1372965) (-821 "OMEXPR.spad" 1372299 1372309 1372455 1372460) (-820 "OMERR.spad" 1371842 1371850 1372289 1372294) (-819 "OMERRK.spad" 1370876 1370884 1371832 1371837) (-818 "OMENC.spad" 1370220 1370228 1370866 1370871) (-817 "OMDEV.spad" 1364509 1364517 1370210 1370215) (-816 "OMCONN.spad" 1363918 1363926 1364499 1364504) (-815 "OINTDOM.spad" 1363681 1363689 1363844 1363913) (-814 "OFMONOID.spad" 1359868 1359878 1363671 1363676) (-813 "ODVAR.spad" 1359129 1359139 1359858 1359863) (-812 "ODR.spad" 1358773 1358799 1358941 1359090) (-811 "ODPOL.spad" 1356119 1356129 1356459 1356586) (-810 "ODP.spad" 1345966 1345986 1346339 1346470) (-809 "ODETOOLS.spad" 1344549 1344568 1345956 1345961) (-808 "ODESYS.spad" 1342199 1342216 1344539 1344544) (-807 "ODERTRIC.spad" 1338140 1338157 1342156 1342161) (-806 "ODERED.spad" 1337527 1337551 1338130 1338135) (-805 "ODERAT.spad" 1335078 1335095 1337517 1337522) (-804 "ODEPRRIC.spad" 1331969 1331991 1335068 1335073) (-803 "ODEPROB.spad" 1331226 1331234 1331959 1331964) (-802 "ODEPRIM.spad" 1328500 1328522 1331216 1331221) (-801 "ODEPAL.spad" 1327876 1327900 1328490 1328495) (-800 "ODEPACK.spad" 1314478 1314486 1327866 1327871) (-799 "ODEINT.spad" 1313909 1313925 1314468 1314473) (-798 "ODEIFTBL.spad" 1311304 1311312 1313899 1313904) (-797 "ODEEF.spad" 1306671 1306687 1311294 1311299) (-796 "ODECONST.spad" 1306190 1306208 1306661 1306666) (-795 "ODECAT.spad" 1304786 1304794 1306180 1306185) (-794 "OCT.spad" 1302924 1302934 1303640 1303679) (-793 "OCTCT2.spad" 1302568 1302589 1302914 1302919) (-792 "OC.spad" 1300342 1300352 1302524 1302563) (-791 "OC.spad" 1297841 1297853 1300025 1300030) (-790 "OCAMON.spad" 1297689 1297697 1297831 1297836) (-789 "OASGP.spad" 1297504 1297512 1297679 1297684) (-788 "OAMONS.spad" 1297024 1297032 1297494 1297499) (-787 "OAMON.spad" 1296885 1296893 1297014 1297019) (-786 "OAGROUP.spad" 1296747 1296755 1296875 1296880) (-785 "NUMTUBE.spad" 1296334 1296350 1296737 1296742) (-784 "NUMQUAD.spad" 1284196 1284204 1296324 1296329) (-783 "NUMODE.spad" 1275332 1275340 1284186 1284191) (-782 "NUMINT.spad" 1272890 1272898 1275322 1275327) (-781 "NUMFMT.spad" 1271730 1271738 1272880 1272885) (-780 "NUMERIC.spad" 1263802 1263812 1271535 1271540) (-779 "NTSCAT.spad" 1262304 1262320 1263770 1263797) (-778 "NTPOLFN.spad" 1261849 1261859 1262221 1262226) (-777 "NSUP.spad" 1254859 1254869 1259399 1259552) (-776 "NSUP2.spad" 1254251 1254263 1254849 1254854) (-775 "NSMP.spad" 1250446 1250465 1250754 1250881) (-774 "NREP.spad" 1248818 1248832 1250436 1250441) (-773 "NPCOEF.spad" 1248064 1248084 1248808 1248813) (-772 "NORMRETR.spad" 1247662 1247701 1248054 1248059) (-771 "NORMPK.spad" 1245564 1245583 1247652 1247657) (-770 "NORMMA.spad" 1245252 1245278 1245554 1245559) (-769 "NONE.spad" 1244993 1245001 1245242 1245247) (-768 "NONE1.spad" 1244669 1244679 1244983 1244988) (-767 "NODE1.spad" 1244138 1244154 1244659 1244664) (-766 "NNI.spad" 1243025 1243033 1244112 1244133) (-765 "NLINSOL.spad" 1241647 1241657 1243015 1243020) (-764 "NIPROB.spad" 1240188 1240196 1241637 1241642) (-763 "NFINTBAS.spad" 1237648 1237665 1240178 1240183) (-762 "NETCLT.spad" 1237622 1237633 1237638 1237643) (-761 "NCODIV.spad" 1235820 1235836 1237612 1237617) (-760 "NCNTFRAC.spad" 1235462 1235476 1235810 1235815) (-759 "NCEP.spad" 1233622 1233636 1235452 1235457) (-758 "NASRING.spad" 1233218 1233226 1233612 1233617) (-757 "NASRING.spad" 1232812 1232822 1233208 1233213) (-756 "NARNG.spad" 1232156 1232164 1232802 1232807) (-755 "NARNG.spad" 1231498 1231508 1232146 1232151) (-754 "NAGSP.spad" 1230571 1230579 1231488 1231493) (-753 "NAGS.spad" 1220096 1220104 1230561 1230566) (-752 "NAGF07.spad" 1218489 1218497 1220086 1220091) (-751 "NAGF04.spad" 1212721 1212729 1218479 1218484) (-750 "NAGF02.spad" 1206530 1206538 1212711 1212716) (-749 "NAGF01.spad" 1202133 1202141 1206520 1206525) (-748 "NAGE04.spad" 1195593 1195601 1202123 1202128) (-747 "NAGE02.spad" 1185935 1185943 1195583 1195588) (-746 "NAGE01.spad" 1181819 1181827 1185925 1185930) (-745 "NAGD03.spad" 1179739 1179747 1181809 1181814) (-744 "NAGD02.spad" 1172270 1172278 1179729 1179734) (-743 "NAGD01.spad" 1166383 1166391 1172260 1172265) (-742 "NAGC06.spad" 1162170 1162178 1166373 1166378) (-741 "NAGC05.spad" 1160639 1160647 1162160 1162165) (-740 "NAGC02.spad" 1159894 1159902 1160629 1160634) (-739 "NAALG.spad" 1159429 1159439 1159862 1159889) (-738 "NAALG.spad" 1158984 1158996 1159419 1159424) (-737 "MULTSQFR.spad" 1155942 1155959 1158974 1158979) (-736 "MULTFACT.spad" 1155325 1155342 1155932 1155937) (-735 "MTSCAT.spad" 1153359 1153380 1155223 1155320) (-734 "MTHING.spad" 1153016 1153026 1153349 1153354) (-733 "MSYSCMD.spad" 1152450 1152458 1153006 1153011) (-732 "MSET.spad" 1150392 1150402 1152156 1152195) (-731 "MSETAGG.spad" 1150237 1150247 1150360 1150387) (-730 "MRING.spad" 1147208 1147220 1149945 1150012) (-729 "MRF2.spad" 1146776 1146790 1147198 1147203) (-728 "MRATFAC.spad" 1146322 1146339 1146766 1146771) (-727 "MPRFF.spad" 1144352 1144371 1146312 1146317) (-726 "MPOLY.spad" 1141787 1141802 1142146 1142273) (-725 "MPCPF.spad" 1141051 1141070 1141777 1141782) (-724 "MPC3.spad" 1140866 1140906 1141041 1141046) (-723 "MPC2.spad" 1140508 1140541 1140856 1140861) (-722 "MONOTOOL.spad" 1138843 1138860 1140498 1140503) (-721 "MONOID.spad" 1138162 1138170 1138833 1138838) (-720 "MONOID.spad" 1137479 1137489 1138152 1138157) (-719 "MONOGEN.spad" 1136225 1136238 1137339 1137474) (-718 "MONOGEN.spad" 1134993 1135008 1136109 1136114) (-717 "MONADWU.spad" 1133007 1133015 1134983 1134988) (-716 "MONADWU.spad" 1131019 1131029 1132997 1133002) (-715 "MONAD.spad" 1130163 1130171 1131009 1131014) (-714 "MONAD.spad" 1129305 1129315 1130153 1130158) (-713 "MOEBIUS.spad" 1127991 1128005 1129285 1129300) (-712 "MODULE.spad" 1127861 1127871 1127959 1127986) (-711 "MODULE.spad" 1127751 1127763 1127851 1127856) (-710 "MODRING.spad" 1127082 1127121 1127731 1127746) (-709 "MODOP.spad" 1125741 1125753 1126904 1126971) (-708 "MODMONOM.spad" 1125470 1125488 1125731 1125736) (-707 "MODMON.spad" 1122229 1122245 1122948 1123101) (-706 "MODFIELD.spad" 1121587 1121626 1122131 1122224) (-705 "MMLFORM.spad" 1120447 1120455 1121577 1121582) (-704 "MMAP.spad" 1120187 1120221 1120437 1120442) (-703 "MLO.spad" 1118614 1118624 1120143 1120182) (-702 "MLIFT.spad" 1117186 1117203 1118604 1118609) (-701 "MKUCFUNC.spad" 1116719 1116737 1117176 1117181) (-700 "MKRECORD.spad" 1116321 1116334 1116709 1116714) (-699 "MKFUNC.spad" 1115702 1115712 1116311 1116316) (-698 "MKFLCFN.spad" 1114658 1114668 1115692 1115697) (-697 "MKCHSET.spad" 1114523 1114533 1114648 1114653) (-696 "MKBCFUNC.spad" 1114008 1114026 1114513 1114518) (-695 "MINT.spad" 1113447 1113455 1113910 1114003) (-694 "MHROWRED.spad" 1111948 1111958 1113437 1113442) (-693 "MFLOAT.spad" 1110464 1110472 1111838 1111943) (-692 "MFINFACT.spad" 1109864 1109886 1110454 1110459) (-691 "MESH.spad" 1107596 1107604 1109854 1109859) (-690 "MDDFACT.spad" 1105789 1105799 1107586 1107591) (-689 "MDAGG.spad" 1105076 1105086 1105769 1105784) (-688 "MCMPLX.spad" 1101062 1101070 1101676 1101865) (-687 "MCDEN.spad" 1100270 1100282 1101052 1101057) (-686 "MCALCFN.spad" 1097372 1097398 1100260 1100265) (-685 "MAYBE.spad" 1096656 1096667 1097362 1097367) (-684 "MATSTOR.spad" 1093932 1093942 1096646 1096651) (-683 "MATRIX.spad" 1092636 1092646 1093120 1093147) (-682 "MATLIN.spad" 1089962 1089986 1092520 1092525) (-681 "MATCAT.spad" 1081547 1081569 1089930 1089957) (-680 "MATCAT.spad" 1073004 1073028 1081389 1081394) (-679 "MATCAT2.spad" 1072272 1072320 1072994 1072999) (-678 "MAPPKG3.spad" 1071171 1071185 1072262 1072267) (-677 "MAPPKG2.spad" 1070505 1070517 1071161 1071166) (-676 "MAPPKG1.spad" 1069323 1069333 1070495 1070500) (-675 "MAPPAST.spad" 1068636 1068644 1069313 1069318) (-674 "MAPHACK3.spad" 1068444 1068458 1068626 1068631) (-673 "MAPHACK2.spad" 1068209 1068221 1068434 1068439) (-672 "MAPHACK1.spad" 1067839 1067849 1068199 1068204) (-671 "MAGMA.spad" 1065629 1065646 1067829 1067834) (-670 "MACROAST.spad" 1065208 1065216 1065619 1065624) (-669 "M3D.spad" 1062904 1062914 1064586 1064591) (-668 "LZSTAGG.spad" 1060132 1060142 1062894 1062899) (-667 "LZSTAGG.spad" 1057358 1057370 1060122 1060127) (-666 "LWORD.spad" 1054063 1054080 1057348 1057353) (-665 "LSTAST.spad" 1053847 1053855 1054053 1054058) (-664 "LSQM.spad" 1052073 1052087 1052471 1052522) (-663 "LSPP.spad" 1051606 1051623 1052063 1052068) (-662 "LSMP.spad" 1050446 1050474 1051596 1051601) (-661 "LSMP1.spad" 1048250 1048264 1050436 1050441) (-660 "LSAGG.spad" 1047919 1047929 1048218 1048245) (-659 "LSAGG.spad" 1047608 1047620 1047909 1047914) (-658 "LPOLY.spad" 1046562 1046581 1047464 1047533) (-657 "LPEFRAC.spad" 1045819 1045829 1046552 1046557) (-656 "LO.spad" 1045220 1045234 1045753 1045780) (-655 "LOGIC.spad" 1044822 1044830 1045210 1045215) (-654 "LOGIC.spad" 1044422 1044432 1044812 1044817) (-653 "LODOOPS.spad" 1043340 1043352 1044412 1044417) (-652 "LODO.spad" 1042724 1042740 1043020 1043059) (-651 "LODOF.spad" 1041768 1041785 1042681 1042686) (-650 "LODOCAT.spad" 1040426 1040436 1041724 1041763) (-649 "LODOCAT.spad" 1039082 1039094 1040382 1040387) (-648 "LODO2.spad" 1038355 1038367 1038762 1038801) (-647 "LODO1.spad" 1037755 1037765 1038035 1038074) (-646 "LODEEF.spad" 1036527 1036545 1037745 1037750) (-645 "LNAGG.spad" 1032329 1032339 1036517 1036522) (-644 "LNAGG.spad" 1028095 1028107 1032285 1032290) (-643 "LMOPS.spad" 1024831 1024848 1028085 1028090) (-642 "LMODULE.spad" 1024473 1024483 1024821 1024826) (-641 "LMDICT.spad" 1023756 1023766 1024024 1024051) (-640 "LITERAL.spad" 1023662 1023673 1023746 1023751) (-639 "LIST.spad" 1021380 1021390 1022809 1022836) (-638 "LIST3.spad" 1020671 1020685 1021370 1021375) (-637 "LIST2.spad" 1019311 1019323 1020661 1020666) (-636 "LIST2MAP.spad" 1016188 1016200 1019301 1019306) (-635 "LINEXP.spad" 1015620 1015630 1016168 1016183) (-634 "LINDEP.spad" 1014397 1014409 1015532 1015537) (-633 "LIMITRF.spad" 1012311 1012321 1014387 1014392) (-632 "LIMITPS.spad" 1011194 1011207 1012301 1012306) (-631 "LIE.spad" 1009208 1009220 1010484 1010629) (-630 "LIECAT.spad" 1008684 1008694 1009134 1009203) (-629 "LIECAT.spad" 1008188 1008200 1008640 1008645) (-628 "LIB.spad" 1006236 1006244 1006847 1006862) (-627 "LGROBP.spad" 1003589 1003608 1006226 1006231) (-626 "LF.spad" 1002508 1002524 1003579 1003584) (-625 "LFCAT.spad" 1001527 1001535 1002498 1002503) (-624 "LEXTRIPK.spad" 997030 997045 1001517 1001522) (-623 "LEXP.spad" 995033 995060 997010 997025) (-622 "LETAST.spad" 994732 994740 995023 995028) (-621 "LEADCDET.spad" 993116 993133 994722 994727) (-620 "LAZM3PK.spad" 991820 991842 993106 993111) (-619 "LAUPOL.spad" 990509 990522 991413 991482) (-618 "LAPLACE.spad" 990082 990098 990499 990504) (-617 "LA.spad" 989522 989536 990004 990043) (-616 "LALG.spad" 989298 989308 989502 989517) (-615 "LALG.spad" 989082 989094 989288 989293) (-614 "KVTFROM.spad" 988817 988827 989072 989077) (-613 "KTVLOGIC.spad" 988240 988248 988807 988812) (-612 "KRCFROM.spad" 987978 987988 988230 988235) (-611 "KOVACIC.spad" 986691 986708 987968 987973) (-610 "KONVERT.spad" 986413 986423 986681 986686) (-609 "KOERCE.spad" 986150 986160 986403 986408) (-608 "KERNEL.spad" 984685 984695 985934 985939) (-607 "KERNEL2.spad" 984388 984400 984675 984680) (-606 "KDAGG.spad" 983491 983513 984368 984383) (-605 "KDAGG.spad" 982602 982626 983481 983486) (-604 "KAFILE.spad" 981565 981581 981800 981827) (-603 "JORDAN.spad" 979392 979404 980855 981000) (-602 "JOINAST.spad" 979086 979094 979382 979387) (-601 "JAVACODE.spad" 978952 978960 979076 979081) (-600 "IXAGG.spad" 977075 977099 978942 978947) (-599 "IXAGG.spad" 975053 975079 976922 976927) (-598 "IVECTOR.spad" 973824 973839 973979 974006) (-597 "ITUPLE.spad" 972969 972979 973814 973819) (-596 "ITRIGMNP.spad" 971780 971799 972959 972964) (-595 "ITFUN3.spad" 971274 971288 971770 971775) (-594 "ITFUN2.spad" 971004 971016 971264 971269) (-593 "ITAYLOR.spad" 968796 968811 970840 970965) (-592 "ISUPS.spad" 961207 961222 967770 967867) (-591 "ISUMP.spad" 960704 960720 961197 961202) (-590 "ISTRING.spad" 959707 959720 959873 959900) (-589 "ISAST.spad" 959426 959434 959697 959702) (-588 "IRURPK.spad" 958139 958158 959416 959421) (-587 "IRSN.spad" 956099 956107 958129 958134) (-586 "IRRF2F.spad" 954574 954584 956055 956060) (-585 "IRREDFFX.spad" 954175 954186 954564 954569) (-584 "IROOT.spad" 952506 952516 954165 954170) (-583 "IR.spad" 950295 950309 952361 952388) (-582 "IR2.spad" 949315 949331 950285 950290) (-581 "IR2F.spad" 948515 948531 949305 949310) (-580 "IPRNTPK.spad" 948275 948283 948505 948510) (-579 "IPF.spad" 947840 947852 948080 948173) (-578 "IPADIC.spad" 947601 947627 947766 947835) (-577 "IP4ADDR.spad" 947158 947166 947591 947596) (-576 "IOMODE.spad" 946779 946787 947148 947153) (-575 "IOBFILE.spad" 946140 946148 946769 946774) (-574 "IOBCON.spad" 946005 946013 946130 946135) (-573 "INVLAPLA.spad" 945650 945666 945995 946000) (-572 "INTTR.spad" 938896 938913 945640 945645) (-571 "INTTOOLS.spad" 936607 936623 938470 938475) (-570 "INTSLPE.spad" 935913 935921 936597 936602) (-569 "INTRVL.spad" 935479 935489 935827 935908) (-568 "INTRF.spad" 933843 933857 935469 935474) (-567 "INTRET.spad" 933275 933285 933833 933838) (-566 "INTRAT.spad" 931950 931967 933265 933270) (-565 "INTPM.spad" 930313 930329 931593 931598) (-564 "INTPAF.spad" 928081 928099 930245 930250) (-563 "INTPACK.spad" 918391 918399 928071 928076) (-562 "INT.spad" 917752 917760 918245 918386) (-561 "INTHERTR.spad" 917018 917035 917742 917747) (-560 "INTHERAL.spad" 916684 916708 917008 917013) (-559 "INTHEORY.spad" 913097 913105 916674 916679) (-558 "INTG0.spad" 906560 906578 913029 913034) (-557 "INTFTBL.spad" 900589 900597 906550 906555) (-556 "INTFACT.spad" 899648 899658 900579 900584) (-555 "INTEF.spad" 897963 897979 899638 899643) (-554 "INTDOM.spad" 896578 896586 897889 897958) (-553 "INTDOM.spad" 895255 895265 896568 896573) (-552 "INTCAT.spad" 893508 893518 895169 895250) (-551 "INTBIT.spad" 893011 893019 893498 893503) (-550 "INTALG.spad" 892193 892220 893001 893006) (-549 "INTAF.spad" 891685 891701 892183 892188) (-548 "INTABL.spad" 890203 890234 890366 890393) (-547 "INT8.spad" 890083 890091 890193 890198) (-546 "INT32.spad" 889962 889970 890073 890078) (-545 "INT16.spad" 889841 889849 889952 889957) (-544 "INS.spad" 887308 887316 889743 889836) (-543 "INS.spad" 884861 884871 887298 887303) (-542 "INPSIGN.spad" 884295 884308 884851 884856) (-541 "INPRODPF.spad" 883361 883380 884285 884290) (-540 "INPRODFF.spad" 882419 882443 883351 883356) (-539 "INNMFACT.spad" 881390 881407 882409 882414) (-538 "INMODGCD.spad" 880874 880904 881380 881385) (-537 "INFSP.spad" 879159 879181 880864 880869) (-536 "INFPROD0.spad" 878209 878228 879149 879154) (-535 "INFORM.spad" 875370 875378 878199 878204) (-534 "INFORM1.spad" 874995 875005 875360 875365) (-533 "INFINITY.spad" 874547 874555 874985 874990) (-532 "INETCLTS.spad" 874524 874532 874537 874542) (-531 "INEP.spad" 873056 873078 874514 874519) (-530 "INDE.spad" 872785 872802 873046 873051) (-529 "INCRMAPS.spad" 872206 872216 872775 872780) (-528 "INBFILE.spad" 871278 871286 872196 872201) (-527 "INBFF.spad" 867048 867059 871268 871273) (-526 "INBCON.spad" 865336 865344 867038 867043) (-525 "INBCON.spad" 863622 863632 865326 865331) (-524 "INAST.spad" 863287 863295 863612 863617) (-523 "IMPTAST.spad" 862995 863003 863277 863282) (-522 "IMATRIX.spad" 861940 861966 862452 862479) (-521 "IMATQF.spad" 861034 861078 861896 861901) (-520 "IMATLIN.spad" 859639 859663 860990 860995) (-519 "ILIST.spad" 858295 858310 858822 858849) (-518 "IIARRAY2.spad" 857683 857721 857902 857929) (-517 "IFF.spad" 857093 857109 857364 857457) (-516 "IFAST.spad" 856707 856715 857083 857088) (-515 "IFARRAY.spad" 854194 854209 855890 855917) (-514 "IFAMON.spad" 854056 854073 854150 854155) (-513 "IEVALAB.spad" 853445 853457 854046 854051) (-512 "IEVALAB.spad" 852832 852846 853435 853440) (-511 "IDPO.spad" 852630 852642 852822 852827) (-510 "IDPOAMS.spad" 852386 852398 852620 852625) (-509 "IDPOAM.spad" 852106 852118 852376 852381) (-508 "IDPC.spad" 851040 851052 852096 852101) (-507 "IDPAM.spad" 850785 850797 851030 851035) (-506 "IDPAG.spad" 850532 850544 850775 850780) (-505 "IDENT.spad" 850304 850312 850522 850527) (-504 "IDECOMP.spad" 847541 847559 850294 850299) (-503 "IDEAL.spad" 842464 842503 847476 847481) (-502 "ICDEN.spad" 841615 841631 842454 842459) (-501 "ICARD.spad" 840804 840812 841605 841610) (-500 "IBPTOOLS.spad" 839397 839414 840794 840799) (-499 "IBITS.spad" 838596 838609 839033 839060) (-498 "IBATOOL.spad" 835471 835490 838586 838591) (-497 "IBACHIN.spad" 833958 833973 835461 835466) (-496 "IARRAY2.spad" 832946 832972 833565 833592) (-495 "IARRAY1.spad" 831991 832006 832129 832156) (-494 "IAN.spad" 830204 830212 831807 831900) (-493 "IALGFACT.spad" 829805 829838 830194 830199) (-492 "HYPCAT.spad" 829229 829237 829795 829800) (-491 "HYPCAT.spad" 828651 828661 829219 829224) (-490 "HOSTNAME.spad" 828459 828467 828641 828646) (-489 "HOMOTOP.spad" 828202 828212 828449 828454) (-488 "HOAGG.spad" 825470 825480 828192 828197) (-487 "HOAGG.spad" 822513 822525 825237 825242) (-486 "HEXADEC.spad" 820615 820623 820980 821073) (-485 "HEUGCD.spad" 819630 819641 820605 820610) (-484 "HELLFDIV.spad" 819220 819244 819620 819625) (-483 "HEAP.spad" 818612 818622 818827 818854) (-482 "HEADAST.spad" 818143 818151 818602 818607) (-481 "HDP.spad" 807986 808002 808363 808494) (-480 "HDMP.spad" 805162 805177 805780 805907) (-479 "HB.spad" 803399 803407 805152 805157) (-478 "HASHTBL.spad" 801869 801900 802080 802107) (-477 "HASAST.spad" 801585 801593 801859 801864) (-476 "HACKPI.spad" 801068 801076 801487 801580) (-475 "GTSET.spad" 800007 800023 800714 800741) (-474 "GSTBL.spad" 798526 798561 798700 798715) (-473 "GSERIES.spad" 795693 795720 796658 796807) (-472 "GROUP.spad" 794962 794970 795673 795688) (-471 "GROUP.spad" 794239 794249 794952 794957) (-470 "GROEBSOL.spad" 792727 792748 794229 794234) (-469 "GRMOD.spad" 791298 791310 792717 792722) (-468 "GRMOD.spad" 789867 789881 791288 791293) (-467 "GRIMAGE.spad" 782472 782480 789857 789862) (-466 "GRDEF.spad" 780851 780859 782462 782467) (-465 "GRAY.spad" 779310 779318 780841 780846) (-464 "GRALG.spad" 778357 778369 779300 779305) (-463 "GRALG.spad" 777402 777416 778347 778352) (-462 "GPOLSET.spad" 776856 776879 777084 777111) (-461 "GOSPER.spad" 776121 776139 776846 776851) (-460 "GMODPOL.spad" 775259 775286 776089 776116) (-459 "GHENSEL.spad" 774328 774342 775249 775254) (-458 "GENUPS.spad" 770429 770442 774318 774323) (-457 "GENUFACT.spad" 770006 770016 770419 770424) (-456 "GENPGCD.spad" 769590 769607 769996 770001) (-455 "GENMFACT.spad" 769042 769061 769580 769585) (-454 "GENEEZ.spad" 766981 766994 769032 769037) (-453 "GDMP.spad" 763999 764016 764775 764902) (-452 "GCNAALG.spad" 757894 757921 763793 763860) (-451 "GCDDOM.spad" 757066 757074 757820 757889) (-450 "GCDDOM.spad" 756300 756310 757056 757061) (-449 "GB.spad" 753818 753856 756256 756261) (-448 "GBINTERN.spad" 749838 749876 753808 753813) (-447 "GBF.spad" 745595 745633 749828 749833) (-446 "GBEUCLID.spad" 743469 743507 745585 745590) (-445 "GAUSSFAC.spad" 742766 742774 743459 743464) (-444 "GALUTIL.spad" 741088 741098 742722 742727) (-443 "GALPOLYU.spad" 739534 739547 741078 741083) (-442 "GALFACTU.spad" 737699 737718 739524 739529) (-441 "GALFACT.spad" 727832 727843 737689 737694) (-440 "FVFUN.spad" 724855 724863 727822 727827) (-439 "FVC.spad" 723907 723915 724845 724850) (-438 "FUNDESC.spad" 723585 723593 723897 723902) (-437 "FUNCTION.spad" 723434 723446 723575 723580) (-436 "FT.spad" 721727 721735 723424 723429) (-435 "FTEM.spad" 720890 720898 721717 721722) (-434 "FSUPFACT.spad" 719790 719809 720826 720831) (-433 "FST.spad" 717876 717884 719780 719785) (-432 "FSRED.spad" 717354 717370 717866 717871) (-431 "FSPRMELT.spad" 716178 716194 717311 717316) (-430 "FSPECF.spad" 714255 714271 716168 716173) (-429 "FS.spad" 708317 708327 714030 714250) (-428 "FS.spad" 702157 702169 707872 707877) (-427 "FSINT.spad" 701815 701831 702147 702152) (-426 "FSERIES.spad" 701002 701014 701635 701734) (-425 "FSCINT.spad" 700315 700331 700992 700997) (-424 "FSAGG.spad" 699432 699442 700271 700310) (-423 "FSAGG.spad" 698511 698523 699352 699357) (-422 "FSAGG2.spad" 697210 697226 698501 698506) (-421 "FS2UPS.spad" 691693 691727 697200 697205) (-420 "FS2.spad" 691338 691354 691683 691688) (-419 "FS2EXPXP.spad" 690461 690484 691328 691333) (-418 "FRUTIL.spad" 689403 689413 690451 690456) (-417 "FR.spad" 683097 683107 688427 688496) (-416 "FRNAALG.spad" 678184 678194 683039 683092) (-415 "FRNAALG.spad" 673283 673295 678140 678145) (-414 "FRNAAF2.spad" 672737 672755 673273 673278) (-413 "FRMOD.spad" 672131 672161 672668 672673) (-412 "FRIDEAL.spad" 671326 671347 672111 672126) (-411 "FRIDEAL2.spad" 670928 670960 671316 671321) (-410 "FRETRCT.spad" 670439 670449 670918 670923) (-409 "FRETRCT.spad" 669816 669828 670297 670302) (-408 "FRAMALG.spad" 668144 668157 669772 669811) (-407 "FRAMALG.spad" 666504 666519 668134 668139) (-406 "FRAC.spad" 663603 663613 664006 664179) (-405 "FRAC2.spad" 663206 663218 663593 663598) (-404 "FR2.spad" 662540 662552 663196 663201) (-403 "FPS.spad" 659349 659357 662430 662535) (-402 "FPS.spad" 656186 656196 659269 659274) (-401 "FPC.spad" 655228 655236 656088 656181) (-400 "FPC.spad" 654356 654366 655218 655223) (-399 "FPATMAB.spad" 654118 654128 654346 654351) (-398 "FPARFRAC.spad" 652591 652608 654108 654113) (-397 "FORTRAN.spad" 651097 651140 652581 652586) (-396 "FORT.spad" 650026 650034 651087 651092) (-395 "FORTFN.spad" 647196 647204 650016 650021) (-394 "FORTCAT.spad" 646880 646888 647186 647191) (-393 "FORMULA.spad" 644344 644352 646870 646875) (-392 "FORMULA1.spad" 643823 643833 644334 644339) (-391 "FORDER.spad" 643514 643538 643813 643818) (-390 "FOP.spad" 642715 642723 643504 643509) (-389 "FNLA.spad" 642139 642161 642683 642710) (-388 "FNCAT.spad" 640726 640734 642129 642134) (-387 "FNAME.spad" 640618 640626 640716 640721) (-386 "FMTC.spad" 640416 640424 640544 640613) (-385 "FMONOID.spad" 637471 637481 640372 640377) (-384 "FM.spad" 637166 637178 637405 637432) (-383 "FMFUN.spad" 634196 634204 637156 637161) (-382 "FMC.spad" 633248 633256 634186 634191) (-381 "FMCAT.spad" 630902 630920 633216 633243) (-380 "FM1.spad" 630259 630271 630836 630863) (-379 "FLOATRP.spad" 627980 627994 630249 630254) (-378 "FLOAT.spad" 621268 621276 627846 627975) (-377 "FLOATCP.spad" 618685 618699 621258 621263) (-376 "FLINEXP.spad" 618397 618407 618665 618680) (-375 "FLINEXP.spad" 618063 618075 618333 618338) (-374 "FLASORT.spad" 617383 617395 618053 618058) (-373 "FLALG.spad" 615029 615048 617309 617378) (-372 "FLAGG.spad" 612047 612057 615009 615024) (-371 "FLAGG.spad" 608966 608978 611930 611935) (-370 "FLAGG2.spad" 607647 607663 608956 608961) (-369 "FINRALG.spad" 605676 605689 607603 607642) (-368 "FINRALG.spad" 603631 603646 605560 605565) (-367 "FINITE.spad" 602783 602791 603621 603626) (-366 "FINAALG.spad" 591764 591774 602725 602778) (-365 "FINAALG.spad" 580757 580769 591720 591725) (-364 "FILE.spad" 580340 580350 580747 580752) (-363 "FILECAT.spad" 578858 578875 580330 580335) (-362 "FIELD.spad" 578264 578272 578760 578853) (-361 "FIELD.spad" 577756 577766 578254 578259) (-360 "FGROUP.spad" 576365 576375 577736 577751) (-359 "FGLMICPK.spad" 575152 575167 576355 576360) (-358 "FFX.spad" 574527 574542 574868 574961) (-357 "FFSLPE.spad" 574016 574037 574517 574522) (-356 "FFPOLY.spad" 565268 565279 574006 574011) (-355 "FFPOLY2.spad" 564328 564345 565258 565263) (-354 "FFP.spad" 563725 563745 564044 564137) (-353 "FF.spad" 563173 563189 563406 563499) (-352 "FFNBX.spad" 561685 561705 562889 562982) (-351 "FFNBP.spad" 560198 560215 561401 561494) (-350 "FFNB.spad" 558663 558684 559879 559972) (-349 "FFINTBAS.spad" 556077 556096 558653 558658) (-348 "FFIELDC.spad" 553652 553660 555979 556072) (-347 "FFIELDC.spad" 551313 551323 553642 553647) (-346 "FFHOM.spad" 550061 550078 551303 551308) (-345 "FFF.spad" 547496 547507 550051 550056) (-344 "FFCGX.spad" 546343 546363 547212 547305) (-343 "FFCGP.spad" 545232 545252 546059 546152) (-342 "FFCG.spad" 544024 544045 544913 545006) (-341 "FFCAT.spad" 537051 537073 543863 544019) (-340 "FFCAT.spad" 530157 530181 536971 536976) (-339 "FFCAT2.spad" 529902 529942 530147 530152) (-338 "FEXPR.spad" 521611 521657 529658 529697) (-337 "FEVALAB.spad" 521317 521327 521601 521606) (-336 "FEVALAB.spad" 520808 520820 521094 521099) (-335 "FDIV.spad" 520250 520274 520798 520803) (-334 "FDIVCAT.spad" 518292 518316 520240 520245) (-333 "FDIVCAT.spad" 516332 516358 518282 518287) (-332 "FDIV2.spad" 515986 516026 516322 516327) (-331 "FCPAK1.spad" 514539 514547 515976 515981) (-330 "FCOMP.spad" 513918 513928 514529 514534) (-329 "FC.spad" 503833 503841 513908 513913) (-328 "FAXF.spad" 496768 496782 503735 503828) (-327 "FAXF.spad" 489755 489771 496724 496729) (-326 "FARRAY.spad" 487901 487911 488938 488965) (-325 "FAMR.spad" 486021 486033 487799 487896) (-324 "FAMR.spad" 484125 484139 485905 485910) (-323 "FAMONOID.spad" 483775 483785 484079 484084) (-322 "FAMONC.spad" 481997 482009 483765 483770) (-321 "FAGROUP.spad" 481603 481613 481893 481920) (-320 "FACUTIL.spad" 479799 479816 481593 481598) (-319 "FACTFUNC.spad" 478975 478985 479789 479794) (-318 "EXPUPXS.spad" 475808 475831 477107 477256) (-317 "EXPRTUBE.spad" 473036 473044 475798 475803) (-316 "EXPRODE.spad" 469908 469924 473026 473031) (-315 "EXPR.spad" 465183 465193 465897 466304) (-314 "EXPR2UPS.spad" 461275 461288 465173 465178) (-313 "EXPR2.spad" 460978 460990 461265 461270) (-312 "EXPEXPAN.spad" 457916 457941 458550 458643) (-311 "EXIT.spad" 457587 457595 457906 457911) (-310 "EXITAST.spad" 457323 457331 457577 457582) (-309 "EVALCYC.spad" 456781 456795 457313 457318) (-308 "EVALAB.spad" 456345 456355 456771 456776) (-307 "EVALAB.spad" 455907 455919 456335 456340) (-306 "EUCDOM.spad" 453449 453457 455833 455902) (-305 "EUCDOM.spad" 451053 451063 453439 453444) (-304 "ESTOOLS.spad" 442893 442901 451043 451048) (-303 "ESTOOLS2.spad" 442494 442508 442883 442888) (-302 "ESTOOLS1.spad" 442179 442190 442484 442489) (-301 "ES.spad" 434726 434734 442169 442174) (-300 "ES.spad" 427179 427189 434624 434629) (-299 "ESCONT.spad" 423952 423960 427169 427174) (-298 "ESCONT1.spad" 423701 423713 423942 423947) (-297 "ES2.spad" 423196 423212 423691 423696) (-296 "ES1.spad" 422762 422778 423186 423191) (-295 "ERROR.spad" 420083 420091 422752 422757) (-294 "EQTBL.spad" 418555 418577 418764 418791) (-293 "EQ.spad" 413429 413439 416228 416340) (-292 "EQ2.spad" 413145 413157 413419 413424) (-291 "EP.spad" 409459 409469 413135 413140) (-290 "ENV.spad" 408161 408169 409449 409454) (-289 "ENTIRER.spad" 407829 407837 408105 408156) (-288 "EMR.spad" 407030 407071 407755 407824) (-287 "ELTAGG.spad" 405270 405289 407020 407025) (-286 "ELTAGG.spad" 403474 403495 405226 405231) (-285 "ELTAB.spad" 402921 402939 403464 403469) (-284 "ELFUTS.spad" 402300 402319 402911 402916) (-283 "ELEMFUN.spad" 401989 401997 402290 402295) (-282 "ELEMFUN.spad" 401676 401686 401979 401984) (-281 "ELAGG.spad" 399619 399629 401656 401671) (-280 "ELAGG.spad" 397499 397511 399538 399543) (-279 "ELABEXPR.spad" 396430 396438 397489 397494) (-278 "EFUPXS.spad" 393206 393236 396386 396391) (-277 "EFULS.spad" 390042 390065 393162 393167) (-276 "EFSTRUC.spad" 387997 388013 390032 390037) (-275 "EF.spad" 382763 382779 387987 387992) (-274 "EAB.spad" 381039 381047 382753 382758) (-273 "E04UCFA.spad" 380575 380583 381029 381034) (-272 "E04NAFA.spad" 380152 380160 380565 380570) (-271 "E04MBFA.spad" 379732 379740 380142 380147) (-270 "E04JAFA.spad" 379268 379276 379722 379727) (-269 "E04GCFA.spad" 378804 378812 379258 379263) (-268 "E04FDFA.spad" 378340 378348 378794 378799) (-267 "E04DGFA.spad" 377876 377884 378330 378335) (-266 "E04AGNT.spad" 373718 373726 377866 377871) (-265 "DVARCAT.spad" 370403 370413 373708 373713) (-264 "DVARCAT.spad" 367086 367098 370393 370398) (-263 "DSMP.spad" 364517 364531 364822 364949) (-262 "DROPT.spad" 358462 358470 364507 364512) (-261 "DROPT1.spad" 358125 358135 358452 358457) (-260 "DROPT0.spad" 352952 352960 358115 358120) (-259 "DRAWPT.spad" 351107 351115 352942 352947) (-258 "DRAW.spad" 343707 343720 351097 351102) (-257 "DRAWHACK.spad" 343015 343025 343697 343702) (-256 "DRAWCX.spad" 340457 340465 343005 343010) (-255 "DRAWCURV.spad" 339994 340009 340447 340452) (-254 "DRAWCFUN.spad" 329166 329174 339984 339989) (-253 "DQAGG.spad" 327334 327344 329134 329161) (-252 "DPOLCAT.spad" 322675 322691 327202 327329) (-251 "DPOLCAT.spad" 318102 318120 322631 322636) (-250 "DPMO.spad" 310328 310344 310466 310767) (-249 "DPMM.spad" 302567 302585 302692 302993) (-248 "DOMCTOR.spad" 302459 302467 302557 302562) (-247 "DOMAIN.spad" 301590 301598 302449 302454) (-246 "DMP.spad" 298812 298827 299384 299511) (-245 "DLP.spad" 298160 298170 298802 298807) (-244 "DLIST.spad" 296739 296749 297343 297370) (-243 "DLAGG.spad" 295150 295160 296729 296734) (-242 "DIVRING.spad" 294692 294700 295094 295145) (-241 "DIVRING.spad" 294278 294288 294682 294687) (-240 "DISPLAY.spad" 292458 292466 294268 294273) (-239 "DIRPROD.spad" 282038 282054 282678 282809) (-238 "DIRPROD2.spad" 280846 280864 282028 282033) (-237 "DIRPCAT.spad" 279788 279804 280710 280841) (-236 "DIRPCAT.spad" 278459 278477 279383 279388) (-235 "DIOSP.spad" 277284 277292 278449 278454) (-234 "DIOPS.spad" 276268 276278 277264 277279) (-233 "DIOPS.spad" 275226 275238 276224 276229) (-232 "DIFRING.spad" 274518 274526 275206 275221) (-231 "DIFRING.spad" 273818 273828 274508 274513) (-230 "DIFEXT.spad" 272977 272987 273798 273813) (-229 "DIFEXT.spad" 272053 272065 272876 272881) (-228 "DIAGG.spad" 271683 271693 272033 272048) (-227 "DIAGG.spad" 271321 271333 271673 271678) (-226 "DHMATRIX.spad" 269625 269635 270778 270805) (-225 "DFSFUN.spad" 263033 263041 269615 269620) (-224 "DFLOAT.spad" 259754 259762 262923 263028) (-223 "DFINTTLS.spad" 257963 257979 259744 259749) (-222 "DERHAM.spad" 255873 255905 257943 257958) (-221 "DEQUEUE.spad" 255191 255201 255480 255507) (-220 "DEGRED.spad" 254806 254820 255181 255186) (-219 "DEFINTRF.spad" 252331 252341 254796 254801) (-218 "DEFINTEF.spad" 250827 250843 252321 252326) (-217 "DEFAST.spad" 250195 250203 250817 250822) (-216 "DECIMAL.spad" 248301 248309 248662 248755) (-215 "DDFACT.spad" 246100 246117 248291 248296) (-214 "DBLRESP.spad" 245698 245722 246090 246095) (-213 "DBASE.spad" 244352 244362 245688 245693) (-212 "DATAARY.spad" 243814 243827 244342 244347) (-211 "D03FAFA.spad" 243642 243650 243804 243809) (-210 "D03EEFA.spad" 243462 243470 243632 243637) (-209 "D03AGNT.spad" 242542 242550 243452 243457) (-208 "D02EJFA.spad" 242004 242012 242532 242537) (-207 "D02CJFA.spad" 241482 241490 241994 241999) (-206 "D02BHFA.spad" 240972 240980 241472 241477) (-205 "D02BBFA.spad" 240462 240470 240962 240967) (-204 "D02AGNT.spad" 235266 235274 240452 240457) (-203 "D01WGTS.spad" 233585 233593 235256 235261) (-202 "D01TRNS.spad" 233562 233570 233575 233580) (-201 "D01GBFA.spad" 233084 233092 233552 233557) (-200 "D01FCFA.spad" 232606 232614 233074 233079) (-199 "D01ASFA.spad" 232074 232082 232596 232601) (-198 "D01AQFA.spad" 231520 231528 232064 232069) (-197 "D01APFA.spad" 230944 230952 231510 231515) (-196 "D01ANFA.spad" 230438 230446 230934 230939) (-195 "D01AMFA.spad" 229948 229956 230428 230433) (-194 "D01ALFA.spad" 229488 229496 229938 229943) (-193 "D01AKFA.spad" 229014 229022 229478 229483) (-192 "D01AJFA.spad" 228537 228545 229004 229009) (-191 "D01AGNT.spad" 224596 224604 228527 228532) (-190 "CYCLOTOM.spad" 224102 224110 224586 224591) (-189 "CYCLES.spad" 220934 220942 224092 224097) (-188 "CVMP.spad" 220351 220361 220924 220929) (-187 "CTRIGMNP.spad" 218841 218857 220341 220346) (-186 "CTOR.spad" 218536 218544 218831 218836) (-185 "CTORKIND.spad" 218139 218147 218526 218531) (-184 "CTORCAT.spad" 217594 217602 218129 218134) (-183 "CTORCAT.spad" 217047 217057 217584 217589) (-182 "CTORCALL.spad" 216627 216635 217037 217042) (-181 "CSTTOOLS.spad" 215870 215883 216617 216622) (-180 "CRFP.spad" 209574 209587 215860 215865) (-179 "CRCEAST.spad" 209294 209302 209564 209569) (-178 "CRAPACK.spad" 208337 208347 209284 209289) (-177 "CPMATCH.spad" 207837 207852 208262 208267) (-176 "CPIMA.spad" 207542 207561 207827 207832) (-175 "COORDSYS.spad" 202435 202445 207532 207537) (-174 "CONTOUR.spad" 201837 201845 202425 202430) (-173 "CONTFRAC.spad" 197449 197459 201739 201832) (-172 "CONDUIT.spad" 197207 197215 197439 197444) (-171 "COMRING.spad" 196881 196889 197145 197202) (-170 "COMPPROP.spad" 196395 196403 196871 196876) (-169 "COMPLPAT.spad" 196162 196177 196385 196390) (-168 "COMPLEX.spad" 190198 190208 190442 190691) (-167 "COMPLEX2.spad" 189911 189923 190188 190193) (-166 "COMPFACT.spad" 189513 189527 189901 189906) (-165 "COMPCAT.spad" 187651 187661 189259 189508) (-164 "COMPCAT.spad" 185470 185482 187080 187085) (-163 "COMMUPC.spad" 185216 185234 185460 185465) (-162 "COMMONOP.spad" 184749 184757 185206 185211) (-161 "COMM.spad" 184558 184566 184739 184744) (-160 "COMMAAST.spad" 184321 184329 184548 184553) (-159 "COMBOPC.spad" 183226 183234 184311 184316) (-158 "COMBINAT.spad" 181971 181981 183216 183221) (-157 "COMBF.spad" 179339 179355 181961 181966) (-156 "COLOR.spad" 178176 178184 179329 179334) (-155 "COLONAST.spad" 177842 177850 178166 178171) (-154 "CMPLXRT.spad" 177551 177568 177832 177837) (-153 "CLLCTAST.spad" 177213 177221 177541 177546) (-152 "CLIP.spad" 173305 173313 177203 177208) (-151 "CLIF.spad" 171944 171960 173261 173300) (-150 "CLAGG.spad" 168429 168439 171934 171939) (-149 "CLAGG.spad" 164785 164797 168292 168297) (-148 "CINTSLPE.spad" 164110 164123 164775 164780) (-147 "CHVAR.spad" 162188 162210 164100 164105) (-146 "CHARZ.spad" 162103 162111 162168 162183) (-145 "CHARPOL.spad" 161611 161621 162093 162098) (-144 "CHARNZ.spad" 161364 161372 161591 161606) (-143 "CHAR.spad" 159232 159240 161354 161359) (-142 "CFCAT.spad" 158548 158556 159222 159227) (-141 "CDEN.spad" 157706 157720 158538 158543) (-140 "CCLASS.spad" 155855 155863 157117 157156) (-139 "CATEGORY.spad" 154945 154953 155845 155850) (-138 "CATCTOR.spad" 154836 154844 154935 154940) (-137 "CATAST.spad" 154463 154471 154826 154831) (-136 "CASEAST.spad" 154177 154185 154453 154458) (-135 "CARTEN.spad" 149280 149304 154167 154172) (-134 "CARTEN2.spad" 148666 148693 149270 149275) (-133 "CARD.spad" 145955 145963 148640 148661) (-132 "CAPSLAST.spad" 145729 145737 145945 145950) (-131 "CACHSET.spad" 145351 145359 145719 145724) (-130 "CABMON.spad" 144904 144912 145341 145346) (-129 "BYTE.spad" 144325 144333 144894 144899) (-128 "BYTEBUF.spad" 142157 142165 143494 143521) (-127 "BTREE.spad" 141226 141236 141764 141791) (-126 "BTOURN.spad" 140229 140239 140833 140860) (-125 "BTCAT.spad" 139617 139627 140197 140224) (-124 "BTCAT.spad" 139025 139037 139607 139612) (-123 "BTAGG.spad" 138147 138155 138993 139020) (-122 "BTAGG.spad" 137289 137299 138137 138142) (-121 "BSTREE.spad" 136024 136034 136896 136923) (-120 "BRILL.spad" 134219 134230 136014 136019) (-119 "BRAGG.spad" 133143 133153 134209 134214) (-118 "BRAGG.spad" 132031 132043 133099 133104) (-117 "BPADICRT.spad" 130012 130024 130267 130360) (-116 "BPADIC.spad" 129676 129688 129938 130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP.spad" 124796 124804 129322 129327) (-113 "BOP1.spad" 122182 122192 124752 124757) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP8.spad" 97774 97787 98721 98726) (-87 "ASP80.spad" 97096 97109 97764 97769) (-86 "ASP7.spad" 96256 96269 97086 97091) (-85 "ASP78.spad" 95707 95720 96246 96251) (-84 "ASP77.spad" 95076 95089 95697 95702) (-83 "ASP74.spad" 94168 94181 95066 95071) (-82 "ASP73.spad" 93439 93452 94158 94163) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP4.spad" 87927 87940 88622 88627) (-77 "ASP49.spad" 86926 86939 87917 87922) (-76 "ASP42.spad" 85333 85372 86916 86921) (-75 "ASP41.spad" 83912 83951 85323 85328) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP1.spad" 67361 67374 67970 67975) (-63 "ASP19.spad" 62047 62060 67351 67356) (-62 "ASP12.spad" 61461 61474 62037 62042) (-61 "ASP10.spad" 60732 60745 61451 61456) (-60 "ARRAY2.spad" 60092 60101 60339 60366) (-59 "ARRAY1.spad" 58927 58936 59275 59302) (-58 "ARRAY12.spad" 57596 57607 58917 58922) (-57 "ARR2CAT.spad" 53258 53279 57564 57591) (-56 "ARR2CAT.spad" 48940 48963 53248 53253) (-55 "ARITY.spad" 48508 48515 48930 48935) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY.spad" 45709 45716 47357 47362) (-51 "ANY1.spad" 44780 44789 45699 45704) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2282316 2282321 2282326 2282331) (-2 NIL 2282296 2282301 2282306 2282311) (-1 NIL 2282276 2282281 2282286 2282291) (0 NIL 2282256 2282261 2282266 2282271) (-1284 "ZMOD.spad" 2282065 2282078 2282194 2282251) (-1283 "ZLINDEP.spad" 2281109 2281120 2282055 2282060) (-1282 "ZDSOLVE.spad" 2270958 2270980 2281099 2281104) (-1281 "YSTREAM.spad" 2270451 2270462 2270948 2270953) (-1280 "XRPOLY.spad" 2269671 2269691 2270307 2270376) (-1279 "XPR.spad" 2267462 2267475 2269389 2269488) (-1278 "XPOLY.spad" 2267017 2267028 2267318 2267387) (-1277 "XPOLYC.spad" 2266334 2266350 2266943 2267012) (-1276 "XPBWPOLY.spad" 2264771 2264791 2266114 2266183) (-1275 "XF.spad" 2263232 2263247 2264673 2264766) (-1274 "XF.spad" 2261673 2261690 2263116 2263121) (-1273 "XFALG.spad" 2258697 2258713 2261599 2261668) (-1272 "XEXPPKG.spad" 2257948 2257974 2258687 2258692) (-1271 "XDPOLY.spad" 2257562 2257578 2257804 2257873) (-1270 "XALG.spad" 2257222 2257233 2257518 2257557) (-1269 "WUTSET.spad" 2253061 2253078 2256868 2256895) (-1268 "WP.spad" 2252260 2252304 2252919 2252986) (-1267 "WHILEAST.spad" 2252058 2252067 2252250 2252255) (-1266 "WHEREAST.spad" 2251729 2251738 2252048 2252053) (-1265 "WFFINTBS.spad" 2249292 2249314 2251719 2251724) (-1264 "WEIER.spad" 2247506 2247517 2249282 2249287) (-1263 "VSPACE.spad" 2247179 2247190 2247474 2247501) (-1262 "VSPACE.spad" 2246872 2246885 2247169 2247174) (-1261 "VOID.spad" 2246549 2246558 2246862 2246867) (-1260 "VIEW.spad" 2244171 2244180 2246539 2246544) (-1259 "VIEWDEF.spad" 2239368 2239377 2244161 2244166) (-1258 "VIEW3D.spad" 2223203 2223212 2239358 2239363) (-1257 "VIEW2D.spad" 2210940 2210949 2223193 2223198) (-1256 "VECTOR.spad" 2209615 2209626 2209866 2209893) (-1255 "VECTOR2.spad" 2208242 2208255 2209605 2209610) (-1254 "VECTCAT.spad" 2206142 2206153 2208210 2208237) (-1253 "VECTCAT.spad" 2203850 2203863 2205920 2205925) (-1252 "VARIABLE.spad" 2203630 2203645 2203840 2203845) (-1251 "UTYPE.spad" 2203274 2203283 2203620 2203625) (-1250 "UTSODETL.spad" 2202567 2202591 2203230 2203235) (-1249 "UTSODE.spad" 2200755 2200775 2202557 2202562) (-1248 "UTS.spad" 2195544 2195572 2199222 2199319) (-1247 "UTSCAT.spad" 2192995 2193011 2195442 2195539) (-1246 "UTSCAT.spad" 2190090 2190108 2192539 2192544) (-1245 "UTS2.spad" 2189683 2189718 2190080 2190085) (-1244 "URAGG.spad" 2184315 2184326 2189673 2189678) (-1243 "URAGG.spad" 2178911 2178924 2184271 2184276) (-1242 "UPXSSING.spad" 2176554 2176580 2177992 2178125) (-1241 "UPXS.spad" 2173702 2173730 2174686 2174835) (-1240 "UPXSCONS.spad" 2171459 2171479 2171834 2171983) (-1239 "UPXSCCA.spad" 2170024 2170044 2171305 2171454) (-1238 "UPXSCCA.spad" 2168731 2168753 2170014 2170019) (-1237 "UPXSCAT.spad" 2167312 2167328 2168577 2168726) (-1236 "UPXS2.spad" 2166853 2166906 2167302 2167307) (-1235 "UPSQFREE.spad" 2165265 2165279 2166843 2166848) (-1234 "UPSCAT.spad" 2162858 2162882 2165163 2165260) (-1233 "UPSCAT.spad" 2160157 2160183 2162464 2162469) (-1232 "UPOLYC.spad" 2155135 2155146 2159999 2160152) (-1231 "UPOLYC.spad" 2150005 2150018 2154871 2154876) (-1230 "UPOLYC2.spad" 2149474 2149493 2149995 2150000) (-1229 "UP.spad" 2146631 2146646 2147024 2147177) (-1228 "UPMP.spad" 2145521 2145534 2146621 2146626) (-1227 "UPDIVP.spad" 2145084 2145098 2145511 2145516) (-1226 "UPDECOMP.spad" 2143321 2143335 2145074 2145079) (-1225 "UPCDEN.spad" 2142528 2142544 2143311 2143316) (-1224 "UP2.spad" 2141890 2141911 2142518 2142523) (-1223 "UNISEG.spad" 2141243 2141254 2141809 2141814) (-1222 "UNISEG2.spad" 2140736 2140749 2141199 2141204) (-1221 "UNIFACT.spad" 2139837 2139849 2140726 2140731) (-1220 "ULS.spad" 2130389 2130417 2131482 2131911) (-1219 "ULSCONS.spad" 2122783 2122803 2123155 2123304) (-1218 "ULSCCAT.spad" 2120512 2120532 2122629 2122778) (-1217 "ULSCCAT.spad" 2118349 2118371 2120468 2120473) (-1216 "ULSCAT.spad" 2116565 2116581 2118195 2118344) (-1215 "ULS2.spad" 2116077 2116130 2116555 2116560) (-1214 "UINT8.spad" 2115954 2115963 2116067 2116072) (-1213 "UINT32.spad" 2115830 2115839 2115944 2115949) (-1212 "UINT16.spad" 2115706 2115715 2115820 2115825) (-1211 "UFD.spad" 2114771 2114780 2115632 2115701) (-1210 "UFD.spad" 2113898 2113909 2114761 2114766) (-1209 "UDVO.spad" 2112745 2112754 2113888 2113893) (-1208 "UDPO.spad" 2110172 2110183 2112701 2112706) (-1207 "TYPE.spad" 2110104 2110113 2110162 2110167) (-1206 "TYPEAST.spad" 2110023 2110032 2110094 2110099) (-1205 "TWOFACT.spad" 2108673 2108688 2110013 2110018) (-1204 "TUPLE.spad" 2108157 2108168 2108572 2108577) (-1203 "TUBETOOL.spad" 2104994 2105003 2108147 2108152) (-1202 "TUBE.spad" 2103635 2103652 2104984 2104989) (-1201 "TS.spad" 2102224 2102240 2103200 2103297) (-1200 "TSETCAT.spad" 2089351 2089368 2102192 2102219) (-1199 "TSETCAT.spad" 2076464 2076483 2089307 2089312) (-1198 "TRMANIP.spad" 2070830 2070847 2076170 2076175) (-1197 "TRIMAT.spad" 2069789 2069814 2070820 2070825) (-1196 "TRIGMNIP.spad" 2068306 2068323 2069779 2069784) (-1195 "TRIGCAT.spad" 2067818 2067827 2068296 2068301) (-1194 "TRIGCAT.spad" 2067328 2067339 2067808 2067813) (-1193 "TREE.spad" 2065899 2065910 2066935 2066962) (-1192 "TRANFUN.spad" 2065730 2065739 2065889 2065894) (-1191 "TRANFUN.spad" 2065559 2065570 2065720 2065725) (-1190 "TOPSP.spad" 2065233 2065242 2065549 2065554) (-1189 "TOOLSIGN.spad" 2064896 2064907 2065223 2065228) (-1188 "TEXTFILE.spad" 2063453 2063462 2064886 2064891) (-1187 "TEX.spad" 2060585 2060594 2063443 2063448) (-1186 "TEX1.spad" 2060141 2060152 2060575 2060580) (-1185 "TEMUTL.spad" 2059696 2059705 2060131 2060136) (-1184 "TBCMPPK.spad" 2057789 2057812 2059686 2059691) (-1183 "TBAGG.spad" 2056825 2056848 2057769 2057784) (-1182 "TBAGG.spad" 2055869 2055894 2056815 2056820) (-1181 "TANEXP.spad" 2055245 2055256 2055859 2055864) (-1180 "TABLE.spad" 2053656 2053679 2053926 2053953) (-1179 "TABLEAU.spad" 2053137 2053148 2053646 2053651) (-1178 "TABLBUMP.spad" 2049920 2049931 2053127 2053132) (-1177 "SYSTEM.spad" 2049194 2049203 2049910 2049915) (-1176 "SYSSOLP.spad" 2046667 2046678 2049184 2049189) (-1175 "SYSNNI.spad" 2045843 2045854 2046657 2046662) (-1174 "SYSINT.spad" 2045316 2045327 2045833 2045838) (-1173 "SYNTAX.spad" 2041586 2041595 2045306 2045311) (-1172 "SYMTAB.spad" 2039642 2039651 2041576 2041581) (-1171 "SYMS.spad" 2035627 2035636 2039632 2039637) (-1170 "SYMPOLY.spad" 2034634 2034645 2034716 2034843) (-1169 "SYMFUNC.spad" 2034109 2034120 2034624 2034629) (-1168 "SYMBOL.spad" 2031536 2031545 2034099 2034104) (-1167 "SWITCH.spad" 2028293 2028302 2031526 2031531) (-1166 "SUTS.spad" 2025192 2025220 2026760 2026857) (-1165 "SUPXS.spad" 2022327 2022355 2023324 2023473) (-1164 "SUP.spad" 2019096 2019107 2019877 2020030) (-1163 "SUPFRACF.spad" 2018201 2018219 2019086 2019091) (-1162 "SUP2.spad" 2017591 2017604 2018191 2018196) (-1161 "SUMRF.spad" 2016557 2016568 2017581 2017586) (-1160 "SUMFS.spad" 2016190 2016207 2016547 2016552) (-1159 "SULS.spad" 2006729 2006757 2007835 2008264) (-1158 "SUCHTAST.spad" 2006498 2006507 2006719 2006724) (-1157 "SUCH.spad" 2006178 2006193 2006488 2006493) (-1156 "SUBSPACE.spad" 1998185 1998200 2006168 2006173) (-1155 "SUBRESP.spad" 1997345 1997359 1998141 1998146) (-1154 "STTF.spad" 1993444 1993460 1997335 1997340) (-1153 "STTFNC.spad" 1989912 1989928 1993434 1993439) (-1152 "STTAYLOR.spad" 1982310 1982321 1989793 1989798) (-1151 "STRTBL.spad" 1980815 1980832 1980964 1980991) (-1150 "STRING.spad" 1980224 1980233 1980238 1980265) (-1149 "STRICAT.spad" 1980012 1980021 1980192 1980219) (-1148 "STREAM.spad" 1976870 1976881 1979537 1979552) (-1147 "STREAM3.spad" 1976415 1976430 1976860 1976865) (-1146 "STREAM2.spad" 1975483 1975496 1976405 1976410) (-1145 "STREAM1.spad" 1975187 1975198 1975473 1975478) (-1144 "STINPROD.spad" 1974093 1974109 1975177 1975182) (-1143 "STEP.spad" 1973294 1973303 1974083 1974088) (-1142 "STBL.spad" 1971820 1971848 1971987 1972002) (-1141 "STAGG.spad" 1970895 1970906 1971810 1971815) (-1140 "STAGG.spad" 1969968 1969981 1970885 1970890) (-1139 "STACK.spad" 1969319 1969330 1969575 1969602) (-1138 "SREGSET.spad" 1967023 1967040 1968965 1968992) (-1137 "SRDCMPK.spad" 1965568 1965588 1967013 1967018) (-1136 "SRAGG.spad" 1960665 1960674 1965536 1965563) (-1135 "SRAGG.spad" 1955782 1955793 1960655 1960660) (-1134 "SQMATRIX.spad" 1953398 1953416 1954314 1954401) (-1133 "SPLTREE.spad" 1947950 1947963 1952834 1952861) (-1132 "SPLNODE.spad" 1944538 1944551 1947940 1947945) (-1131 "SPFCAT.spad" 1943315 1943324 1944528 1944533) (-1130 "SPECOUT.spad" 1941865 1941874 1943305 1943310) (-1129 "SPADXPT.spad" 1934004 1934013 1941855 1941860) (-1128 "spad-parser.spad" 1933469 1933478 1933994 1933999) (-1127 "SPADAST.spad" 1933170 1933179 1933459 1933464) (-1126 "SPACEC.spad" 1917183 1917194 1933160 1933165) (-1125 "SPACE3.spad" 1916959 1916970 1917173 1917178) (-1124 "SORTPAK.spad" 1916504 1916517 1916915 1916920) (-1123 "SOLVETRA.spad" 1914261 1914272 1916494 1916499) (-1122 "SOLVESER.spad" 1912781 1912792 1914251 1914256) (-1121 "SOLVERAD.spad" 1908791 1908802 1912771 1912776) (-1120 "SOLVEFOR.spad" 1907211 1907229 1908781 1908786) (-1119 "SNTSCAT.spad" 1906811 1906828 1907179 1907206) (-1118 "SMTS.spad" 1905071 1905097 1906376 1906473) (-1117 "SMP.spad" 1902510 1902530 1902900 1903027) (-1116 "SMITH.spad" 1901353 1901378 1902500 1902505) (-1115 "SMATCAT.spad" 1899463 1899493 1901297 1901348) (-1114 "SMATCAT.spad" 1897505 1897537 1899341 1899346) (-1113 "SKAGG.spad" 1896466 1896477 1897473 1897500) (-1112 "SINT.spad" 1895292 1895301 1896332 1896461) (-1111 "SIMPAN.spad" 1895020 1895029 1895282 1895287) (-1110 "SIG.spad" 1894348 1894357 1895010 1895015) (-1109 "SIGNRF.spad" 1893456 1893467 1894338 1894343) (-1108 "SIGNEF.spad" 1892725 1892742 1893446 1893451) (-1107 "SIGAST.spad" 1892106 1892115 1892715 1892720) (-1106 "SHP.spad" 1890024 1890039 1892062 1892067) (-1105 "SHDP.spad" 1879735 1879762 1880244 1880375) (-1104 "SGROUP.spad" 1879343 1879352 1879725 1879730) (-1103 "SGROUP.spad" 1878949 1878960 1879333 1879338) (-1102 "SGCF.spad" 1871830 1871839 1878939 1878944) (-1101 "SFRTCAT.spad" 1870758 1870775 1871798 1871825) (-1100 "SFRGCD.spad" 1869821 1869841 1870748 1870753) (-1099 "SFQCMPK.spad" 1864458 1864478 1869811 1869816) (-1098 "SFORT.spad" 1863893 1863907 1864448 1864453) (-1097 "SEXOF.spad" 1863736 1863776 1863883 1863888) (-1096 "SEX.spad" 1863628 1863637 1863726 1863731) (-1095 "SEXCAT.spad" 1861179 1861219 1863618 1863623) (-1094 "SET.spad" 1859479 1859490 1860600 1860639) (-1093 "SETMN.spad" 1857913 1857930 1859469 1859474) (-1092 "SETCAT.spad" 1857398 1857407 1857903 1857908) (-1091 "SETCAT.spad" 1856881 1856892 1857388 1857393) (-1090 "SETAGG.spad" 1853402 1853413 1856861 1856876) (-1089 "SETAGG.spad" 1849931 1849944 1853392 1853397) (-1088 "SEQAST.spad" 1849634 1849643 1849921 1849926) (-1087 "SEGXCAT.spad" 1848756 1848769 1849624 1849629) (-1086 "SEG.spad" 1848569 1848580 1848675 1848680) (-1085 "SEGCAT.spad" 1847476 1847487 1848559 1848564) (-1084 "SEGBIND.spad" 1846548 1846559 1847431 1847436) (-1083 "SEGBIND2.spad" 1846244 1846257 1846538 1846543) (-1082 "SEGAST.spad" 1845958 1845967 1846234 1846239) (-1081 "SEG2.spad" 1845383 1845396 1845914 1845919) (-1080 "SDVAR.spad" 1844659 1844670 1845373 1845378) (-1079 "SDPOL.spad" 1842049 1842060 1842340 1842467) (-1078 "SCPKG.spad" 1840128 1840139 1842039 1842044) (-1077 "SCOPE.spad" 1839273 1839282 1840118 1840123) (-1076 "SCACHE.spad" 1837955 1837966 1839263 1839268) (-1075 "SASTCAT.spad" 1837864 1837873 1837945 1837950) (-1074 "SAOS.spad" 1837736 1837745 1837854 1837859) (-1073 "SAERFFC.spad" 1837449 1837469 1837726 1837731) (-1072 "SAE.spad" 1835624 1835640 1836235 1836370) (-1071 "SAEFACT.spad" 1835325 1835345 1835614 1835619) (-1070 "RURPK.spad" 1832966 1832982 1835315 1835320) (-1069 "RULESET.spad" 1832407 1832431 1832956 1832961) (-1068 "RULE.spad" 1830611 1830635 1832397 1832402) (-1067 "RULECOLD.spad" 1830463 1830476 1830601 1830606) (-1066 "RSTRCAST.spad" 1830180 1830189 1830453 1830458) (-1065 "RSETGCD.spad" 1826558 1826578 1830170 1830175) (-1064 "RSETCAT.spad" 1816342 1816359 1826526 1826553) (-1063 "RSETCAT.spad" 1806146 1806165 1816332 1816337) (-1062 "RSDCMPK.spad" 1804598 1804618 1806136 1806141) (-1061 "RRCC.spad" 1802982 1803012 1804588 1804593) (-1060 "RRCC.spad" 1801364 1801396 1802972 1802977) (-1059 "RPTAST.spad" 1801066 1801075 1801354 1801359) (-1058 "RPOLCAT.spad" 1780426 1780441 1800934 1801061) (-1057 "RPOLCAT.spad" 1759500 1759517 1780010 1780015) (-1056 "ROUTINE.spad" 1755363 1755372 1758147 1758174) (-1055 "ROMAN.spad" 1754691 1754700 1755229 1755358) (-1054 "ROIRC.spad" 1753771 1753803 1754681 1754686) (-1053 "RNS.spad" 1752674 1752683 1753673 1753766) (-1052 "RNS.spad" 1751663 1751674 1752664 1752669) (-1051 "RNG.spad" 1751398 1751407 1751653 1751658) (-1050 "RMODULE.spad" 1751036 1751047 1751388 1751393) (-1049 "RMCAT2.spad" 1750444 1750501 1751026 1751031) (-1048 "RMATRIX.spad" 1749268 1749287 1749611 1749650) (-1047 "RMATCAT.spad" 1744801 1744832 1749224 1749263) (-1046 "RMATCAT.spad" 1740224 1740257 1744649 1744654) (-1045 "RINTERP.spad" 1740112 1740132 1740214 1740219) (-1044 "RING.spad" 1739582 1739591 1740092 1740107) (-1043 "RING.spad" 1739060 1739071 1739572 1739577) (-1042 "RIDIST.spad" 1738444 1738453 1739050 1739055) (-1041 "RGCHAIN.spad" 1737023 1737039 1737929 1737956) (-1040 "RGBCSPC.spad" 1736804 1736816 1737013 1737018) (-1039 "RGBCMDL.spad" 1736334 1736346 1736794 1736799) (-1038 "RF.spad" 1733948 1733959 1736324 1736329) (-1037 "RFFACTOR.spad" 1733410 1733421 1733938 1733943) (-1036 "RFFACT.spad" 1733145 1733157 1733400 1733405) (-1035 "RFDIST.spad" 1732133 1732142 1733135 1733140) (-1034 "RETSOL.spad" 1731550 1731563 1732123 1732128) (-1033 "RETRACT.spad" 1730978 1730989 1731540 1731545) (-1032 "RETRACT.spad" 1730404 1730417 1730968 1730973) (-1031 "RETAST.spad" 1730216 1730225 1730394 1730399) (-1030 "RESULT.spad" 1728276 1728285 1728863 1728890) (-1029 "RESRING.spad" 1727623 1727670 1728214 1728271) (-1028 "RESLATC.spad" 1726947 1726958 1727613 1727618) (-1027 "REPSQ.spad" 1726676 1726687 1726937 1726942) (-1026 "REP.spad" 1724228 1724237 1726666 1726671) (-1025 "REPDB.spad" 1723933 1723944 1724218 1724223) (-1024 "REP2.spad" 1713505 1713516 1723775 1723780) (-1023 "REP1.spad" 1707495 1707506 1713455 1713460) (-1022 "REGSET.spad" 1705292 1705309 1707141 1707168) (-1021 "REF.spad" 1704621 1704632 1705247 1705252) (-1020 "REDORDER.spad" 1703797 1703814 1704611 1704616) (-1019 "RECLOS.spad" 1702580 1702600 1703284 1703377) (-1018 "REALSOLV.spad" 1701712 1701721 1702570 1702575) (-1017 "REAL.spad" 1701584 1701593 1701702 1701707) (-1016 "REAL0Q.spad" 1698866 1698881 1701574 1701579) (-1015 "REAL0.spad" 1695694 1695709 1698856 1698861) (-1014 "RDUCEAST.spad" 1695415 1695424 1695684 1695689) (-1013 "RDIV.spad" 1695066 1695091 1695405 1695410) (-1012 "RDIST.spad" 1694629 1694640 1695056 1695061) (-1011 "RDETRS.spad" 1693425 1693443 1694619 1694624) (-1010 "RDETR.spad" 1691532 1691550 1693415 1693420) (-1009 "RDEEFS.spad" 1690605 1690622 1691522 1691527) (-1008 "RDEEF.spad" 1689601 1689618 1690595 1690600) (-1007 "RCFIELD.spad" 1686787 1686796 1689503 1689596) (-1006 "RCFIELD.spad" 1684059 1684070 1686777 1686782) (-1005 "RCAGG.spad" 1681971 1681982 1684049 1684054) (-1004 "RCAGG.spad" 1679810 1679823 1681890 1681895) (-1003 "RATRET.spad" 1679170 1679181 1679800 1679805) (-1002 "RATFACT.spad" 1678862 1678874 1679160 1679165) (-1001 "RANDSRC.spad" 1678181 1678190 1678852 1678857) (-1000 "RADUTIL.spad" 1677935 1677944 1678171 1678176) (-999 "RADIX.spad" 1674837 1674850 1676402 1676495) (-998 "RADFF.spad" 1673251 1673287 1673369 1673525) (-997 "RADCAT.spad" 1672845 1672853 1673241 1673246) (-996 "RADCAT.spad" 1672437 1672447 1672835 1672840) (-995 "QUEUE.spad" 1671780 1671790 1672044 1672071) (-994 "QUAT.spad" 1670362 1670372 1670704 1670769) (-993 "QUATCT2.spad" 1669981 1669999 1670352 1670357) (-992 "QUATCAT.spad" 1668146 1668156 1669911 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1016032 1016042 1016580 1016595) (-634 "LINDEP.spad" 1014809 1014821 1015944 1015949) (-633 "LIMITRF.spad" 1012723 1012733 1014799 1014804) (-632 "LIMITPS.spad" 1011606 1011619 1012713 1012718) (-631 "LIE.spad" 1009620 1009632 1010896 1011041) (-630 "LIECAT.spad" 1009096 1009106 1009546 1009615) (-629 "LIECAT.spad" 1008600 1008612 1009052 1009057) (-628 "LIB.spad" 1006648 1006656 1007259 1007274) (-627 "LGROBP.spad" 1004001 1004020 1006638 1006643) (-626 "LF.spad" 1002920 1002936 1003991 1003996) (-625 "LFCAT.spad" 1001939 1001947 1002910 1002915) (-624 "LEXTRIPK.spad" 997442 997457 1001929 1001934) (-623 "LEXP.spad" 995445 995472 997422 997437) (-622 "LETAST.spad" 995144 995152 995435 995440) (-621 "LEADCDET.spad" 993528 993545 995134 995139) (-620 "LAZM3PK.spad" 992232 992254 993518 993523) (-619 "LAUPOL.spad" 990921 990934 991825 991894) (-618 "LAPLACE.spad" 990494 990510 990911 990916) (-617 "LA.spad" 989934 989948 990416 990455) (-616 "LALG.spad" 989710 989720 989914 989929) (-615 "LALG.spad" 989494 989506 989700 989705) (-614 "KVTFROM.spad" 989229 989239 989484 989489) (-613 "KTVLOGIC.spad" 988652 988660 989219 989224) (-612 "KRCFROM.spad" 988390 988400 988642 988647) (-611 "KOVACIC.spad" 987103 987120 988380 988385) (-610 "KONVERT.spad" 986825 986835 987093 987098) (-609 "KOERCE.spad" 986562 986572 986815 986820) (-608 "KERNEL.spad" 985097 985107 986346 986351) (-607 "KERNEL2.spad" 984800 984812 985087 985092) (-606 "KDAGG.spad" 983903 983925 984780 984795) (-605 "KDAGG.spad" 983014 983038 983893 983898) (-604 "KAFILE.spad" 981977 981993 982212 982239) (-603 "JORDAN.spad" 979804 979816 981267 981412) (-602 "JOINAST.spad" 979498 979506 979794 979799) (-601 "JAVACODE.spad" 979364 979372 979488 979493) (-600 "IXAGG.spad" 977487 977511 979354 979359) (-599 "IXAGG.spad" 975465 975491 977334 977339) (-598 "IVECTOR.spad" 974236 974251 974391 974418) (-597 "ITUPLE.spad" 973381 973391 974226 974231) (-596 "ITRIGMNP.spad" 972192 972211 973371 973376) (-595 "ITFUN3.spad" 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(-574 "IOBCON.spad" 946417 946425 946542 946547) (-573 "INVLAPLA.spad" 946062 946078 946407 946412) (-572 "INTTR.spad" 939308 939325 946052 946057) (-571 "INTTOOLS.spad" 937019 937035 938882 938887) (-570 "INTSLPE.spad" 936325 936333 937009 937014) (-569 "INTRVL.spad" 935891 935901 936239 936320) (-568 "INTRF.spad" 934255 934269 935881 935886) (-567 "INTRET.spad" 933687 933697 934245 934250) (-566 "INTRAT.spad" 932362 932379 933677 933682) (-565 "INTPM.spad" 930725 930741 932005 932010) (-564 "INTPAF.spad" 928493 928511 930657 930662) (-563 "INTPACK.spad" 918803 918811 928483 928488) (-562 "INT.spad" 918164 918172 918657 918798) (-561 "INTHERTR.spad" 917430 917447 918154 918159) (-560 "INTHERAL.spad" 917096 917120 917420 917425) (-559 "INTHEORY.spad" 913509 913517 917086 917091) (-558 "INTG0.spad" 906972 906990 913441 913446) (-557 "INTFTBL.spad" 901001 901009 906962 906967) (-556 "INTFACT.spad" 900060 900070 900991 900996) (-555 "INTEF.spad" 898375 898391 900050 900055) (-554 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875417 875772 875777) (-533 "INFINITY.spad" 874959 874967 875397 875402) (-532 "INETCLTS.spad" 874936 874944 874949 874954) (-531 "INEP.spad" 873468 873490 874926 874931) (-530 "INDE.spad" 873197 873214 873458 873463) (-529 "INCRMAPS.spad" 872618 872628 873187 873192) (-528 "INBFILE.spad" 871690 871698 872608 872613) (-527 "INBFF.spad" 867460 867471 871680 871685) (-526 "INBCON.spad" 865748 865756 867450 867455) (-525 "INBCON.spad" 864034 864044 865738 865743) (-524 "INAST.spad" 863699 863707 864024 864029) (-523 "IMPTAST.spad" 863407 863415 863689 863694) (-522 "IMATRIX.spad" 862352 862378 862864 862891) (-521 "IMATQF.spad" 861446 861490 862308 862313) (-520 "IMATLIN.spad" 860051 860075 861402 861407) (-519 "ILIST.spad" 858707 858722 859234 859261) (-518 "IIARRAY2.spad" 858095 858133 858314 858341) (-517 "IFF.spad" 857505 857521 857776 857869) (-516 "IFAST.spad" 857119 857127 857495 857500) (-515 "IFARRAY.spad" 854606 854621 856302 856329) (-514 "IFAMON.spad" 854468 854485 854562 854567) (-513 "IEVALAB.spad" 853857 853869 854458 854463) (-512 "IEVALAB.spad" 853244 853258 853847 853852) (-511 "IDPO.spad" 853042 853054 853234 853239) (-510 "IDPOAMS.spad" 852798 852810 853032 853037) (-509 "IDPOAM.spad" 852518 852530 852788 852793) (-508 "IDPC.spad" 851452 851464 852508 852513) (-507 "IDPAM.spad" 851197 851209 851442 851447) (-506 "IDPAG.spad" 850944 850956 851187 851192) (-505 "IDENT.spad" 850716 850724 850934 850939) (-504 "IDECOMP.spad" 847953 847971 850706 850711) (-503 "IDEAL.spad" 842876 842915 847888 847893) (-502 "ICDEN.spad" 842027 842043 842866 842871) (-501 "ICARD.spad" 841216 841224 842017 842022) (-500 "IBPTOOLS.spad" 839809 839826 841206 841211) (-499 "IBITS.spad" 839008 839021 839445 839472) (-498 "IBATOOL.spad" 835883 835902 838998 839003) (-497 "IBACHIN.spad" 834370 834385 835873 835878) (-496 "IARRAY2.spad" 833358 833384 833977 834004) (-495 "IARRAY1.spad" 832403 832418 832541 832568) (-494 "IAN.spad" 830616 830624 832219 832312) (-493 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514946) (-329 "FC.spad" 504245 504253 514320 514325) (-328 "FAXF.spad" 497180 497194 504147 504240) (-327 "FAXF.spad" 490167 490183 497136 497141) (-326 "FARRAY.spad" 488313 488323 489350 489377) (-325 "FAMR.spad" 486433 486445 488211 488308) (-324 "FAMR.spad" 484537 484551 486317 486322) (-323 "FAMONOID.spad" 484187 484197 484491 484496) (-322 "FAMONC.spad" 482409 482421 484177 484182) (-321 "FAGROUP.spad" 482015 482025 482305 482332) (-320 "FACUTIL.spad" 480211 480228 482005 482010) (-319 "FACTFUNC.spad" 479387 479397 480201 480206) (-318 "EXPUPXS.spad" 476220 476243 477519 477668) (-317 "EXPRTUBE.spad" 473448 473456 476210 476215) (-316 "EXPRODE.spad" 470320 470336 473438 473443) (-315 "EXPR.spad" 465595 465605 466309 466716) (-314 "EXPR2UPS.spad" 461687 461700 465585 465590) (-313 "EXPR2.spad" 461390 461402 461677 461682) (-312 "EXPEXPAN.spad" 458328 458353 458962 459055) (-311 "EXIT.spad" 457999 458007 458318 458323) (-310 "EXITAST.spad" 457735 457743 457989 457994) (-309 "EVALCYC.spad" 457193 457207 457725 457730) (-308 "EVALAB.spad" 456757 456767 457183 457188) (-307 "EVALAB.spad" 456319 456331 456747 456752) (-306 "EUCDOM.spad" 453861 453869 456245 456314) (-305 "EUCDOM.spad" 451465 451475 453851 453856) (-304 "ESTOOLS.spad" 443305 443313 451455 451460) (-303 "ESTOOLS2.spad" 442906 442920 443295 443300) (-302 "ESTOOLS1.spad" 442591 442602 442896 442901) (-301 "ES.spad" 435138 435146 442581 442586) (-300 "ES.spad" 427591 427601 435036 435041) (-299 "ESCONT.spad" 424364 424372 427581 427586) (-298 "ESCONT1.spad" 424113 424125 424354 424359) (-297 "ES2.spad" 423608 423624 424103 424108) (-296 "ES1.spad" 423174 423190 423598 423603) (-295 "ERROR.spad" 420495 420503 423164 423169) (-294 "EQTBL.spad" 418967 418989 419176 419203) (-293 "EQ.spad" 413841 413851 416640 416752) (-292 "EQ2.spad" 413557 413569 413831 413836) (-291 "EP.spad" 409871 409881 413547 413552) (-290 "ENV.spad" 408573 408581 409861 409866) (-289 "ENTIRER.spad" 408241 408249 408517 408568) (-288 "EMR.spad" 407442 407483 408167 408236) (-287 "ELTAGG.spad" 405682 405701 407432 407437) (-286 "ELTAGG.spad" 403886 403907 405638 405643) (-285 "ELTAB.spad" 403333 403351 403876 403881) (-284 "ELFUTS.spad" 402712 402731 403323 403328) (-283 "ELEMFUN.spad" 402401 402409 402702 402707) (-282 "ELEMFUN.spad" 402088 402098 402391 402396) (-281 "ELAGG.spad" 400031 400041 402068 402083) (-280 "ELAGG.spad" 397911 397923 399950 399955) (-279 "ELABEXPR.spad" 396842 396850 397901 397906) (-278 "EFUPXS.spad" 393618 393648 396798 396803) (-277 "EFULS.spad" 390454 390477 393574 393579) (-276 "EFSTRUC.spad" 388409 388425 390444 390449) (-275 "EF.spad" 383175 383191 388399 388404) (-274 "EAB.spad" 381451 381459 383165 383170) (-273 "E04UCFA.spad" 380987 380995 381441 381446) (-272 "E04NAFA.spad" 380564 380572 380977 380982) (-271 "E04MBFA.spad" 380144 380152 380554 380559) (-270 "E04JAFA.spad" 379680 379688 380134 380139) (-269 "E04GCFA.spad" 379216 379224 379670 379675) (-268 "E04FDFA.spad" 378752 378760 379206 379211) (-267 "E04DGFA.spad" 378288 378296 378742 378747) (-266 "E04AGNT.spad" 374130 374138 378278 378283) (-265 "DVARCAT.spad" 370815 370825 374120 374125) (-264 "DVARCAT.spad" 367498 367510 370805 370810) (-263 "DSMP.spad" 364929 364943 365234 365361) (-262 "DROPT.spad" 358874 358882 364919 364924) (-261 "DROPT1.spad" 358537 358547 358864 358869) (-260 "DROPT0.spad" 353364 353372 358527 358532) (-259 "DRAWPT.spad" 351519 351527 353354 353359) (-258 "DRAW.spad" 344119 344132 351509 351514) (-257 "DRAWHACK.spad" 343427 343437 344109 344114) (-256 "DRAWCX.spad" 340869 340877 343417 343422) (-255 "DRAWCURV.spad" 340406 340421 340859 340864) (-254 "DRAWCFUN.spad" 329578 329586 340396 340401) (-253 "DQAGG.spad" 327746 327756 329546 329573) (-252 "DPOLCAT.spad" 323087 323103 327614 327741) (-251 "DPOLCAT.spad" 318514 318532 323043 323048) (-250 "DPMO.spad" 310740 310756 310878 311179) (-249 "DPMM.spad" 302979 302997 303104 303405) (-248 "DOMCTOR.spad" 302871 302879 302969 302974) (-247 "DOMAIN.spad" 302002 302010 302861 302866) (-246 "DMP.spad" 299224 299239 299796 299923) (-245 "DLP.spad" 298572 298582 299214 299219) (-244 "DLIST.spad" 297151 297161 297755 297782) (-243 "DLAGG.spad" 295562 295572 297141 297146) (-242 "DIVRING.spad" 295104 295112 295506 295557) (-241 "DIVRING.spad" 294690 294700 295094 295099) (-240 "DISPLAY.spad" 292870 292878 294680 294685) (-239 "DIRPROD.spad" 282450 282466 283090 283221) (-238 "DIRPROD2.spad" 281258 281276 282440 282445) (-237 "DIRPCAT.spad" 280200 280216 281122 281253) (-236 "DIRPCAT.spad" 278871 278889 279795 279800) (-235 "DIOSP.spad" 277696 277704 278861 278866) (-234 "DIOPS.spad" 276680 276690 277676 277691) (-233 "DIOPS.spad" 275638 275650 276636 276641) (-232 "DIFRING.spad" 274930 274938 275618 275633) (-231 "DIFRING.spad" 274230 274240 274920 274925) (-230 "DIFEXT.spad" 273389 273399 274210 274225) (-229 "DIFEXT.spad" 272465 272477 273288 273293) (-228 "DIAGG.spad" 272095 272105 272445 272460) (-227 "DIAGG.spad" 271733 271745 272085 272090) (-226 "DHMATRIX.spad" 270037 270047 271190 271217) (-225 "DFSFUN.spad" 263445 263453 270027 270032) (-224 "DFLOAT.spad" 260166 260174 263335 263440) (-223 "DFINTTLS.spad" 258375 258391 260156 260161) (-222 "DERHAM.spad" 256285 256317 258355 258370) (-221 "DEQUEUE.spad" 255603 255613 255892 255919) (-220 "DEGRED.spad" 255218 255232 255593 255598) (-219 "DEFINTRF.spad" 252743 252753 255208 255213) (-218 "DEFINTEF.spad" 251239 251255 252733 252738) (-217 "DEFAST.spad" 250607 250615 251229 251234) (-216 "DECIMAL.spad" 248713 248721 249074 249167) (-215 "DDFACT.spad" 246512 246529 248703 248708) (-214 "DBLRESP.spad" 246110 246134 246502 246507) (-213 "DBASE.spad" 244764 244774 246100 246105) (-212 "DATAARY.spad" 244226 244239 244754 244759) (-211 "D03FAFA.spad" 244054 244062 244216 244221) (-210 "D03EEFA.spad" 243874 243882 244044 244049) (-209 "D03AGNT.spad" 242954 242962 243864 243869) (-208 "D02EJFA.spad" 242416 242424 242944 242949) (-207 "D02CJFA.spad" 241894 241902 242406 242411) (-206 "D02BHFA.spad" 241384 241392 241884 241889) (-205 "D02BBFA.spad" 240874 240882 241374 241379) (-204 "D02AGNT.spad" 235678 235686 240864 240869) (-203 "D01WGTS.spad" 233997 234005 235668 235673) (-202 "D01TRNS.spad" 233974 233982 233987 233992) (-201 "D01GBFA.spad" 233496 233504 233964 233969) (-200 "D01FCFA.spad" 233018 233026 233486 233491) (-199 "D01ASFA.spad" 232486 232494 233008 233013) (-198 "D01AQFA.spad" 231932 231940 232476 232481) (-197 "D01APFA.spad" 231356 231364 231922 231927) (-196 "D01ANFA.spad" 230850 230858 231346 231351) (-195 "D01AMFA.spad" 230360 230368 230840 230845) (-194 "D01ALFA.spad" 229900 229908 230350 230355) (-193 "D01AKFA.spad" 229426 229434 229890 229895) (-192 "D01AJFA.spad" 228949 228957 229416 229421) (-191 "D01AGNT.spad" 225008 225016 228939 228944) (-190 "CYCLOTOM.spad" 224514 224522 224998 225003) (-189 "CYCLES.spad" 221346 221354 224504 224509) (-188 "CVMP.spad" 220763 220773 221336 221341) (-187 "CTRIGMNP.spad" 219253 219269 220753 220758) (-186 "CTOR.spad" 218948 218956 219243 219248) (-185 "CTORKIND.spad" 218551 218559 218938 218943) (-184 "CTORCAT.spad" 217800 217808 218541 218546) (-183 "CTORCAT.spad" 217047 217057 217790 217795) (-182 "CTORCALL.spad" 216627 216635 217037 217042) (-181 "CSTTOOLS.spad" 215870 215883 216617 216622) (-180 "CRFP.spad" 209574 209587 215860 215865) (-179 "CRCEAST.spad" 209294 209302 209564 209569) (-178 "CRAPACK.spad" 208337 208347 209284 209289) (-177 "CPMATCH.spad" 207837 207852 208262 208267) (-176 "CPIMA.spad" 207542 207561 207827 207832) (-175 "COORDSYS.spad" 202435 202445 207532 207537) (-174 "CONTOUR.spad" 201837 201845 202425 202430) (-173 "CONTFRAC.spad" 197449 197459 201739 201832) (-172 "CONDUIT.spad" 197207 197215 197439 197444) (-171 "COMRING.spad" 196881 196889 197145 197202) (-170 "COMPPROP.spad" 196395 196403 196871 196876) (-169 "COMPLPAT.spad" 196162 196177 196385 196390) (-168 "COMPLEX.spad" 190198 190208 190442 190691) (-167 "COMPLEX2.spad" 189911 189923 190188 190193) (-166 "COMPFACT.spad" 189513 189527 189901 189906) (-165 "COMPCAT.spad" 187651 187661 189259 189508) (-164 "COMPCAT.spad" 185470 185482 187080 187085) (-163 "COMMUPC.spad" 185216 185234 185460 185465) (-162 "COMMONOP.spad" 184749 184757 185206 185211) (-161 "COMM.spad" 184558 184566 184739 184744) (-160 "COMMAAST.spad" 184321 184329 184548 184553) (-159 "COMBOPC.spad" 183226 183234 184311 184316) (-158 "COMBINAT.spad" 181971 181981 183216 183221) (-157 "COMBF.spad" 179339 179355 181961 181966) (-156 "COLOR.spad" 178176 178184 179329 179334) (-155 "COLONAST.spad" 177842 177850 178166 178171) (-154 "CMPLXRT.spad" 177551 177568 177832 177837) (-153 "CLLCTAST.spad" 177213 177221 177541 177546) (-152 "CLIP.spad" 173305 173313 177203 177208) (-151 "CLIF.spad" 171944 171960 173261 173300) (-150 "CLAGG.spad" 168429 168439 171934 171939) (-149 "CLAGG.spad" 164785 164797 168292 168297) (-148 "CINTSLPE.spad" 164110 164123 164775 164780) (-147 "CHVAR.spad" 162188 162210 164100 164105) (-146 "CHARZ.spad" 162103 162111 162168 162183) (-145 "CHARPOL.spad" 161611 161621 162093 162098) (-144 "CHARNZ.spad" 161364 161372 161591 161606) (-143 "CHAR.spad" 159232 159240 161354 161359) (-142 "CFCAT.spad" 158548 158556 159222 159227) (-141 "CDEN.spad" 157706 157720 158538 158543) (-140 "CCLASS.spad" 155855 155863 157117 157156) (-139 "CATEGORY.spad" 154945 154953 155845 155850) (-138 "CATCTOR.spad" 154836 154844 154935 154940) (-137 "CATAST.spad" 154463 154471 154826 154831) (-136 "CASEAST.spad" 154177 154185 154453 154458) (-135 "CARTEN.spad" 149280 149304 154167 154172) (-134 "CARTEN2.spad" 148666 148693 149270 149275) (-133 "CARD.spad" 145955 145963 148640 148661) (-132 "CAPSLAST.spad" 145729 145737 145945 145950) (-131 "CACHSET.spad" 145351 145359 145719 145724) (-130 "CABMON.spad" 144904 144912 145341 145346) (-129 "BYTE.spad" 144325 144333 144894 144899) (-128 "BYTEBUF.spad" 142157 142165 143494 143521) (-127 "BTREE.spad" 141226 141236 141764 141791) (-126 "BTOURN.spad" 140229 140239 140833 140860) (-125 "BTCAT.spad" 139617 139627 140197 140224) (-124 "BTCAT.spad" 139025 139037 139607 139612) (-123 "BTAGG.spad" 138147 138155 138993 139020) (-122 "BTAGG.spad" 137289 137299 138137 138142) (-121 "BSTREE.spad" 136024 136034 136896 136923) (-120 "BRILL.spad" 134219 134230 136014 136019) (-119 "BRAGG.spad" 133143 133153 134209 134214) (-118 "BRAGG.spad" 132031 132043 133099 133104) (-117 "BPADICRT.spad" 130012 130024 130267 130360) (-116 "BPADIC.spad" 129676 129688 129938 130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP.spad" 124796 124804 129322 129327) (-113 "BOP1.spad" 122182 122192 124752 124757) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP8.spad" 97774 97787 98721 98726) (-87 "ASP80.spad" 97096 97109 97764 97769) (-86 "ASP7.spad" 96256 96269 97086 97091) (-85 "ASP78.spad" 95707 95720 96246 96251) (-84 "ASP77.spad" 95076 95089 95697 95702) (-83 "ASP74.spad" 94168 94181 95066 95071) (-82 "ASP73.spad" 93439 93452 94158 94163) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP4.spad" 87927 87940 88622 88627) (-77 "ASP49.spad" 86926 86939 87917 87922) (-76 "ASP42.spad" 85333 85372 86916 86921) (-75 "ASP41.spad" 83912 83951 85323 85328) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP1.spad" 67361 67374 67970 67975) (-63 "ASP19.spad" 62047 62060 67351 67356) (-62 "ASP12.spad" 61461 61474 62037 62042) (-61 "ASP10.spad" 60732 60745 61451 61456) (-60 "ARRAY2.spad" 60092 60101 60339 60366) (-59 "ARRAY1.spad" 58927 58936 59275 59302) (-58 "ARRAY12.spad" 57596 57607 58917 58922) (-57 "ARR2CAT.spad" 53258 53279 57564 57591) (-56 "ARR2CAT.spad" 48940 48963 53248 53253) (-55 "ARITY.spad" 48508 48515 48930 48935) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY.spad" 45709 45716 47357 47362) (-51 "ANY1.spad" 44780 44789 45699 45704) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 7d2ad6a5..9c3dd555 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,6 +1,6 @@ -(162070 . 3442535953) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) #0#) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) +(162070 . 3442698070) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) #0#) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) ((((-562)) . T) (($) -4037 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-554))) (((-406 (-562))) -4037 (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-1033 (-406 (-562))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-562)) . T)) @@ -52,7 +52,7 @@ (((|#1| (-530 (-1168))) . T)) (((#0=(-865 |#1|) #0#) . T) ((#1=(-406 (-562)) #1#) . T) (($ $) . T)) ((((-1150)) . T) (((-857)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (|has| |#4| (-367)) (|has| |#3| (-367)) (((|#1|) . T)) @@ -68,7 +68,7 @@ ((((-562)) . T) (((-406 (-562))) -4037 (|has| |#2| (-38 (-406 (-562)))) (|has| |#2| (-1033 (-406 (-562))))) ((|#2|) . T) (($) -4037 (|has| |#2| (-451)) (|has| |#2| (-554)) (|has| |#2| (-904))) (((-859 |#1|)) . T)) (-4037 (|has| |#1| (-362)) (|has| |#1| (-554))) (-4037 (|has| |#1| (-362)) (|has| |#1| (-554))) -((((-2 (|:| -2466 |#1|) (|:| -1960 |#2|))) . T)) +((((-2 (|:| -2464 |#1|) (|:| -1300 |#2|))) . T)) ((($) . T)) ((((-562)) . T) (((-406 (-562))) -4037 (|has| |#1| (-38 (-406 (-562)))) (|has| |#1| (-1033 (-406 (-562))))) ((|#1|) . T) (($) -4037 (|has| |#1| (-451)) (|has| |#1| (-554)) (|has| |#1| (-904))) (((-1168)) . T)) ((((-857)) -4037 (|has| |#1| (-609 (-857))) (|has| |#1| (-845)) (|has| |#1| (-1092)))) @@ -112,7 +112,7 @@ (|has| |#1| (-367)) (((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092)))) ((((-857)) . T)) (((|#1| |#2|) . T)) @@ -236,8 +236,8 @@ (((|#1|) . T)) ((((-406 (-562))) |has| |#1| (-1033 (-406 (-562)))) (((-562)) |has| |#1| (-1033 (-562))) ((|#1|) . T)) (((|#1|) . T) (((-562)) |has| |#1| (-635 (-562)))) -(((|#2|) . T) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) . T)) (|has| |#1| (-554)) ((((-562)) -4037 (|has| |#4| (-171)) (|has| |#4| (-843)) (-12 (|has| |#4| (-1033 (-562))) (|has| |#4| (-1092))) (|has| |#4| (-1044))) ((|#4|) -4037 (|has| |#4| (-171)) (|has| |#4| (-1092))) (((-406 (-562))) -12 (|has| |#4| (-1033 (-406 (-562)))) (|has| |#4| (-1092)))) ((((-562)) -4037 (|has| |#3| (-171)) (|has| |#3| (-843)) (-12 (|has| |#3| (-1033 (-562))) (|has| |#3| (-1092))) (|has| |#3| (-1044))) ((|#3|) -4037 (|has| |#3| (-171)) (|has| |#3| (-1092))) (((-406 (-562))) -12 (|has| |#3| (-1033 (-406 (-562)))) (|has| |#3| (-1092)))) @@ -264,11 +264,11 @@ ((((-535)) |has| |#2| (-610 (-535))) (((-887 (-378))) |has| |#2| (-610 (-887 (-378)))) (((-887 (-562))) |has| |#2| (-610 (-887 (-562))))) ((((-857)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-2 (|:| -2466 |#1|) (|:| -1960 |#2|))) . T) (((-857)) . T)) +((((-2 (|:| -2464 |#1|) (|:| -1300 |#2|))) . T) (((-857)) . T)) ((((-535)) |has| |#1| (-610 (-535))) (((-887 (-378))) |has| |#1| (-610 (-887 (-378)))) (((-887 (-562))) |has| |#1| (-610 (-887 (-562))))) (((|#4|) -4037 (|has| |#4| (-171)) (|has| |#4| (-362)) (|has| |#4| (-1044))) (($) |has| |#4| (-171))) (((|#3|) -4037 (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-1044))) (($) |has| |#3| (-171))) -((((-2 (|:| -2466 |#1|) (|:| -1960 |#2|))) . T)) +((((-2 (|:| -2464 |#1|) (|:| -1300 |#2|))) . T)) ((((-857)) . T)) ((((-857)) . T)) ((((-535)) . T) (((-562)) . T) (((-887 (-562))) . T) (((-378)) . T) (((-224)) . T)) @@ -276,7 +276,7 @@ (((|#1|) . T) (((-562)) |has| |#1| (-1033 (-562))) (((-406 (-562))) |has| |#1| (-1033 (-406 (-562))))) ((($) . T) (((-406 (-562))) |has| |#2| (-38 (-406 (-562)))) ((|#2|) . T)) ((((-406 $) (-406 $)) |has| |#2| (-554)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -2320 (-1150)) (|:| -2694 (-52)))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-904)) ((((-1150) (-52)) . T)) @@ -312,7 +312,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1143)) -((((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) . T)) (|has| (-1242 |#1| |#2| |#3| |#4|) (-144)) (|has| (-1242 |#1| |#2| |#3| |#4|) (-146)) (|has| |#1| (-144)) @@ -330,10 +330,10 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-1044))) ((((-857)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) #0#) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) #0#) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) (((|#1|) . T)) -((((-1256 (-338 (-4066) (-4066 (QUOTE X)) (-693)))) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092))) ((#0=(-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) #0#) |has| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (-308 (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))))) +((((-1256 (-338 (-4064) (-4064 (QUOTE X)) (-693)))) . T)) +(((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092))) ((#0=(-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) #0#) |has| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (-308 (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))))) ((((-857)) . T)) ((((-562) |#1|) . T)) ((((-535)) -12 (|has| |#1| (-610 (-535))) (|has| |#2| (-610 (-535)))) (((-887 (-378))) -12 (|has| |#1| (-610 (-887 (-378)))) (|has| |#2| (-610 (-887 (-378))))) (((-887 (-562))) -12 (|has| |#1| (-610 (-887 (-562)))) (|has| |#2| (-610 (-887 (-562)))))) @@ -430,11 +430,11 @@ ((((-143)) . T)) (((|#3|) |has| |#3| (-1092)) (((-562)) -12 (|has| |#3| (-1033 (-562))) (|has| |#3| (-1092))) (((-406 (-562))) -12 (|has| |#3| (-1033 (-406 (-562)))) (|has| |#3| (-1092)))) ((((-857)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (((|#1|) . T)) ((((-857)) -4037 (|has| |#1| (-609 (-857))) (|has| |#1| (-845)) (|has| |#1| (-1092)))) ((((-535)) |has| |#1| (-610 (-535)))) -((((-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))) . T)) +((((-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))) . T)) (|has| |#1| (-362)) ((((-1173)) . T)) (-4037 (|has| |#1| (-21)) (|has| |#1| (-843))) @@ -444,13 +444,13 @@ (|has| |#1| (-843)) (-4037 (|has| |#1| (-845)) (|has| |#1| (-1092))) ((((-857)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-535)) |has| |#1| (-610 (-535)))) (((|#1| |#2|) . T)) ((((-1168)) -12 (|has| |#1| (-362)) (|has| |#1| (-895 (-1168))))) ((((-1150) |#1|) . T)) (((|#1| |#2| |#3| (-530 |#3|)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (|has| |#1| (-367)) (|has| |#1| (-367)) (|has| |#1| (-367)) @@ -654,7 +654,7 @@ (((|#4| |#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1092)))) (((|#2|) . T) (((-562)) |has| |#2| (-1033 (-562))) (((-406 (-562))) |has| |#2| (-1033 (-406 (-562))))) (((|#3| |#3|) -12 (|has| |#3| (-308 |#3|)) (|has| |#3| (-1092)))) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((($) . T)) @@ -662,7 +662,7 @@ (((|#2|) . T)) (((|#3|) . T)) (-4037 (|has| |#1| (-845)) (|has| |#1| (-1092))) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) (((|#2|) . T)) ((((-857)) -4037 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-609 (-857))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-721)) (|has| |#2| (-788)) (|has| |#2| (-843)) (|has| |#2| (-1044)) (|has| |#2| (-1092))) (((-1256 |#2|)) . T)) ((((-406 (-562))) |has| |#1| (-1033 (-406 (-562)))) ((|#1|) . T) (((-562)) . T) (($) . T)) @@ -742,9 +742,9 @@ (-4037 (|has| |#1| (-451)) (|has| |#1| (-904))) ((((-562) |#2|) . T)) ((((-857)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092)))) ((($) -4037 (|has| |#3| (-171)) (|has| |#3| (-843)) (|has| |#3| (-1044))) ((|#3|) -4037 (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-1044)))) ((((-562) |#1|) . T)) @@ -759,11 +759,11 @@ (|has| |#1| (-554)) (|has| |#1| (-38 (-406 (-562)))) (|has| |#1| (-38 (-406 (-562)))) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-857)) . T)) -((((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) . T)) (|has| |#1| (-38 (-406 (-562)))) -((((-387) (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) . T)) +((((-387) (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) . T)) (|has| |#1| (-38 (-406 (-562)))) (|has| |#2| (-1143)) (-4037 (|has| |#1| (-362)) (|has| |#1| (-554))) @@ -982,7 +982,7 @@ (|has| |#2| (-171)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-232)) (|has| |#2| (-1044))) -(((|#2|) . T) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (-4037 (|has| |#3| (-788)) (|has| |#3| (-843))) (-4037 (|has| |#3| (-788)) (|has| |#3| (-843))) ((((-857)) . T)) @@ -1013,10 +1013,10 @@ (((|#1| (-406 (-562))) . T)) (((|#3|) . T) (((-608 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092)))) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-562)) -4037 (|has| |#2| (-171)) (|has| |#2| (-843)) (-12 (|has| |#2| (-1033 (-562))) (|has| |#2| (-1092))) (|has| |#2| (-1044))) ((|#2|) -4037 (|has| |#2| (-171)) (|has| |#2| (-1092))) (((-406 (-562))) -12 (|has| |#2| (-1033 (-406 (-562)))) (|has| |#2| (-1092)))) (((|#1|) . T) (((-406 (-562))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) @@ -1025,8 +1025,8 @@ ((((-857)) . T)) ((((-857)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) -(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092))) (((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) |has| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (-308 (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) +(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092))) (((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) |has| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (-308 (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))))) ((((-857)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1039,7 +1039,7 @@ (|has| |#1| (-1092)) (((|#2| |#2|) -4037 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1044))) (($ $) |has| |#2| (-171))) (((|#2|) -4037 (|has| |#2| (-171)) (|has| |#2| (-362)))) -((((-562) (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T) ((|#1| |#2|) . T)) +((((-562) (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T) ((|#1| |#2|) . T)) (((|#2|) -4037 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1044))) (($) |has| |#2| (-171))) ((((-1173)) . T)) ((((-766)) . T)) @@ -1072,7 +1072,7 @@ (-4037 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-721)) (|has| |#2| (-788)) (|has| |#2| (-843)) (|has| |#2| (-1044)) (|has| |#2| (-1092))) (-12 (|has| |#3| (-232)) (|has| |#3| (-1044))) (|has| |#2| (-1143)) -(((#0=(-52)) . T) (((-2 (|:| -2320 (-1168)) (|:| -2694 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2319 (-1168)) (|:| -2693 #0#))) . T)) (((|#1| |#2|) . T)) (-4037 (|has| |#3| (-171)) (|has| |#3| (-843)) (|has| |#3| (-1044))) (((|#1| (-562) (-1074)) . T)) @@ -1099,7 +1099,7 @@ ((((-562)) -4037 (|has| |#3| (-171)) (|has| |#3| (-843)) (-12 (|has| |#3| (-1033 (-562))) (|has| |#3| (-1092))) (|has| |#3| (-1044))) ((|#3|) -4037 (|has| |#3| (-171)) (|has| |#3| (-1092))) (((-406 (-562))) -12 (|has| |#3| (-1033 (-406 (-562)))) (|has| |#3| (-1092)))) (((|#1|) . T)) (((|#4|) . T) (((-857)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) #0#) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) #0#) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) (|has| |#1| (-554)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092)))) ((((-857)) . T)) @@ -1159,7 +1159,7 @@ (-12 (|has| |#1| (-788)) (|has| |#2| (-788))) (-4037 (|has| |#2| (-171)) (|has| |#2| (-843)) (|has| |#2| (-1044))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (|has| |#1| (-1192)) (((#0=(-562) #0#) . T) ((#1=(-406 (-562)) #1#) . T) (($ $) . T)) ((((-406 (-562))) . T) (($) . T)) @@ -1189,7 +1189,7 @@ ((($) . T) (((-406 (-562))) -4037 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) (-4037 (|has| |#1| (-171)) (|has| |#1| (-554))) ((($) . T)) -(((#0=(-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) #0#) |has| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (-308 (-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))))) +(((#0=(-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) #0#) |has| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (-308 (-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))))) (|has| |#2| (-845)) ((($) . T)) (((|#2|) |has| |#2| (-1092))) @@ -1202,10 +1202,10 @@ ((((-562)) |has| #0=(-406 |#2|) (-635 (-562))) ((#0#) . T)) ((($) . T) (((-562)) . T)) ((((-562) (-143)) . T)) -((((-562) (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T) ((|#1| |#2|) . T)) +((((-562) (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T) ((|#1| |#2|) . T)) ((((-406 (-562))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-857)) . T)) ((((-905 |#1|)) . T)) (|has| |#1| (-362)) @@ -1232,7 +1232,7 @@ ((((-857)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-562) (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T) ((|#1| |#2|) . T)) +((((-562) (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-171))) ((($) |has| |#1| (-554)) ((|#1|) |has| |#1| (-171)) (((-406 (-562))) |has| |#1| (-38 (-406 (-562))))) @@ -1246,7 +1246,7 @@ (((|#1|) . T)) ((((-535)) |has| |#1| (-610 (-535))) (((-887 (-378))) |has| |#1| (-610 (-887 (-378)))) (((-887 (-562))) |has| |#1| (-610 (-887 (-562))))) ((((-857)) . T)) -(((|#2|) . T) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-505)) . T)) (|has| |#2| (-843)) ((((-505)) . T)) @@ -1275,7 +1275,7 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1168)) |has| (-406 |#2|) (-895 (-1168)))) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) #0#) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) #0#) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) @@ -1286,7 +1286,7 @@ (((|#2|) . T) (((-562)) . T)) ((((-857)) . T)) ((((-857)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T) ((|#2|) . T)) ((((-857)) . T)) ((((-857)) . T)) ((((-1150) (-1168) (-562) (-224) (-857)) . T)) @@ -1375,7 +1375,7 @@ ((((-994 |#1|)) . T) ((|#1|) . T)) ((((-857)) . T)) ((((-857)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-406 (-562))) . T) (((-406 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1164 |#1|)) . T)) ((((-562)) . T) (($) . T) (((-406 (-562))) . T)) @@ -1383,7 +1383,7 @@ (|has| |#1| (-845)) (((|#2|) . T)) ((((-562)) . T) (($) . T) (((-406 (-562))) . T)) -((((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) . T)) ((((-562) |#2|) . T)) ((((-857)) -4037 (|has| |#1| (-609 (-857))) (|has| |#1| (-1092)))) (((|#2|) . T)) @@ -1398,7 +1398,7 @@ (|has| |#1| (-1092)) (|has| |#1| (-38 (-406 (-562)))) (|has| |#1| (-38 (-406 (-562)))) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) #0#) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) #0#) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-38 (-406 (-562)))) (((|#2|) . T)) @@ -1433,7 +1433,7 @@ (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092)))) (((|#1| |#2|) . T)) ((((-562) (-143)) . T)) -(((#0=(-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) #0#) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092)))) +(((#0=(-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) #0#) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092)))) ((($) -4037 (|has| |#1| (-451)) (|has| |#1| (-554)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-171)) (((-406 (-562))) |has| |#1| (-38 (-406 (-562))))) (|has| |#1| (-845)) (((|#2| (-766) (-1074)) . T)) @@ -1477,7 +1477,7 @@ ((((-387) (-1150)) . T)) ((($) |has| |#1| (-554)) ((|#1|) |has| |#1| (-171)) (((-406 (-562))) |has| |#1| (-38 (-406 (-562))))) ((((-857)) -4037 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-609 (-857))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-721)) (|has| |#2| (-788)) (|has| |#2| (-843)) (|has| |#2| (-1044)) (|has| |#2| (-1092))) (((-1256 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2320 (-1150)) (|:| -2694 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2319 (-1150)) (|:| -2693 #0#))) . T)) (((|#1|) . T)) ((((-857)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092)))) @@ -1526,11 +1526,11 @@ (|has| |#1| (-146)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) -((((-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) +((((-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))) . T)) ((((-1166 |#1| |#2| |#3|)) |has| |#1| (-362))) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-1168) (-52)) . T)) ((($ $) . T)) (((|#1| (-562)) . T)) @@ -1577,11 +1577,11 @@ (|has| |#1| (-38 (-406 (-562)))) (-4037 (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-38 (-406 (-562)))) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-1168)) |has| |#1| (-895 (-1168))) (((-1074)) . T)) (((|#1|) . T)) (|has| |#1| (-843)) -(((#0=(-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) #0#) |has| (-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) (-308 (-2 (|:| -2320 (-1150)) (|:| -2694 (-52)))))) +(((#0=(-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) #0#) |has| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (-308 (-2 (|:| -2319 (-1150)) (|:| -2693 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092)))) (|has| |#1| (-1092)) ((((-857)) . T) (((-1173)) . T)) @@ -1627,7 +1627,7 @@ (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092))) ((#0=(-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) #0#) |has| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (-308 (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))))) +(((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092))) ((#0=(-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) #0#) |has| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (-308 (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))))) (-4037 (|has| |#2| (-451)) (|has| |#2| (-904))) (-4037 (|has| |#1| (-451)) (|has| |#1| (-904))) (((|#1|) . T) (($) . T)) @@ -1652,7 +1652,7 @@ ((((-406 (-562))) -4037 (|has| |#1| (-38 (-406 (-562)))) (|has| |#1| (-362))) (($) -4037 (|has| |#1| (-362)) (|has| |#1| (-554))) (((-1166 |#1| |#2| |#3|)) |has| |#1| (-362)) ((|#1|) |has| |#1| (-171))) (((|#1|) |has| |#1| (-171)) (((-406 (-562))) -4037 (|has| |#1| (-38 (-406 (-562)))) (|has| |#1| (-362))) (($) -4037 (|has| |#1| (-362)) (|has| |#1| (-554)))) ((($) |has| |#1| (-554)) ((|#1|) |has| |#1| (-171)) (((-406 (-562))) |has| |#1| (-38 (-406 (-562))))) -((((-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))) . T)) +((((-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))) . T)) ((((-406 |#2|)) . T) (((-406 (-562))) . T) (($) . T)) ((((-666 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1720,7 +1720,7 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092)))) ((($ $) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((($ $) . T)) ((((-562) (-112)) . T)) ((($) . T)) @@ -1749,7 +1749,7 @@ (((|#1| (-1220 |#1| |#2| |#3|)) . T)) (((|#1| (-766)) . T)) (((|#1|) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-857)) . T)) (|has| |#1| (-1092)) ((((-1150) |#1|) . T)) @@ -1788,7 +1788,7 @@ (|has| |#1| (-554)) (((|#1|) . T)) ((((-857)) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) (((|#1|) |has| |#1| (-171))) ((($) |has| |#1| (-554)) ((|#1|) |has| |#1| (-171)) (((-406 (-562))) |has| |#1| (-38 (-406 (-562))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092)))) @@ -1807,7 +1807,7 @@ (|has| |#1| (-843)) (((|#1| (-562) (-1074)) . T)) (-4037 (|has| |#1| (-895 (-1168))) (|has| |#1| (-1044))) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (((|#1| (-406 (-562)) (-1074)) . T)) (((|#1| (-766) (-1074)) . T)) (|has| |#1| (-845)) @@ -1825,11 +1825,11 @@ (|has| |#1| (-1092)) ((((-562)) -12 (|has| |#1| (-362)) (|has| |#2| (-635 (-562)))) ((|#2|) |has| |#1| (-362))) (-4037 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-721)) (|has| |#2| (-788)) (|has| |#2| (-843)) (|has| |#2| (-1044)) (|has| |#2| (-1092))) -((((-683 (-338 (-4066) (-4066 (QUOTE X) (QUOTE HESS)) (-693)))) . T)) +((((-683 (-338 (-4064) (-4064 (QUOTE X) (QUOTE HESS)) (-693)))) . T)) (((|#2|) |has| |#2| (-171))) (((|#1|) |has| |#1| (-171))) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) -((((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) . T)) ((((-857)) . T)) (|has| |#3| (-843)) ((((-857)) . T)) @@ -1843,9 +1843,9 @@ (((|#2|) |has| |#2| (-362))) ((($) . T) ((|#1|) . T) (((-406 (-562))) |has| |#1| (-362))) (|has| |#1| (-845)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))) |has| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (-308 (-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))))) +((((-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))) |has| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (-308 (-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))))) (-4037 (|has| |#1| (-451)) (|has| |#1| (-904))) (((|#2|) . T) (((-562)) |has| |#2| (-635 (-562)))) ((((-857)) . T)) @@ -1895,7 +1895,7 @@ ((((-639 |#1|)) . T)) (|has| |#1| (-904)) (((|#2|) |has| |#2| (-1044))) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) (|has| |#1| (-362)) (((|#1|) |has| |#1| (-171))) (((|#1| |#1|) . T)) @@ -1946,14 +1946,14 @@ ((((-112)) |has| |#1| (-1092)) (((-857)) -4037 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-472)) (|has| |#1| (-721)) (|has| |#1| (-895 (-1168))) (|has| |#1| (-1044)) (|has| |#1| (-1104)) (|has| |#1| (-1092)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2320 (-1150)) (|:| -2694 (-52)))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 (-52)))) . T)) ((((-857)) . T)) ((((-562) |#1|) . T)) ((((-857)) . T)) ((((-693)) . T) (((-406 (-562))) . T) (((-562)) . T)) (((|#1| |#1|) |has| |#1| (-171))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) ((((-378)) . T)) ((((-693)) . T)) ((((-406 (-562))) . #0=(|has| |#2| (-362))) (($) . #0#)) @@ -1972,7 +1972,7 @@ (((|#3|) |has| |#3| (-1044))) ((((-1168)) |has| |#2| (-895 (-1168)))) ((((-857)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-406 (-562))) . T) (($) . T)) (|has| |#1| (-472)) (|has| |#1| (-367)) @@ -2000,11 +2000,11 @@ (|has| |#1| (-38 (-406 (-562)))) (|has| |#1| (-38 (-406 (-562)))) (|has| |#1| (-845)) -((((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-146)) (|has| |#1| (-144)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)))) ((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092)))) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)))) ((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2022,7 +2022,7 @@ ((((-535)) |has| |#1| (-610 (-535))) (((-887 (-562))) |has| |#1| (-610 (-887 (-562)))) (((-887 (-378))) |has| |#1| (-610 (-887 (-378)))) (((-378)) . #0=(|has| |#1| (-1017))) (((-224)) . #0#)) (((|#1|) |has| |#1| (-362))) ((((-857)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((($ $) . T) (((-608 $) $) . T)) (-4037 (|has| |#1| (-362)) (|has| |#1| (-554))) ((($) . T) (((-1242 |#1| |#2| |#3| |#4|)) . T) (((-406 (-562))) . T)) @@ -2084,7 +2084,7 @@ ((((-947 |#1|)) . T) (((-857)) . T)) (((|#3|) . T)) (((|#1| |#1|) . T) (($ $) -4037 (|has| |#1| (-289)) (|has| |#1| (-362))) ((#0=(-406 (-562)) #0#) |has| |#1| (-362))) -((((-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))) . T)) +((((-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))) . T)) ((((-947 |#1|)) . T)) ((($) . T)) ((((-562) |#1|) . T)) @@ -2124,7 +2124,7 @@ ((($) -4037 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-562))) -4037 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) ((((-562)) . T)) (|has| |#1| (-38 (-406 (-562)))) -((((-2 (|:| -2320 (-1150)) (|:| -2694 (-52)))) |has| (-2 (|:| -2320 (-1150)) (|:| -2694 (-52))) (-308 (-2 (|:| -2320 (-1150)) (|:| -2694 (-52)))))) +((((-2 (|:| -2319 (-1150)) (|:| -2693 (-52)))) |has| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (-308 (-2 (|:| -2319 (-1150)) (|:| -2693 (-52)))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092)))) (|has| |#1| (-843)) (|has| |#1| (-38 (-406 (-562)))) @@ -2166,10 +2166,10 @@ ((($) -4037 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-451)) (|has| |#1| (-554)) (|has| |#1| (-904))) ((|#1|) . T) (((-406 (-562))) |has| |#1| (-38 (-406 (-562))))) ((((-535)) |has| |#4| (-610 (-535)))) ((((-857)) . T) (((-639 |#4|)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-843)) -(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092))) (((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) |has| (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|)) (-308 (-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))))) +(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092))) (((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) |has| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (-308 (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))))) (|has| |#1| (-1092)) (|has| |#1| (-362)) (|has| |#1| (-845)) @@ -2211,7 +2211,7 @@ ((((-857)) . T)) ((((-857)) . T)) ((((-535)) |has| |#1| (-610 (-535)))) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-1168) |#1|) |has| |#1| (-513 (-1168) |#1|)) ((|#1| |#1|) |has| |#1| (-308 |#1|))) (((|#1|) -4037 (|has| |#1| (-171)) (|has| |#1| (-362)))) ((((-315 |#1|)) . T)) @@ -2239,7 +2239,7 @@ (|has| |#1| (-554)) (((|#2|) . T)) ((((-562)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (((|#1|) . T)) (-4037 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-554)) (|has| |#1| (-1044))) ((((-579 |#1|)) . T)) @@ -2250,7 +2250,7 @@ ((($) . T)) (((|#1|) . T)) ((((-857)) . T)) -(((|#2|) |has| |#2| (-6 (-4404 "*")))) +(((|#2|) |has| |#2| (-6 (-4405 "*")))) (((|#1|) . T)) (((|#1|) . T)) (((|#3|) . T)) @@ -2351,21 +2351,21 @@ (((|#1|) |has| |#1| (-171))) ((((-857)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1092)))) -(((|#2|) -4037 (|has| |#2| (-6 (-4404 "*"))) (|has| |#2| (-171)))) +(((|#2|) -4037 (|has| |#2| (-6 (-4405 "*"))) (|has| |#2| (-171)))) (-4037 (|has| |#2| (-451)) (|has| |#2| (-554)) (|has| |#2| (-904))) (-4037 (|has| |#1| (-451)) (|has| |#1| (-554)) (|has| |#1| (-904))) (|has| |#2| (-845)) (|has| |#2| (-904)) (|has| |#1| (-904)) (((|#2|) |has| |#2| (-171))) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-1248 |#1| |#2| |#3|)) |has| |#1| (-362))) ((((-857)) . T)) ((((-857)) . T)) ((((-535)) . T) (((-562)) . T) (((-887 (-562))) . T) (((-378)) . T) (((-224)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) -((((-2 (|:| -2320 (-1150)) (|:| -2694 (-52)))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 (-52)))) . T)) (((|#1|) . T)) ((((-857)) . T)) (((|#1| |#2|) . T)) @@ -2387,7 +2387,7 @@ ((((-857)) . T)) ((((-857)) . T)) ((((-186)) . T) (((-857)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-857)) . T)) ((((-857)) . T)) @@ -2400,7 +2400,7 @@ ((((-857)) . T)) ((((-1150)) . T)) ((((-1168) |#1|) |has| |#1| (-513 (-1168) |#1|)) ((|#1| |#1|) |has| |#1| (-308 |#1|))) -((((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) . T)) (|has| |#1| (-845)) ((((-857)) . T)) ((((-535)) |has| |#1| (-610 (-535)))) @@ -2457,8 +2457,8 @@ (-4037 (|has| |#1| (-144)) (|has| |#1| (-367))) (-4037 (|has| |#1| (-144)) (|has| |#1| (-367))) (-4037 (|has| |#1| (-144)) (|has| |#1| (-367))) -((((-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2320 (-1168)) (|:| -2694 #0#))) . T)) +((((-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2319 (-1168)) (|:| -2693 #0#))) . T)) (|has| |#1| (-348)) ((((-562)) . T)) ((((-857)) . T)) @@ -2535,7 +2535,7 @@ (|has| |#2| (-1017)) ((($) . T)) (|has| |#1| (-904)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2561,7 +2561,7 @@ ((((-406 (-562))) . T)) (-4037 (|has| |#1| (-451)) (|has| |#1| (-554)) (|has| |#1| (-904))) ((((-1150)) . T) (((-857)) . T)) -(((#0=(-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) #0#) |has| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (-308 (-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))))) +(((#0=(-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) #0#) |has| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (-308 (-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))))) ((((-1150)) . T)) (|has| |#1| (-904)) (|has| |#2| (-362)) @@ -2597,7 +2597,7 @@ (((|#2|) |has| |#1| (-362))) (((|#2|) |has| |#1| (-362))) ((((-562)) . T) (($) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) @@ -2637,9 +2637,9 @@ (((|#2|) . T)) (((|#2|) . T)) (-4037 (|has| |#2| (-171)) (|has| |#2| (-721)) (|has| |#2| (-843)) (|has| |#2| (-1044))) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) -((((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (|has| |#1| (-38 (-406 (-562)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-406 (-562)))) @@ -2761,7 +2761,7 @@ (|has| |#2| (-362)) ((((-579 |#1|)) . T) (((-406 (-562))) . T) (($) . T) (((-562)) . T)) ((((-562)) . T) (((-406 (-562))) . T) (($) . T)) -((((-2 (|:| -2320 (-1150)) (|:| -2694 (-52)))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-562)) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092)))) @@ -2791,7 +2791,7 @@ ((((-579 |#1|)) . T) (($) . T) (((-406 (-562))) . T)) ((($) . T) (((-406 (-562))) . T)) ((($) . T) (((-406 (-562))) . T)) -(((|#2|) |has| |#2| (-6 (-4404 "*")))) +(((|#2|) |has| |#2| (-6 (-4405 "*")))) (((|#1|) . T)) ((((-406 (-562))) |has| |#1| (-1033 (-406 (-562)))) ((|#1|) . T) (((-562)) . T)) (((|#1|) . T)) @@ -2819,7 +2819,7 @@ ((($) -4037 (|has| |#1| (-171)) (|has| |#1| (-451)) (|has| |#1| (-554)) (|has| |#1| (-904))) ((|#1|) . T) (((-406 (-562))) |has| |#1| (-38 (-406 (-562))))) ((((-857)) . T)) (((|#1|) . T)) -((((-2 (|:| -2320 (-1150)) (|:| -2694 |#1|))) . T)) +((((-2 (|:| -2319 (-1150)) (|:| -2693 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2936,7 +2936,7 @@ (((|#1|) . T)) ((((-857)) . T)) (|has| |#2| (-904)) -((((-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))) . T)) +((((-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))) . T)) ((((-535)) |has| |#2| (-610 (-535))) (((-887 (-378))) |has| |#2| (-610 (-887 (-378)))) (((-887 (-562))) |has| |#2| (-610 (-887 (-562))))) ((((-857)) . T)) ((((-857)) . T)) @@ -3119,7 +3119,7 @@ ((((-1206)) . T) (((-857)) . T) (((-1173)) . T)) ((((-1173)) . T)) ((((-1173)) . T)) -((((-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))) |has| (-2 (|:| -2320 (-1168)) (|:| -2694 (-52))) (-308 (-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))))) +((((-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))) |has| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (-308 (-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))))) (-4037 (|has| |#2| (-451)) (|has| |#2| (-554)) (|has| |#2| (-904))) ((((-562) |#1|) . T)) ((((-562) |#1|) . T)) @@ -3311,7 +3311,7 @@ (-4037 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-130)) (|has| |#2| (-130))) (-12 (|has| |#1| (-788)) (|has| |#2| (-788)))) ((((-562)) . T)) ((((-562)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) (-4037 (|has| |#2| (-171)) (|has| |#2| (-721)) (|has| |#2| (-843)) (|has| |#2| (-1044))) @@ -3411,11 +3411,11 @@ ((((-1166 |#1| |#2| |#3|)) |has| |#1| (-362))) ((((-1132 |#1| |#2|)) . T)) ((((-1166 |#1| |#2| |#3|)) |has| |#1| (-362))) -(((|#2|) . T) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) -((((-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) +((((-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1017)) -(((|#2|) . T) (((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) ((((-857)) . T)) ((((-535)) |has| |#2| (-610 (-535))) (((-887 (-562))) |has| |#2| (-610 (-887 (-562)))) (((-887 (-378))) |has| |#2| (-610 (-887 (-378)))) (((-378)) . #0=(|has| |#2| (-1017))) (((-224)) . #0#)) ((((-293 |#3|)) . T)) @@ -3469,7 +3469,7 @@ ((((-857)) . T)) ((((-857)) . T)) (((|#1| (-530 |#2|)) . T)) -((((-2 (|:| -2320 (-1168)) (|:| -2694 (-52)))) . T)) +((((-2 (|:| -2319 (-1168)) (|:| -2693 (-52)))) . T)) ((((-562) (-129)) . T)) (((|#1| (-562)) . T)) (((|#1| (-406 (-562))) . T)) @@ -3505,7 +3505,7 @@ (((|#1| |#2|) . T)) ((((-1150) |#1|) . T)) ((((-406 |#2|)) . T)) -((((-2 (|:| -2320 |#1|) (|:| -2694 |#2|))) . T)) +((((-2 (|:| -2319 |#1|) (|:| -2693 |#2|))) . T)) (|has| |#1| (-554)) (|has| |#1| (-554)) ((($) . T) ((|#2|) . T)) @@ -3533,7 +3533,7 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1132 |#1| |#2|) #0#) |has| (-1132 |#1| |#2|) (-308 (-1132 |#1| |#2|)))) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) #0#) |has| (-2 (|:| -2320 |#1|) (|:| -2694 |#2|)) (-308 (-2 (|:| -2320 |#1|) (|:| -2694 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((#0=(-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) #0#) |has| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (-308 (-2 (|:| -2319 |#1|) (|:| -2693 |#2|))))) (((#0=(-116 |#1|)) |has| #0# (-308 #0#))) ((($ $) . T)) (-4037 (|has| |#1| (-845)) (|has| |#1| (-1092))) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 8ff9c59d..5f51ab94 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3442535945) -(4405 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3442698062) +(4406 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -477,662 +477,662 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |conditionP| |externalList| |rational| - |positiveRemainder| |exptMod| |changeThreshhold| |cTan| |iisin| - |forLoop| |fortranLiteral| |f02bbf| |recoverAfterFail| |approxSqrt| - |readLineIfCan!| |lfextlimint| |mapGen| |leftDiscriminant| - |fractRadix| |slash| |multiple?| |reduceLODE| |inf| - |componentUpperBound| |multiEuclidean| |OMgetSymbol| - |monomialIntegrate| |powern| |normal?| |complexIntegrate| |rotatey| - |ignore?| |iiacoth| |powerAssociative?| |primitive?| |e02dff| - |addBadValue| |nor| |patternMatchTimes| |normalise| |exponents| - |divisor| |reverseLex| |s17def| |fortran| |exprToGenUPS| |npcoef| - |antisymmetric?| |nonSingularModel| |extendedResultant| |startStats!| - |sncndn| |setIntersection| |midpoint| |selectPDERoutines| - |OMgetInteger| |closeComponent| |infinite?| |radicalEigenvectors| - |droot| |consnewpol| |setUnion| |stoseInvertible?| |factorial| - |characteristicSet| |extend| |loopPoints| |OMgetAtp| |tanNa| |B1solve| - |routines| |intcompBasis| |apply| |mapMatrixIfCan| |pointColorDefault| - |vspace| |basisOfMiddleNucleus| |imagi| |ideal| |baseRDEsys| - |currentEnv| |commutativeEquality| |nil| |upperCase?| |convergents| - |e04naf| |setClosed| |exportedOperators| |chainSubResultants| - |constantKernel| |monomial| |rightPower| |f01brf| |insertBottom!| - |size| |paren| |karatsuba| |call| |cross| |intPatternMatch| - |getStream| |ScanFloatIgnoreSpaces| |multivariate| |hconcat| - |torsion?| |diophantineSystem| |postfix| |sort| |commutative?| - |product| |OMcloseConn| |sorted?| |solveLinear| |createGenericMatrix| - |variables| UTS2UP |zerosOf| |nthr| |approximate| |function| - |infRittWu?| |chvar| |primitivePart!| |cAsin| |redPol| - |quasiAlgebraicSet| |d03faf| |monicModulo| |id| |optpair| |complex| - |resultantEuclidean| |qelt| |first| |evaluateInverse| |clipSurface| - |twist| |insertRoot!| |usingTable?| |linear| |OMUnknownSymbol?| - |normalizedAssociate| |internalAugment| |qsetelt| |birth| |eval| - |rest| |HermiteIntegrate| |semiSubResultantGcdEuclidean1| - |outputAsScript| |sn| |symmetricPower| |shallowExpand| - |fortranCharacter| |asinIfCan| |table| |elseBranch| |unitNormal| - |identification| |substitute| |random| |xRange| |close| |printInfo!| - |paraboloidal| |zeroDimensional?| |polynomial| |coleman| - |algebraicDecompose| |s17adf| |new| |removeDuplicates| |point| - |pdf2df| |yRange| |cot2trig| |connect| |obj| |intermediateResultsIF| - |createMultiplicationMatrix| |leadingTerm| |taylor| |expandPower| - |clearDenominator| |search| |prepareSubResAlgo| |cup| |remove| - |getConstant| |readBytes!| |zRange| |display| |cylindrical| |cache| - |script| BY |doubleFloatFormat| |laurent| |setMinPoints3D| |bat| - |block| |getGraph| |map!| |varselect| |dAndcExp| |rationalFunction| - |pushuconst| |tower| |pushdterm| |constant| |primitivePart| |puiseux| - |getVariableOrder| |rk4qc| |rootOf| |series| |last| |qsetelt!| - |setref| |numFunEvals3D| |subSet| |drawComplex| |factors| |solid| - |setvalue!| |OMlistCDs| |tensorProduct| |assoc| - |reducedContinuedFraction| |generalizedEigenvectors| - |genericLeftTrace| |nextColeman| |keys| |nextsousResultant2| |tex| - |fortranReal| |times!| |inv| |viewWriteDefault| |limitedIntegrate| - |subresultantSequence| |scopes| |divideExponents| - |useSingleFactorBound| |headReduce| |idealSimplify| |ground?| - |leftDivide| |imagK| |zoom| |iprint| |curve| |linkToFortran| |input| - |d02bhf| |cotIfCan| |diagonal?| |mat| |isPlus| |ground| |normalForm| - |leftMult| |d01amf| |min| |tubeRadius| |splitSquarefree| |library| - |BumInSepFFE| |fortranComplex| |iiatan| |gcdcofact| |noKaratsuba| - |leadingMonomial| |subTriSet?| |complexNumeric| |adjoint| |lcm| - |minimalPolynomial| |acsch| |solveInField| |collect| - |linearlyDependent?| |index?| |maximumExponent| |showArrayValues| - |leadingCoefficient| |evenlambert| |rules| |upperCase| |euclideanSize| - |indicialEquations| |factorGroebnerBasis| |mainValue| |backOldPos| - |mapUp!| |kernels| |leadingExponent| |rischDE| |primitiveMonomials| - |permutations| |left| |nonQsign| |range| |cAcsc| |append| |subMatrix| - |dmpToHdmp| |completeHensel| |rangePascalTriangle| |safetyMargin| - |dimensionsOf| |univariate| |super| |reductum| |right| |clikeUniv| - |rootRadius| |overlap| |gcd| |trueEqual| |set| - |lastSubResultantElseSplit| |merge| |divisorCascade| |augment| - |pointColor| |lowerCase!| |false| |lazyPseudoRemainder| |seriesSolve| - |integerIfCan| |solve1| |cosSinInfo| |basisOfRightNucleus| |bringDown| - |closed?| |complementaryBasis| |sum| |semiIndiceSubResultantEuclidean| - |s21baf| |isExpt| |argumentList!| |impliesOperands| |exponentialOrder| - |getMeasure| |intensity| |univariatePolynomials| |factor| - |traceMatrix| |primextendedint| |lagrange| |leftRemainder| - |semiResultantEuclideannaif| |functionIsOscillatory| |splitLinear| - |sqrt| |permutationRepresentation| |int| |complexRoots| - |fortranLogical| |f02akf| |predicates| |lambert| |setFieldInfo| - |rootProduct| |df2fi| |palglimint0| |numeric| |thetaCoord| |real| - |saturate| |distdfact| |leftFactorIfCan| |list?| |makeResult| |lp| - |monicRightDivide| |genericRightTrace| |radical| |cAtan| |reseed| - |member?| |imag| |leftRegularRepresentation| |ptree| - |subscriptedVariables| |argscript| |trigs| |eigenMatrix| |minPoly| - |decrease| |directProduct| |leftNorm| |leftUnits| |multMonom| - |realEigenvectors| |OMputEndError| |symmetricRemainder| |mapDown!| - |clearTable!| |showSummary| |sequences| |increase| |UpTriBddDenomInv| - |setFormula!| |iipow| |numberOfMonomials| |cycles| |generalSqFr| - |tValues| |constantOpIfCan| |acscIfCan| |subNodeOf?| |specialTrigs| - |e01sef| |brace| |addPointLast| |deepExpand| |groebSolve| - |innerSolve1| |equivOperands| |hash| |mathieu12| |showAttributes| - |chiSquare| |vconcat| |monomRDEsys| |coord| |destruct| |getOrder| - |setright!| |branchPoint?| |parts| |resultantEuclideannaif| |show| - |count| |var1StepsDefault| |subHeight| |rationalIfCan| |bat1| - |modularGcdPrimitive| |OMgetEndAtp| |symbol| = |resultantReduit| - |xCoord| |numberOfImproperPartitions| |readInt8!| |monicLeftDivide| - |makeprod| |imagj| |functionIsContinuousAtEndPoints| |nlde| |unravel| - |leviCivitaSymbol| |expression| |any?| |pToDmp| |perfectSquare?| - |semiSubResultantGcdEuclidean2| |trace| |cot2tan| |rightRank| |lo| - |newSubProgram| F2FG |modifyPointData| |highCommonTerms| |pole?| - |integer| |d01gbf| < |acothIfCan| |legendre| |exquo| |every?| - |printStats!| |newLine| |incr| |ScanRoman| |identity| - |SturmHabichtMultiple| |doubleResultant| |qfactor| > |div| |cosh2sech| - |radPoly| |is?| |tanh2coth| |removeCosSq| |satisfy?| - |stoseSquareFreePart| |iiacsch| |subscript| |rootSplit| |limitedint| - <= |opeval| |quo| |constantOperator| |generalPosition| |c06fuf| - |fortranDouble| |c06fpf| |removeIrreducibleRedundantFactors| - |halfExtendedResultant1| |mainForm| |distFact| |separateFactors| >= - |label| |sample| |superHeight| |mathieu22| |rightFactorIfCan| - |duplicates?| |read!| |ref| |curveColor| - |initializeGroupForWordProblem| |invmod| |screenResolution3D| |rem| - |collectUpper| |equiv?| |invertibleSet| |setProperty| |rootPoly| - |tubePlot| |simplifyLog| |infieldIntegrate| |predicate| |zeroOf| |zag| - |bezoutDiscriminant| |fortranInteger| |inR?| |imagE| - |parabolicCylindrical| |iiabs| |totalfract| |redpps| - |axesColorDefault| |doubleRank| |genericLeftNorm| |symmetricGroup| + - |numFunEvals| |leadingIdeal| |currentSubProgram| |multiset| - |listLoops| |setVariableOrder| |combineFeatureCompatibility| - |graphStates| |hMonic| |xn| |normalElement| |linearDependence| - - |initiallyReduce| |readByte!| |lastSubResultant| |subresultantVector| - |copyInto!| |showFortranOutputStack| |assign| |oddintegers| |maxint| - |ScanArabic| / |makeop| |readIfCan!| |open?| |coth2tanh| |binding| - |idealiserMatrix| |lflimitedint| |completeSmith| |besselK| |c06gbf| - |nthExpon| |OMgetFloat| |triangulate| |symbol?| |term| |inconsistent?| - |constructor| |rationalPoint?| |iilog| |fi2df| |weights| |trunc| - |mkIntegral| |parabolic| |lazyPseudoQuotient| |euclideanGroebner| - |inRadical?| |OMmakeConn| |sqfree| |monomials| |readInt32!| |nthRoot| - |lazyEvaluate| |indiceSubResultantEuclidean| |binarySearchTree| - |option| |rightRemainder| |realEigenvalues| |tanIfCan| - |defineProperty| |order| |addMatchRestricted| |structuralConstants| - |moreAlgebraic?| |extract!| |complexForm| |trailingCoefficient| - |reciprocalPolynomial| |computeCycleLength| |cAcos| |OMputEndBVar| - |commutator| |members| |parameters| |palgextint| - |antisymmetricTensors| |setEpilogue!| |commonDenominator| |nothing| - |e02bdf| |roughSubIdeal?| |d02kef| |shuffle| |selectOrPolynomials| - |rename!| |f04axf| |imagk| |leadingIndex| |setRow!| |weight| - |internalZeroSetSplit| |setOrder| |bag| |readable?| |number?| |equiv| - |setOfMinN| |var2StepsDefault| |terms| |derivative| |safeFloor| - |makeEq| |s17acf| |lift| |showTypeInOutput| |fortranCompilerName| - |branchPointAtInfinity?| |OMopenFile| |minPoints3D| |sincos| - |invertibleElseSplit?| |matrixConcat3D| |zero?| |rowEchelonLocal| - |univariate?| |reduce| |polar| |one?| |regularRepresentation| - |ScanFloatIgnoreSpacesIfCan| |exponent| |FormatRoman| |complexZeros| - |outputGeneral| |SFunction| |rightScalarTimes!| |fullDisplay| - |outputList| |rightTrim| |f02fjf| |s17dlf| |nthFractionalTerm| - |calcRanges| |viewWriteAvailable| |bivariateSLPEBR| |biRank| |gcdprim| - |continuedFraction| |balancedBinaryTree| |style| |leftTrim| - |antiCommutative?| |integral| |Lazard2| |complexElementary| |Is| - |totalDegree| |ran| |sPol| |hclf| |minPoints| |printStatement| - |definingEquations| |central?| |primPartElseUnitCanonical| - |outputForm| |triangularSystems| |s17dhf| |reducedDiscriminant| - |lookup| |c06gqf| |cAcot| |iExquo| |cExp| |univariatePolynomial| - |build| |symFunc| |permanent| |generalTwoFactor| |oddlambert| |low| - |findCycle| |boundOfCauchy| UP2UTS |factorAndSplit| - |decreasePrecision| |realRoots| |explicitlyFinite?| |decompose| - |showTheSymbolTable| |restorePrecision| |invertible?| |divideIfCan| - |socf2socdf| |transcendent?| |problemPoints| |leftMinimalPolynomial| - |iicoth| |sech2cosh| |graphImage| |cCos| |tRange| |sinhcosh| |li| - |binaryTree| |createIrreduciblePoly| |stopMusserTrials| - |factorsOfDegree| |stoseInvertibleSetsqfreg| |weakBiRank| |reorder| - |OMgetBVar| |isTimes| |iicsch| |HenselLift| |indiceSubResultant| - |bindings| |algint| |OMgetEndApp| |green| |sizeMultiplication| - |c06ecf| |updatF| |OMgetType| |returnType!| |aCubic| |mathieu24| - |iicosh| |cyclePartition| |bipolar| |curve?| |rootSimp| - |halfExtendedSubResultantGcd1| |f02ajf| |karatsubaOnce| |shellSort| - |c06gcf| |tubeRadiusDefault| |poisson| |getExplanations| |adaptive3D?| - |mainVariable?| |shiftRoots| |meshPar1Var| |presub| - |leftExactQuotient| |minimumDegree| |iteratedInitials| |hessian| - |component| |divide| |iiacos| |and?| |singularAtInfinity?| - |splitNodeOf!| |d02bbf| |complexEigenvectors| |e04fdf| |Beta| |hi| - |leftAlternative?| |normDeriv2| |eulerE| |indices| |exactQuotient| - |ellipticCylindrical| |definingPolynomial| |quotient| |rowEch| - |c06frf| |showAllElements| |numberOfFactors| |s19acf| |pushdown| - |listConjugateBases| |froot| |particularSolution| - |fullPartialFraction| |localAbs| |updateStatus!| |moebius| - |setPosition| |imaginary| |signAround| |exprex| |OMsupportsCD?| - |genus| |rightUnit| |harmonic| |factorByRecursion| |nextSublist| - |quatern| |knownInfBasis| |elRow2!| |eyeDistance| |e02baf| - |radicalSimplify| |mathieu11| |gramschmidt| |symmetricDifference| - |perfectNthPower?| |minimumExponent| |recur| |quadraticForm| |nand| - |pr2dmp| |repeating| |nthFlag| |lyndon| |elliptic?| |linSolve| - |setTopPredicate| |normalizeAtInfinity| |primlimitedint| - |jordanAlgebra?| |useSingleFactorBound?| |lex| |dioSolve| |iiacosh| - |iibinom| |solveid| |ip4Address| |maxrow| |test| |unitNormalize| - |symmetricSquare| |printingInfo?| |tan2cot| |f04jgf| |eulerPhi| - |e02agf| |clipParametric| |s21bcf| |maxrank| |f02aaf| |PDESolve| - |limit| |generate| |leadingCoefficientRicDE| |top!| |rdregime| - |palgextint0| |measure| |rank| |findBinding| |hermite| |split| - |bounds| |prefix| |selectFiniteRoutines| |toseInvertibleSet| - |returnTypeOf| |clipPointsDefault| |randnum| |lighting| - |GospersMethod| |string?| |associatedSystem| |swapRows!| - |leftExtendedGcd| |airyBi| |OMputInteger| |OMreadStr| |depth| - |leftRank| |messagePrint| |extendedSubResultantGcd| |f04asf| |e04jaf| - |genericRightNorm| |evenInfiniteProduct| |att2Result| |showTheIFTable| - |squareMatrix| |arbitrary| |basisOfLeftAnnihilator| |corrPoly| - |roughUnitIdeal?| |patternVariable| |setProperties!| - |outputBinaryFile| |column| |showRegion| |identitySquareMatrix| - |sortConstraints| |lowerPolynomial| |mappingAst| |rootPower| - |Vectorise| |double?| |null| |lquo| |d01bbf| |s17ajf| |hspace| - |setScreenResolution| |iiasec| |rightDivide| - |stoseIntegralLastSubResultant| |critMonD1| |nil?| |zeroDim?| - |innerEigenvectors| |computeBasis| |OMreceive| - |halfExtendedSubResultantGcd2| |not| |legendreP| |character?| - |createThreeSpace| |external?| |dim| |readInt16!| |sumOfDivisors| - |uniform01| |startTableInvSet!| |and| |norm| |setValue!| - |LazardQuotient| |s14baf| |setPredicates| |radicalEigenvalues| - |cyclicGroup| |split!| |or| |complete| - |removeRoughlyRedundantFactorsInContents| |frobenius| - |setAttributeButtonStep| |meatAxe| |sh| |mathieu23| |s13acf| - |remainder| |xor| |rCoord| |quasiComponent| |critT| |setLabelValue| - |e01bgf| |createNormalPoly| |tubePointsDefault| |inputBinaryFile| - |e01saf| |qualifier| |case| |sign| |diag| |squareFreePrim| |minordet| - |OMputObject| |outputSpacing| |createPrimitiveElement| |cTanh| - |exactQuotient!| |Zero| |laurentIfCan| |rubiksGroup| |univariateSolve| - |aLinear| |swap| |bezoutMatrix| |polyred| |One| |totalGroebner| - |cycleLength| |directSum| |/\\| - |generalizedContinuumHypothesisAssumed?| |gethi| |setProperty!| - |exQuo| |sqfrFactor| |zeroSetSplit| |partitions| - |nativeModuleExtension| |returns| |\\/| |horizConcat| |lazyPquo| - |monic?| |solveLinearPolynomialEquationByRecursion| |ksec| |expIfCan| - |mainCharacterization| |extractClosed| |finiteBound| |nullSpace| - |removeCoshSq| |key| |complexNumericIfCan| |delay| |makeSketch| - |unary?| |viewport2D| |s18aff| |getSyntaxFormsFromFile| |center| - |strongGenerators| |subset?| |categoryFrame| |limitPlus| - |partialQuotients| |OMsetEncoding| |dn| |filename| |addMatch| - |polygon| |monicRightFactorIfCan| |iiasinh| |alphabetic?| - |appendPoint| |elt| |overlabel| |fintegrate| |coerceS| |hexDigit| - |nextNormalPoly| |not?| |second| |LyndonWordsList1| |plot| |iisinh| - |toseInvertible?| |rightNorm| |stFuncN| |curry| |parse| |third| - |zeroVector| |f04faf| |polarCoordinates| |tablePow| |logGamma| - |OMencodingXML| |e02daf| |alphabetic| |quotedOperators| |getOperands| - |representationType| |laplacian| |dec| |leftScalarTimes!| |acoshIfCan| - |pseudoQuotient| |point?| |numberOfFractionalTerms| |mesh| |quickSort| - |rightAlternative?| |mkAnswer| |semiResultantReduitEuclidean| - |trace2PowMod| |c06eaf| |curveColorPalette| |absolutelyIrreducible?| - |removeZero| |lintgcd| |deepestTail| |acschIfCan| |enqueue!| - |showScalarValues| |linearAssociatedExp| |lazyGintegrate| |viewport3D| - |e04gcf| |topPredicate| |infiniteProduct| |laguerreL| |qroot| - |polyPart| |palgRDE0| |f01rdf| |expr| |e02zaf| |reducedSystem| - |innerint| |heap| |bytes| |pquo| |entries| |shanksDiscLogAlgorithm| - |reopen!| |lazyVariations| |rquo| |kmax| |e02aef| |measure2Result| - |OMencodingSGML| |systemCommand| |kind| |rightTrace| |e02akf| - |cyclic?| |numberOfDivisors| |wrregime| |unmakeSUP| |element?| - |fixedPoint| |palgintegrate| |op| |nextPrimitivePoly| |logical?| - |removeSquaresIfCan| |reduceBasisAtInfinity| |associator| |divisors| - |localIntegralBasis| |e01daf| |stack| |scaleRoots| |RittWuCompare| - |se2rfi| |variable| |extractPoint| |aQuartic| |reverse!| - |abelianGroup| |complement| |complex?| |normal| - |inverseIntegralMatrixAtInfinity| |maxColIndex| |iterators| - |discriminant| |printHeader| |selectSumOfSquaresRoutines| - |genericLeftTraceForm| |deleteRoutine!| |domainOf| |lexGroebner| - |stoseInvertibleSetreg| |nilFactor| |changeWeightLevel| - |primextintfrac| |index| |swapColumns!| |isOpen?| |argumentListOf| - |iiasin| |extractProperty| |integral?| |basisOfCommutingElements| - |f02agf| |writeUInt8!| |viewZoomDefault| |sylvesterMatrix| - |OMunhandledSymbol| |OMclose| |radix| |endSubProgram| - |extendedIntegrate| |infinityNorm| |compiledFunction| |ode1| - |nextLatticePermutation| |loadNativeModule| |rightLcm| - |replaceKthElement| |elRow1!| |OMreadFile| |leftQuotient| |lowerCase?| - |union| |inverseLaplace| |zeroMatrix| |pair| |startTable!| - 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|createRandomElement| |getMultiplicationMatrix| |youngGroup| - |roughEqualIdeals?| |isMult| |powmod| |mesh?| |root?| - |irreducibleRepresentation| |OMputFloat| |sumOfSquares| |ratpart| - |iicsc| |parent| |heapSort| SEGMENT |getProperties| - |degreeSubResultant| |tube| |mainExpression| |cycleElt| - |expressIdealMember| |fortranLinkerArgs| |dequeue!| |getZechTable| - |maxIndex| |viewDeltaYDefault| |exponential| |drawComplexVectorField| - |scale| |complexLimit| |subNode?| |c06ebf| |extractIndex| |message| - |rewriteIdealWithRemainder| |elements| |squareTop| |rroot| |e04dgf| - |exprToXXP| |changeName| |viewpoint| |linearAssociatedOrder| - |resultantnaif| |matrixGcd| |setMaxPoints| |e02adf| |mapSolve| - |removeSinhSq| |diagonals| |content| |unitVector| |iflist2Result| - |f01rcf| |quartic| |f01maf| |coefficient| |ptFunc| |chebyshevU| - |scalarTypeOf| |cSech| |getProperty| |parseString| |cycleEntry| - |setprevious!| |compound?| |getGoodPrime| |fixedPointExquo| |infix?| - |realElementary| |showTheRoutinesTable| |bothWays| |nullity| |s17dgf| - |interpret| |generalizedEigenvector| |mapdiv| |cyclicCopy| |basis| - |d02gaf| |mask| |unit| |psolve| |integralMatrix| |subQuasiComponent?| - |createNormalPrimitivePoly| |operators| |fracPart| |cAtanh| - |removeRedundantFactorsInContents| |atanIfCan| |basisOfCenter| - |binaryTournament| |surface| |replace| |laplace| |mantissa| - |partialDenominators| |close!| |cons| |setlast!| |clipWithRanges| - |rationalPower| |genericLeftDiscriminant| |curryRight| |factor1| - |compdegd| |OMputEndApp| |tanQ| |setScreenResolution3D| |e02ajf| - |retract| |OMputAtp| |removeSuperfluousCases| |error| |s17agf| - |writeByte!| |fTable| |f04mcf| |gradient| |overbar| |yCoordinates| - |vark| |f07aef| |aromberg| |OMsupportsSymbol?| |shufflein| |assert| - |exp1| |wholeRagits| |elementary| |status| |ratDsolve| |bright| - |tableForDiscreteLogarithm| |radicalEigenvector| - |factorSquareFreePolynomial| |bumprow| |insertTop!| |constant?| - |basisOfRightAnnihilator| |OMread| |makeYoungTableau| |mr| |implies| - |mapUnivariate| |trigs2explogs| |relerror| |firstUncouplingMatrix| - |normInvertible?| |remove!| |nonLinearPart| |lepol| |showAll?| - |vector| |option?| |sin?| |leaves| |signatureAst| |irreducible?| - |screenResolution| |repeatUntilLoop| |startTableGcd!| - |noLinearFactor?| |floor| |mkPrim| |stirling2| |optAttributes| - |represents| |quadraticNorm| |source| |erf| |getDatabase| NOT - |splitConstant| |OMputAttr| |getMatch| |cschIfCan| |outputAsTex| - |differentiate| |hypergeometric0F1| |LiePoly| |monomialIntPoly| - |fprindINFO| |intChoose| |bitLength| |categories| OR |totolex| - |s01eaf| |yCoord| ~= |lyndonIfCan| |cCosh| |totalDifferential| - |unaryFunction| |OMencodingUnknown| |monomRDE| |retractIfCan| - |resetAttributeButtons| AND |reindex| |subResultantChain| |c05nbf| - |coerce| |child?| |dilog| |identityMatrix| |OMgetVariable| |coshIfCan| - |null?| |typeList| |copies| |edf2efi| |computePowers| |numer| - |construct| |scanOneDimSubspaces| |getOperator| |radicalSolve| |df2mf| - |infieldint| |stosePrepareSubResAlgo| |SturmHabichtCoefficients| |sin| - |critM| |denom| |mix| |powers| |purelyTranscendental?| - |selectMultiDimensionalRoutines| |drawCurves| |internalIntegrate0| - |Si| |target| |removeRoughlyRedundantFactorsInPols| |deriv| |cos| - |maxRowIndex| |algebraicVariables| |decomposeFunc| |reduced?| - |BasicMethod| |prem| |OMlistSymbols| |constantCoefficientRicDE| - |splitDenominator| |tan| |laurentRep| |bandedJacobian| |pi| - |readLine!| |extendedEuclidean| |round| |primaryDecomp| |makeTerm| - |s20acf| |insertionSort!| |cot| |continue| |s17aff| |countable?| - |qinterval| |infinity| |alternative?| |nextPartition| |iicos| - |constantIfCan| |linears| |sec| |simplify| |extensionDegree| |d01akf| - |midpoints| |rightZero| |eigenvector| |OMputApp| |rspace| |wholeRadix| - |integralLastSubResultant| |csc| |goto| |leftLcm| |factorSFBRlcUnit| - |interReduce| |s18adf| |conditionsForIdempotents| |inc| |asin| - |userOrdered?| |numberOfPrimitivePoly| |kernel| |concat!| |stFunc1| - |chiSquare1| |pointPlot| |incrementKthElement| |tan2trig| |ravel| - |createLowComplexityTable| |solveLinearPolynomialEquation| |acos| - |map| |leftTrace| * |draw| |enterInCache| |separate| |ratPoly| - |finiteBasis| |exteriorDifferential| |graphState| - |brillhartIrreducible?| |singularitiesOf| |reshape| |atan| |palgLODE0| - |digit| |nextNormalPrimitivePoly| |has?| |trivialIdeal?| - |rootNormalize| |numberOfComposites| |nthCoef| |acot| - |interpretString| |palginfieldint| |dot| |setClipValue| |hexDigit?| - |f2st| |tracePowMod| |asec| |direction| |char| |getPickedPoints| - |iisec| |internalSubQuasiComponent?| |OMconnInDevice| |f04adf| - |controlPanel| |lllip| |printInfo| |algSplitSimple| - |sizePascalTriangle| |acsc| |mainMonomials| |minIndex| |f04mbf| - |makeObject| |setelt| |cCsc| |bezoutResultant| |linearAssociatedLog| - |OMputBVar| |dimensionOfIrreducibleRepresentation| |chebyshevT| |sinh| - |convert| |wordInStrongGenerators| |reify| |algebraicCoefficients?| - |setsubMatrix!| |expintegrate| |makeMulti| |primes| |update| - |minColIndex| |outputFloating| |outlineRender| |copy| |coef| - |multiplyCoefficients| |f01qef| |showClipRegion| |subCase?| - |taylorRep| |byteBuffer| |brillhartTrials| |minGbasis| |polygamma| - |toScale| |cyclicEntries| |applyRules| |cardinality| |float| - |enterPointData| |cCsch| |leftRecip| |complexEigenvalues| - |ramifiedAtInfinity?| |maxdeg| |generic| |f07adf| |var1Steps| - |inverseIntegralMatrix| |wholePart| |autoCoerce| - |rationalApproximation| |polCase| |shrinkable| |An| |autoReduced?| - |failed| |solveLinearPolynomialEquationByFractions| |c05adf| |d01ajf| - |removeConstantTerm| |lieAdmissible?| |OMputEndBind| |cAcoth| - |typeLists| |linearlyDependentOverZ?| |match?| |position| |key?| - |besselJ| |pseudoRemainder| |exponential1| |binary| - |integralCoordinates| |critBonD| |stirling1| |imports| |triangular?| - |tubePoints| |clearTheFTable| |deleteProperty!| |changeNameToObjf| - |pmintegrate| |bivariatePolynomials| |prindINFO| |rightGcd| |plus!| - |numberOfOperations| |fractRagits| |kovacic| |iidprod| - |standardBasisOfCyclicSubmodule| |cubic| |startPolynomial| - |eisensteinIrreducible?| |semiDegreeSubResultantEuclidean| |rst| |po| - |just| |freeOf?| |explogs2trigs| |makeSUP| |currentScope| |insert!| - |resize| |linearPart| |contractSolve| |powerSum| |simplifyPower| - |countRealRootsMultiple| |empty| |dflist| |module| |comp| |e02dcf| - |sechIfCan| GE |viewDeltaXDefault| |crest| |lhs| |listYoungTableaus| - |rewriteSetByReducingWithParticularGenerators| |setnext!| |rombergo| - |zeroDimPrime?| |partialFraction| |flexible?| GT |multisect| - |jacobian| |cycleSplit!| |rhs| |generalInfiniteProduct| |diff| - |singleFactorBound| |pack!| |differentialVariables| |root| |next| - |size?| LE |groebgen| |mvar| |redmat| |rename| |euler| |mainMonomial| - |hdmpToP| |bubbleSort!| |integralAtInfinity?| LT |randomR| |create| - |removeRoughlyRedundantFactorsInPol| |solve| |constantRight| - |sinhIfCan| |removeDuplicates!| |csch2sinh| |rightTraceMatrix| - |exprHasAlgebraicWeight| |coefficients| |ord| |implies?| |Ci| - |permutationGroup| |createMultiplicationTable| |lfunc| |log| - |solveRetract| |mainKernel| |pdct| |mergeFactors| |unit?| - |OMgetEndError| |possiblyNewVariety?| |virtualDegree| |Frobenius| - |submod| |intersect| |stronglyReduced?| |unknown| |node?| |pol| - |basisOfRightNucloid| |expenseOfEvaluationIF| |nil| |infinite| - |arbitraryExponent| |approximate| |complex| |shallowMutable| - |canonical| |noetherian| |central| |partiallyOrderedSet| - |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| - |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| - |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| - |shallowlyMutable| |commutative|)
\ No newline at end of file + |Record| |Union| |tanintegrate| |cAtanh| |ScanFloatIgnoreSpacesIfCan| + |alternating| |polynomialZeros| |clearTheFTable| + |functionIsOscillatory| |denominators| |s14baf| |byte| + |removeRedundantFactorsInContents| |exponent| |iisqrt3| |truncate| + |deleteProperty!| |splitLinear| |setPredicates| |dmp2rfi| |totalLex| + |atanIfCan| |FormatRoman| |cyclic| |iiacsc| |changeNameToObjf| + |permutationRepresentation| |edf2ef| |radicalEigenvalues| + |basisOfCenter| |coerceP| |complexZeros| |clearFortranOutputStack| + |hasoln| |pmintegrate| |int| |lfinfieldint| |cyclicGroup| + |binaryTournament| |OMReadError?| |forLoop| |outputGeneral| |or?| + |zeroSetSplitIntoTriangularSystems| |bivariatePolynomials| |fortran| + |complexRoots| |sturmSequence| |split!| |surface| |generalLambert| + |fortranLiteral| |SFunction| |setIntersection| |palgint0| |f04atf| + |prindINFO| |fortranLogical| |complete| |queue| |credPol| |replace| + |setUnion| |rightScalarTimes!| |increment| |pade| |rightGcd| |f02akf| + |f02adf| |removeRoughlyRedundantFactorsInContents| |laplace| |points| + |fullDisplay| |apply| |makeViewport2D| |dimensions| |plus!| + |partialDenominators| |predicates| |frobenius| |rk4| |currentEnv| + |mapExpon| |nil| |f02fjf| |e02ahf| |removeSinSq| |numberOfOperations| + |setAttributeButtonStep| |lambert| |monomial| |LazardQuotient2| + |getIdentifier| |close!| |s17dlf| |size| |palglimint| |triangSolve| + |call| |fractRagits| |ideal| |setFieldInfo| |multivariate| |OMbindTCP| + |meatAxe| |perfectSqrt| |setlast!| |nthFractionalTerm| |sort| + |spherical| |pointSizeDefault| |kovacic| |rootProduct| |baseRDEsys| + |variables| |imagI| |sh| |clipWithRanges| |constantLeft| |approximate| + |function| |calcRanges| |createLowComplexityNormalBasis| + |removeRedundantFactorsInPols| |iidprod| |nary?| |df2fi| + |completeEval| |mathieu23| |id| |rationalPower| |complex| + |viewWriteAvailable| |qelt| |first| |alternatingGroup| |distance| + |standardBasisOfCyclicSubmodule| |rootOfIrreduciblePoly| |palglimint0| + |s13acf| |linear| |genericLeftDiscriminant| |transform| |rootsOf| + |bivariateSLPEBR| |eval| |rest| |qsetelt| |sizeLess?| |cubic| |Aleph| + |thetaCoord| |leftZero| |remainder| |curryRight| |table| |biRank| + |equality| |substitute| |random| |xRange| |close| |OMopenString| + |startPolynomial| |eq?| |saturate| |factor1| |polynomial| |rCoord| + |pToHdmp| |new| |removeDuplicates| |point| |gcdprim| |yRange| + |semiResultantEuclidean1| |nthRootIfCan| |obj| + |eisensteinIrreducible?| |distdfact| |musserTrials| |rightUnits| + |taylor| |quasiComponent| |search| |compdegd| |log2| |remove| + |bandedHessian| |continuedFraction| |zRange| |display| + |semiDegreeSubResultantEuclidean| |cache| |script| BY |critT| + |leftFactorIfCan| |expextendedint| |laurent| |principal?| + |OMputEndApp| |balancedBinaryTree| |map!| |plenaryPower| |normalized?| + |rst| |tanQ| |setLabelValue| |constant| |list?| |puiseux| |smith| + |tower| |operator| |series| |last| |capacity| |style| |qsetelt!| + |polyRicDE| |po| |makeResult| |irreducibleFactor| |e01bgf| + |setScreenResolution3D| |inverseColeman| |assoc| |getlo| + |antiCommutative?| |OMgetAtp| |notOperand| |just| |keys| |tex| + |createNormalPoly| |monicRightDivide| |inv| |hitherPlane| |delete!| + |e02ajf| |integral| |OMParseError?| |middle| |tanNa| |freeOf?| + |ground?| |genericRightTrace| |trapezoidalo| |tubePointsDefault| + |rk4a| |OMputAtp| |someBasis| |Lazard2| |input| |LyndonWordsList| + |explogs2trigs| |mapCoef| |cAtan| |ground| |inputBinaryFile| |s21bdf| + |removeSuperfluousCases| |min| |library| |complexElementary| |d01aqf| + |scan| |makeSUP| |sumOfKthPowerDivisors| |e01saf| |reseed| + |leadingMonomial| |OMputString| |s17agf| |complexNumeric| |lcm| + |f02abf| |Is| |acsch| |characteristic| |currentScope| + |associatedEquations| |writeByte!| |member?| |leadingCoefficient| + |qualifier| |rules| |setEmpty!| |basisOfMiddleNucleus| |totalDegree| + |jordanAdmissible?| |denominator| |insert!| |kernels| + |leftRegularRepresentation| |btwFact| |primitiveMonomials| + |algebraicSort| |sign| |fTable| |left| |ran| |append| |imagi| |sup| + |mindeg| |resize| |diag| |c06ekf| |f04mcf| |super| |reductum| |fmecg| + |univariate| |right| |sPol| |coerceL| |gcd| |set| |newTypeLists| + |linearPart| |divideExponents| |isobaric?| |squareFreePrim| |gradient| + |shade| |false| |hclf| |readUInt16!| |writeLine!| |contractSolve| + |useSingleFactorBound| |genericPosition| |minordet| |besselI| + |overbar| |sum| |minPoints| |bsolve| |invmultisect| |powerSum| + |headReduce| |yCoordinates| |moebiusMu| |OMputObject| |mainContent| + |factor| |leftDiscriminant| |explicitlyEmpty?| |retractable?| + |simplifyPower| |idealSimplify| |bfKeys| |outputSpacing| |vark| |sqrt| + |initiallyReduced?| |nthExpon| |fractRadix| |lazyPremWithDefault| + |unitsColorDefault| |countRealRootsMultiple| |leftDivide| |ipow| + |createPrimitiveElement| |tryFunctionalDecomposition| |numeric| + |f07aef| |real| |OMgetFloat| |slash| |conjugate| |check| |lp| |empty| + |imagK| |numerators| |radical| |cTanh| |f02aff| |aromberg| |imag| + |triangulate| |ptree| |primintegrate| |lazyResidueClass| |multiple?| + |dflist| |zoom| |directProduct| |d01apf| |OMsupportsSymbol?| |symbol?| + |df2st| |completeHermite| |reduceLODE| |module| |showSummary| |iprint| + |d03edf| |s21bcf| |vedf2vef| |shufflein| |term| |inf| |recip| + |sinh2csch| |OMcloseConn| |e02dcf| |curve| |maxrank| |deref| |exp1| + |brace| |composites| |inconsistent?| |quadratic?| |sorted?| |setPoly| + |componentUpperBound| |hash| |sechIfCan| |eigenvectors| + |linkToFortran| |showAttributes| |f02aaf| |wholeRagits| |destruct| + |unrankImproperPartitions1| |rationalPoint?| |multiEuclidean| |parts| + |solveLinear| |show| |count| |viewDeltaXDefault| |d02bhf| |f02awf| + |PDESolve| |elementary| |symbol| |shiftRight| |iilog| |ranges| = + |writeUInt8!| |OMgetSymbol| |createGenericMatrix| |crest| |cotIfCan| + |limit| |pointData| |algDsolve| |ratDsolve| |expression| + |oneDimensionalArray| |fi2df| |monomialIntegrate| |viewZoomDefault| + |trace| UTS2UP |lo| |listYoungTableaus| |diagonal?| + |factorsOfCyclicGroupSize| |leadingCoefficientRicDE| + |tableForDiscreteLogarithm| |host| |integer| |sylvesterMatrix| + |weights| |binomThmExpt| < |exquo| |zerosOf| |powern| |incr| + |rewriteSetByReducingWithParticularGenerators| |mat| |top!| |newReduc| + |computeCycleEntry| > |trunc| |OMunhandledSymbol| |div| |normal?| + |nthr| |setnext!| |isPlus| |f07fef| |rdregime| |iicsc| |OMgetString| + |mkIntegral| GF2FG <= |OMclose| |quo| |complexIntegrate| |infRittWu?| + |rombergo| |normalForm| |palgextint0| |getBadValues| |whatInfinity| + |parent| |parabolic| |cSin| >= |label| |radix| |chvar| |rotatey| + |zeroDimPrime?| |leftMult| |nullary?| |measure| |heapSort| + |minRowIndex| |lazyPseudoQuotient| |rem| |setStatus!| |endSubProgram| + |ignore?| |primitivePart!| |basisOfLeftNucleus| |d01amf| |findBinding| + |countRealRoots| |getProperties| |predicate| |iiacoth| + |euclideanGroebner| |associatorDependence| |extendedIntegrate| + |sizePascalTriangle| |cAsin| |tubeRadius| |s18def| |hermite| + |generalizedInverse| |degreeSubResultant| |powerAssociative?| + |infinityNorm| |inRadical?| |bitCoef| + |redPol| |mainMonomials| + |splitSquarefree| |rarrow| |split| |child| |tube| |primitive?| + |compiledFunction| |OMmakeConn| - |light| |minIndex| + |quasiAlgebraicSet| |BumInSepFFE| |bounds| |monicDecomposeIfCan| + |expenseOfEvaluation| |mainExpression| |leastPower| |d03faf| |sqfree| + / |ode1| |e02dff| |f04mbf| |fortranComplex| |selectFiniteRoutines| + |resetNew| |cycleElt| |linGenPos| |cCsc| |monomials| |conditionP| + |f07fdf| |nextLatticePermutation| |addBadValue| |monicModulo| + |constructor| |iiatan| |pointLists| |toseInvertibleSet| + |expressIdealMember| |graphs| |bezoutResultant| |readInt32!| + |externalList| |rightLcm| |maxPoints| |nor| |optpair| |gcdcofact| + |makeSeries| |returnTypeOf| |cSec| |fortranLinkerArgs| |option| + |linearAssociatedLog| |nthRoot| |resultantReduitEuclidean| + |replaceKthElement| |patternMatchTimes| |resultantEuclidean| + |noKaratsuba| |clipPointsDefault| |branchIfCan| |dequeue!| |digamma| + |intcompBasis| |lazyEvaluate| |elRow1!| |numericalIntegration| + |OMputBVar| |evaluateInverse| |normalise| |ramified?| |getZechTable| + |subTriSet?| |randnum| |mapmult| |parameters| |nothing| + |mapMatrixIfCan| |exponents| |indiceSubResultantEuclidean| + |OMreadFile| |sub| |dimensionOfIrreducibleRepresentation| + |clipSurface| |adjoint| |OMconnOutDevice| |lighting| |maxIndex| + |numberOfVariables| |binarySearchTree| |dictionary| |divisor| + |leftQuotient| |twist| |chebyshevT| |minimalPolynomial| + |GospersMethod| |hasSolution?| |permutation| |viewDeltaYDefault| + |lift| |insertRoot!| |rightRemainder| |lowerCase?| |movedPoints| + |wordInStrongGenerators| |reverseLex| |solveInField| |string?| + |setTex!| |exponential| |csc2sin| |reduce| |reify| |realEigenvalues| + |space| |inverseLaplace| |s17def| |usingTable?| |associatedSystem| + |collect| |find| |drawComplexVectorField| |unitCanonical| |outputList| + |rightTrim| |exprToGenUPS| |tanIfCan| |zeroMatrix| |d02raf| + |algebraicCoefficients?| |OMUnknownSymbol?| |linearlyDependent?| + |swapRows!| |positiveSolve| |squareFreePart| |scale| |leftTrim| + |setsubMatrix!| |defineProperty| |sylvesterSequence| |startTable!| + |normalizedAssociate| |npcoef| |gbasis| |index?| |getStream| + |leftExtendedGcd| |complexLimit| |characteristicSerie| |eigenvalues| + |order| |expintegrate| |s18dcf| |antisymmetric?| |internalAugment| + |dihedral| |maximumExponent| |ScanFloatIgnoreSpaces| |airyBi| + |subNode?| |makeViewport3D| |nonSingularModel| |addMatchRestricted| + |leadingSupport| |firstNumer| |makeMulti| |birth| |showArrayValues| + |OMputInteger| RF2UTS |exprToUPS| |c06ebf| |HermiteIntegrate| + |structuralConstants| |c06gsf| |minset| |extendedResultant| |primes| + |evenlambert| |OMreadStr| |unprotectedRemoveRedundantFactors| + |anfactor| |extractIndex| |moduleSum| |moreAlgebraic?| |minColIndex| + |expandTrigProducts| |semiSubResultantGcdEuclidean1| |startStats!| + |li| |upperCase| |leftRank| |subResultantGcd| |belong?| + |rewriteIdealWithRemainder| |extract!| |sncndn| |s17akf| |axes| + |outputFloating| |outputAsScript| |euclideanSize| |messagePrint| + |deepCopy| |setErrorBound| |elements| |sn| |complexForm| |mulmod| + |cRationalPower| |outlineRender| |midpoint| |indicialEquations| + |setLegalFortranSourceExtensions| |extendedSubResultantGcd| + |squareTop| |charthRoot| |trailingCoefficient| |symmetricPower| + |numberOfComputedEntries| |initials| |multiplyCoefficients| + |selectPDERoutines| |factorGroebnerBasis| |f04asf| |binomial| + |iterationVar| |rroot| |reciprocalPolynomial| |shallowExpand| + |asechIfCan| |stoseInternalLastSubResultant| |f01qef| |OMgetInteger| + |mainValue| |inspect| |e04jaf| |cap| |e04dgf| |computeCycleLength| + |createPrimitivePoly| |fortranCharacter| |SturmHabicht| + |showClipRegion| |closeComponent| |hi| |backOldPos| |genericRightNorm| + |real?| |exprToXXP| |s20adf| |createPrimitiveNormalPoly| |cAcos| + |squareFreeFactors| |subCase?| |infinite?| |asinIfCan| |mapUp!| + |possiblyInfinite?| |evenInfiniteProduct| |changeName| + |jacobiIdentity?| |OMputEndBVar| |orthonormalBasis| |realSolve| + |taylorRep| |leadingExponent| |att2Result| |charpol| |lyndon?| + |viewpoint| |commutator| |withPredicates| |bivariate?| |byteBuffer| + |rischDE| |showTheIFTable| |padicallyExpand| |linearAssociatedOrder| + |aspFilename| |members| |padicFraction| |stopTableGcd!| + |brillhartTrials| |rightPower| |permutations| |kroneckerDelta| + |squareMatrix| |OMgetApp| |resultantnaif| |palgextint| |cCoth| + |pushup| |minGbasis| |f01brf| |nonQsign| |arbitrary| |normalize| + |matrixGcd| |d01alf| |antisymmetricTensors| |invertIfCan| |zCoord| + |polygamma| |range| |basisOfLeftAnnihilator| |normalDenom| + |setMaxPoints| |Hausdorff| |test| |setEpilogue!| + |showIntensityFunctions| |composite| |toScale| |cAcsc| |corrPoly| + |simplifyExp| |cSinh| |e02adf| |commonDenominator| |s14abf| + |changeVar| |cyclicEntries| |generate| |subMatrix| + |halfExtendedResultant2| |roughUnitIdeal?| |iicot| |mapSolve| |rank| + |e02bdf| |ListOfTerms| |htrigs| |applyRules| |prefix| |dmpToHdmp| + |patternVariable| |collectUnder| |extension| |removeSinhSq| + |roughSubIdeal?| |primeFrobenius| |OMputVariable| |cardinality| + |setProperties!| |completeHensel| |e02gaf| |factorset| |depth| + |diagonals| |d02kef| |degreePartition| |OMputEndAtp| |enterPointData| + |rangePascalTriangle| |outputBinaryFile| |subResultantGcdEuclidean| + |rightDiscriminant| |content| |consnewpol| |shuffle| |lSpaceBasis| + |coordinates| |cCsch| |safetyMargin| |column| |collectQuasiMonic| + |expint| |unitVector| |stoseInvertible?| |selectOrPolynomials| + |systemSizeIF| |karatsubaDivide| |insertBottom!| |leftRecip| + |charClass| |iflist2Result| |dimensionsOf| |primlimintfrac| + |showRegion| |approxSqrt| |null| |rename!| |validExponential| + |reduceByQuasiMonic| |complexEigenvalues| |paren| + |identitySquareMatrix| |f01rcf| |clikeUniv| |LowTriBddDenomInv| |not| + |readLineIfCan!| |optional?| |reducedQPowers| |f04axf| |rowEchelon| + |dim| |ramifiedAtInfinity?| |rootRadius| |sortConstraints| |digits| + |and| |quartic| |listOfLists| |imagk| |extractIfCan| |degree| |maxdeg| + |lowerPolynomial| |e04mbf| |lazyIntegrate| |f01maf| |or| + |leadingIndex| |OMgetEndBind| |listBranches| |generic| |elseBranch| + |mappingAst| |cycle| |xor| |prefixRagits| |coefficient| |setRow!| + |callForm?| |dominantTerm| |f07adf| |unitNormal| |rootPower| + |processTemplate| |twoFactor| |ptFunc| |case| |weight| |in?| |dark| + |var1Steps| |identification| |argument| |Vectorise| + |transcendenceDegree| |Zero| |chebyshevU| |e02bbf| |principalIdeal| + |inverseIntegralMatrix| |printInfo!| |double?| |scalarTypeOf| + |approxNthRoot| |One| |viewDefaults| |invmod| |/\\| |makeVariable| + |f02xef| |wholePart| |paraboloidal| |laguerre| |lquo| |getButtonValue| + |cSech| |\\/| |screenResolution3D| |perfectNthRoot| |transpose| + |rationalApproximation| |zeroDimensional?| |logpart| |d01bbf| + |getProperty| |compactFraction| |collectUpper| |s13aaf| + |areEquivalent?| |key| |polCase| |coleman| |parseString| |henselFact| + |equiv?| |leastAffineMultiple| |minPol| |shrinkable| |center| + |algebraicDecompose| |simpson| |froot| |OMwrite| |cycleEntry| + |invertibleSet| |filename| |fixedPoints| |patternMatch| |An| |s17adf| + |palgint| |particularSolution| |setprevious!| |elt| |quoByVar| + |setProperty| |ratDenom| |seed| |not?| |second| |autoReduced?| + |pdf2df| |fullPartialFraction| |superscript| |compound?| |resultant| + |rootPoly| |parse| |third| |solveLinearPolynomialEquationByFractions| + |cot2trig| |basisOfNucleus| |localAbs| |mapExponents| |getGoodPrime| + |tubePlot| |entries| |rightFactorCandidate| |c05adf| |dec| |connect| + |pushNewContour| |updateStatus!| |trapezoidal| |fixedPointExquo| + |simplifyLog| |shanksDiscLogAlgorithm| |closedCurve| |d01ajf| + |intermediateResultsIF| |recolor| |moebius| |realElementary| |conjug| + |infieldIntegrate| |reopen!| |insertMatch| |removeConstantTerm| + |createMultiplicationMatrix| |setPosition| + |genericRightMinimalPolynomial| |zeroOf| |lazyVariations| |tab| + |lieAdmissible?| |leadingTerm| |imaginary| |acosIfCan| + |wordsForStrongGenerators| |diagonal| |expr| |zag| |complexNormalize| + |rquo| |OMputEndBind| |expandPower| |signAround| |goodnessOfFit| + |divideIfCan!| |nodes| |bezoutDiscriminant| |kmax| |iFTable| |cAcoth| + |clearDenominator| |exprex| |internal?| |principalAncestors| + |mightHaveRoots| |systemCommand| |kind| |fortranInteger| |e02aef| + |gderiv| |prepareSubResAlgo| |e02bcf| |OMsupportsCD?| |comparison| + |maxPoints3D| |op| |inR?| |stiffnessAndStabilityOfODEIF| + |measure2Result| |midpoints| |cup| |genus| |failed?| + |mainDefiningPolynomial| |even?| |stack| |OMencodingSGML| |imagE| + |setPrologue!| |variable| |rightZero| |getConstant| |localUnquote| + |rightUnit| |outputMeasure| |removeZeroes| |normal| + |parabolicCylindrical| |rightTrace| |iterators| |hostPlatform| + |eigenvector| |readBytes!| |bitTruth| |harmonic| |ReduceOrder| + |makingStats?| |iiabs| |e02akf| |inverse| |index| |OMputApp| + |cylindrical| |semicolonSeparate| |factorByRecursion| + |factorSquareFreeByRecursion| |regime| |totalfract| |alphanumeric?| + |cyclic?| |rspace| |doubleFloatFormat| |setLength!| |nextSublist| + |debug3D| |stoseInvertible?reg| |lfextlimint| |redpps| + |numberOfDivisors| |lexico| |wholeRadix| |setMinPoints3D| + |loadNativeModule| |quatern| |rischDEsys| |alphanumeric| + |oddInfiniteProduct| |mapGen| |union| |axesColorDefault| |errorInfo| + |wrregime| |pair| |integralLastSubResultant| |bat| |knownInfBasis| + |iisqrt2| |logIfCan| |buildSyntax| |doubleRank| |yellow| |unmakeSUP| + |goto| |commutativeEquality| |block| |iiGamma| |elRow2!| |whileLoop| + |prinpolINFO| |genericLeftNorm| |compBound| |element?| |leftLcm| + |upperCase?| |getGraph| |colorFunction| |eyeDistance| |explimitedint| + |term?| |symmetricGroup| |fixedPoint| |constDsolve| |factorSFBRlcUnit| + |varselect| |e02baf| |hdmpToDmp| |double| + |noncommutativeJordanAlgebra?| |complexExpand| |value| |numFunEvals| + |palgintegrate| |setCondition!| |interReduce| |dAndcExp| + |derivationCoordinates| |radicalSimplify| |putColorInfo| |expt| + |leadingIdeal| |nextPrimitivePoly| |janko2| |s18adf| + |rationalFunction| |edf2fi| |mathieu11| |partialNumerators| |nullary| + |currentSubProgram| |logical?| |c06fqf| |conditionsForIdempotents| + |f02bbf| |pushuconst| |physicalLength| |gramschmidt| |e01bhf| + |fractionPart| |multiset| |blankSeparate| |removeSquaresIfCan| + |recoverAfterFail| |userOrdered?| |convergents| |pushdterm| + |genericRightTraceForm| |symmetricDifference| |push!| |mirror| + |listLoops| |leftOne| |reduceBasisAtInfinity| |numberOfPrimitivePoly| + |e04naf| |primitivePart| |perfectNthPower?| |internalLastSubResultant| + |color| |Gamma| |setVariableOrder| |associator| |acotIfCan| |rule| + |concat!| |getVariableOrder| |readUInt32!| |minimumExponent| |unparse| + |f04arf| |say| |combineFeatureCompatibility| |divisors| + |binaryFunction| |stFunc1| |recur| |rk4qc| |polyRDE| |declare!| + |gcdPolynomial| |RemainderList| |graphStates| |numericalOptimization| + |localIntegralBasis| |chiSquare1| |rootOf| |testDim| |quadraticForm| + |genericRightDiscriminant| |fortranTypeOf| |hMonic| |setleaves!| + |e01daf| |pointPlot| |setref| |nand| |lineColorDefault| + |leftRankPolynomial| |generic?| |xn| |scaleRoots| |adaptive?| + |incrementKthElement| |numFunEvals3D| |pr2dmp| |csubst| |upperCase!| + |sin2csc| |normalElement| |RittWuCompare| + |purelyAlgebraicLeadingMonomial?| |tan2trig| |subSet| + |antiAssociative?| |repeating| |stiffnessAndStabilityFactor| + |integralBasis| |linearDependence| |se2rfi| |overset?| + |createLowComplexityTable| |drawComplex| |nthFlag| |doubleComplex?| + |tanhIfCan| |inputOutputBinaryFile| |void| |reset| |initiallyReduce| + |extractPoint| |prologue| |solveLinearPolynomialEquation| |formula| + |factors| |clip| |lyndon| |isConnected?| |viewThetaDefault| + |readByte!| |front| |aQuartic| |leftTrace| |solid| |elliptic?| + |writeInt8!| |segment| |uncouplingMatrices| |stripCommentsAndBlanks| + |write| |lastSubResultant| |reverse!| |uniform| |enterInCache| + |reverse| |setvalue!| |constantToUnaryFunction| |linSolve| |iidsum| + |mindegTerm| |save| |directory| |subresultantVector| |modulus| + |abelianGroup| |separate| |OMlistCDs| FG2F |setTopPredicate| |iiperm| + |prevPrime| |entry| |copyInto!| |complement| |positive?| |ratPoly| + |nrows| |tensorProduct| |normalizeAtInfinity| |stoseInvertibleSet| + |OMputError| |addiag| |showFortranOutputStack| |normalDeriv| + |complex?| |finiteBasis| |ncols| |reducedContinuedFraction| + |internalIntegrate| |primlimitedint| |extractBottom!| |rationalPoints| + |assign| |inverseIntegralMatrixAtInfinity| |entry?| + |exteriorDifferential| |comment| |generalizedEigenvectors| + |jordanAlgebra?| |meshFun2Var| |e01sbf| |prod| |checkPrecision| + |oddintegers| |cartesian| |maxColIndex| |graphState| + |genericLeftTrace| |useSingleFactorBound?| |definingInequation| + |mkcomm| |solveLinearlyOverQ| |maxint| |iomode| |discriminant| + |brillhartIrreducible?| |parents| |nextColeman| |atoms| |lex| + |linearMatrix| |UP2ifCan| |ScanArabic| |box| |nextsubResultant2| + |printHeader| |singularitiesOf| |nextsousResultant2| |dioSolve| + |coercePreimagesImages| |padecf| |addPoint| |flatten| |makeop| + |selectSumOfSquaresRoutines| |abs| |palgLODE0| |fortranReal| + |dualSignature| |iiacosh| |escape| |closedCurve?| |makeSin| + |readIfCan!| |genericLeftTraceForm| |concat| |digit| |times!| + |iibinom| |f2df| |zeroSquareMatrix| |OMconnectTCP| |top| |open?| + |refine| |deleteRoutine!| |nextNormalPrimitivePoly| |setClosed| + |viewWriteDefault| |subtractIfCan| |solveid| |rootBound| + |relationsIdeal| |coth2tanh| |domainOf| |primitiveElement| |has?| + |exportedOperators| |limitedIntegrate| |mapBivariate| |ip4Address| + |ldf2lst| |pow| |binding| |true| |lexGroebner| |baseRDE| + |trivialIdeal?| |subresultantSequence| |setMinPoints| |maxrow| + |d02ejf| |selectsecond| |idealiserMatrix| |iitanh| + |stoseInvertibleSetreg| |rootNormalize| |scopes| |unitNormalize| + |isPower| |numberOfHues| |purelyAlgebraic?| |lflimitedint| + |outputFixed| |nilFactor| |numberOfComposites| |symmetricSquare| + |square?| |leadingBasisTerm| |red| |lists| |completeSmith| + |coerceListOfPairs| |changeWeightLevel| |nthCoef| + |primPartElseUnitCanonical!| |printingInfo?| |minrank| |headReduced?| + |besselK| |primextintfrac| |monomial?| |interpretString| + |create3Space| |tan2cot| |createRandomElement| |internalSubPolSet?| + |c06gbf| |outerProduct| |lexTriangular| |swapColumns!| + |palginfieldint| |signature| |f04jgf| |transcendentalDecompose| + |getMultiplicationMatrix| |groebner| |d02gbf| |varList| |isOpen?| + |dot| |morphism| |eulerPhi| |youngGroup| |setStatus| |nlde| |makeFR| + |argumentListOf| |setClipValue| |setleft!| |e02agf| |expintfldpoly| + |roughEqualIdeals?| |unravel| |iiasin| |addPoint2| |hexDigit?| + |clipParametric| |setRealSteps| |isMult| |orbit| |leviCivitaSymbol| + |setAdaptive| |extractProperty| |f2st| |powmod| + |semiDiscriminantEuclidean| |any?| |delete| |integral?| + |selectAndPolynomials| |tracePowMod| |matrix| |OMgetEndApp| |putGraph| + |selectIntegrationRoutines| |mesh?| |pToDmp| + |basisOfCommutingElements| |dequeue| |direction| |schwerpunkt| |green| + |denomLODE| |root?| |perfectSquare?| |increasePrecision| |f02agf| + |getPickedPoints| |sizeMultiplication| |choosemon| + |irreducibleRepresentation| |cothIfCan| + |semiSubResultantGcdEuclidean2| |optimize| |iisec| |c06ecf| |untab| + |zero| |OMputFloat| |endOfFile?| |cot2tan| |checkRur| + |LyndonWordsList1| |internalSubQuasiComponent?| |updatF| + |relativeApprox| |sumOfSquares| |moduloP| |rightRank| |cPower| |plot| + |OMconnInDevice| |normalizedDivide| |OMgetType| |And| + |PollardSmallFactor| |ratpart| |newSubProgram| |iisinh| |printCode| + |f04adf| |pureLex| |Or| |returnType!| F2FG |hcrf| |toseInvertible?| + |digit?| |controlPanel| |cond| |Not| |aCubic| |epilogue| |reflect| + |exists?| |modifyPointData| |rightNorm| |mpsode| |lllip| |mathieu24| + |rotate!| |nextSubsetGray| |vertConcat| |highCommonTerms| |numerator| + |stFuncN| |plus| |algSplitSimple| |iicosh| |subspace| |omError| |slex| + |pole?| |curry| |roughBasicSet| |select!| |cyclePartition| |jacobi| + |cCot| |zeroVector| |d01gbf| |rightCharacteristicPolynomial| + |commaSeparate| |c05nbf| |cosh| |bipolar| |idealiser| |sayLength| + |iiatanh| |log10| |f04faf| |acothIfCan| |child?| |clearTheSymbolTable| + |tanh| |cfirst| |rowEchLocal| |curve?| |inGroundField?| |simpsono| + |max| |polarCoordinates| |rightRegularRepresentation| |legendre| + |bitand| |explicitEntries?| |identityMatrix| |coth| |times| |rootSimp| + |unrankImproperPartitions0| |partition| |stopTableInvSet!| + |isQuotient| |tablePow| |every?| |bitior| |fractionFreeGauss!| + |OMgetVariable| |plotPolar| |sech| |octon| + |halfExtendedSubResultantGcd1| |drawToScale| |unvectorise| |logGamma| + |printStats!| |ocf2ocdf| |coshIfCan| |csch| |shallowCopy| + |fortranDoubleComplex| |f02ajf| |indicialEquationAtInfinity| + |linearDependenceOverZ| |balancedFactorisation| |newLine| |cAsec| + |OMencodingXML| |null?| |asinh| |sumSquares| |karatsubaOnce| + |makeUnit| |e01bef| |e02daf| |ScanRoman| |acosh| |typeList| + |diagonalProduct| |revert| |monom| |shellSort| |d01anf| + |setMaxPoints3D| |drawStyle| |alphabetic| |identity| |copies| + |integers| |discriminantEuclidean| |atanh| |c06gcf| |quasiRegular?| + |objectOf| |normal01| |height| |edf2efi| |SturmHabichtMultiple| + |meshPar2Var| |quotedOperators| |selectOptimizationRoutines| |acoth| + |pomopo!| |tubeRadiusDefault| |flagFactor| |ODESolve| |cn| |conical| + |doubleResultant| |common| |supersub| |getOperands| |computePowers| + |asech| |numberOfNormalPoly| |poisson| |aQuadratic| |integrate| + |representationType| |qfactor| |selectfirst| |tree| + |scanOneDimSubspaces| |empty?| |exprHasLogarithmicWeights| + |getExplanations| |algintegrate| |cyclicEqual?| |elliptic| |declare| + |cosh2sech| |getRef| |laplacian| |multiple| |getOperator| + |leftCharacteristicPolynomial| |hasPredicate?| |adaptive3D?| |s13adf| + |debug| |radPoly| |applyQuote| |leftScalarTimes!| |quoted?| + |changeMeasure| |radicalSolve| |duplicates| |nthFactor| + |mainVariable?| D |semiLastSubResultantEuclidean| |is?| |d01asf| + |acoshIfCan| |df2mf| |quotientByP| |tail| |shiftRoots| |s17dcf| + |ldf2vmf| |merge!| |tanh2coth| |bernoulliB| |pseudoQuotient| + |integralDerivationMatrix| |infieldint| |meshPar1Var| |listexp| + |cAsinh| |mainVariables| |symbolTable| |functionIsFracPolynomial?| + |removeCosSq| |integralBasisAtInfinity| |point?| |ruleset| + |stosePrepareSubResAlgo| |rk4f| |presub| |chineseRemainder| + |companionBlocks| |qPot| |satisfy?| |generator| + |numberOfFractionalTerms| |multinomial| |SturmHabichtCoefficients| + |leftExactQuotient| |odd?| |hyperelliptic| |iCompose| + |stoseSquareFreePart| |mergeDifference| |mesh| |computeInt| |critM| + |addmod| |minimumDegree| |getCode| |s18acf| |subst| |iiacsch| + |quickSort| |mix| |diagonalMatrix| |gcdPrimitive| |suchThat| Y + |f01qcf| |iteratedInitials| |integralRepresents| |printTypes| + |pushFortranOutputStack| |subscript| |rightAlternative?| |leaf?| + |powers| |mainSquareFreePart| |randomLC| |hessian| |critB| |power| + |rootSplit| |mkAnswer| |bumptab1| |purelyTranscendental?| LODO2FUN + |component| |LiePolyIfCan| |createZechTable| |radicalRoots| + |popFortranOutputStack| F |limitedint| |semiResultantReduitEuclidean| + |quasiRegular| |selectMultiDimensionalRoutines| |rotate| + |radicalOfLeftTraceForm| |interval| |divide| |sturmVariationsOf| + |print| |cTan| |opeval| |findConstructor| |trace2PowMod| |drawCurves| + |qqq| |Nul| |iiacos| |subResultantsChain| |resolve| + |toseSquareFreePart| |outputAsFortran| |constantOperator| |iisin| + |c06eaf| |numberOfCycles| |internalIntegrate0| |cAcsch| |karatsuba| + |graeffe| |and?| |goodPoint| |clearTheIFTable| |objects| + |generalPosition| |curveColorPalette| |lifting1| |Si| |leftPower| + |singularAtInfinity?| |SturmHabichtSequence| |whitePoint| |setfirst!| + |base| |torsion?| |c06fuf| |absolutelyIrreducible?| + |univariatePolynomialsGcds| |removeRoughlyRedundantFactorsInPols| + |contours| |cross| |splitNodeOf!| |lowerCase| |makeCos| |f02wef| + |fortranDouble| |name| |bfEntry| |removeZero| |deriv| |coth2trigh| + |intPatternMatch| |d02bbf| |infix| |crushedSet| |ode| |datalist| + |c06fpf| |body| |lintgcd| |listRepresentation| |topFortranOutputStack| + |maxRowIndex| |complexEigenvectors| |isOp| |raisePolynomial| |cAsech| + |removeIrreducibleRedundantFactors| |sinIfCan| |deepestTail| + |fortranLiteralLine| |algebraicVariables| |e04fdf| |firstDenom| + |curryLeft| |determinant| ** |halfExtendedResultant1| + |cyclotomicFactorization| |acschIfCan| |cAcosh| |decomposeFunc| + |checkForZero| |secIfCan| |Beta| |stop| |deepestInitial| ~ |insert| + |mainForm| |enqueue!| |nodeOf?| |rightMult| |reduced?| |iitan| + |leftAlternative?| |e04ycf| |selectODEIVPRoutines| |distFact| + |doublyTransitive?| |showScalarValues| |BasicMethod| |e01baf| EQ + |normDeriv2| |sec2cos| |rotatez| |s19adf| |open| |condition| + |separateFactors| |separateDegrees| |linearAssociatedExp| |setColumn!| + |prem| |eulerE| |tab1| |integralMatrixAtInfinity| |tanh2trigh| + |precision| |level| |port| |sample| |lazyGintegrate| |scripted?| + |OMputSymbol| |OMlistSymbols| |B1solve| |palgLODE| |indices| + |integerBound| |internalInfRittWu?| |eq| |superHeight| + |internalDecompose| |viewport3D| |e04ucf| |constantCoefficientRicDE| + |routines| |phiCoord| |exactQuotient| |skewSFunction| + |mainPrimitivePart| |factorial| |iter| |e04gcf| |mathieu22| |t| + |shift| |unexpand| |taylorIfCan| |splitDenominator| + |ellipticCylindrical| |operations| |lazyIrreducibleFactors| + |nextIrreduciblePoly| |minus!| |previous| |characteristicSet| + |rightFactorIfCan| |beauzamyBound| |topPredicate| |seriesToOutputForm| + |laurentRep| |definingPolynomial| |getCurve| |normFactors| + |hasTopPredicate?| |duplicates?| |adaptive| |infiniteProduct| + |bandedJacobian| |modifyPoint| |quotient| |blue| |expPot| |components| + |category| |read!| |f01mcf| |laguerreL| |changeBase| |readLine!| + |rowEch| |pair?| |rightExtendedGcd| |hermiteH| |property| |domain| + |ref| |qroot| |linearPolynomials| |extendedEuclidean| |setrest!| + |inHallBasis?| |c06frf| |FormatArabic| |stFunc2| |package| + |curveColor| |rightMinimalPolynomial| |polyPart| |f01bsf| |round| + |clearCache| |cycleRagits| |showAllElements| |pdf2ef| |supRittWu?| + |chainSubResultants| |initializeGroupForWordProblem| |firstSubsetGray| + |palgRDE0| |rangeIsFinite| |primaryDecomp| + |generalizedContinuumHypothesisAssumed| |numberOfFactors| + |viewPhiDefault| |selectPolynomials| |units| |constantKernel| + |modularFactor| |f01rdf| |exp| |var2Steps| |makeTerm| |arguments| + |s19acf| |LagrangeInterpolation| |quote| |rur| |subscriptedVariables| + |setButtonValue| |e02zaf| |useEisensteinCriterion?| |s20acf| + |bernoulli| |pushdown| |writeBytes!| |quasiMonic?| |argscript| + |makeGraphImage| |reducedSystem| |insertionSort!| |medialSet| + |listConjugateBases| |matrixDimensions| |denomRicDE| |conjugates| + |trigs| |innerint| |palgRDE| |s17aff| |orOperands| |distribute| + |output| |certainlySubVariety?| |compile| |eigenMatrix| |any| |heap| + |factorPolynomial| |countable?| |torsionIfCan| |printStatement| + |initTable!| |code| |contract| |tanAn| |minPoly| |bytes| |isList| + |qinterval| |ParCond| |definingEquations| |expandLog| + |useEisensteinCriterion| |perspective| |decrease| |pquo| |hasHi| + |alternative?| |fixedDivisor| |central?| |numberOfChildren| |#| + |lazyPrem| |currentCategoryFrame| |leftNorm| |nextPartition| |ode2| + |rational?| |primPartElseUnitCanonical| |OMgetEndAttr| |generators| + |leftUnits| |ricDsolve| |exactQuotient!| |iicos| |leftTraceMatrix| + |compose| |outputForm| |dom| |fill!| |row| |multMonom| |incrementBy| + |lprop| |laurentIfCan| |constantIfCan| |squareFreePolynomial| + |genericLeftMinimalPolynomial| |triangularSystems| |singular?| + |prime?| |iifact| |realEigenvectors| |rubiksGroup| |expand| + |radicalEigenvectors| |linears| |part?| |frst| |s17dhf| |droot| |node| + |push| |OMputEndError| |filterWhile| |univariateSolve| |simplify| + |shiftLeft| |elem?| |reducedDiscriminant| |prinshINFO| |const| + |discreteLog| |symmetricRemainder| |aLinear| |filterUntil| |e01sff| + |extensionDegree| |lookup| |outputArgs| |anticoord| |leftGcd| + |mapDown!| |swap| |factorOfDegree| |select| |d01akf| |schema| |c06gqf| + |rightExactQuotient| |c02agf| |parametric?| |title| |bezoutMatrix| + |clearTable!| |divergence| |options| |cAcot| |OMgetAttr| |elColumn2!| + |e01bff| |sequences| |bits| |polyred| |pile| |radicalEigenvector| + |iExquo| |infLex?| |prepareDecompose| |bumptab| |increase| |operation| + |euclideanNormalForm| |totalGroebner| |accuracyIF| + |factorSquareFreePolynomial| |bombieriNorm| |cExp| |s17ahf| + |supDimElseRittWu?| |e| |initial| |OMserve| |UpTriBddDenomInv| + |cycleLength| |string| |setProperties| |bumprow| |nextPrime| + |univariatePolynomial| |symbolTableOf| |monicCompleteDecompose| + |setFormula!| |plusInfinity| |prinb| |directSum| |insertTop!| + |KrullNumber| |build| |evaluate| |separant| |cyclotomic| + |partialFraction| |generalizedContinuumHypothesisAssumed?| |iipow| + |minusInfinity| |makeRecord| |enumerate| |minimize| |constant?| + |pointColorDefault| |symFunc| |stronglyReduce| |OMencodingBinary| + |asinhIfCan| |flexible?| |numberOfMonomials| |gethi| |safeCeiling| + |basisOfRightAnnihilator| |s19aaf| |vspace| |rischNormalize| + |permanent| |redPo| |ceiling| |multisect| |setProperty!| |cycles| + |mainVariable| |length| |OMread| |children| |dmpToP| + |generalTwoFactor| |e02bef| |linear?| |jacobian| |exQuo| |generalSqFr| + |stoseInvertible?sqfreg| |scripts| |pushucoef| |makeYoungTableau| + |swap!| |oddlambert| |nthExponent| |factorFraction| |cycleSplit!| + |tValues| |sqfrFactor| |multiplyExponents| |position!| |implies| |low| + |resetVariableOrder| |interpolate| |numberOfComponents| + |generalInfiniteProduct| |constantOpIfCan| |lieAlgebra?| + |zeroSetSplit| |mapUnivariate| |removeRedundantFactors| + |zeroDimPrimary?| |findCycle| |ffactor| |ddFact| |diff| |equation| + |type| |acscIfCan| |characteristicPolynomial| |partitions| + |trigs2explogs| |f02axf| |errorKind| |boundOfCauchy| |arrayStack| + |back| |singleFactorBound| |subNodeOf?| |integer?| + |nativeModuleExtension| |relerror| |latex| |width| + |lastSubResultantEuclidean| UP2UTS |decimal| |pmComplexintegrate| + |pack!| |specialTrigs| |toroidal| |returns| |packageCall| + |firstUncouplingMatrix| |iiasech| |factorAndSplit| |OMgetEndBVar| + |rightQuotient| |differentialVariables| |horizConcat| |e01sef| + |viewPosDefault| |list| |power!| |normInvertible?| |decreasePrecision| + |d02cjf| |fortranCarriageReturn| |lifting| |root| |multiEuclideanTree| + |lazyPquo| |addPointLast| |OMUnknownCD?| |car| |remove!| |init| + |inrootof| |realRoots| |besselY| |cycleTail| |size?| |leader| |sort!| + |deepExpand| |monic?| |cdr| |nonLinearPart| |setchildren!| |arg1| + |figureUnits| |explicitlyFinite?| |readUInt8!| |roman| |groebgen| + |oblateSpheroidal| |groebSolve| |setDifference| + |solveLinearPolynomialEquationByRecursion| |lepol| |symbolIfCan| + |arg2| |delta| |head| |decompose| |extendedint| |s18aef| |mvar| + |innerSolve1| |ksec| |preprocess| |llprop| |showAll?| |pop!| + |showTheSymbolTable| |f02aef| |polygon?| |redmat| |equivOperands| + |wordInGenerators| |expIfCan| |option?| |nextPrimitiveNormalPoly| + |conditions| |optional| |fglmIfCan| |restorePrecision| |UnVectorise| + |algebraic?| |rename| |mathieu12| |pleskenSplit| + |mainCharacterization| |sin?| |squareFree| |match| |rightOne| |write!| + |invertible?| |normalizeIfCan| |result| |euler| |chiSquare| |cosIfCan| + |extractClosed| |associates?| |signatureAst| |substring?| + |divideIfCan| |move| |groebnerIdeal| |factorSquareFree| |properties| + |mainMonomial| |vconcat| |finiteBound| |localReal?| |irreducible?| + |badValues| |socf2socdf| |groebnerFactorize| |fillPascalTriangle| + |lllp| |hdmpToP| |translate| |monomRDEsys| |irreducibleFactors| + |nullSpace| |screenResolution| |lazyPseudoDivide| |suffix?| + |LyndonCoordinates| |transcendent?| |c05pbf| |nextItem| |bubbleSort!| + |coord| |myDegree| |removeCoshSq| |repeatUntilLoop| |reduction| + |lambda| |factorials| |problemPoints| |pattern| |leftUnit| + |pseudoDivide| |integralAtInfinity?| |getOrder| |s15aef| + |complexNumericIfCan| |startTableGcd!| |parametersOf| |prefix?| + |solid?| |leftMinimalPolynomial| |leftFactor| |monicDivide| |randomR| + |setright!| |rational| |negative?| |delay| |noLinearFactor?| + |viewSizeDefault| |iicoth| |f02bjf| |createNormalElement| |hex| + SEGMENT |create| |makeSketch| |branchPoint?| |positiveRemainder| + |OMputEndObject| |bit?| |floor| |sech2cosh| |magnitude| |rdHack1| + |difference| |removeRoughlyRedundantFactorsInPol| |diophantineSystem| + |iroot| |resultantEuclideannaif| |unary?| |exptMod| |mkPrim| + |cscIfCan| |graphImage| |nsqfree| |message| |basisOfCentroid| + |critMTonD1| |solve| |postfix| |changeThreshhold| |var1StepsDefault| + |OMgetBind| |viewport2D| |stirling2| |sequence| |rotatex| |cCos| + |OMputEndAttr| |OMsend| |constantRight| |commutative?| |subHeight| + |s18aff| |trim| |optAttributes| |sdf2lst| |tRange| |asecIfCan| + |basisOfLeftNucloid| |cyclotomicDecomposition| |sinhIfCan| |product| + |rationalIfCan| |asimpson| |getSyntaxFormsFromFile| |represents| + |physicalLength!| |infix?| |wronskianMatrix| |sinhcosh| + |tryFunctionalDecomposition?| |OMputBind| |removeDuplicates!| + |interpret| |bat1| |strongGenerators| |variable?| |neglist| + |quadraticNorm| |mask| |binaryTree| |region| |modTree| |dfRange| + |csch2sinh| |modularGcdPrimitive| |makeFloatFunction| |subset?| + |critpOrder| |getDatabase| |homogeneous?| |createIrreduciblePoly| + |headAst| |realZeros| |rightTraceMatrix| |mantissa| |categoryFrame| + |OMgetEndAtp| |cons| |airyAi| |splitConstant| |singRicDE| + |stopMusserTrials| |over| |fixPredicate| |traverse| + |exprHasAlgebraicWeight| |OMgetObject| |resultantReduit| |retract| + |limitPlus| |OMputAttr| |atanhIfCan| |error| |factorsOfDegree| |imagJ| + |updatD| |stoseLastSubResultant| |coefficients| |xCoord| + |partialQuotients| |andOperands| |finite?| |getMatch| |arity| |assert| + |stoseInvertibleSetsqfreg| |mapUnivariateIfCan| |high| |ord| |status| + |bright| |numberOfImproperPartitions| |s17aef| |OMsetEncoding| + |cschIfCan| |ridHack1| |weakBiRank| |completeEchelonBasis| + |sparsityIF| |numericIfCan| |implies?| |mr| |readInt8!| |dn| + |rightRankPolynomial| |lfintegrate| |outputAsTex| |reorder| + |squareFreeLexTriangular| |setImagSteps| |dihedralGroup| |Ci| |vector| + |s14aaf| |monicLeftDivide| |addMatch| |leaves| |hypergeometric0F1| + |atrapezoidal| |e02ddf| |OMgetBVar| |makeCrit| |float?| + |permutationGroup| |LiePoly| |source| |makeprod| |Lazard| |polygon| + |erf| |colorDef| NOT |thenBranch| |isTimes| |summation| |quadratic| + |createMultiplicationTable| |differentiate| |imagj| |hue| + |monicRightFactorIfCan| |approximants| |monomialIntPoly| |iicsch| + |repSq| OR |categories| |symmetricProduct| |lazy?| ~= |lfunc| + |functionIsContinuousAtEndPoints| |iiasinh| |taylorQuoByVar| + |fprindINFO| |generateIrredPoly| |retractIfCan| |simpleBounds?| AND + |HenselLift| |connectTo| |coerce| |toseLastSubResultant| + |solveRetract| |alphabetic?| |dilog| |indicialEquation| |hconcat| + |intChoose| |rewriteIdealWithQuasiMonicGenerators| |writable?| |numer| + |construct| |indiceSubResultant| |prime| |tanSum| |mainKernel| + |overlap| |appendPoint| |gcdcofactprim| |factorList| |bitLength| |sin| + |bindings| |universe| |subPolSet?| |f01ref| |denom| |pdct| |trueEqual| + |totolex| |s21bbf| |target| |overlabel| |probablyZeroDim?| |cos| + |algint| |stopTable!| |s15adf| |mdeg| |mergeFactors| + |lastSubResultantElseSplit| |s01eaf| |rectangularMatrix| |fintegrate| + |symmetric?| |tan| |notelem| |pi| |extractSplittingLeaf| |unit?| + |merge| |iiacot| |primintfldpoly| |coerceS| |yCoord| |cot| |continue| + |internalZeroSetSplit| |reducedForm| |pointColorPalette| |infinity| + |OMgetEndError| |divisorCascade| |hexDigit| |lyndonIfCan| |pastel| + |mainCoefficients| |sec| |setOrder| |showTheFTable| |headRemainder| + |possiblyNewVariety?| |augment| |useNagFunctions| |nextNormalPoly| + |isAbsolutelyIrreducible?| |cCosh| |csc| |bag| |eof?| |geometric| + |virtualDegree| |pointColor| |totalDifferential| |inc| |bracket| + |asin| |readable?| |kernel| |romberg| |coerceImages| |Frobenius| + |lowerCase!| |s17ajf| |less?| |ravel| |unaryFunction| + |symmetricTensors| |acos| |map| |number?| * |draw| |univcase| + |coHeight| |submod| |lazyPseudoRemainder| |hspace| + |semiResultantEuclidean2| |reshape| |OMgetEndObject| + |OMencodingUnknown| |atan| |equiv| |ef2edf| |basicSet| |intersect| + |seriesSolve| |setScreenResolution| |more?| |monomRDE| |weighted| + |acot| |setOfMinN| |stronglyReduced?| |integerIfCan| |iiasec| + |innerSolve| |resetAttributeButtons| |resetBadValues| |asec| |char| + |var2StepsDefault| |exprHasWeightCosWXorSinWX| |coefChoose| |node?| + |solve1| |rightDivide| |ParCondList| |printInfo| |reindex| |orbits| + |acsc| |terms| |prolateSpheroidal| |Ei| |makeObject| |setelt| |pol| + |cosSinInfo| |rootKerSimp| |stoseIntegralLastSubResultant| + |subResultantChain| |sinh| |cyclicParents| |convert| |derivative| + |complexSolve| |upDateBranches| |basisOfRightNucloid| + |basisOfRightNucleus| |critMonD1| |d01gaf| |update| |safeFloor| + |iisech| |roughBase?| |copy| |coef| |expenseOfEvaluationIF| + |bringDown| |nil?| |cos2sec| |showTheRoutinesTable| + |rewriteSetWithReduction| |makeEq| |testModulus| + |rewriteIdealWithHeadRemainder| |closed?| |zeroDim?| |badNum| + |extractTop!| |bothWays| |s17acf| |float| |f04maf| |cyclicSubmodule| + |complementaryBasis| |innerEigenvectors| |weierstrass| |edf2df| + |nullity| |showTypeInOutput| |d01fcf| |coordinate| |autoCoerce| + |iiexp| |semiIndiceSubResultantEuclidean| |contains?| |computeBasis| + |s17dgf| |failed| |fortranCompilerName| |pascalTriangle| + |removeSuperfluousQuasiComponents| |typeLists| + |generalizedEigenvector| |s21baf| |lfextendedint| |OMreceive| + |vectorise| |match?| |position| |branchPointAtInfinity?| |copy!| + |algebraicOf| |linearlyDependentOverZ?| |isExpt| |wreath| + |halfExtendedSubResultantGcd2| |f01qdf| |mapdiv| |OMopenFile| + |rightRecip| |selectNonFiniteRoutines| |key?| |argumentList!| + |legendreP| |quasiMonicPolynomials| |leastMonomial| |cyclicCopy| + |minPoints3D| |groebner?| |presuper| |besselJ| |impliesOperands| + |numberOfIrreduciblePoly| |character?| |basis| |LyndonBasis| |sincos| + |primeFactor| |largest| |pseudoRemainder| |exponentialOrder| + |listOfMonoms| |createThreeSpace| |d02gaf| |atom?| + |invertibleElseSplit?| |OMgetError| |graphCurves| |exponential1| + |getMeasure| |external?| |c02aff| |associative?| |unit| |bottom!| + |comp| |matrixConcat3D| GE |rootDirectory| |extend| |binary| |lhs| + |intensity| |readInt16!| |modularGcd| |flexibleArray| |psolve| + |antiCommutator| |zero?| GT |doubleDisc| |loopPoints| + |integralCoordinates| |rhs| |univariatePolynomials| |sumOfDivisors| + |extendIfCan| |clipBoolean| |integralMatrix| |next| |rowEchelonLocal| + LE |getMultiplicationTable| |dimension| |critBonD| |traceMatrix| + |df2ef| |uniform01| |d03eef| |subQuasiComponent?| |univariate?| LT + |fibonacci| |f04qaf| |stirling1| |primextendedint| |s19abf| + |startTableInvSet!| |createNormalPrimitivePoly| |e02def| |polar| + |setelt!| |degreeSubResultantEuclidean| |imports| |lagrange| |cLog| + |norm| |operators| |variationOfParameters| |log| |one?| + |bipolarCylindrical| |scalarMatrix| |triangular?| |leftRemainder| + |setAdaptive3D| |setValue!| |fracPart| |sts2stst| + |regularRepresentation| |repeating?| |tableau| |tubePoints| |unknown| + |semiResultantEuclideannaif| |LazardQuotient| |allRootsOf| |nil| + |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-406 (-562))) -4037 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-38 |#1|) . T) ((-38 $) -4037 (|has| |#1| (-554)) (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-35) |has| |#1| (-1192)) ((-95) |has| |#1| (-1192)) ((-102) . T) ((-111 #0# #0#) -4037 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-130) . T) ((-144) -4037 (|has| |#1| (-348)) (|has| |#1| (-144))) ((-146) |has| |#1| (-146)) ((-612 #0#) -4037 (|has| |#1| (-1033 (-406 (-562)))) (|has| |#1| (-348)) (|has| |#1| (-362))) ((-612 (-562)) . T) ((-612 |#1|) . T) ((-612 $) -4037 (|has| |#1| (-554)) (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-609 (-857)) . T) ((-171) . T) ((-610 (-168 (-224))) |has| |#1| (-1017)) ((-610 (-168 (-378))) |has| |#1| (-1017)) ((-610 (-535)) |has| |#1| (-610 (-535))) ((-610 (-887 (-378))) |has| |#1| (-610 (-887 (-378)))) ((-610 (-887 (-562))) |has| |#1| (-610 (-887 (-562)))) ((-610 #1=(-1164 |#1|)) . T) ((-230 |#1|) . T) ((-232) -4037 (|has| |#1| (-348)) (|has| |#1| (-232))) ((-242) -4037 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-283) |has| |#1| (-1192)) ((-285 |#1| $) |has| |#1| (-285 |#1| |#1|)) ((-289) -4037 (|has| |#1| (-554)) (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-306) -4037 (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-308 |#1|) |has| |#1| (-308 |#1|)) ((-362) -4037 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-401) |has| |#1| (-348)) ((-367) -4037 (|has| |#1| (-367)) (|has| |#1| (-348))) ((-348) |has| |#1| (-348)) ((-369 |#1| #1#) . T) ((-408 |#1| #1#) . T) ((-337 |#1|) . T) ((-376 |#1|) . T) ((-399 |#1|) . T) ((-410 |#1|) . T) ((-451) -4037 (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-492) |has| |#1| (-1192)) ((-513 (-1168) |#1|) |has| |#1| (-513 (-1168) |#1|)) ((-513 |#1| |#1|) |has| |#1| (-308 |#1|)) ((-554) -4037 (|has| |#1| (-554)) (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-642 #0#) -4037 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-642 |#1|) . T) ((-642 $) . T) ((-635 (-562)) |has| |#1| (-635 (-562))) ((-635 |#1|) . T) ((-712 #0#) -4037 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-712 |#1|) . T) ((-712 $) -4037 (|has| |#1| (-554)) (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-719 |#1| #1#) . T) ((-721) . T) ((-845) |has| |#1| (-845)) ((-895 (-1168)) |has| |#1| (-895 (-1168))) ((-881 (-378)) |has| |#1| (-881 (-378))) ((-881 (-562)) |has| |#1| (-881 (-562))) ((-879 |#1|) . T) ((-904) -12 (|has| |#1| (-306)) (|has| |#1| (-904))) ((-915) -4037 (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-997) -12 (|has| |#1| (-997)) (|has| |#1| (-1192))) ((-1033 (-406 (-562))) |has| |#1| (-1033 (-406 (-562)))) ((-1033 (-562)) |has| |#1| (-1033 (-562))) ((-1033 |#1|) . T) ((-1050 #0#) -4037 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-1050 |#1|) . T) ((-1050 $) . T) ((-1044) . T) ((-1051) . T) ((-1104) . T) ((-1092) . T) ((-1143) |has| |#1| (-348)) ((-1192) |has| |#1| (-1192)) ((-1195) |has| |#1| (-1192)) ((-1207) . 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T) ((-38 |#2|) |has| |#2| (-171)) ((-102) -4037 (|has| |#2| (-1092)) (|has| |#2| (-1044)) (|has| |#2| (-843)) (|has| |#2| (-788)) (|has| |#2| (-721)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -4037 (|has| |#2| (-1044)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-111 $ $) |has| |#2| (-171)) ((-130) -4037 (|has| |#2| (-1044)) (|has| |#2| (-843)) (|has| |#2| (-788)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130))) ((-612 #0=(-406 (-562))) -12 (|has| |#2| (-1033 (-406 (-562)))) (|has| |#2| (-1092))) ((-612 (-562)) -4037 (|has| |#2| (-1044)) (-12 (|has| |#2| (-1033 (-562))) (|has| |#2| (-1092))) (|has| |#2| (-843)) (|has| |#2| (-171))) ((-612 |#2|) -4037 (|has| |#2| (-1092)) (|has| |#2| (-171))) ((-609 (-857)) -4037 (|has| |#2| (-1092)) (|has| |#2| (-1044)) (|has| |#2| (-843)) (|has| |#2| (-788)) (|has| |#2| (-721)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-609 (-857))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-609 (-1256 |#2|)) . T) ((-171) |has| |#2| (-171)) ((-230 |#2|) |has| |#2| (-1044)) ((-232) -12 (|has| |#2| (-232)) (|has| |#2| (-1044))) ((-285 #1=(-562) |#2|) . T) ((-287 #1# |#2|) . T) ((-308 |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((-367) |has| |#2| (-367)) ((-376 |#2|) |has| |#2| (-1044)) ((-410 |#2|) |has| |#2| (-1092)) ((-488 |#2|) . T) ((-600 #1# |#2|) . T) ((-513 |#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1092))) ((-642 |#2|) -4037 (|has| |#2| (-1044)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-642 $) -4037 (|has| |#2| (-1044)) (|has| |#2| (-843)) (|has| |#2| (-171))) ((-635 (-562)) -12 (|has| |#2| (-635 (-562))) (|has| |#2| (-1044))) ((-635 |#2|) |has| |#2| (-1044)) ((-712 |#2|) -4037 (|has| |#2| (-362)) (|has| |#2| (-171))) ((-721) -4037 (|has| |#2| (-1044)) (|has| |#2| (-843)) (|has| |#2| (-721)) (|has| |#2| (-171))) ((-786) |has| |#2| (-843)) ((-787) -4037 (|has| |#2| (-843)) (|has| |#2| (-788))) ((-788) |has| |#2| (-788)) ((-789) -4037 (|has| |#2| (-843)) (|has| |#2| (-788))) ((-790) -4037 (|has| |#2| (-843)) (|has| |#2| (-788))) ((-843) |has| |#2| (-843)) ((-845) -4037 (|has| |#2| (-843)) (|has| |#2| (-788))) ((-895 (-1168)) -12 (|has| |#2| (-895 (-1168))) (|has| |#2| (-1044))) ((-1033 #0#) -12 (|has| |#2| (-1033 (-406 (-562)))) (|has| |#2| (-1092))) ((-1033 (-562)) -12 (|has| |#2| (-1033 (-562))) (|has| |#2| (-1092))) ((-1033 |#2|) |has| |#2| (-1092)) ((-1050 |#2|) -4037 (|has| |#2| (-1044)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-1050 $) |has| |#2| (-171)) ((-1044) -4037 (|has| |#2| (-1044)) (|has| |#2| (-843)) (|has| |#2| (-171))) ((-1051) -4037 (|has| |#2| (-1044)) (|has| |#2| (-843)) (|has| |#2| (-171))) ((-1104) -4037 (|has| |#2| (-1044)) (|has| |#2| (-843)) (|has| |#2| (-721)) (|has| |#2| (-171))) ((-1092) -4037 (|has| |#2| (-1092)) (|has| |#2| (-1044)) (|has| |#2| (-843)) (|has| |#2| (-788)) (|has| |#2| (-721)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1207) . T) ((-1263 |#2|) |has| |#2| (-362))) -((-2578 (((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 21)) (-1955 ((|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 23)) (-4152 (((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)) 18))) -(((-238 |#1| |#2| |#3|) (-10 -7 (-15 -2578 ((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -1955 (|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -4152 ((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)))) (-766) (-1207) (-1207)) (T -238)) -((-4152 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-239 *5 *6)) (-14 *5 (-766)) (-4 *6 (-1207)) (-4 *7 (-1207)) (-5 *2 (-239 *5 *7)) (-5 *1 (-238 *5 *6 *7)))) (-1955 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-239 *5 *6)) (-14 *5 (-766)) (-4 *6 (-1207)) (-4 *2 (-1207)) (-5 *1 (-238 *5 *6 *2)))) (-2578 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-239 *6 *7)) (-14 *6 (-766)) (-4 *7 (-1207)) (-4 *5 (-1207)) (-5 *2 (-239 *6 *5)) (-5 *1 (-238 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-171) -4037 (|has| |#1| (-554)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-610 (-224)) -12 (|has| |#1| (-362)) (|has| |#2| (-1017))) ((-610 (-378)) -12 (|has| |#1| (-362)) (|has| |#2| (-1017))) ((-610 (-535)) -12 (|has| |#1| (-362)) (|has| |#2| (-610 (-535)))) ((-610 (-887 (-378))) -12 (|has| |#1| (-362)) (|has| |#2| (-610 (-887 (-378))))) ((-610 (-887 (-562))) -12 (|has| |#1| (-362)) (|has| |#2| (-610 (-887 (-562))))) ((-230 |#2|) |has| |#1| (-362)) ((-232) -4037 (-12 (|has| |#1| (-362)) (|has| |#2| (-232))) (|has| |#1| (-15 * (|#1| (-562) |#1|)))) ((-242) |has| |#1| (-362)) ((-283) |has| |#1| (-38 (-406 (-562)))) ((-285 |#2| $) -12 (|has| |#1| (-362)) (|has| |#2| (-285 |#2| |#2|))) ((-285 $ $) |has| (-562) (-1104)) ((-289) -4037 (|has| |#1| (-554)) (|has| |#1| (-362))) ((-306) |has| |#1| (-362)) ((-308 |#2|) -12 (|has| |#1| (-362)) (|has| |#2| (-308 |#2|))) ((-362) |has| |#1| (-362)) ((-337 |#2|) |has| |#1| (-362)) ((-376 |#2|) |has| |#1| (-362)) ((-399 |#2|) |has| |#1| (-362)) ((-451) |has| |#1| (-362)) ((-492) |has| |#1| (-38 (-406 (-562)))) ((-513 (-1168) |#2|) -12 (|has| |#1| (-362)) (|has| |#2| (-513 (-1168) |#2|))) ((-513 |#2| |#2|) -12 (|has| |#1| (-362)) (|has| |#2| (-308 |#2|))) ((-554) -4037 (|has| |#1| (-554)) (|has| |#1| (-362))) ((-642 #1#) -4037 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-562))))) ((-642 |#1|) . T) ((-642 |#2|) |has| |#1| (-362)) ((-642 $) . T) ((-635 (-562)) -12 (|has| |#1| (-362)) (|has| |#2| (-635 (-562)))) ((-635 |#2|) |has| |#1| (-362)) ((-712 #1#) -4037 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-562))))) ((-712 |#1|) |has| |#1| (-171)) ((-712 |#2|) |has| |#1| (-362)) ((-712 $) -4037 (|has| |#1| (-554)) (|has| |#1| (-362))) ((-721) . T) ((-786) -12 (|has| |#1| (-362)) (|has| |#2| (-815))) ((-787) -12 (|has| |#1| (-362)) (|has| |#2| (-815))) ((-789) -12 (|has| |#1| (-362)) (|has| |#2| (-815))) ((-790) -12 (|has| |#1| (-362)) (|has| |#2| (-815))) ((-815) -12 (|has| |#1| (-362)) (|has| |#2| (-815))) ((-843) -12 (|has| |#1| (-362)) (|has| |#2| (-815))) ((-845) -4037 (-12 (|has| |#1| (-362)) (|has| |#2| (-845))) (-12 (|has| |#1| (-362)) (|has| |#2| (-815)))) ((-895 (-1168)) -4037 (-12 (|has| |#1| (-362)) (|has| |#2| (-895 (-1168)))) (-12 (|has| |#1| (-15 * (|#1| (-562) |#1|))) (|has| |#1| (-895 (-1168))))) ((-881 (-378)) -12 (|has| |#1| (-362)) (|has| |#2| (-881 (-378)))) ((-881 (-562)) -12 (|has| |#1| (-362)) (|has| |#2| (-881 (-562)))) ((-879 |#2|) |has| |#1| (-362)) ((-904) -12 (|has| |#1| (-362)) (|has| |#2| (-904))) ((-968 |#1| #0# (-1074)) . T) ((-915) |has| |#1| (-362)) ((-987 |#2|) |has| |#1| (-362)) ((-997) |has| |#1| (-38 (-406 (-562)))) ((-1017) -12 (|has| |#1| (-362)) (|has| |#2| (-1017))) ((-1033 (-406 (-562))) -12 (|has| |#1| (-362)) (|has| |#2| (-1033 (-562)))) ((-1033 (-562)) -12 (|has| |#1| (-362)) (|has| |#2| (-1033 (-562)))) ((-1033 #2#) -12 (|has| |#1| (-362)) (|has| |#2| (-1033 (-1168)))) ((-1033 |#2|) . T) ((-1050 #1#) -4037 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-562))))) ((-1050 |#1|) . T) ((-1050 |#2|) |has| |#1| (-362)) ((-1050 $) -4037 (|has| |#1| (-554)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-1044) . T) ((-1051) . T) ((-1104) . T) ((-1092) . T) ((-1143) -12 (|has| |#1| (-362)) (|has| |#2| (-1143))) ((-1192) |has| |#1| (-38 (-406 (-562)))) ((-1195) |has| |#1| (-38 (-406 (-562)))) ((-1207) |has| |#1| (-362)) ((-1211) |has| |#1| (-362)) ((-1216 |#1|) . T) ((-1234 |#1| #0#) . 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(NIL T T) -8 NIL NIL NIL) (-1275 3163591 3165843 3165885 "XF" 3166506 NIL XF (NIL T) -9 NIL 3166906 NIL) (-1274 3163212 3163300 3163469 "XF-" 3163474 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1273 3158546 3159801 3159856 "XFALG" 3162028 NIL XFALG (NIL T T) -9 NIL 3162817 NIL) (-1272 3157679 3157783 3157988 "XEXPPKG" 3158438 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1271 3155823 3157529 3157625 "XDPOLY" 3157630 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1270 3154768 3155334 3155377 "XALG" 3155382 NIL XALG (NIL T) -9 NIL 3155493 NIL) (-1269 3148237 3152745 3153239 "WUTSET" 3154360 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1268 3146528 3147289 3147612 "WP" 3148048 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1267 3146157 3146350 3146420 "WHILEAST" 3146480 T WHILEAST (NIL) -8 NIL NIL NIL) (-1266 3145656 3145874 3145968 "WHEREAST" 3146085 T WHEREAST (NIL) -8 NIL NIL NIL) (-1265 3144542 3144740 3145035 "WFFINTBS" 3145453 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1264 3142446 3142873 3143335 "WEIER" 3144114 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1263 3141593 3142017 3142059 "VSPACE" 3142195 NIL VSPACE (NIL T) -9 NIL 3142269 NIL) (-1262 3141431 3141458 3141549 "VSPACE-" 3141554 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1261 3141239 3141282 3141350 "VOID" 3141385 T VOID (NIL) -8 NIL NIL NIL) (-1260 3139375 3139734 3140140 "VIEW" 3140855 T VIEW (NIL) -7 NIL NIL NIL) (-1259 3135800 3136438 3137175 "VIEWDEF" 3138660 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1258 3125136 3127348 3129521 "VIEW3D" 3133649 T VIEW3D (NIL) -8 NIL NIL NIL) (-1257 3117418 3119047 3120626 "VIEW2D" 3123579 T VIEW2D (NIL) -8 NIL NIL NIL) (-1256 3112822 3117188 3117280 "VECTOR" 3117361 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1255 3111399 3111658 3111976 "VECTOR2" 3112552 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1254 3104926 3109183 3109226 "VECTCAT" 3110219 NIL VECTCAT (NIL T) -9 NIL 3110805 NIL) (-1253 3103940 3104194 3104584 "VECTCAT-" 3104589 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1252 3103421 3103591 3103711 "VARIABLE" 3103855 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1251 3103354 3103359 3103389 "UTYPE" 3103394 T UTYPE (NIL) -9 NIL NIL NIL) (-1250 3102184 3102338 3102600 "UTSODETL" 3103180 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1249 3099624 3100084 3100608 "UTSODE" 3101725 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1248 3091500 3097250 3097739 "UTS" 3099193 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1247 3082743 3088067 3088110 "UTSCAT" 3089222 NIL UTSCAT (NIL T) -9 NIL 3089979 NIL) (-1246 3080098 3080813 3081802 "UTSCAT-" 3081807 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1245 3079725 3079768 3079901 "UTS2" 3080049 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1244 3073998 3076563 3076606 "URAGG" 3078676 NIL URAGG (NIL T) -9 NIL 3079399 NIL) (-1243 3070937 3071800 3072923 "URAGG-" 3072928 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1242 3066661 3069551 3070023 "UPXSSING" 3070601 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1241 3058763 3065908 3066181 "UPXS" 3066446 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1240 3051876 3058667 3058739 "UPXSCONS" 3058744 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1239 3042121 3048871 3048933 "UPXSCCA" 3049507 NIL UPXSCCA (NIL T T) -9 NIL 3049740 NIL) (-1238 3041759 3041844 3042018 "UPXSCCA-" 3042023 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1237 3031857 3038380 3038423 "UPXSCAT" 3039071 NIL UPXSCAT (NIL T) -9 NIL 3039679 NIL) (-1236 3031287 3031366 3031545 "UPXS2" 3031772 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1235 3029941 3030194 3030545 "UPSQFREE" 3031030 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1234 3023729 3026743 3026798 "UPSCAT" 3027959 NIL UPSCAT (NIL T T) -9 NIL 3028733 NIL) (-1233 3022933 3023140 3023467 "UPSCAT-" 3023472 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1232 3008783 3016781 3016824 "UPOLYC" 3018925 NIL UPOLYC (NIL T) -9 NIL 3020146 NIL) (-1231 3000112 3002537 3005684 "UPOLYC-" 3005689 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1230 2999739 2999782 2999915 "UPOLYC2" 3000063 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1229 2991313 2999422 2999551 "UP" 2999658 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1228 2990652 2990759 2990923 "UPMP" 2991202 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1227 2990205 2990286 2990425 "UPDIVP" 2990565 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1226 2988773 2989022 2989338 "UPDECOMP" 2989954 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1225 2988008 2988120 2988305 "UPCDEN" 2988657 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1224 2987527 2987596 2987745 "UP2" 2987933 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1223 2986044 2986731 2987008 "UNISEG" 2987285 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1222 2985259 2985386 2985591 "UNISEG2" 2985887 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1221 2984319 2984499 2984725 "UNIFACT" 2985075 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1220 2968286 2983496 2983747 "ULS" 2984126 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1219 2956326 2968190 2968262 "ULSCONS" 2968267 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1218 2938942 2950884 2950946 "ULSCCAT" 2951584 NIL ULSCCAT (NIL T T) -9 NIL 2951872 NIL) (-1217 2937992 2938237 2938625 "ULSCCAT-" 2938630 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1216 2927867 2934304 2934347 "ULSCAT" 2935210 NIL ULSCAT (NIL T) -9 NIL 2935940 NIL) (-1215 2927297 2927376 2927555 "ULS2" 2927782 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1214 2926434 2926909 2927010 "UINT8" 2927121 T UINT8 (NIL) -8 NIL NIL 2927200) (-1213 2925570 2926045 2926146 "UINT32" 2926257 T UINT32 (NIL) -8 NIL NIL 2926336) (-1212 2924706 2925181 2925282 "UINT16" 2925393 T UINT16 (NIL) -8 NIL NIL 2925472) (-1211 2923109 2924032 2924062 "UFD" 2924274 T UFD (NIL) -9 NIL 2924388 NIL) (-1210 2922903 2922949 2923044 "UFD-" 2923049 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1209 2921985 2922168 2922384 "UDVO" 2922709 T UDVO (NIL) -7 NIL NIL NIL) (-1208 2919801 2920210 2920681 "UDPO" 2921549 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1207 2919734 2919739 2919769 "TYPE" 2919774 T TYPE (NIL) -9 NIL NIL NIL) (-1206 2919521 2919689 2919720 "TYPEAST" 2919725 T TYPEAST (NIL) -8 NIL NIL NIL) (-1205 2918492 2918694 2918934 "TWOFACT" 2919315 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1204 2917564 2917901 2918136 "TUPLE" 2918292 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1203 2915255 2915774 2916313 "TUBETOOL" 2917047 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1202 2914104 2914309 2914550 "TUBE" 2915048 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1201 2908868 2913076 2913359 "TS" 2913856 NIL TS (NIL T) -8 NIL NIL NIL) (-1200 2897535 2901627 2901724 "TSETCAT" 2906993 NIL TSETCAT (NIL T T T T) -9 NIL 2908524 NIL) (-1199 2892270 2893867 2895758 "TSETCAT-" 2895763 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1198 2886533 2887379 2888321 "TRMANIP" 2891406 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1197 2885974 2886037 2886200 "TRIMAT" 2886465 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1196 2883770 2884007 2884371 "TRIGMNIP" 2885723 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1195 2883290 2883403 2883433 "TRIGCAT" 2883646 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1194 2882959 2883038 2883179 "TRIGCAT-" 2883184 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1193 2879856 2881817 2882098 "TREE" 2882713 NIL TREE (NIL T) -8 NIL NIL NIL) (-1192 2879130 2879658 2879688 "TRANFUN" 2879723 T TRANFUN (NIL) -9 NIL 2879789 NIL) (-1191 2878409 2878600 2878880 "TRANFUN-" 2878885 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1190 2878213 2878245 2878306 "TOPSP" 2878370 T TOPSP (NIL) -7 NIL NIL NIL) (-1189 2877561 2877676 2877830 "TOOLSIGN" 2878094 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1188 2876222 2876738 2876977 "TEXTFILE" 2877344 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1187 2874161 2874675 2875104 "TEX" 2875815 T TEX (NIL) -8 NIL NIL NIL) (-1186 2873942 2873973 2874045 "TEX1" 2874124 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1185 2873590 2873653 2873743 "TEMUTL" 2873874 T TEMUTL (NIL) -7 NIL NIL NIL) (-1184 2871744 2872024 2872349 "TBCMPPK" 2873313 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1183 2863632 2869904 2869960 "TBAGG" 2870360 NIL TBAGG (NIL T T) -9 NIL 2870571 NIL) (-1182 2858702 2860190 2861944 "TBAGG-" 2861949 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1181 2858086 2858193 2858338 "TANEXP" 2858591 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1180 2851587 2857943 2858036 "TABLE" 2858041 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1179 2850999 2851098 2851236 "TABLEAU" 2851484 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1178 2845607 2846827 2848075 "TABLBUMP" 2849785 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1177 2845035 2845135 2845263 "SYSTEM" 2845501 T SYSTEM (NIL) -7 NIL NIL NIL) (-1176 2841498 2842193 2842976 "SYSSOLP" 2844286 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1175 2840555 2841022 2841135 "SYSNNI" 2841321 NIL SYSNNI (NIL NIL) -8 NIL NIL 2841400) (-1174 2840008 2840413 2840455 "SYSINT" 2840460 NIL SYSINT (NIL NIL) -8 NIL NIL 2840468) (-1173 2836342 2837269 2837985 "SYNTAX" 2839314 T SYNTAX (NIL) -8 NIL NIL NIL) (-1172 2833500 2834102 2834734 "SYMTAB" 2835732 T SYMTAB (NIL) -8 NIL NIL NIL) (-1171 2828749 2829651 2830634 "SYMS" 2832539 T SYMS (NIL) -8 NIL NIL NIL) (-1170 2826021 2828207 2828437 "SYMPOLY" 2828554 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1169 2825538 2825613 2825736 "SYMFUNC" 2825933 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1168 2821590 2822850 2823663 "SYMBOL" 2824747 T SYMBOL (NIL) -8 NIL NIL NIL) (-1167 2815129 2816818 2818538 "SWITCH" 2819892 T SWITCH (NIL) -8 NIL NIL NIL) (-1166 2808399 2813950 2814253 "SUTS" 2814884 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2800500 2807646 2807919 "SUPXS" 2808184 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1164 2792030 2800118 2800244 "SUP" 2800409 NIL SUP (NIL T) -8 NIL NIL NIL) (-1163 2791189 2791316 2791533 "SUPFRACF" 2791898 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1162 2790810 2790869 2790982 "SUP2" 2791124 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1161 2789223 2789497 2789860 "SUMRF" 2790509 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1160 2788537 2788603 2788802 "SUMFS" 2789144 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1159 2772544 2787714 2787965 "SULS" 2788344 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1158 2772173 2772366 2772436 "SUCHTAST" 2772496 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1157 2771495 2771698 2771838 "SUCH" 2772081 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1156 2765389 2766401 2767360 "SUBSPACE" 2770583 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1155 2764819 2764909 2765073 "SUBRESP" 2765277 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1154 2758188 2759484 2760795 "STTF" 2763555 NIL STTF (NIL T) -7 NIL NIL NIL) (-1153 2752361 2753481 2754628 "STTFNC" 2757088 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1152 2743676 2745543 2747337 "STTAYLOR" 2750602 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1151 2736920 2743540 2743623 "STRTBL" 2743628 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1150 2732311 2736875 2736906 "STRING" 2736911 T STRING (NIL) -8 NIL NIL NIL) (-1149 2727199 2731684 2731714 "STRICAT" 2731773 T STRICAT (NIL) -9 NIL 2731835 NIL) (-1148 2720009 2724818 2725429 "STREAM" 2726623 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1147 2719519 2719596 2719740 "STREAM3" 2719926 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1146 2718501 2718684 2718919 "STREAM2" 2719332 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1145 2718189 2718241 2718334 "STREAM1" 2718443 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1144 2717205 2717386 2717617 "STINPROD" 2718005 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1143 2716783 2716967 2716997 "STEP" 2717077 T STEP (NIL) -9 NIL 2717155 NIL) (-1142 2710326 2716682 2716759 "STBL" 2716764 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1141 2705500 2709547 2709590 "STAGG" 2709743 NIL STAGG (NIL T) -9 NIL 2709832 NIL) (-1140 2703202 2703804 2704676 "STAGG-" 2704681 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1139 2701397 2702972 2703064 "STACK" 2703145 NIL STACK (NIL T) -8 NIL NIL NIL) (-1138 2694122 2699538 2699994 "SREGSET" 2701027 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1137 2686548 2687916 2689429 "SRDCMPK" 2692728 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1136 2679515 2683988 2684018 "SRAGG" 2685321 T SRAGG (NIL) -9 NIL 2685929 NIL) (-1135 2678532 2678787 2679166 "SRAGG-" 2679171 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1134 2673027 2677479 2677900 "SQMATRIX" 2678158 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1133 2666776 2669745 2670472 "SPLTREE" 2672372 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1132 2662766 2663432 2664078 "SPLNODE" 2666202 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1131 2661813 2662046 2662076 "SPFCAT" 2662520 T SPFCAT (NIL) -9 NIL NIL NIL) (-1130 2660550 2660760 2661024 "SPECOUT" 2661571 T SPECOUT (NIL) -7 NIL NIL NIL) (-1129 2652202 2653946 2653976 "SPADXPT" 2658368 T SPADXPT (NIL) -9 NIL 2660402 NIL) (-1128 2651963 2652003 2652072 "SPADPRSR" 2652155 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1127 2650146 2651918 2651949 "SPADAST" 2651954 T SPADAST (NIL) -8 NIL NIL NIL) (-1126 2642117 2643864 2643907 "SPACEC" 2648280 NIL SPACEC (NIL T) -9 NIL 2650096 NIL) (-1125 2640288 2642049 2642098 "SPACE3" 2642103 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1124 2639040 2639211 2639502 "SORTPAK" 2640093 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1123 2637090 2637393 2637812 "SOLVETRA" 2638704 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1122 2636101 2636323 2636597 "SOLVESER" 2636863 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1121 2631321 2632202 2633204 "SOLVERAD" 2635153 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1120 2627136 2627745 2628474 "SOLVEFOR" 2630688 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1119 2621433 2626485 2626582 "SNTSCAT" 2626587 NIL SNTSCAT (NIL T T T T) -9 NIL 2626657 NIL) (-1118 2615576 2619756 2620147 "SMTS" 2621123 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1117 2610027 2615464 2615541 "SMP" 2615546 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1116 2608186 2608487 2608885 "SMITH" 2609724 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1115 2601081 2605237 2605340 "SMATCAT" 2606691 NIL SMATCAT (NIL NIL T T T) -9 NIL 2607241 NIL) (-1114 2598021 2598844 2600022 "SMATCAT-" 2600027 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1113 2595734 2597257 2597300 "SKAGG" 2597561 NIL SKAGG (NIL T) -9 NIL 2597696 NIL) (-1112 2592076 2595150 2595345 "SINT" 2595532 T SINT (NIL) -8 NIL NIL 2595705) (-1111 2591848 2591886 2591952 "SIMPAN" 2592032 T SIMPAN (NIL) -7 NIL NIL NIL) (-1110 2591155 2591383 2591523 "SIG" 2591730 T SIG (NIL) -8 NIL NIL NIL) (-1109 2589993 2590214 2590489 "SIGNRF" 2590914 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1108 2588798 2588949 2589240 "SIGNEF" 2589822 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1107 2588131 2588381 2588505 "SIGAST" 2588696 T SIGAST (NIL) -8 NIL NIL NIL) (-1106 2585821 2586275 2586781 "SHP" 2587672 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1105 2579727 2585722 2585798 "SHDP" 2585803 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1104 2579326 2579492 2579522 "SGROUP" 2579615 T SGROUP (NIL) -9 NIL 2579677 NIL) (-1103 2579184 2579210 2579283 "SGROUP-" 2579288 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1102 2576020 2576717 2577440 "SGCF" 2578483 T SGCF (NIL) -7 NIL NIL NIL) (-1101 2570415 2575467 2575564 "SFRTCAT" 2575569 NIL SFRTCAT (NIL T T T T) -9 NIL 2575608 NIL) (-1100 2563839 2564854 2565990 "SFRGCD" 2569398 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1099 2556967 2558038 2559224 "SFQCMPK" 2562772 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1098 2556589 2556678 2556788 "SFORT" 2556908 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1097 2555734 2556429 2556550 "SEXOF" 2556555 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1096 2554868 2555615 2555683 "SEX" 2555688 T SEX (NIL) -8 NIL NIL NIL) (-1095 2550407 2551096 2551191 "SEXCAT" 2554128 NIL SEXCAT (NIL T T T T T) -9 NIL 2554706 NIL) (-1094 2547587 2550341 2550389 "SET" 2550394 NIL SET (NIL T) -8 NIL NIL NIL) (-1093 2545838 2546300 2546605 "SETMN" 2547328 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1092 2545444 2545570 2545600 "SETCAT" 2545717 T SETCAT (NIL) -9 NIL 2545802 NIL) (-1091 2545224 2545276 2545375 "SETCAT-" 2545380 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1090 2541611 2543685 2543728 "SETAGG" 2544598 NIL SETAGG (NIL T) -9 NIL 2544938 NIL) (-1089 2541069 2541185 2541422 "SETAGG-" 2541427 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1088 2540539 2540765 2540866 "SEQAST" 2540990 T SEQAST (NIL) -8 NIL NIL NIL) (-1087 2539738 2540032 2540093 "SEGXCAT" 2540379 NIL SEGXCAT (NIL T T) -9 NIL 2540499 NIL) (-1086 2538794 2539404 2539586 "SEG" 2539591 NIL SEG (NIL T) -8 NIL NIL NIL) (-1085 2537773 2537987 2538030 "SEGCAT" 2538552 NIL SEGCAT (NIL T) -9 NIL 2538773 NIL) (-1084 2536822 2537152 2537352 "SEGBIND" 2537608 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1083 2536443 2536502 2536615 "SEGBIND2" 2536757 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1082 2536044 2536244 2536321 "SEGAST" 2536388 T SEGAST (NIL) -8 NIL NIL NIL) (-1081 2535263 2535389 2535593 "SEG2" 2535888 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1080 2534700 2535198 2535245 "SDVAR" 2535250 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1079 2526990 2534470 2534600 "SDPOL" 2534605 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1078 2525583 2525849 2526168 "SCPKG" 2526705 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1077 2524719 2524899 2525099 "SCOPE" 2525405 T SCOPE (NIL) -8 NIL NIL NIL) (-1076 2523940 2524073 2524252 "SCACHE" 2524574 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1075 2523612 2523772 2523802 "SASTCAT" 2523807 T SASTCAT (NIL) -9 NIL 2523820 NIL) (-1074 2523126 2523447 2523523 "SAOS" 2523558 T SAOS (NIL) -8 NIL NIL NIL) (-1073 2522691 2522726 2522899 "SAERFFC" 2523085 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1072 2516665 2522588 2522668 "SAE" 2522673 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1071 2516258 2516293 2516452 "SAEFACT" 2516624 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1070 2514579 2514893 2515294 "RURPK" 2515924 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1069 2513215 2513494 2513806 "RULESET" 2514413 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1068 2510402 2510905 2511370 "RULE" 2512896 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1067 2510041 2510196 2510279 "RULECOLD" 2510354 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1066 2509539 2509758 2509852 "RSTRCAST" 2509969 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1065 2504388 2505182 2506102 "RSETGCD" 2508738 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1064 2493645 2498697 2498794 "RSETCAT" 2502913 NIL RSETCAT (NIL T T T T) -9 NIL 2504010 NIL) (-1063 2491572 2492111 2492935 "RSETCAT-" 2492940 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1062 2483959 2485334 2486854 "RSDCMPK" 2490171 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1061 2481964 2482405 2482479 "RRCC" 2483565 NIL RRCC (NIL T T) -9 NIL 2483909 NIL) (-1060 2481315 2481489 2481768 "RRCC-" 2481773 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1059 2480785 2481011 2481112 "RPTAST" 2481236 T RPTAST (NIL) -8 NIL NIL NIL) (-1058 2454791 2464378 2464445 "RPOLCAT" 2475109 NIL RPOLCAT (NIL T T T) -9 NIL 2478268 NIL) (-1057 2446291 2448629 2451751 "RPOLCAT-" 2451756 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1056 2437338 2444502 2444984 "ROUTINE" 2445831 T ROUTINE (NIL) -8 NIL NIL NIL) (-1055 2434171 2436964 2437104 "ROMAN" 2437220 T ROMAN (NIL) -8 NIL NIL NIL) (-1054 2432446 2433031 2433291 "ROIRC" 2433976 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1053 2428839 2431082 2431112 "RNS" 2431416 T RNS (NIL) -9 NIL 2431689 NIL) (-1052 2427348 2427731 2428265 "RNS-" 2428340 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1051 2426797 2427179 2427209 "RNG" 2427214 T RNG (NIL) -9 NIL 2427235 NIL) (-1050 2426189 2426551 2426594 "RMODULE" 2426656 NIL RMODULE (NIL T) -9 NIL 2426698 NIL) (-1049 2425025 2425119 2425455 "RMCAT2" 2426090 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1048 2421902 2424371 2424668 "RMATRIX" 2424787 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1047 2414844 2417078 2417193 "RMATCAT" 2420552 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2421534 NIL) (-1046 2414219 2414366 2414673 "RMATCAT-" 2414678 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1045 2413786 2413861 2413989 "RINTERP" 2414138 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1044 2412919 2413439 2413469 "RING" 2413525 T RING (NIL) -9 NIL 2413611 NIL) (-1043 2412711 2412755 2412852 "RING-" 2412857 NIL RING- (NIL T) -8 NIL NIL NIL) (-1042 2411552 2411789 2412047 "RIDIST" 2412475 T RIDIST (NIL) -7 NIL NIL NIL) (-1041 2402868 2411020 2411226 "RGCHAIN" 2411400 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1040 2402244 2402624 2402665 "RGBCSPC" 2402723 NIL RGBCSPC (NIL T) -9 NIL 2402775 NIL) (-1039 2401428 2401783 2401824 "RGBCMDL" 2402056 NIL RGBCMDL (NIL T) -9 NIL 2402170 NIL) (-1038 2398422 2399036 2399706 "RF" 2400792 NIL RF (NIL T) -7 NIL NIL NIL) (-1037 2398068 2398131 2398234 "RFFACTOR" 2398353 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1036 2397793 2397828 2397925 "RFFACT" 2398027 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1035 2395910 2396274 2396656 "RFDIST" 2397433 T RFDIST (NIL) -7 NIL NIL NIL) (-1034 2395363 2395455 2395618 "RETSOL" 2395812 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1033 2394999 2395079 2395122 "RETRACT" 2395255 NIL RETRACT (NIL T) -9 NIL 2395342 NIL) (-1032 2394848 2394873 2394960 "RETRACT-" 2394965 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1031 2394477 2394670 2394740 "RETAST" 2394800 T RETAST (NIL) -8 NIL NIL NIL) (-1030 2387331 2394130 2394257 "RESULT" 2394372 T RESULT (NIL) -8 NIL NIL NIL) (-1029 2385957 2386600 2386799 "RESRING" 2387234 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1028 2385593 2385642 2385740 "RESLATC" 2385894 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1027 2385299 2385333 2385440 "REPSQ" 2385552 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1026 2382721 2383301 2383903 "REP" 2384719 T REP (NIL) -7 NIL NIL NIL) (-1025 2382419 2382453 2382564 "REPDB" 2382680 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1024 2376329 2377708 2378931 "REP2" 2381231 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1023 2372706 2373387 2374195 "REP1" 2375556 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1022 2365432 2370847 2371303 "REGSET" 2372336 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1021 2364245 2364580 2364830 "REF" 2365217 NIL REF (NIL T) -8 NIL NIL NIL) (-1020 2363622 2363725 2363892 "REDORDER" 2364129 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1019 2359627 2362835 2363062 "RECLOS" 2363450 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1018 2358679 2358860 2359075 "REALSOLV" 2359434 T REALSOLV (NIL) -7 NIL NIL NIL) (-1017 2358525 2358566 2358596 "REAL" 2358601 T REAL (NIL) -9 NIL 2358636 NIL) (-1016 2355008 2355810 2356694 "REAL0Q" 2357690 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1015 2350609 2351597 2352658 "REAL0" 2353989 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1014 2350107 2350326 2350420 "RDUCEAST" 2350537 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1013 2349512 2349584 2349791 "RDIV" 2350029 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1012 2348580 2348754 2348967 "RDIST" 2349334 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1011 2347177 2347464 2347836 "RDETRS" 2348288 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1010 2344989 2345443 2345981 "RDETR" 2346719 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1009 2343600 2343878 2344282 "RDEEFS" 2344705 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1008 2342095 2342401 2342833 "RDEEF" 2343288 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1007 2336356 2339231 2339261 "RCFIELD" 2340556 T RCFIELD (NIL) -9 NIL 2341286 NIL) (-1006 2334420 2334924 2335620 "RCFIELD-" 2335695 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1005 2330736 2332521 2332564 "RCAGG" 2333648 NIL RCAGG (NIL T) -9 NIL 2334113 NIL) (-1004 2330364 2330458 2330621 "RCAGG-" 2330626 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1003 2329699 2329811 2329976 "RATRET" 2330248 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1002 2329252 2329319 2329440 "RATFACT" 2329627 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1001 2328560 2328680 2328832 "RANDSRC" 2329122 T RANDSRC (NIL) -7 NIL NIL NIL) (-1000 2328294 2328338 2328411 "RADUTIL" 2328509 T RADUTIL (NIL) -7 NIL NIL NIL) (-999 2321456 2327136 2327444 "RADIX" 2328018 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-998 2313113 2321300 2321428 "RADFF" 2321433 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-997 2312765 2312840 2312868 "RADCAT" 2313025 T RADCAT (NIL) -9 NIL NIL NIL) (-996 2312550 2312598 2312695 "RADCAT-" 2312700 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-995 2310701 2312325 2312414 "QUEUE" 2312494 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-994 2307277 2310638 2310683 "QUAT" 2310688 NIL QUAT (NIL T) -8 NIL NIL NIL) (-993 2306915 2306958 2307085 "QUATCT2" 2307228 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-992 2300662 2303964 2304004 "QUATCAT" 2304784 NIL QUATCAT (NIL T) -9 NIL 2305550 NIL) (-991 2296806 2297843 2299230 "QUATCAT-" 2299324 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-990 2294326 2295890 2295931 "QUAGG" 2296306 NIL QUAGG (NIL T) -9 NIL 2296481 NIL) (-989 2293958 2294151 2294219 "QQUTAST" 2294278 T QQUTAST (NIL) -8 NIL NIL NIL) (-988 2292883 2293356 2293528 "QFORM" 2293830 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-987 2284095 2289300 2289340 "QFCAT" 2289998 NIL QFCAT (NIL T) -9 NIL 2290999 NIL) (-986 2279667 2280868 2282459 "QFCAT-" 2282553 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-985 2279305 2279348 2279475 "QFCAT2" 2279618 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-984 2278765 2278875 2279005 "QEQUAT" 2279195 T QEQUAT (NIL) -8 NIL NIL NIL) (-983 2271913 2272984 2274168 "QCMPACK" 2277698 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-982 2269489 2269910 2270338 "QALGSET" 2271568 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-981 2268734 2268908 2269140 "QALGSET2" 2269309 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-980 2267425 2267648 2267965 "PWFFINTB" 2268507 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-979 2265607 2265775 2266129 "PUSHVAR" 2267239 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-978 2261525 2262579 2262620 "PTRANFN" 2264504 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-977 2259927 2260218 2260540 "PTPACK" 2261236 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-976 2259559 2259616 2259725 "PTFUNC2" 2259864 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-975 2254086 2258431 2258472 "PTCAT" 2258768 NIL PTCAT (NIL T) -9 NIL 2258921 NIL) (-974 2253744 2253779 2253903 "PSQFR" 2254045 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-973 2252339 2252637 2252971 "PSEUDLIN" 2253442 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-972 2239109 2241473 2243797 "PSETPK" 2250099 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-971 2232153 2234867 2234963 "PSETCAT" 2237984 NIL PSETCAT (NIL T T T T) -9 NIL 2238798 NIL) (-970 2229989 2230623 2231444 "PSETCAT-" 2231449 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-969 2229338 2229503 2229531 "PSCURVE" 2229799 T PSCURVE (NIL) -9 NIL 2229966 NIL) (-968 2225694 2227176 2227241 "PSCAT" 2228085 NIL PSCAT (NIL T T T) -9 NIL 2228325 NIL) (-967 2224757 2224973 2225373 "PSCAT-" 2225378 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-966 2223489 2224122 2224327 "PRTITION" 2224572 T PRTITION (NIL) -8 NIL NIL NIL) (-965 2222991 2223210 2223302 "PRTDAST" 2223417 T PRTDAST (NIL) -8 NIL NIL NIL) (-964 2212089 2214295 2216483 "PRS" 2220853 NIL PRS (NIL T T) -7 NIL NIL NIL) (-963 2209947 2211439 2211479 "PRQAGG" 2211662 NIL PRQAGG (NIL T) -9 NIL 2211764 NIL) (-962 2209333 2209562 2209590 "PROPLOG" 2209775 T PROPLOG (NIL) -9 NIL 2209897 NIL) (-961 2206503 2207147 2207611 "PROPFRML" 2208901 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-960 2205963 2206073 2206203 "PROPERTY" 2206393 T PROPERTY (NIL) -8 NIL NIL NIL) (-959 2200048 2204129 2204949 "PRODUCT" 2205189 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-958 2197361 2199506 2199740 "PR" 2199859 NIL PR (NIL T T) -8 NIL NIL NIL) (-957 2197157 2197189 2197248 "PRINT" 2197322 T PRINT (NIL) -7 NIL NIL NIL) (-956 2196497 2196614 2196766 "PRIMES" 2197037 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-955 2194562 2194963 2195429 "PRIMELT" 2196076 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-954 2194291 2194340 2194368 "PRIMCAT" 2194492 T PRIMCAT (NIL) -9 NIL NIL NIL) (-953 2190452 2194229 2194274 "PRIMARR" 2194279 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-952 2189459 2189637 2189865 "PRIMARR2" 2190270 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-951 2189102 2189158 2189269 "PREASSOC" 2189397 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-950 2188577 2188710 2188738 "PPCURVE" 2188943 T PPCURVE (NIL) -9 NIL 2189079 NIL) (-949 2188199 2188372 2188455 "PORTNUM" 2188514 T PORTNUM (NIL) -8 NIL NIL NIL) (-948 2185558 2185957 2186549 "POLYROOT" 2187780 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-947 2179503 2185162 2185322 "POLY" 2185431 NIL POLY (NIL T) -8 NIL NIL NIL) (-946 2178886 2178944 2179178 "POLYLIFT" 2179439 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-945 2175161 2175610 2176239 "POLYCATQ" 2178431 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-944 2161978 2167336 2167401 "POLYCAT" 2170915 NIL POLYCAT (NIL T T T) -9 NIL 2172843 NIL) (-943 2155428 2157289 2159673 "POLYCAT-" 2159678 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-942 2155015 2155083 2155203 "POLY2UP" 2155354 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-941 2154647 2154704 2154813 "POLY2" 2154952 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-940 2153332 2153571 2153847 "POLUTIL" 2154421 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-939 2151687 2151964 2152295 "POLTOPOL" 2153054 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-938 2147205 2151623 2151669 "POINT" 2151674 NIL POINT (NIL T) -8 NIL NIL NIL) (-937 2145392 2145749 2146124 "PNTHEORY" 2146850 T PNTHEORY (NIL) -7 NIL NIL NIL) (-936 2143811 2144108 2144520 "PMTOOLS" 2145090 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-935 2143404 2143482 2143599 "PMSYM" 2143727 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-934 2142914 2142983 2143157 "PMQFCAT" 2143329 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-933 2142269 2142379 2142535 "PMPRED" 2142791 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-932 2141665 2141751 2141912 "PMPREDFS" 2142170 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-931 2140308 2140516 2140901 "PMPLCAT" 2141427 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-930 2139840 2139919 2140071 "PMLSAGG" 2140223 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-929 2139315 2139391 2139572 "PMKERNEL" 2139758 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-928 2138932 2139007 2139120 "PMINS" 2139234 NIL PMINS (NIL T) -7 NIL NIL NIL) (-927 2138360 2138429 2138645 "PMFS" 2138857 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-926 2137588 2137706 2137911 "PMDOWN" 2138237 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-925 2136751 2136910 2137092 "PMASS" 2137426 T PMASS (NIL) -7 NIL NIL NIL) (-924 2136025 2136136 2136299 "PMASSFS" 2136637 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-923 2135680 2135748 2135842 "PLOTTOOL" 2135951 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-922 2130302 2131491 2132639 "PLOT" 2134552 T PLOT (NIL) -8 NIL NIL NIL) (-921 2126116 2127150 2128071 "PLOT3D" 2129401 T PLOT3D (NIL) -8 NIL NIL NIL) (-920 2125028 2125205 2125440 "PLOT1" 2125920 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-919 2100422 2105094 2109945 "PLEQN" 2120294 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-918 2099740 2099862 2100042 "PINTERP" 2100287 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-917 2099433 2099480 2099583 "PINTERPA" 2099687 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-916 2098681 2099202 2099289 "PI" 2099329 T PI (NIL) -8 NIL NIL 2099396) (-915 2097078 2098019 2098047 "PID" 2098229 T PID (NIL) -9 NIL 2098363 NIL) (-914 2096803 2096840 2096928 "PICOERCE" 2097035 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-913 2096123 2096262 2096438 "PGROEB" 2096659 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-912 2091710 2092524 2093429 "PGE" 2095238 T PGE (NIL) -7 NIL NIL NIL) (-911 2089834 2090080 2090446 "PGCD" 2091427 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-910 2089172 2089275 2089436 "PFRPAC" 2089718 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-909 2085852 2087720 2088073 "PFR" 2088851 NIL PFR (NIL T) -8 NIL NIL NIL) (-908 2084241 2084485 2084810 "PFOTOOLS" 2085599 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-907 2082774 2083013 2083364 "PFOQ" 2083998 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-906 2081247 2081459 2081822 "PFO" 2082558 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-905 2077835 2081136 2081205 "PF" 2081210 NIL PF (NIL NIL) -8 NIL NIL NIL) (-904 2075269 2076506 2076534 "PFECAT" 2077119 T PFECAT (NIL) -9 NIL 2077503 NIL) (-903 2074714 2074868 2075082 "PFECAT-" 2075087 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-902 2073318 2073569 2073870 "PFBRU" 2074463 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-901 2071185 2071536 2071968 "PFBR" 2072969 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-900 2067101 2068561 2069237 "PERM" 2070542 NIL PERM (NIL T) -8 NIL NIL NIL) (-899 2062367 2063308 2064178 "PERMGRP" 2066264 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-898 2060499 2061430 2061471 "PERMCAT" 2061917 NIL PERMCAT (NIL T) -9 NIL 2062222 NIL) (-897 2060152 2060193 2060317 "PERMAN" 2060452 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-896 2057688 2059817 2059939 "PENDTREE" 2060063 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-895 2055781 2056515 2056556 "PDRING" 2057213 NIL PDRING (NIL T) -9 NIL 2057499 NIL) (-894 2054884 2055102 2055464 "PDRING-" 2055469 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-893 2052126 2052877 2053545 "PDEPROB" 2054236 T PDEPROB (NIL) -8 NIL NIL NIL) (-892 2049673 2050175 2050730 "PDEPACK" 2051591 T PDEPACK (NIL) -7 NIL NIL NIL) (-891 2048585 2048775 2049026 "PDECOMP" 2049472 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-890 2046190 2047007 2047035 "PDECAT" 2047822 T PDECAT (NIL) -9 NIL 2048535 NIL) (-889 2045941 2045974 2046064 "PCOMP" 2046151 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-888 2044146 2044742 2045039 "PBWLB" 2045670 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-887 2036651 2038219 2039557 "PATTERN" 2042829 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-886 2036283 2036340 2036449 "PATTERN2" 2036588 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-885 2034040 2034428 2034885 "PATTERN1" 2035872 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-884 2031435 2031989 2032470 "PATRES" 2033605 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-883 2030999 2031066 2031198 "PATRES2" 2031362 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-882 2028882 2029287 2029694 "PATMATCH" 2030666 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-881 2028418 2028601 2028642 "PATMAB" 2028749 NIL PATMAB (NIL T) -9 NIL 2028832 NIL) (-880 2026963 2027272 2027530 "PATLRES" 2028223 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-879 2026509 2026632 2026673 "PATAB" 2026678 NIL PATAB (NIL T) -9 NIL 2026850 NIL) (-878 2023990 2024522 2025095 "PARTPERM" 2025956 T PARTPERM (NIL) -7 NIL NIL NIL) (-877 2023611 2023674 2023776 "PARSURF" 2023921 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-876 2023243 2023300 2023409 "PARSU2" 2023548 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-875 2023007 2023047 2023114 "PARSER" 2023196 T PARSER (NIL) -7 NIL NIL NIL) (-874 2022628 2022691 2022793 "PARSCURV" 2022938 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-873 2022260 2022317 2022426 "PARSC2" 2022565 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-872 2021899 2021957 2022054 "PARPCURV" 2022196 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-871 2021531 2021588 2021697 "PARPC2" 2021836 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-870 2021051 2021137 2021256 "PAN2EXPR" 2021432 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-869 2019857 2020172 2020400 "PALETTE" 2020843 T PALETTE (NIL) -8 NIL NIL NIL) (-868 2018325 2018862 2019222 "PAIR" 2019543 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-867 2012231 2017584 2017778 "PADICRC" 2018180 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-866 2005495 2011577 2011761 "PADICRAT" 2012079 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-865 2003845 2005432 2005477 "PADIC" 2005482 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-864 2001055 2002585 2002625 "PADICCT" 2003206 NIL PADICCT (NIL NIL) -9 NIL 2003488 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1980590 1980875 "ORTHPOL" 1981365 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-850 1977949 1980198 1980319 "OREUP" 1980324 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-849 1975387 1977640 1977767 "ORESUP" 1977891 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-848 1972915 1973415 1973976 "OREPCTO" 1974876 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-847 1966739 1968906 1968947 "OREPCAT" 1971295 NIL OREPCAT (NIL T) -9 NIL 1972399 NIL) (-846 1963886 1964668 1965726 "OREPCAT-" 1965731 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-845 1963063 1963335 1963363 "ORDSET" 1963672 T ORDSET (NIL) -9 NIL 1963836 NIL) (-844 1962582 1962704 1962897 "ORDSET-" 1962902 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-843 1961216 1961973 1962001 "ORDRING" 1962203 T ORDRING (NIL) -9 NIL 1962328 NIL) (-842 1960861 1960955 1961099 "ORDRING-" 1961104 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-841 1960267 1960704 1960732 "ORDMON" 1960737 T ORDMON (NIL) -9 NIL 1960758 NIL) (-840 1959429 1959576 1959771 "ORDFUNS" 1960116 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-839 1958793 1959186 1959214 "ORDFIN" 1959279 T ORDFIN (NIL) -9 NIL 1959353 NIL) (-838 1955385 1957379 1957788 "ORDCOMP" 1958417 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-837 1954651 1954778 1954964 "ORDCOMP2" 1955245 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-836 1951259 1952142 1952956 "OPTPROB" 1953857 T OPTPROB (NIL) -8 NIL NIL NIL) (-835 1948061 1948700 1949404 "OPTPACK" 1950575 T OPTPACK (NIL) -7 NIL NIL NIL) (-834 1945774 1946514 1946542 "OPTCAT" 1947361 T OPTCAT (NIL) -9 NIL 1948011 NIL) (-833 1945217 1945451 1945556 "OPSIG" 1945689 T OPSIG (NIL) -8 NIL NIL NIL) (-832 1944985 1945024 1945090 "OPQUERY" 1945171 T OPQUERY (NIL) -7 NIL NIL NIL) (-831 1942151 1943296 1943800 "OP" 1944514 NIL OP (NIL T) -8 NIL NIL NIL) (-830 1941686 1941857 1941898 "OPERCAT" 1942033 NIL OPERCAT (NIL T) -9 NIL 1942101 NIL) (-829 1941532 1941559 1941645 "OPERCAT-" 1941650 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-828 1938377 1940329 1940698 "ONECOMP" 1941196 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-827 1937682 1937797 1937971 "ONECOMP2" 1938249 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-826 1937101 1937207 1937337 "OMSERVER" 1937572 T OMSERVER (NIL) -7 NIL NIL NIL) (-825 1933989 1936541 1936581 "OMSAGG" 1936642 NIL OMSAGG (NIL T) -9 NIL 1936706 NIL) (-824 1932612 1932875 1933157 "OMPKG" 1933727 T OMPKG (NIL) -7 NIL NIL NIL) (-823 1932042 1932145 1932173 "OM" 1932472 T OM (NIL) -9 NIL NIL NIL) (-822 1930624 1931591 1931760 "OMLO" 1931923 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-821 1929549 1929696 1929923 "OMEXPR" 1930450 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-820 1928867 1929095 1929231 "OMERR" 1929433 T OMERR (NIL) -8 NIL NIL NIL) (-819 1928045 1928288 1928448 "OMERRK" 1928727 T OMERRK (NIL) -8 NIL NIL NIL) (-818 1927523 1927722 1927830 "OMENC" 1927957 T OMENC (NIL) -8 NIL NIL NIL) (-817 1921418 1922603 1923774 "OMDEV" 1926372 T OMDEV (NIL) -8 NIL NIL NIL) (-816 1920487 1920658 1920852 "OMCONN" 1921244 T OMCONN (NIL) -8 NIL NIL NIL) (-815 1919108 1920050 1920078 "OINTDOM" 1920083 T OINTDOM (NIL) -9 NIL 1920104 NIL) (-814 1914914 1916098 1916814 "OFMONOID" 1918424 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-813 1914352 1914851 1914896 "ODVAR" 1914901 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-812 1911810 1914097 1914252 "ODR" 1914257 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-811 1904154 1911586 1911712 "ODPOL" 1911717 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-810 1898030 1904026 1904131 "ODP" 1904136 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-809 1896796 1897011 1897286 "ODETOOLS" 1897804 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-808 1893765 1894421 1895137 "ODESYS" 1896129 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-807 1888647 1889555 1890580 "ODERTRIC" 1892840 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-806 1888073 1888155 1888349 "ODERED" 1888559 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-805 1884961 1885509 1886186 "ODERAT" 1887496 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-804 1881921 1882385 1882982 "ODEPRRIC" 1884490 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-803 1879891 1880460 1880946 "ODEPROB" 1881455 T ODEPROB (NIL) -8 NIL NIL NIL) (-802 1876413 1876896 1877543 "ODEPRIM" 1879370 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-801 1875662 1875764 1876024 "ODEPAL" 1876305 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-800 1871824 1872615 1873479 "ODEPACK" 1874818 T ODEPACK (NIL) -7 NIL NIL NIL) (-799 1870857 1870964 1871193 "ODEINT" 1871713 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-798 1864958 1866383 1867830 "ODEIFTBL" 1869430 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-797 1860293 1861079 1862038 "ODEEF" 1864117 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-796 1859628 1859717 1859947 "ODECONST" 1860198 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-795 1857779 1858414 1858442 "ODECAT" 1859047 T ODECAT (NIL) -9 NIL 1859578 NIL) (-794 1854686 1857491 1857610 "OCT" 1857692 NIL OCT (NIL T) -8 NIL NIL NIL) (-793 1854324 1854367 1854494 "OCTCT2" 1854637 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-792 1849098 1851498 1851538 "OC" 1852635 NIL OC (NIL T) -9 NIL 1853493 NIL) (-791 1846325 1847073 1848063 "OC-" 1848157 NIL OC- (NIL T T) -8 NIL NIL NIL) (-790 1845703 1846145 1846173 "OCAMON" 1846178 T OCAMON (NIL) -9 NIL 1846199 NIL) (-789 1845260 1845575 1845603 "OASGP" 1845608 T OASGP (NIL) -9 NIL 1845628 NIL) (-788 1844547 1845010 1845038 "OAMONS" 1845078 T OAMONS (NIL) -9 NIL 1845121 NIL) (-787 1843987 1844394 1844422 "OAMON" 1844427 T OAMON (NIL) -9 NIL 1844447 NIL) (-786 1843291 1843783 1843811 "OAGROUP" 1843816 T OAGROUP (NIL) -9 NIL 1843836 NIL) (-785 1842981 1843031 1843119 "NUMTUBE" 1843235 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-784 1836554 1838072 1839608 "NUMQUAD" 1841465 T NUMQUAD (NIL) -7 NIL NIL NIL) (-783 1832310 1833298 1834323 "NUMODE" 1835549 T NUMODE (NIL) -7 NIL NIL NIL) (-782 1829691 1830545 1830573 "NUMINT" 1831496 T NUMINT (NIL) -9 NIL 1832260 NIL) (-781 1828639 1828836 1829054 "NUMFMT" 1829493 T NUMFMT (NIL) -7 NIL NIL NIL) (-780 1814998 1817943 1820475 "NUMERIC" 1826146 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-779 1809395 1814447 1814542 "NTSCAT" 1814547 NIL NTSCAT (NIL T T T T) -9 NIL 1814586 NIL) (-778 1808589 1808754 1808947 "NTPOLFN" 1809234 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-777 1796429 1805414 1806226 "NSUP" 1807810 NIL NSUP (NIL T) -8 NIL NIL NIL) (-776 1796061 1796118 1796227 "NSUP2" 1796366 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-775 1786058 1795835 1795968 "NSMP" 1795973 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-774 1784490 1784791 1785148 "NREP" 1785746 NIL NREP (NIL T) -7 NIL NIL NIL) (-773 1783081 1783333 1783691 "NPCOEF" 1784233 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-772 1782147 1782262 1782478 "NORMRETR" 1782962 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-771 1780188 1780478 1780887 "NORMPK" 1781855 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-770 1779873 1779901 1780025 "NORMMA" 1780154 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-769 1779700 1779830 1779859 "NONE" 1779864 T NONE (NIL) -8 NIL NIL NIL) (-768 1779489 1779518 1779587 "NONE1" 1779664 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-767 1778972 1779034 1779220 "NODE1" 1779421 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-766 1777243 1778066 1778321 "NNI" 1778668 T NNI (NIL) -8 NIL NIL 1778903) (-765 1775663 1775976 1776340 "NLINSOL" 1776911 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-764 1771931 1772899 1773798 "NIPROB" 1774784 T NIPROB (NIL) -8 NIL NIL NIL) (-763 1770688 1770922 1771224 "NFINTBAS" 1771693 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-762 1769862 1770338 1770379 "NETCLT" 1770551 NIL NETCLT (NIL T) -9 NIL 1770633 NIL) (-761 1768570 1768801 1769082 "NCODIV" 1769630 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-760 1768332 1768369 1768444 "NCNTFRAC" 1768527 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-759 1766512 1766876 1767296 "NCEP" 1767957 NIL NCEP (NIL T) -7 NIL NIL NIL) (-758 1765423 1766162 1766190 "NASRING" 1766300 T NASRING (NIL) -9 NIL 1766374 NIL) (-757 1765218 1765262 1765356 "NASRING-" 1765361 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-756 1764371 1764870 1764898 "NARNG" 1765015 T NARNG (NIL) -9 NIL 1765106 NIL) (-755 1764063 1764130 1764264 "NARNG-" 1764269 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-754 1762942 1763149 1763384 "NAGSP" 1763848 T NAGSP (NIL) -7 NIL NIL NIL) (-753 1754214 1755898 1757571 "NAGS" 1761289 T NAGS (NIL) -7 NIL NIL NIL) (-752 1752762 1753070 1753401 "NAGF07" 1753903 T NAGF07 (NIL) -7 NIL NIL NIL) (-751 1747300 1748591 1749898 "NAGF04" 1751475 T NAGF04 (NIL) -7 NIL NIL NIL) (-750 1740268 1741882 1743515 "NAGF02" 1745687 T NAGF02 (NIL) -7 NIL NIL NIL) (-749 1735492 1736592 1737709 "NAGF01" 1739171 T NAGF01 (NIL) -7 NIL NIL NIL) (-748 1729120 1730686 1732271 "NAGE04" 1733927 T NAGE04 (NIL) -7 NIL NIL NIL) (-747 1720289 1722410 1724540 "NAGE02" 1727010 T NAGE02 (NIL) -7 NIL NIL NIL) (-746 1716242 1717189 1718153 "NAGE01" 1719345 T NAGE01 (NIL) -7 NIL NIL NIL) (-745 1714037 1714571 1715129 "NAGD03" 1715704 T NAGD03 (NIL) -7 NIL NIL NIL) (-744 1705787 1707715 1709669 "NAGD02" 1712103 T NAGD02 (NIL) -7 NIL NIL NIL) (-743 1699598 1701023 1702463 "NAGD01" 1704367 T NAGD01 (NIL) -7 NIL NIL NIL) (-742 1695807 1696629 1697466 "NAGC06" 1698781 T NAGC06 (NIL) -7 NIL NIL NIL) (-741 1694272 1694604 1694960 "NAGC05" 1695471 T NAGC05 (NIL) -7 NIL NIL NIL) (-740 1693648 1693767 1693911 "NAGC02" 1694148 T NAGC02 (NIL) -7 NIL NIL NIL) (-739 1692708 1693265 1693305 "NAALG" 1693384 NIL NAALG (NIL T) -9 NIL 1693445 NIL) (-738 1692543 1692572 1692662 "NAALG-" 1692667 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-737 1686493 1687601 1688788 "MULTSQFR" 1691439 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-736 1685812 1685887 1686071 "MULTFACT" 1686405 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-735 1678905 1682775 1682828 "MTSCAT" 1683898 NIL MTSCAT (NIL T T) -9 NIL 1684412 NIL) (-734 1678617 1678671 1678763 "MTHING" 1678845 NIL MTHING (NIL T) -7 NIL NIL NIL) (-733 1678409 1678442 1678502 "MSYSCMD" 1678577 T MSYSCMD (NIL) -7 NIL NIL NIL) (-732 1674521 1677164 1677484 "MSET" 1678122 NIL MSET (NIL T) -8 NIL NIL NIL) (-731 1671616 1674082 1674123 "MSETAGG" 1674128 NIL MSETAGG (NIL T) -9 NIL 1674162 NIL) (-730 1667499 1668995 1669740 "MRING" 1670916 NIL MRING (NIL T T) -8 NIL NIL NIL) (-729 1667065 1667132 1667263 "MRF2" 1667426 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-728 1666683 1666718 1666862 "MRATFAC" 1667024 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-727 1664295 1664590 1665021 "MPRFF" 1666388 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-726 1658355 1664149 1664246 "MPOLY" 1664251 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-725 1657845 1657880 1658088 "MPCPF" 1658314 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-724 1657359 1657402 1657586 "MPC3" 1657796 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1656554 1656635 1656856 "MPC2" 1657274 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-722 1654855 1655192 1655582 "MONOTOOL" 1656214 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-721 1654106 1654397 1654425 "MONOID" 1654644 T MONOID (NIL) -9 NIL 1654791 NIL) (-720 1653652 1653771 1653952 "MONOID-" 1653957 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-719 1644511 1650419 1650478 "MONOGEN" 1651152 NIL MONOGEN (NIL T T) -9 NIL 1651608 NIL) (-718 1641729 1642464 1643464 "MONOGEN-" 1643583 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-717 1640588 1641008 1641036 "MONADWU" 1641428 T MONADWU (NIL) -9 NIL 1641666 NIL) (-716 1639960 1640119 1640367 "MONADWU-" 1640372 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-715 1639345 1639563 1639591 "MONAD" 1639798 T MONAD (NIL) -9 NIL 1639910 NIL) (-714 1639030 1639108 1639240 "MONAD-" 1639245 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-713 1637346 1637943 1638222 "MOEBIUS" 1638783 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-712 1636738 1637116 1637156 "MODULE" 1637161 NIL MODULE (NIL T) -9 NIL 1637187 NIL) (-711 1636306 1636402 1636592 "MODULE-" 1636597 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-710 1634021 1634670 1634997 "MODRING" 1636130 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-709 1631007 1632126 1632647 "MODOP" 1633550 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-708 1629622 1630074 1630351 "MODMONOM" 1630870 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-707 1619429 1627913 1628327 "MODMON" 1629259 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-706 1616620 1618273 1618549 "MODFIELD" 1619304 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-705 1615624 1615901 1616091 "MMLFORM" 1616450 T MMLFORM (NIL) -8 NIL NIL NIL) (-704 1615150 1615193 1615372 "MMAP" 1615575 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-703 1613367 1614100 1614141 "MLO" 1614564 NIL MLO (NIL T) -9 NIL 1614806 NIL) (-702 1610734 1611249 1611851 "MLIFT" 1612848 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-701 1610125 1610209 1610363 "MKUCFUNC" 1610645 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-700 1609724 1609794 1609917 "MKRECORD" 1610048 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-699 1608772 1608933 1609161 "MKFUNC" 1609535 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-698 1608160 1608264 1608420 "MKFLCFN" 1608655 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-697 1607703 1608070 1608129 "MKCHSET" 1608134 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-696 1606980 1607082 1607267 "MKBCFUNC" 1607596 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-695 1603722 1606534 1606670 "MINT" 1606864 T MINT (NIL) -8 NIL NIL NIL) (-694 1602534 1602777 1603054 "MHROWRED" 1603477 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-693 1597960 1601069 1601474 "MFLOAT" 1602149 T MFLOAT (NIL) -8 NIL NIL NIL) (-692 1597317 1597393 1597564 "MFINFACT" 1597872 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-691 1593632 1594480 1595364 "MESH" 1596453 T MESH (NIL) -7 NIL NIL NIL) (-690 1592022 1592334 1592687 "MDDFACT" 1593319 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-689 1588864 1591181 1591222 "MDAGG" 1591477 NIL MDAGG (NIL T) -9 NIL 1591620 NIL) (-688 1578642 1588157 1588364 "MCMPLX" 1588677 T MCMPLX (NIL) -8 NIL NIL NIL) (-687 1577783 1577929 1578129 "MCDEN" 1578491 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-686 1575673 1575943 1576323 "MCALCFN" 1577513 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-685 1574598 1574838 1575071 "MAYBE" 1575479 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-684 1572210 1572733 1573295 "MATSTOR" 1574069 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-683 1568216 1571582 1571830 "MATRIX" 1571995 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-682 1563985 1564689 1565425 "MATLIN" 1567573 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-681 1554139 1557277 1557354 "MATCAT" 1562234 NIL MATCAT (NIL T T T) -9 NIL 1563651 NIL) (-680 1550503 1551516 1552872 "MATCAT-" 1552877 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-679 1549097 1549250 1549583 "MATCAT2" 1550338 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-678 1547209 1547533 1547917 "MAPPKG3" 1548772 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-677 1546190 1546363 1546585 "MAPPKG2" 1547033 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-676 1544689 1544973 1545300 "MAPPKG1" 1545896 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-675 1543795 1544095 1544272 "MAPPAST" 1544532 T MAPPAST (NIL) -8 NIL NIL NIL) (-674 1543406 1543464 1543587 "MAPHACK3" 1543731 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-673 1542998 1543059 1543173 "MAPHACK2" 1543338 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-672 1542436 1542539 1542681 "MAPHACK1" 1542889 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-671 1540542 1541136 1541440 "MAGMA" 1542164 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-670 1540048 1540266 1540357 "MACROAST" 1540471 T MACROAST (NIL) -8 NIL NIL NIL) (-669 1536515 1538287 1538748 "M3D" 1539620 NIL M3D (NIL T) -8 NIL NIL NIL) (-668 1530669 1534884 1534925 "LZSTAGG" 1535707 NIL LZSTAGG (NIL T) -9 NIL 1536002 NIL) (-667 1526643 1527800 1529257 "LZSTAGG-" 1529262 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-666 1523757 1524534 1525021 "LWORD" 1526188 NIL LWORD (NIL T) -8 NIL NIL NIL) (-665 1523360 1523561 1523636 "LSTAST" 1523702 T LSTAST (NIL) -8 NIL NIL NIL) (-664 1516561 1523131 1523265 "LSQM" 1523270 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-663 1515785 1515924 1516152 "LSPP" 1516416 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-662 1513597 1513898 1514354 "LSMP" 1515474 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-661 1510376 1511050 1511780 "LSMP1" 1512899 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-660 1504301 1509543 1509584 "LSAGG" 1509646 NIL LSAGG (NIL T) -9 NIL 1509724 NIL) (-659 1500996 1501920 1503133 "LSAGG-" 1503138 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-658 1498622 1500140 1500389 "LPOLY" 1500791 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-657 1498204 1498289 1498412 "LPEFRAC" 1498531 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-656 1496551 1497298 1497551 "LO" 1498036 NIL LO (NIL T T T) -8 NIL NIL NIL) (-655 1496203 1496315 1496343 "LOGIC" 1496454 T LOGIC (NIL) -9 NIL 1496535 NIL) (-654 1496065 1496088 1496159 "LOGIC-" 1496164 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-653 1495258 1495398 1495591 "LODOOPS" 1495921 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-652 1492716 1495174 1495240 "LODO" 1495245 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-651 1491254 1491489 1491842 "LODOF" 1492463 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-650 1487610 1490007 1490048 "LODOCAT" 1490486 NIL LODOCAT (NIL T) -9 NIL 1490697 NIL) (-649 1487343 1487401 1487528 "LODOCAT-" 1487533 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-648 1484698 1487184 1487302 "LODO2" 1487307 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-647 1482168 1484635 1484680 "LODO1" 1484685 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-646 1481028 1481193 1481505 "LODEEF" 1481991 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-645 1476314 1479158 1479199 "LNAGG" 1480146 NIL LNAGG (NIL T) -9 NIL 1480590 NIL) (-644 1475461 1475675 1476017 "LNAGG-" 1476022 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-643 1471624 1472386 1473025 "LMOPS" 1474876 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-642 1471019 1471381 1471422 "LMODULE" 1471483 NIL LMODULE (NIL T) -9 NIL 1471525 NIL) (-641 1468265 1470664 1470787 "LMDICT" 1470929 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-640 1467991 1468173 1468233 "LITERAL" 1468238 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-639 1461218 1466937 1467235 "LIST" 1467726 NIL LIST (NIL T) -8 NIL NIL NIL) (-638 1460743 1460817 1460956 "LIST3" 1461138 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-637 1459750 1459928 1460156 "LIST2" 1460561 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-636 1457884 1458196 1458595 "LIST2MAP" 1459397 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-635 1456614 1457250 1457291 "LINEXP" 1457546 NIL LINEXP (NIL T) -9 NIL 1457695 NIL) (-634 1455261 1455521 1455818 "LINDEP" 1456366 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-633 1452028 1452747 1453524 "LIMITRF" 1454516 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-632 1450304 1450599 1451015 "LIMITPS" 1451723 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-631 1444759 1449815 1450043 "LIE" 1450125 NIL LIE (NIL T T) -8 NIL NIL NIL) (-630 1443808 1444251 1444291 "LIECAT" 1444431 NIL LIECAT (NIL T) -9 NIL 1444582 NIL) (-629 1443649 1443676 1443764 "LIECAT-" 1443769 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-628 1436261 1443098 1443263 "LIB" 1443504 T LIB (NIL) -8 NIL NIL NIL) (-627 1431898 1432779 1433714 "LGROBP" 1435378 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-626 1429764 1430038 1430400 "LF" 1431619 NIL LF (NIL T T) -7 NIL NIL NIL) (-625 1428604 1429296 1429324 "LFCAT" 1429531 T LFCAT (NIL) -9 NIL 1429670 NIL) (-624 1425508 1426136 1426824 "LEXTRIPK" 1427968 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-623 1422279 1423078 1423581 "LEXP" 1425088 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-622 1421782 1422000 1422092 "LETAST" 1422207 T LETAST (NIL) -8 NIL NIL NIL) (-621 1420180 1420493 1420894 "LEADCDET" 1421464 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-620 1419370 1419444 1419673 "LAZM3PK" 1420101 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-619 1414325 1417447 1417985 "LAUPOL" 1418882 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-618 1413890 1413934 1414102 "LAPLACE" 1414275 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-617 1411864 1412991 1413242 "LA" 1413723 NIL LA (NIL T T T) -8 NIL NIL NIL) (-616 1410945 1411495 1411536 "LALG" 1411598 NIL LALG (NIL T) -9 NIL 1411657 NIL) (-615 1410659 1410718 1410854 "LALG-" 1410859 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-614 1410494 1410518 1410559 "KVTFROM" 1410621 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-613 1409297 1409711 1409940 "KTVLOGIC" 1410285 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-612 1409132 1409156 1409197 "KRCFROM" 1409259 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-611 1408036 1408223 1408522 "KOVACIC" 1408932 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-610 1407871 1407895 1407936 "KONVERT" 1407998 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-609 1407706 1407730 1407771 "KOERCE" 1407833 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-608 1405440 1406200 1406593 "KERNEL" 1407345 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-607 1404942 1405023 1405153 "KERNEL2" 1405354 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-606 1398793 1403481 1403535 "KDAGG" 1403912 NIL KDAGG (NIL T T) -9 NIL 1404118 NIL) (-605 1398322 1398446 1398651 "KDAGG-" 1398656 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-604 1391497 1397983 1398138 "KAFILE" 1398200 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-603 1385952 1391008 1391236 "JORDAN" 1391318 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-602 1385358 1385601 1385722 "JOINAST" 1385851 T JOINAST (NIL) -8 NIL NIL NIL) (-601 1385204 1385263 1385318 "JAVACODE" 1385323 T JAVACODE (NIL) -8 NIL NIL NIL) (-600 1381503 1383409 1383463 "IXAGG" 1384392 NIL IXAGG (NIL T T) -9 NIL 1384851 NIL) (-599 1380422 1380728 1381147 "IXAGG-" 1381152 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-598 1376002 1380344 1380403 "IVECTOR" 1380408 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-597 1374768 1375005 1375271 "ITUPLE" 1375769 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-596 1373204 1373381 1373687 "ITRIGMNP" 1374590 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-595 1371949 1372153 1372436 "ITFUN3" 1372980 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-594 1371581 1371638 1371747 "ITFUN2" 1371886 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-593 1369418 1370443 1370742 "ITAYLOR" 1371315 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-592 1358401 1363555 1364718 "ISUPS" 1368288 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-591 1357505 1357645 1357881 "ISUMP" 1358248 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-590 1352769 1357306 1357385 "ISTRING" 1357458 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-589 1352272 1352490 1352582 "ISAST" 1352697 T ISAST (NIL) -8 NIL NIL NIL) (-588 1351482 1351563 1351779 "IRURPK" 1352186 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-587 1350418 1350619 1350859 "IRSN" 1351262 T IRSN (NIL) -7 NIL NIL NIL) (-586 1348447 1348802 1349238 "IRRF2F" 1350056 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-585 1348194 1348232 1348308 "IRREDFFX" 1348403 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-584 1346809 1347068 1347367 "IROOT" 1347927 NIL IROOT (NIL T) -7 NIL NIL NIL) (-583 1343441 1344493 1345185 "IR" 1346149 NIL IR (NIL T) -8 NIL NIL NIL) (-582 1341054 1341549 1342115 "IR2" 1342919 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-581 1340126 1340239 1340460 "IR2F" 1340937 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-580 1339917 1339951 1340011 "IPRNTPK" 1340086 T IPRNTPK (NIL) -7 NIL NIL NIL) (-579 1336536 1339806 1339875 "IPF" 1339880 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-578 1334899 1336461 1336518 "IPADIC" 1336523 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-577 1334239 1334459 1334589 "IP4ADDR" 1334789 T IP4ADDR (NIL) -8 NIL NIL NIL) (-576 1333739 1333943 1334053 "IOMODE" 1334149 T IOMODE (NIL) -8 NIL NIL NIL) (-575 1332812 1333336 1333463 "IOBFILE" 1333632 T IOBFILE (NIL) -8 NIL NIL NIL) (-574 1332300 1332716 1332744 "IOBCON" 1332749 T IOBCON (NIL) -9 NIL 1332770 NIL) (-573 1331797 1331855 1332045 "INVLAPLA" 1332236 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-572 1321446 1323799 1326185 "INTTR" 1329461 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-571 1317790 1318532 1319396 "INTTOOLS" 1320631 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-570 1317376 1317467 1317584 "INTSLPE" 1317693 T INTSLPE (NIL) -7 NIL NIL NIL) (-569 1315371 1317299 1317358 "INTRVL" 1317363 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-568 1312973 1313485 1314060 "INTRF" 1314856 NIL INTRF (NIL T) -7 NIL NIL NIL) (-567 1312384 1312481 1312623 "INTRET" 1312871 NIL INTRET (NIL T) -7 NIL NIL NIL) (-566 1310381 1310770 1311240 "INTRAT" 1311992 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-565 1307609 1308192 1308818 "INTPM" 1309866 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-564 1304312 1304911 1305656 "INTPAF" 1306995 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-563 1299491 1300453 1301504 "INTPACK" 1303281 T INTPACK (NIL) -7 NIL NIL NIL) (-562 1296403 1299220 1299347 "INT" 1299384 T INT (NIL) -8 NIL NIL NIL) (-561 1295655 1295807 1296015 "INTHERTR" 1296245 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-560 1295094 1295174 1295362 "INTHERAL" 1295569 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-559 1292940 1293383 1293840 "INTHEORY" 1294657 T INTHEORY (NIL) -7 NIL NIL NIL) (-558 1284248 1285869 1287648 "INTG0" 1291292 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-557 1264821 1269611 1274421 "INTFTBL" 1279458 T INTFTBL (NIL) -8 NIL NIL NIL) (-556 1264070 1264208 1264381 "INTFACT" 1264680 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-555 1261455 1261901 1262465 "INTEF" 1263624 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-554 1259922 1260627 1260655 "INTDOM" 1260956 T INTDOM (NIL) -9 NIL 1261163 NIL) (-553 1259291 1259465 1259707 "INTDOM-" 1259712 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-552 1255786 1257675 1257729 "INTCAT" 1258528 NIL INTCAT (NIL T) -9 NIL 1258848 NIL) (-551 1255259 1255361 1255489 "INTBIT" 1255678 T INTBIT (NIL) -7 NIL NIL NIL) (-550 1253930 1254084 1254398 "INTALG" 1255104 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-549 1253387 1253477 1253647 "INTAF" 1253834 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-548 1246841 1253197 1253337 "INTABL" 1253342 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-547 1246301 1246714 1246742 "INT8" 1246747 T INT8 (NIL) -8 NIL NIL 1246755) (-546 1245760 1246173 1246201 "INT32" 1246206 T INT32 (NIL) -8 NIL NIL 1246214) (-545 1245219 1245632 1245660 "INT16" 1245665 T INT16 (NIL) -8 NIL NIL 1245673) (-544 1240234 1242908 1242936 "INS" 1243870 T INS (NIL) -9 NIL 1244535 NIL) (-543 1237474 1238245 1239219 "INS-" 1239292 NIL INS- (NIL T) -8 NIL NIL NIL) (-542 1236249 1236476 1236774 "INPSIGN" 1237227 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-541 1235367 1235484 1235681 "INPRODPF" 1236129 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-540 1234261 1234378 1234615 "INPRODFF" 1235247 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-539 1233261 1233413 1233673 "INNMFACT" 1234097 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-538 1232458 1232555 1232743 "INMODGCD" 1233160 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-537 1230967 1231211 1231535 "INFSP" 1232203 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-536 1230151 1230268 1230451 "INFPROD0" 1230847 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-535 1227033 1228216 1228731 "INFORM" 1229644 T INFORM (NIL) -8 NIL NIL NIL) (-534 1226643 1226703 1226801 "INFORM1" 1226968 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-533 1226166 1226255 1226369 "INFINITY" 1226549 T INFINITY (NIL) -7 NIL NIL NIL) (-532 1225342 1225886 1225987 "INETCLTS" 1226085 T INETCLTS (NIL) -8 NIL NIL NIL) (-531 1223959 1224208 1224529 "INEP" 1225090 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-530 1223235 1223856 1223921 "INDE" 1223926 NIL INDE (NIL T) -8 NIL NIL NIL) (-529 1222799 1222867 1222984 "INCRMAPS" 1223162 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-528 1221617 1222068 1222274 "INBFILE" 1222613 T INBFILE (NIL) -8 NIL NIL NIL) (-527 1216928 1217853 1218797 "INBFF" 1220705 NIL INBFF (NIL T) -7 NIL NIL NIL) (-526 1215836 1216105 1216133 "INBCON" 1216646 T INBCON (NIL) -9 NIL 1216912 NIL) (-525 1215088 1215311 1215587 "INBCON-" 1215592 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-524 1214590 1214809 1214901 "INAST" 1215016 T INAST (NIL) -8 NIL NIL NIL) (-523 1214044 1214269 1214375 "IMPTAST" 1214504 T IMPTAST (NIL) -8 NIL NIL NIL) (-522 1210538 1213888 1213992 "IMATRIX" 1213997 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-521 1209250 1209373 1209688 "IMATQF" 1210394 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-520 1207470 1207697 1208034 "IMATLIN" 1209006 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-519 1202096 1207394 1207452 "ILIST" 1207457 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-518 1200049 1201956 1202069 "IIARRAY2" 1202074 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-517 1195482 1199960 1200024 "IFF" 1200029 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-516 1194856 1195099 1195215 "IFAST" 1195386 T IFAST (NIL) -8 NIL NIL NIL) (-515 1189899 1194148 1194336 "IFARRAY" 1194713 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-514 1189106 1189803 1189876 "IFAMON" 1189881 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-513 1188690 1188755 1188809 "IEVALAB" 1189016 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-512 1188365 1188433 1188593 "IEVALAB-" 1188598 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-511 1188023 1188279 1188342 "IDPO" 1188347 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-510 1187300 1187912 1187987 "IDPOAMS" 1187992 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-509 1186634 1187189 1187264 "IDPOAM" 1187269 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-508 1185719 1185969 1186022 "IDPC" 1186435 NIL IDPC (NIL T T) -9 NIL 1186584 NIL) (-507 1185215 1185611 1185684 "IDPAM" 1185689 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-506 1184618 1185107 1185180 "IDPAG" 1185185 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-505 1184386 1184533 1184583 "IDENT" 1184588 T IDENT (NIL) -8 NIL NIL NIL) (-504 1180641 1181489 1182384 "IDECOMP" 1183543 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-503 1173515 1174564 1175611 "IDEAL" 1179677 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-502 1172679 1172791 1172990 "ICDEN" 1173399 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-501 1171778 1172159 1172306 "ICARD" 1172552 T ICARD (NIL) -8 NIL NIL NIL) (-500 1169838 1170151 1170556 "IBPTOOLS" 1171455 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-499 1165472 1169458 1169571 "IBITS" 1169757 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-498 1162195 1162771 1163466 "IBATOOL" 1164889 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-497 1159975 1160436 1160969 "IBACHIN" 1161730 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-496 1157852 1159821 1159924 "IARRAY2" 1159929 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-495 1154005 1157778 1157835 "IARRAY1" 1157840 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-494 1147999 1152417 1152898 "IAN" 1153544 T IAN (NIL) -8 NIL NIL NIL) (-493 1147510 1147567 1147740 "IALGFACT" 1147936 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-492 1147038 1147151 1147179 "HYPCAT" 1147386 T HYPCAT (NIL) -9 NIL NIL NIL) (-491 1146576 1146693 1146879 "HYPCAT-" 1146884 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-490 1146198 1146371 1146454 "HOSTNAME" 1146513 T HOSTNAME (NIL) -8 NIL NIL NIL) (-489 1146043 1146080 1146121 "HOMOTOP" 1146126 NIL HOMOTOP (NIL T) -9 NIL 1146159 NIL) (-488 1142722 1144053 1144094 "HOAGG" 1145075 NIL HOAGG (NIL T) -9 NIL 1145754 NIL) (-487 1141316 1141715 1142241 "HOAGG-" 1142246 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-486 1135358 1140913 1141061 "HEXADEC" 1141188 T HEXADEC (NIL) -8 NIL NIL NIL) (-485 1134106 1134328 1134591 "HEUGCD" 1135135 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-484 1133209 1133943 1134073 "HELLFDIV" 1134078 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-483 1131437 1132986 1133074 "HEAP" 1133153 NIL HEAP (NIL T) -8 NIL NIL NIL) (-482 1130728 1130989 1131123 "HEADAST" 1131323 T HEADAST (NIL) -8 NIL NIL NIL) (-481 1124648 1130643 1130705 "HDP" 1130710 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-480 1118399 1124283 1124435 "HDMP" 1124549 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-479 1117724 1117863 1118027 "HB" 1118255 T HB (NIL) -7 NIL NIL NIL) (-478 1111221 1117570 1117674 "HASHTBL" 1117679 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-477 1110724 1110942 1111034 "HASAST" 1111149 T HASAST (NIL) -8 NIL NIL NIL) (-476 1108536 1110346 1110528 "HACKPI" 1110562 T HACKPI (NIL) -8 NIL NIL NIL) (-475 1104231 1108389 1108502 "GTSET" 1108507 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-474 1097757 1104109 1104207 "GSTBL" 1104212 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-473 1090070 1096788 1097053 "GSERIES" 1097548 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-472 1089237 1089628 1089656 "GROUP" 1089859 T GROUP (NIL) -9 NIL 1089993 NIL) (-471 1088603 1088762 1089013 "GROUP-" 1089018 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-470 1086972 1087291 1087678 "GROEBSOL" 1088280 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-469 1085912 1086174 1086225 "GRMOD" 1086754 NIL GRMOD (NIL T T) -9 NIL 1086922 NIL) (-468 1085680 1085716 1085844 "GRMOD-" 1085849 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-467 1081006 1082034 1083034 "GRIMAGE" 1084700 T GRIMAGE (NIL) -8 NIL NIL NIL) (-466 1079473 1079733 1080057 "GRDEF" 1080702 T GRDEF (NIL) -7 NIL NIL NIL) (-465 1078917 1079033 1079174 "GRAY" 1079352 T GRAY (NIL) -7 NIL NIL NIL) (-464 1078130 1078510 1078561 "GRALG" 1078714 NIL GRALG (NIL T T) -9 NIL 1078807 NIL) (-463 1077791 1077864 1078027 "GRALG-" 1078032 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-462 1074595 1077376 1077554 "GPOLSET" 1077698 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-461 1073949 1074006 1074264 "GOSPER" 1074532 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-460 1069708 1070387 1070913 "GMODPOL" 1073648 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-459 1068713 1068897 1069135 "GHENSEL" 1069520 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-458 1062764 1063607 1064634 "GENUPS" 1067797 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-457 1062461 1062512 1062601 "GENUFACT" 1062707 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-456 1061873 1061950 1062115 "GENPGCD" 1062379 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-455 1061347 1061382 1061595 "GENMFACT" 1061832 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-454 1059915 1060170 1060477 "GENEEZ" 1061090 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-453 1053828 1059526 1059688 "GDMP" 1059838 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-452 1043205 1047599 1048705 "GCNAALG" 1052811 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-451 1041632 1042460 1042488 "GCDDOM" 1042743 T GCDDOM (NIL) -9 NIL 1042900 NIL) (-450 1041102 1041229 1041444 "GCDDOM-" 1041449 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-449 1039774 1039959 1040263 "GB" 1040881 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-448 1028394 1030720 1033112 "GBINTERN" 1037465 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-447 1026231 1026523 1026944 "GBF" 1028069 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-446 1025012 1025177 1025444 "GBEUCLID" 1026047 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-445 1024361 1024486 1024635 "GAUSSFAC" 1024883 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-444 1022728 1023030 1023344 "GALUTIL" 1024080 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-443 1021036 1021310 1021634 "GALPOLYU" 1022455 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-442 1018401 1018691 1019098 "GALFACTU" 1020733 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-441 1010207 1011706 1013314 "GALFACT" 1016833 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-440 1007595 1008253 1008281 "FVFUN" 1009437 T FVFUN (NIL) -9 NIL 1010157 NIL) (-439 1006861 1007043 1007071 "FVC" 1007362 T FVC (NIL) -9 NIL 1007545 NIL) (-438 1006531 1006686 1006754 "FUNDESC" 1006813 T FUNDESC (NIL) -8 NIL NIL NIL) (-437 1006173 1006328 1006409 "FUNCTION" 1006483 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1003944 1004495 1004961 "FT" 1005727 T FT (NIL) -8 NIL NIL NIL) (-435 1002762 1003245 1003448 "FTEM" 1003761 T FTEM (NIL) -8 NIL NIL NIL) (-434 1001018 1001307 1001711 "FSUPFACT" 1002453 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999415 999704 1000036 "FST" 1000706 T FST (NIL) -8 NIL NIL NIL) (-432 998586 998692 998887 "FSRED" 999297 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 997265 997520 997874 "FSPRMELT" 998301 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994350 994788 995287 "FSPECF" 996828 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976410 984853 984893 "FS" 988741 NIL FS (NIL T) -9 NIL 991030 NIL) (-428 965060 968050 972106 "FS-" 972403 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964574 964628 964805 "FSINT" 965001 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 962901 963567 963870 "FSERIES" 964353 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 961915 962031 962262 "FSCINT" 962781 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 958149 960859 960900 "FSAGG" 961270 NIL FSAGG (NIL T) -9 NIL 961529 NIL) (-423 955911 956512 957308 "FSAGG-" 957403 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 954953 955096 955323 "FSAGG2" 955764 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952608 952887 953441 "FS2UPS" 954671 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 952190 952233 952388 "FS2" 952559 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 951047 951218 951527 "FS2EXPXP" 952015 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950473 950588 950740 "FRUTIL" 950927 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 941928 945968 947326 "FR" 949147 NIL FR (NIL T) -8 NIL NIL NIL) (-416 937003 939646 939686 "FRNAALG" 941082 NIL FRNAALG (NIL T) -9 NIL 941689 NIL) (-415 932681 933752 935027 "FRNAALG-" 935777 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 932319 932362 932489 "FRNAAF2" 932632 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 930726 931173 931468 "FRMOD" 932131 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928505 929109 929426 "FRIDEAL" 930517 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 927700 927787 928076 "FRIDEAL2" 928412 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 926833 927247 927288 "FRETRCT" 927293 NIL FRETRCT (NIL T) -9 NIL 927469 NIL) (-409 925945 926176 926527 "FRETRCT-" 926532 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 923157 924333 924392 "FRAMALG" 925274 NIL FRAMALG (NIL T T) -9 NIL 925566 NIL) (-407 921291 921746 922376 "FRAMALG-" 922599 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 915249 920766 921042 "FRAC" 921047 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 914885 914942 915049 "FRAC2" 915186 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914521 914578 914685 "FR2" 914822 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 909194 912046 912074 "FPS" 913193 T FPS (NIL) -9 NIL 913750 NIL) (-402 908643 908752 908916 "FPS-" 909062 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 906097 907732 907760 "FPC" 907985 T FPC (NIL) -9 NIL 908127 NIL) (-400 905890 905930 906027 "FPC-" 906032 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 904768 905378 905419 "FPATMAB" 905424 NIL FPATMAB (NIL T) -9 NIL 905576 NIL) (-398 902468 902944 903370 "FPARFRAC" 904405 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 897862 898360 899042 "FORTRAN" 901900 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895578 896078 896617 "FORT" 897343 T FORT (NIL) -7 NIL NIL NIL) (-395 893254 893816 893844 "FORTFN" 894904 T FORTFN (NIL) -9 NIL 895528 NIL) (-394 893018 893068 893096 "FORTCAT" 893155 T FORTCAT (NIL) -9 NIL 893217 NIL) (-393 891151 891634 892024 "FORMULA" 892648 T FORMULA (NIL) -8 NIL NIL NIL) (-392 890939 890969 891038 "FORMULA1" 891115 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890462 890514 890687 "FORDER" 890881 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889558 889722 889915 "FOP" 890289 T FOP (NIL) -7 NIL NIL NIL) (-389 888166 888838 889012 "FNLA" 889440 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 886921 887310 887338 "FNCAT" 887798 T FNCAT (NIL) -9 NIL 888058 NIL) (-387 886487 886880 886908 "FNAME" 886913 T FNAME (NIL) -8 NIL NIL NIL) (-386 885150 886079 886107 "FMTC" 886112 T FMTC (NIL) -9 NIL 886148 NIL) (-385 881512 882673 883302 "FMONOID" 884554 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 880731 881254 881403 "FM" 881408 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 878155 878801 878829 "FMFUN" 879973 T FMFUN (NIL) -9 NIL 880681 NIL) (-382 877424 877605 877633 "FMC" 877923 T FMC (NIL) -9 NIL 878105 NIL) (-381 874618 875452 875506 "FMCAT" 876701 NIL FMCAT (NIL T T) -9 NIL 877196 NIL) (-380 873511 874384 874484 "FM1" 874563 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 871285 871701 872195 "FLOATRP" 873062 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 864909 869014 869635 "FLOAT" 870684 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862347 862847 863425 "FLOATCP" 864376 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 861156 861960 862001 "FLINEXP" 862006 NIL FLINEXP (NIL T) -9 NIL 862099 NIL) (-375 860310 860545 860873 "FLINEXP-" 860878 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859386 859530 859754 "FLASORT" 860162 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856603 857445 857497 "FLALG" 858724 NIL FLALG (NIL T T) -9 NIL 859191 NIL) (-372 850387 854089 854130 "FLAGG" 855392 NIL FLAGG (NIL T) -9 NIL 856044 NIL) (-371 849113 849452 849942 "FLAGG-" 849947 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 848155 848298 848525 "FLAGG2" 848966 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 845130 846104 846163 "FINRALG" 847291 NIL FINRALG (NIL T T) -9 NIL 847799 NIL) (-368 844290 844519 844858 "FINRALG-" 844863 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 843696 843909 843937 "FINITE" 844133 T FINITE (NIL) -9 NIL 844240 NIL) (-366 836154 838315 838355 "FINAALG" 842022 NIL FINAALG (NIL T) -9 NIL 843475 NIL) (-365 831495 832536 833680 "FINAALG-" 835059 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 830890 831250 831353 "FILE" 831425 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829574 829886 829940 "FILECAT" 830624 NIL FILECAT (NIL T T) -9 NIL 830840 NIL) (-362 827442 828936 828964 "FIELD" 829004 T FIELD (NIL) -9 NIL 829084 NIL) (-361 826062 826447 826958 "FIELD-" 826963 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 823940 824697 825044 "FGROUP" 825748 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 823030 823194 823414 "FGLMICPK" 823772 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 818897 822955 823012 "FFX" 823017 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818498 818559 818694 "FFSLPE" 818830 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814491 815270 816066 "FFPOLY" 817734 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 813995 814031 814240 "FFPOLY2" 814449 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 809881 813914 813977 "FFP" 813982 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 805314 809792 809856 "FF" 809861 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800475 804657 804847 "FFNBX" 805168 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795449 799610 799868 "FFNBP" 800329 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 790117 794733 794944 "FFNB" 795282 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 788949 789147 789462 "FFINTBAS" 789914 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 785177 787356 787384 "FFIELDC" 788004 T FFIELDC (NIL) -9 NIL 788380 NIL) (-347 783840 784210 784707 "FFIELDC-" 784712 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783410 783455 783579 "FFHOM" 783782 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 781108 781592 782109 "FFF" 782925 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 776761 780850 780951 "FFCGX" 781051 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772428 776493 776600 "FFCGP" 776704 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767646 772155 772263 "FFCG" 772364 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749479 758517 758603 "FFCAT" 763768 NIL FFCAT (NIL T T T) -9 NIL 765219 NIL) (-340 744677 745724 747038 "FFCAT-" 748268 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 744088 744131 744366 "FFCAT2" 744628 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 733300 737060 738280 "FEXPR" 742940 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 732300 732735 732776 "FEVALAB" 732860 NIL FEVALAB (NIL T) -9 NIL 733121 NIL) (-336 731459 731669 732007 "FEVALAB-" 732012 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 730052 730842 731045 "FDIV" 731358 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 727118 727833 727948 "FDIVCAT" 729516 NIL FDIVCAT (NIL T T T T) -9 NIL 729953 NIL) (-333 726880 726907 727077 "FDIVCAT-" 727082 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 726100 726187 726464 "FDIV2" 726787 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 724786 725045 725334 "FCPAK1" 725831 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 723914 724286 724427 "FCOMP" 724677 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707651 711064 714602 "FC" 720396 T FC (NIL) -8 NIL NIL NIL) (-328 700230 704215 704255 "FAXF" 706057 NIL FAXF (NIL T) -9 NIL 706749 NIL) (-327 697509 698164 698989 "FAXF-" 699454 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692609 696885 697061 "FARRAY" 697366 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 687862 689894 689947 "FAMR" 690970 NIL FAMR (NIL T T) -9 NIL 691430 NIL) (-324 686752 687054 687489 "FAMR-" 687494 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 685948 686674 686727 "FAMONOID" 686732 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 683760 684444 684497 "FAMONC" 685438 NIL FAMONC (NIL T T) -9 NIL 685824 NIL) (-321 682452 683514 683651 "FAGROUP" 683656 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 680247 680566 680969 "FACUTIL" 682133 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679346 679531 679753 "FACTFUNC" 680057 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 671751 678597 678809 "EXPUPXS" 679202 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 669234 669774 670360 "EXPRTUBE" 671185 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665428 666020 666757 "EXPRODE" 668573 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 650802 664083 664511 "EXPR" 665032 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 645209 645796 646609 "EXPR2UPS" 650100 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 644845 644902 645009 "EXPR2" 645146 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 636250 643977 644274 "EXPEXPAN" 644682 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 636077 636207 636236 "EXIT" 636241 T EXIT (NIL) -8 NIL NIL NIL) (-310 635584 635801 635892 "EXITAST" 636006 T EXITAST (NIL) -8 NIL NIL NIL) (-309 635211 635273 635386 "EVALCYC" 635516 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 634752 634870 634911 "EVALAB" 635081 NIL EVALAB (NIL T) -9 NIL 635185 NIL) (-307 634233 634355 634576 "EVALAB-" 634581 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 631701 632969 632997 "EUCDOM" 633552 T EUCDOM (NIL) -9 NIL 633902 NIL) (-305 630106 630548 631138 "EUCDOM-" 631143 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617646 620404 623154 "ESTOOLS" 627376 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 617278 617335 617444 "ESTOOLS2" 617583 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 617029 617071 617151 "ESTOOLS1" 617230 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 610934 612662 612690 "ES" 615458 T ES (NIL) -9 NIL 616867 NIL) (-300 605882 607168 608985 "ES-" 609149 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 602257 603017 603797 "ESCONT" 605122 T ESCONT (NIL) -7 NIL NIL NIL) (-298 602002 602034 602116 "ESCONT1" 602219 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601677 601727 601827 "ES2" 601946 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 601307 601365 601474 "ES1" 601613 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600523 600652 600828 "ERROR" 601151 T ERROR (NIL) -7 NIL NIL NIL) (-294 594026 600382 600473 "EQTBL" 600478 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586583 589340 590789 "EQ" 592610 NIL -3311 (NIL T) -8 NIL NIL NIL) (-292 586215 586272 586381 "EQ2" 586520 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581507 582553 583646 "EP" 585154 NIL EP (NIL T) -7 NIL NIL NIL) (-290 580089 580390 580707 "ENV" 581210 T ENV (NIL) -8 NIL NIL NIL) (-289 579268 579788 579816 "ENTIRER" 579821 T ENTIRER (NIL) -9 NIL 579867 NIL) (-288 575770 577223 577593 "EMR" 579067 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 574914 575099 575153 "ELTAGG" 575533 NIL ELTAGG (NIL T T) -9 NIL 575744 NIL) (-286 574633 574695 574836 "ELTAGG-" 574841 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574422 574451 574505 "ELTAB" 574589 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573548 573694 573893 "ELFUTS" 574273 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 573290 573346 573374 "ELEMFUN" 573479 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 573160 573181 573249 "ELEMFUN-" 573254 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 568051 571260 571301 "ELAGG" 572241 NIL ELAGG (NIL T) -9 NIL 572704 NIL) (-280 566336 566770 567433 "ELAGG-" 567438 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 564993 565273 565568 "ELABEXPR" 566061 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 557859 559660 560487 "EFUPXS" 564269 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 551309 553110 553920 "EFULS" 557135 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 548731 549089 549568 "EFSTRUC" 550941 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 537803 539368 540928 "EF" 547246 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 536904 537288 537437 "EAB" 537674 T EAB (NIL) -8 NIL NIL NIL) (-273 536113 536863 536891 "E04UCFA" 536896 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 535322 536072 536100 "E04NAFA" 536105 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534531 535281 535309 "E04MBFA" 535314 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 533740 534490 534518 "E04JAFA" 534523 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 532951 533699 533727 "E04GCFA" 533732 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 532162 532910 532938 "E04FDFA" 532943 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531371 532121 532149 "E04DGFA" 532154 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525549 526896 528260 "E04AGNT" 530027 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 524255 524735 524775 "DVARCAT" 525250 NIL DVARCAT (NIL T) -9 NIL 525449 NIL) (-264 523459 523671 523985 "DVARCAT-" 523990 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516359 523258 523387 "DSMP" 523392 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 511169 512304 513372 "DROPT" 515311 T DROPT (NIL) -8 NIL NIL NIL) (-261 510834 510893 510991 "DROPT1" 511104 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 505949 507075 508212 "DROPT0" 509717 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 504294 504619 505005 "DRAWPT" 505583 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 498881 499804 500883 "DRAW" 503268 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498514 498567 498685 "DRAWHACK" 498822 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 497245 497514 497805 "DRAWCX" 498243 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 496761 496829 496980 "DRAWCURV" 497171 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 487232 489191 491306 "DRAWCFUN" 494666 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 484045 485927 485968 "DQAGG" 486597 NIL DQAGG (NIL T) -9 NIL 486870 NIL) (-252 472324 479023 479106 "DPOLCAT" 480958 NIL DPOLCAT (NIL T T T T) -9 NIL 481503 NIL) (-251 467163 468509 470467 "DPOLCAT-" 470472 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 460318 467024 467122 "DPMO" 467127 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453376 460098 460265 "DPMM" 460270 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 453040 453295 453343 "DOMCTOR" 453348 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452335 452562 452699 "DOMAIN" 452923 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 446086 451970 452122 "DMP" 452236 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445686 445742 445886 "DLP" 446024 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439556 445013 445203 "DLIST" 445528 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436400 438409 438450 "DLAGG" 439000 NIL DLAGG (NIL T) -9 NIL 439230 NIL) (-242 435213 435843 435871 "DIVRING" 435963 T DIVRING (NIL) -9 NIL 436046 NIL) (-241 434450 434640 434940 "DIVRING-" 434945 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432552 432909 433315 "DISPLAY" 434064 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426494 432466 432529 "DIRPROD" 432534 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425342 425545 425810 "DIRPROD2" 426287 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414605 420557 420610 "DIRPCAT" 421020 NIL DIRPCAT (NIL NIL T) -9 NIL 421860 NIL) (-236 411931 412573 413454 "DIRPCAT-" 413791 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 411218 411378 411564 "DIOSP" 411765 T DIOSP (NIL) -7 NIL NIL NIL) (-234 407920 410130 410171 "DIOPS" 410605 NIL DIOPS (NIL T) -9 NIL 410834 NIL) (-233 407469 407583 407774 "DIOPS-" 407779 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406361 406955 406983 "DIFRING" 407170 T DIFRING (NIL) -9 NIL 407280 NIL) (-231 406007 406084 406236 "DIFRING-" 406241 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 403812 405050 405091 "DIFEXT" 405454 NIL DIFEXT (NIL T) -9 NIL 405748 NIL) (-229 402097 402525 403191 "DIFEXT-" 403196 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399419 401629 401670 "DIAGG" 401675 NIL DIAGG (NIL T) -9 NIL 401695 NIL) (-227 398803 398960 399212 "DIAGG-" 399217 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 394268 397762 398039 "DHMATRIX" 398572 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 389880 390789 391799 "DFSFUN" 393278 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 384996 388811 389123 "DFLOAT" 389588 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 383224 383505 383901 "DFINTTLS" 384704 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 380289 381245 381645 "DERHAM" 382890 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 378138 380064 380153 "DEQUEUE" 380233 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377353 377486 377682 "DEGRED" 378000 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 373748 374493 375346 "DEFINTRF" 376581 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 371275 371744 372343 "DEFINTEF" 373267 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370652 370895 371010 "DEFAST" 371180 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364694 370249 370397 "DECIMAL" 370524 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 362206 362664 363170 "DDFACT" 364238 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 361802 361845 361996 "DBLRESP" 362157 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359701 360035 360395 "DBASE" 361569 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 358970 359181 359327 "DATAARY" 359600 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 358103 358929 358957 "D03FAFA" 358962 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 357237 358062 358090 "D03EEFA" 358095 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 355187 355653 356142 "D03AGNT" 356768 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354503 355146 355174 "D02EJFA" 355179 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 353819 354462 354490 "D02CJFA" 354495 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 353135 353778 353806 "D02BHFA" 353811 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352451 353094 353122 "D02BBFA" 353127 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345649 347237 348843 "D02AGNT" 350865 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343418 343940 344486 "D01WGTS" 345123 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342513 343377 343405 "D01TRNS" 343410 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341608 342472 342500 "D01GBFA" 342505 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340703 341567 341595 "D01FCFA" 341600 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 339798 340662 340690 "D01ASFA" 340695 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 338893 339757 339785 "D01AQFA" 339790 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 337988 338852 338880 "D01APFA" 338885 T D01APFA (NIL) -8 NIL NIL NIL) (-196 337083 337947 337975 "D01ANFA" 337980 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 336178 337042 337070 "D01AMFA" 337075 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 335273 336137 336165 "D01ALFA" 336170 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334368 335232 335260 "D01AKFA" 335265 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333463 334327 334355 "D01AJFA" 334360 T D01AJFA (NIL) -8 NIL NIL NIL) (-191 326760 328311 329872 "D01AGNT" 331922 T D01AGNT (NIL) -7 NIL NIL NIL) (-190 326097 326225 326377 "CYCLOTOM" 326628 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-189 322832 323545 324272 "CYCLES" 325390 T CYCLES (NIL) -7 NIL NIL NIL) (-188 322144 322278 322449 "CVMP" 322693 NIL CVMP (NIL T) -7 NIL NIL NIL) (-187 319915 320173 320549 "CTRIGMNP" 321872 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-186 319438 319706 319780 "CTOR" 319861 T CTOR (NIL) -8 NIL NIL NIL) (-185 318974 319169 319270 "CTORKIND" 319357 T CTORKIND (NIL) -8 NIL NIL NIL) (-184 318445 318673 318701 "CTORCAT" 318821 T CTORCAT (NIL) -9 NIL 318904 NIL) (-183 318140 318220 318346 "CTORCAT-" 318351 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-182 317656 317843 317941 "CTORCALL" 318062 T CTORCALL (NIL) -8 NIL NIL NIL) (-181 317030 317129 317282 "CSTTOOLS" 317553 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-180 312829 313486 314244 "CRFP" 316342 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-179 312331 312550 312642 "CRCEAST" 312757 T CRCEAST (NIL) -8 NIL NIL NIL) (-178 311378 311563 311791 "CRAPACK" 312135 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-177 310762 310863 311067 "CPMATCH" 311254 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-176 310487 310515 310621 "CPIMA" 310728 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-175 306851 307523 308241 "COORDSYS" 309822 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-174 306235 306364 306514 "CONTOUR" 306721 T CONTOUR (NIL) -8 NIL NIL NIL) (-173 302161 304238 304730 "CONTFRAC" 305775 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-172 302041 302062 302090 "CONDUIT" 302127 T CONDUIT (NIL) -9 NIL NIL NIL) (-171 301214 301734 301762 "COMRING" 301767 T COMRING (NIL) -9 NIL 301819 NIL) (-170 300295 300572 300756 "COMPPROP" 301050 T COMPPROP (NIL) -8 NIL NIL NIL) (-169 299956 299991 300119 "COMPLPAT" 300254 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-168 290013 299765 299874 "COMPLEX" 299879 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289649 289706 289813 "COMPLEX2" 289950 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-166 289367 289402 289500 "COMPFACT" 289608 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-165 273540 283760 283800 "COMPCAT" 284804 NIL COMPCAT (NIL T) -9 NIL 286189 NIL) (-164 263056 265979 269606 "COMPCAT-" 269962 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-163 262785 262813 262916 "COMMUPC" 263022 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-162 262580 262613 262672 "COMMONOP" 262746 T COMMONOP (NIL) -7 NIL NIL NIL) (-161 262163 262331 262418 "COMM" 262513 T COMM (NIL) -8 NIL NIL NIL) (-160 261767 261967 262042 "COMMAAST" 262108 T COMMAAST (NIL) -8 NIL NIL NIL) (-159 261016 261210 261238 "COMBOPC" 261576 T COMBOPC (NIL) -9 NIL 261751 NIL) (-158 259912 260122 260364 "COMBINAT" 260806 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-157 256110 256683 257323 "COMBF" 259334 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-156 254896 255226 255461 "COLOR" 255895 T COLOR (NIL) -8 NIL NIL NIL) (-155 254399 254617 254709 "COLONAST" 254824 T COLONAST (NIL) -8 NIL NIL NIL) (-154 254039 254086 254211 "CMPLXRT" 254346 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-153 253514 253739 253838 "CLLCTAST" 253960 T CLLCTAST (NIL) -8 NIL NIL NIL) (-152 249016 250044 251124 "CLIP" 252454 T CLIP (NIL) -7 NIL NIL NIL) (-151 247398 248122 248361 "CLIF" 248843 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-150 243620 245544 245585 "CLAGG" 246514 NIL CLAGG (NIL T) -9 NIL 247050 NIL) (-149 242042 242499 243082 "CLAGG-" 243087 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-148 241586 241671 241811 "CINTSLPE" 241951 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-147 239087 239558 240106 "CHVAR" 241114 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-146 238330 238850 238878 "CHARZ" 238883 T CHARZ (NIL) -9 NIL 238898 NIL) (-145 238084 238124 238202 "CHARPOL" 238284 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-144 237211 237764 237792 "CHARNZ" 237839 T CHARNZ (NIL) -9 NIL 237895 NIL) (-143 235200 235901 236236 "CHAR" 236896 T CHAR (NIL) -8 NIL NIL NIL) (-142 234926 234987 235015 "CFCAT" 235126 T CFCAT (NIL) -9 NIL NIL NIL) (-141 234171 234282 234464 "CDEN" 234810 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-140 230163 233324 233604 "CCLASS" 233911 T CCLASS (NIL) -8 NIL NIL NIL) (-139 229470 229613 229776 "CATEGORY" 230020 T -10 (NIL) -8 NIL NIL NIL) (-138 229134 229389 229437 "CATCTOR" 229442 T CATCTOR (NIL) -8 NIL NIL NIL) (-137 228608 228834 228933 "CATAST" 229055 T CATAST (NIL) -8 NIL NIL NIL) (-136 228111 228329 228421 "CASEAST" 228536 T CASEAST (NIL) -8 NIL NIL NIL) (-135 223163 224140 224893 "CARTEN" 227414 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 222271 222419 222640 "CARTEN2" 223010 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-133 220613 221421 221678 "CARD" 222034 T CARD (NIL) -8 NIL NIL NIL) (-132 220216 220417 220492 "CAPSLAST" 220558 T CAPSLAST (NIL) -8 NIL NIL NIL) (-131 219588 219916 219944 "CACHSET" 220076 T CACHSET (NIL) -9 NIL 220153 NIL) (-130 219084 219380 219408 "CABMON" 219458 T CABMON (NIL) -9 NIL 219514 NIL) (-129 218107 218630 218766 "BYTE" 218929 T BYTE (NIL) -8 NIL NIL 219045) (-128 213516 217575 217738 "BYTEBUF" 217964 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211073 213208 213315 "BTREE" 213442 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208571 210721 210843 "BTOURN" 210983 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 205988 208041 208082 "BTCAT" 208150 NIL BTCAT (NIL T) -9 NIL 208227 NIL) (-124 205655 205735 205884 "BTCAT-" 205889 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 200947 204798 204826 "BTAGG" 205048 T BTAGG (NIL) -9 NIL 205209 NIL) (-122 200437 200562 200768 "BTAGG-" 200773 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197481 199715 199930 "BSTREE" 200254 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196619 196745 196929 "BRILL" 197337 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193318 195345 195386 "BRAGG" 196035 NIL BRAGG (NIL T) -9 NIL 196293 NIL) (-118 191847 192253 192808 "BRAGG-" 192813 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185111 191193 191377 "BPADICRT" 191695 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183461 185048 185093 "BPADIC" 185098 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183159 183189 183303 "BOUNDZRO" 183425 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL NIL) (-113 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 174997 175719 175912 "BOOLEAN" 176122 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174359 174737 174791 "BMODULE" 174796 NIL BMODULE (NIL T T) -9 NIL 174861 NIL) (-110 170189 174157 174230 "BITS" 174306 T BITS (NIL) -8 NIL NIL NIL) (-109 169601 169723 169865 "BINDING" 170067 T BINDING (NIL) -8 NIL NIL NIL) (-108 163646 169200 169347 "BINARY" 169474 T BINARY (NIL) -8 NIL NIL NIL) (-107 161473 162901 162942 "BGAGG" 163202 NIL BGAGG (NIL T) -9 NIL 163339 NIL) (-106 161304 161336 161427 "BGAGG-" 161432 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150169 150329 150355 "ASTCAT" 150360 T ASTCAT (NIL) -9 NIL 150390 NIL) (-92 149896 149955 150074 "ASTCAT-" 150079 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148093 149672 149760 "ASTACK" 149839 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146598 146895 147260 "ASSOCEQ" 147775 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145630 146257 146381 "ASP9" 146505 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145394 145578 145617 "ASP8" 145622 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144263 144999 145141 "ASP80" 145283 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143162 143898 144030 "ASP7" 144162 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142116 142839 142957 "ASP78" 143075 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141085 141796 141913 "ASP77" 142030 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 139997 140723 140854 "ASP74" 140985 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138897 139632 139764 "ASP73" 139896 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138001 138723 138823 "ASP6" 138828 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 136949 137678 137796 "ASP55" 137914 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135899 136623 136742 "ASP50" 136861 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 134987 135600 135710 "ASP4" 135820 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134075 134688 134798 "ASP49" 134908 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132860 133614 133782 "ASP42" 133964 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131637 132393 132563 "ASP41" 132747 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130587 131314 131432 "ASP35" 131550 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130352 130535 130574 "ASP34" 130579 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130089 130156 130232 "ASP33" 130307 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 128984 129724 129856 "ASP31" 129988 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128749 128932 128971 "ASP30" 128976 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128484 128553 128629 "ASP29" 128704 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128249 128432 128471 "ASP28" 128476 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128014 128197 128236 "ASP27" 128241 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127098 127712 127823 "ASP24" 127934 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126175 126900 127012 "ASP20" 127017 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125263 125876 125986 "ASP1" 126096 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124207 124937 125056 "ASP19" 125175 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 123944 124011 124087 "ASP12" 124162 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122796 123543 123687 "ASP10" 123831 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120695 122640 122731 "ARRAY2" 122736 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116511 120343 120457 "ARRAY1" 120612 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115543 115716 115937 "ARRAY12" 116334 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109902 111773 111848 "ARR2CAT" 114478 NIL ARR2CAT (NIL T T T) -9 NIL 115236 NIL) (-56 107336 108080 109034 "ARR2CAT-" 109039 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106930 107163 107242 "ARITY" 107275 T ARITY (NIL) -8 NIL NIL NIL) (-54 105678 105830 106136 "APPRULE" 106766 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105329 105377 105496 "APPLYORE" 105624 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104303 104594 104789 "ANY" 105152 T ANY (NIL) -8 NIL NIL NIL) (-51 103581 103704 103861 "ANY1" 104177 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101146 102018 102345 "ANTISYM" 103305 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100661 100850 100947 "ANON" 101067 T ANON (NIL) -8 NIL NIL NIL) (-48 94793 99200 99654 "AN" 100225 T AN (NIL) -8 NIL NIL NIL) (-47 91049 92403 92454 "AMR" 93202 NIL AMR (NIL T T) -9 NIL 93802 NIL) (-46 90161 90382 90745 "AMR-" 90750 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74711 90078 90139 "ALIST" 90144 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71548 74305 74474 "ALGSC" 74629 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68104 68658 69265 "ALGPKG" 70988 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67381 67482 67666 "ALGMFACT" 67990 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63120 63805 64460 "ALGMANIP" 66904 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54526 62746 62896 "ALGFF" 63053 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53722 53853 54032 "ALGFACT" 54384 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52787 53353 53391 "ALGEBRA" 53396 NIL ALGEBRA (NIL T) -9 NIL 53437 NIL) (-37 52505 52564 52696 "ALGEBRA-" 52701 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34764 50507 50559 "ALAGG" 50695 NIL ALAGG (NIL T T) -9 NIL 50856 NIL) (-35 34300 34413 34439 "AHYP" 34640 T AHYP (NIL) -9 NIL NIL NIL) (-34 33231 33479 33505 "AGG" 34004 T AGG (NIL) -9 NIL 34283 NIL) (-33 32665 32827 33041 "AGG-" 33046 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30342 30764 31182 "AF" 32307 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29849 30067 30157 "ADDAST" 30270 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29118 29376 29532 "ACPLOT" 29711 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18410 26331 26382 "ACFS" 27093 NIL ACFS (NIL T) -9 NIL 27332 NIL) (-28 16424 16914 17689 "ACFS-" 17694 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3194841 3194846 3194851 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3194826 3194831 3194836 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3194811 3194816 3194821 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3194796 3194801 3194806 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1284 3193972 3194671 3194748 "ZMOD" 3194753 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1283 3193082 3193246 3193455 "ZLINDEP" 3193804 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1282 3182386 3184150 3186122 "ZDSOLVE" 3191212 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1281 3181632 3181773 3181962 "YSTREAM" 3182232 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1280 3179443 3180933 3181137 "XRPOLY" 3181475 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1279 3176031 3177314 3177889 "XPR" 3178915 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1278 3173787 3175362 3175566 "XPOLY" 3175862 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1277 3171578 3172912 3172967 "XPOLYC" 3173255 NIL XPOLYC (NIL T T) -9 NIL 3173368 NIL) (-1276 3167996 3170095 3170483 "XPBWPOLY" 3171236 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1275 3163907 3166159 3166201 "XF" 3166822 NIL XF (NIL T) -9 NIL 3167222 NIL) (-1274 3163528 3163616 3163785 "XF-" 3163790 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1273 3158862 3160117 3160172 "XFALG" 3162344 NIL XFALG (NIL T T) -9 NIL 3163133 NIL) (-1272 3157995 3158099 3158304 "XEXPPKG" 3158754 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1271 3156139 3157845 3157941 "XDPOLY" 3157946 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1270 3155084 3155650 3155693 "XALG" 3155698 NIL XALG (NIL T) -9 NIL 3155809 NIL) (-1269 3148553 3153061 3153555 "WUTSET" 3154676 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1268 3146844 3147605 3147928 "WP" 3148364 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1267 3146473 3146666 3146736 "WHILEAST" 3146796 T WHILEAST (NIL) -8 NIL NIL NIL) (-1266 3145972 3146190 3146284 "WHEREAST" 3146401 T WHEREAST (NIL) -8 NIL NIL NIL) (-1265 3144858 3145056 3145351 "WFFINTBS" 3145769 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1264 3142762 3143189 3143651 "WEIER" 3144430 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1263 3141909 3142333 3142375 "VSPACE" 3142511 NIL VSPACE (NIL T) -9 NIL 3142585 NIL) (-1262 3141747 3141774 3141865 "VSPACE-" 3141870 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1261 3141555 3141598 3141666 "VOID" 3141701 T VOID (NIL) -8 NIL NIL NIL) (-1260 3139691 3140050 3140456 "VIEW" 3141171 T VIEW (NIL) -7 NIL NIL NIL) (-1259 3136116 3136754 3137491 "VIEWDEF" 3138976 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1258 3125452 3127664 3129837 "VIEW3D" 3133965 T VIEW3D (NIL) -8 NIL NIL NIL) (-1257 3117734 3119363 3120942 "VIEW2D" 3123895 T VIEW2D (NIL) -8 NIL NIL NIL) (-1256 3113138 3117504 3117596 "VECTOR" 3117677 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1255 3111715 3111974 3112292 "VECTOR2" 3112868 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1254 3105242 3109499 3109542 "VECTCAT" 3110535 NIL VECTCAT (NIL T) -9 NIL 3111121 NIL) (-1253 3104256 3104510 3104900 "VECTCAT-" 3104905 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1252 3103737 3103907 3104027 "VARIABLE" 3104171 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1251 3103670 3103675 3103705 "UTYPE" 3103710 T UTYPE (NIL) -9 NIL NIL NIL) (-1250 3102500 3102654 3102916 "UTSODETL" 3103496 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1249 3099940 3100400 3100924 "UTSODE" 3102041 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1248 3091816 3097566 3098055 "UTS" 3099509 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1247 3083059 3088383 3088426 "UTSCAT" 3089538 NIL UTSCAT (NIL T) -9 NIL 3090295 NIL) (-1246 3080414 3081129 3082118 "UTSCAT-" 3082123 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1245 3080041 3080084 3080217 "UTS2" 3080365 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1244 3074314 3076879 3076922 "URAGG" 3078992 NIL URAGG (NIL T) -9 NIL 3079715 NIL) (-1243 3071253 3072116 3073239 "URAGG-" 3073244 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1242 3066977 3069867 3070339 "UPXSSING" 3070917 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1241 3059079 3066224 3066497 "UPXS" 3066762 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1240 3052192 3058983 3059055 "UPXSCONS" 3059060 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1239 3042437 3049187 3049249 "UPXSCCA" 3049823 NIL UPXSCCA (NIL T T) -9 NIL 3050056 NIL) (-1238 3042075 3042160 3042334 "UPXSCCA-" 3042339 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1237 3032173 3038696 3038739 "UPXSCAT" 3039387 NIL UPXSCAT (NIL T) -9 NIL 3039995 NIL) (-1236 3031603 3031682 3031861 "UPXS2" 3032088 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1235 3030257 3030510 3030861 "UPSQFREE" 3031346 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1234 3024045 3027059 3027114 "UPSCAT" 3028275 NIL UPSCAT (NIL T T) -9 NIL 3029049 NIL) (-1233 3023249 3023456 3023783 "UPSCAT-" 3023788 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1232 3009099 3017097 3017140 "UPOLYC" 3019241 NIL UPOLYC (NIL T) -9 NIL 3020462 NIL) (-1231 3000428 3002853 3006000 "UPOLYC-" 3006005 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1230 3000055 3000098 3000231 "UPOLYC2" 3000379 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1229 2991629 2999738 2999867 "UP" 2999974 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1228 2990968 2991075 2991239 "UPMP" 2991518 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1227 2990521 2990602 2990741 "UPDIVP" 2990881 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1226 2989089 2989338 2989654 "UPDECOMP" 2990270 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1225 2988324 2988436 2988621 "UPCDEN" 2988973 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1224 2987843 2987912 2988061 "UP2" 2988249 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1223 2986360 2987047 2987324 "UNISEG" 2987601 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1222 2985575 2985702 2985907 "UNISEG2" 2986203 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1221 2984635 2984815 2985041 "UNIFACT" 2985391 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1220 2968602 2983812 2984063 "ULS" 2984442 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1219 2956642 2968506 2968578 "ULSCONS" 2968583 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1218 2939258 2951200 2951262 "ULSCCAT" 2951900 NIL ULSCCAT (NIL T T) -9 NIL 2952188 NIL) (-1217 2938308 2938553 2938941 "ULSCCAT-" 2938946 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1216 2928183 2934620 2934663 "ULSCAT" 2935526 NIL ULSCAT (NIL T) -9 NIL 2936256 NIL) (-1215 2927613 2927692 2927871 "ULS2" 2928098 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1214 2926750 2927225 2927326 "UINT8" 2927437 T UINT8 (NIL) -8 NIL NIL 2927516) (-1213 2925886 2926361 2926462 "UINT32" 2926573 T UINT32 (NIL) -8 NIL NIL 2926652) (-1212 2925022 2925497 2925598 "UINT16" 2925709 T UINT16 (NIL) -8 NIL NIL 2925788) (-1211 2923425 2924348 2924378 "UFD" 2924590 T UFD (NIL) -9 NIL 2924704 NIL) (-1210 2923219 2923265 2923360 "UFD-" 2923365 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1209 2922301 2922484 2922700 "UDVO" 2923025 T UDVO (NIL) -7 NIL NIL NIL) (-1208 2920117 2920526 2920997 "UDPO" 2921865 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1207 2920050 2920055 2920085 "TYPE" 2920090 T TYPE (NIL) -9 NIL NIL NIL) (-1206 2919837 2920005 2920036 "TYPEAST" 2920041 T TYPEAST (NIL) -8 NIL NIL NIL) (-1205 2918808 2919010 2919250 "TWOFACT" 2919631 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1204 2917880 2918217 2918452 "TUPLE" 2918608 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1203 2915571 2916090 2916629 "TUBETOOL" 2917363 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1202 2914420 2914625 2914866 "TUBE" 2915364 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1201 2909184 2913392 2913675 "TS" 2914172 NIL TS (NIL T) -8 NIL NIL NIL) (-1200 2897851 2901943 2902040 "TSETCAT" 2907309 NIL TSETCAT (NIL T T T T) -9 NIL 2908840 NIL) (-1199 2892586 2894183 2896074 "TSETCAT-" 2896079 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1198 2886849 2887695 2888637 "TRMANIP" 2891722 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1197 2886290 2886353 2886516 "TRIMAT" 2886781 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1196 2884086 2884323 2884687 "TRIGMNIP" 2886039 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1195 2883606 2883719 2883749 "TRIGCAT" 2883962 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1194 2883275 2883354 2883495 "TRIGCAT-" 2883500 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1193 2880172 2882133 2882414 "TREE" 2883029 NIL TREE (NIL T) -8 NIL NIL NIL) (-1192 2879446 2879974 2880004 "TRANFUN" 2880039 T TRANFUN (NIL) -9 NIL 2880105 NIL) (-1191 2878725 2878916 2879196 "TRANFUN-" 2879201 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1190 2878529 2878561 2878622 "TOPSP" 2878686 T TOPSP (NIL) -7 NIL NIL NIL) (-1189 2877877 2877992 2878146 "TOOLSIGN" 2878410 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1188 2876538 2877054 2877293 "TEXTFILE" 2877660 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1187 2874477 2874991 2875420 "TEX" 2876131 T TEX (NIL) -8 NIL NIL NIL) (-1186 2874258 2874289 2874361 "TEX1" 2874440 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1185 2873906 2873969 2874059 "TEMUTL" 2874190 T TEMUTL (NIL) -7 NIL NIL NIL) (-1184 2872060 2872340 2872665 "TBCMPPK" 2873629 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1183 2863948 2870220 2870276 "TBAGG" 2870676 NIL TBAGG (NIL T T) -9 NIL 2870887 NIL) (-1182 2859018 2860506 2862260 "TBAGG-" 2862265 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1181 2858402 2858509 2858654 "TANEXP" 2858907 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1180 2851903 2858259 2858352 "TABLE" 2858357 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1179 2851315 2851414 2851552 "TABLEAU" 2851800 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1178 2845923 2847143 2848391 "TABLBUMP" 2850101 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1177 2845351 2845451 2845579 "SYSTEM" 2845817 T SYSTEM (NIL) -7 NIL NIL NIL) (-1176 2841814 2842509 2843292 "SYSSOLP" 2844602 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1175 2840871 2841338 2841451 "SYSNNI" 2841637 NIL SYSNNI (NIL NIL) -8 NIL NIL 2841716) (-1174 2840324 2840729 2840771 "SYSINT" 2840776 NIL SYSINT (NIL NIL) -8 NIL NIL 2840784) (-1173 2836658 2837585 2838301 "SYNTAX" 2839630 T SYNTAX (NIL) -8 NIL NIL NIL) (-1172 2833816 2834418 2835050 "SYMTAB" 2836048 T SYMTAB (NIL) -8 NIL NIL NIL) (-1171 2829065 2829967 2830950 "SYMS" 2832855 T SYMS (NIL) -8 NIL NIL NIL) (-1170 2826337 2828523 2828753 "SYMPOLY" 2828870 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1169 2825854 2825929 2826052 "SYMFUNC" 2826249 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1168 2821906 2823166 2823979 "SYMBOL" 2825063 T SYMBOL (NIL) -8 NIL NIL NIL) (-1167 2815445 2817134 2818854 "SWITCH" 2820208 T SWITCH (NIL) -8 NIL NIL NIL) (-1166 2808715 2814266 2814569 "SUTS" 2815200 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2800816 2807962 2808235 "SUPXS" 2808500 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1164 2792346 2800434 2800560 "SUP" 2800725 NIL SUP (NIL T) -8 NIL NIL NIL) (-1163 2791505 2791632 2791849 "SUPFRACF" 2792214 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1162 2791126 2791185 2791298 "SUP2" 2791440 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1161 2789539 2789813 2790176 "SUMRF" 2790825 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1160 2788853 2788919 2789118 "SUMFS" 2789460 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1159 2772860 2788030 2788281 "SULS" 2788660 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1158 2772489 2772682 2772752 "SUCHTAST" 2772812 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1157 2771811 2772014 2772154 "SUCH" 2772397 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1156 2765705 2766717 2767676 "SUBSPACE" 2770899 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1155 2765135 2765225 2765389 "SUBRESP" 2765593 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1154 2758504 2759800 2761111 "STTF" 2763871 NIL STTF (NIL T) -7 NIL NIL NIL) (-1153 2752677 2753797 2754944 "STTFNC" 2757404 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1152 2743992 2745859 2747653 "STTAYLOR" 2750918 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1151 2737236 2743856 2743939 "STRTBL" 2743944 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1150 2732627 2737191 2737222 "STRING" 2737227 T STRING (NIL) -8 NIL NIL NIL) (-1149 2727515 2732000 2732030 "STRICAT" 2732089 T STRICAT (NIL) -9 NIL 2732151 NIL) (-1148 2720325 2725134 2725745 "STREAM" 2726939 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1147 2719835 2719912 2720056 "STREAM3" 2720242 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1146 2718817 2719000 2719235 "STREAM2" 2719648 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1145 2718505 2718557 2718650 "STREAM1" 2718759 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1144 2717521 2717702 2717933 "STINPROD" 2718321 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1143 2717099 2717283 2717313 "STEP" 2717393 T STEP (NIL) -9 NIL 2717471 NIL) (-1142 2710642 2716998 2717075 "STBL" 2717080 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1141 2705816 2709863 2709906 "STAGG" 2710059 NIL STAGG (NIL T) -9 NIL 2710148 NIL) (-1140 2703518 2704120 2704992 "STAGG-" 2704997 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1139 2701713 2703288 2703380 "STACK" 2703461 NIL STACK (NIL T) -8 NIL NIL NIL) (-1138 2694438 2699854 2700310 "SREGSET" 2701343 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1137 2686864 2688232 2689745 "SRDCMPK" 2693044 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1136 2679831 2684304 2684334 "SRAGG" 2685637 T SRAGG (NIL) -9 NIL 2686245 NIL) (-1135 2678848 2679103 2679482 "SRAGG-" 2679487 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1134 2673343 2677795 2678216 "SQMATRIX" 2678474 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1133 2667092 2670061 2670788 "SPLTREE" 2672688 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1132 2663082 2663748 2664394 "SPLNODE" 2666518 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1131 2662129 2662362 2662392 "SPFCAT" 2662836 T SPFCAT (NIL) -9 NIL NIL NIL) (-1130 2660866 2661076 2661340 "SPECOUT" 2661887 T SPECOUT (NIL) -7 NIL NIL NIL) (-1129 2652518 2654262 2654292 "SPADXPT" 2658684 T SPADXPT (NIL) -9 NIL 2660718 NIL) (-1128 2652279 2652319 2652388 "SPADPRSR" 2652471 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1127 2650462 2652234 2652265 "SPADAST" 2652270 T SPADAST (NIL) -8 NIL NIL NIL) (-1126 2642433 2644180 2644223 "SPACEC" 2648596 NIL SPACEC (NIL T) -9 NIL 2650412 NIL) (-1125 2640604 2642365 2642414 "SPACE3" 2642419 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1124 2639356 2639527 2639818 "SORTPAK" 2640409 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1123 2637406 2637709 2638128 "SOLVETRA" 2639020 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1122 2636417 2636639 2636913 "SOLVESER" 2637179 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1121 2631637 2632518 2633520 "SOLVERAD" 2635469 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1120 2627452 2628061 2628790 "SOLVEFOR" 2631004 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1119 2621749 2626801 2626898 "SNTSCAT" 2626903 NIL SNTSCAT (NIL T T T T) -9 NIL 2626973 NIL) (-1118 2615892 2620072 2620463 "SMTS" 2621439 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1117 2610343 2615780 2615857 "SMP" 2615862 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1116 2608502 2608803 2609201 "SMITH" 2610040 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1115 2601397 2605553 2605656 "SMATCAT" 2607007 NIL SMATCAT (NIL NIL T T T) -9 NIL 2607557 NIL) (-1114 2598337 2599160 2600338 "SMATCAT-" 2600343 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1113 2596050 2597573 2597616 "SKAGG" 2597877 NIL SKAGG (NIL T) -9 NIL 2598012 NIL) (-1112 2592392 2595466 2595661 "SINT" 2595848 T SINT (NIL) -8 NIL NIL 2596021) (-1111 2592164 2592202 2592268 "SIMPAN" 2592348 T SIMPAN (NIL) -7 NIL NIL NIL) (-1110 2591471 2591699 2591839 "SIG" 2592046 T SIG (NIL) -8 NIL NIL NIL) (-1109 2590309 2590530 2590805 "SIGNRF" 2591230 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1108 2589114 2589265 2589556 "SIGNEF" 2590138 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1107 2588447 2588697 2588821 "SIGAST" 2589012 T SIGAST (NIL) -8 NIL NIL NIL) (-1106 2586137 2586591 2587097 "SHP" 2587988 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1105 2580043 2586038 2586114 "SHDP" 2586119 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1104 2579642 2579808 2579838 "SGROUP" 2579931 T SGROUP (NIL) -9 NIL 2579993 NIL) (-1103 2579500 2579526 2579599 "SGROUP-" 2579604 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1102 2576336 2577033 2577756 "SGCF" 2578799 T SGCF (NIL) -7 NIL NIL NIL) (-1101 2570731 2575783 2575880 "SFRTCAT" 2575885 NIL SFRTCAT (NIL T T T T) -9 NIL 2575924 NIL) (-1100 2564155 2565170 2566306 "SFRGCD" 2569714 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1099 2557283 2558354 2559540 "SFQCMPK" 2563088 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1098 2556905 2556994 2557104 "SFORT" 2557224 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1097 2556050 2556745 2556866 "SEXOF" 2556871 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1096 2555184 2555931 2555999 "SEX" 2556004 T SEX (NIL) -8 NIL NIL NIL) (-1095 2550723 2551412 2551507 "SEXCAT" 2554444 NIL SEXCAT (NIL T T T T T) -9 NIL 2555022 NIL) (-1094 2547903 2550657 2550705 "SET" 2550710 NIL SET (NIL T) -8 NIL NIL NIL) (-1093 2546154 2546616 2546921 "SETMN" 2547644 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1092 2545760 2545886 2545916 "SETCAT" 2546033 T SETCAT (NIL) -9 NIL 2546118 NIL) (-1091 2545540 2545592 2545691 "SETCAT-" 2545696 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1090 2541927 2544001 2544044 "SETAGG" 2544914 NIL SETAGG (NIL T) -9 NIL 2545254 NIL) (-1089 2541385 2541501 2541738 "SETAGG-" 2541743 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1088 2540855 2541081 2541182 "SEQAST" 2541306 T SEQAST (NIL) -8 NIL NIL NIL) (-1087 2540054 2540348 2540409 "SEGXCAT" 2540695 NIL SEGXCAT (NIL T T) -9 NIL 2540815 NIL) (-1086 2539110 2539720 2539902 "SEG" 2539907 NIL SEG (NIL T) -8 NIL NIL NIL) (-1085 2538089 2538303 2538346 "SEGCAT" 2538868 NIL SEGCAT (NIL T) -9 NIL 2539089 NIL) (-1084 2537138 2537468 2537668 "SEGBIND" 2537924 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1083 2536759 2536818 2536931 "SEGBIND2" 2537073 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1082 2536360 2536560 2536637 "SEGAST" 2536704 T SEGAST (NIL) -8 NIL NIL NIL) (-1081 2535579 2535705 2535909 "SEG2" 2536204 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1080 2535016 2535514 2535561 "SDVAR" 2535566 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1079 2527306 2534786 2534916 "SDPOL" 2534921 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1078 2525899 2526165 2526484 "SCPKG" 2527021 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1077 2525035 2525215 2525415 "SCOPE" 2525721 T SCOPE (NIL) -8 NIL NIL NIL) (-1076 2524256 2524389 2524568 "SCACHE" 2524890 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1075 2523928 2524088 2524118 "SASTCAT" 2524123 T SASTCAT (NIL) -9 NIL 2524136 NIL) (-1074 2523442 2523763 2523839 "SAOS" 2523874 T SAOS (NIL) -8 NIL NIL NIL) (-1073 2523007 2523042 2523215 "SAERFFC" 2523401 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1072 2516981 2522904 2522984 "SAE" 2522989 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1071 2516574 2516609 2516768 "SAEFACT" 2516940 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1070 2514895 2515209 2515610 "RURPK" 2516240 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1069 2513531 2513810 2514122 "RULESET" 2514729 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1068 2510718 2511221 2511686 "RULE" 2513212 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1067 2510357 2510512 2510595 "RULECOLD" 2510670 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1066 2509855 2510074 2510168 "RSTRCAST" 2510285 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1065 2504704 2505498 2506418 "RSETGCD" 2509054 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1064 2493961 2499013 2499110 "RSETCAT" 2503229 NIL RSETCAT (NIL T T T T) -9 NIL 2504326 NIL) (-1063 2491888 2492427 2493251 "RSETCAT-" 2493256 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1062 2484275 2485650 2487170 "RSDCMPK" 2490487 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1061 2482280 2482721 2482795 "RRCC" 2483881 NIL RRCC (NIL T T) -9 NIL 2484225 NIL) (-1060 2481631 2481805 2482084 "RRCC-" 2482089 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1059 2481101 2481327 2481428 "RPTAST" 2481552 T RPTAST (NIL) -8 NIL NIL NIL) (-1058 2455107 2464694 2464761 "RPOLCAT" 2475425 NIL RPOLCAT (NIL T T T) -9 NIL 2478584 NIL) (-1057 2446607 2448945 2452067 "RPOLCAT-" 2452072 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1056 2437654 2444818 2445300 "ROUTINE" 2446147 T ROUTINE (NIL) -8 NIL NIL NIL) (-1055 2434487 2437280 2437420 "ROMAN" 2437536 T ROMAN (NIL) -8 NIL NIL NIL) (-1054 2432762 2433347 2433607 "ROIRC" 2434292 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1053 2429155 2431398 2431428 "RNS" 2431732 T RNS (NIL) -9 NIL 2432005 NIL) (-1052 2427664 2428047 2428581 "RNS-" 2428656 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1051 2427113 2427495 2427525 "RNG" 2427530 T RNG (NIL) -9 NIL 2427551 NIL) (-1050 2426505 2426867 2426910 "RMODULE" 2426972 NIL RMODULE (NIL T) -9 NIL 2427014 NIL) (-1049 2425341 2425435 2425771 "RMCAT2" 2426406 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1048 2422218 2424687 2424984 "RMATRIX" 2425103 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1047 2415160 2417394 2417509 "RMATCAT" 2420868 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2421850 NIL) (-1046 2414535 2414682 2414989 "RMATCAT-" 2414994 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1045 2414102 2414177 2414305 "RINTERP" 2414454 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1044 2413235 2413755 2413785 "RING" 2413841 T RING (NIL) -9 NIL 2413927 NIL) (-1043 2413027 2413071 2413168 "RING-" 2413173 NIL RING- (NIL T) -8 NIL NIL NIL) (-1042 2411868 2412105 2412363 "RIDIST" 2412791 T RIDIST (NIL) -7 NIL NIL NIL) (-1041 2403184 2411336 2411542 "RGCHAIN" 2411716 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1040 2402560 2402940 2402981 "RGBCSPC" 2403039 NIL RGBCSPC (NIL T) -9 NIL 2403091 NIL) (-1039 2401744 2402099 2402140 "RGBCMDL" 2402372 NIL RGBCMDL (NIL T) -9 NIL 2402486 NIL) (-1038 2398738 2399352 2400022 "RF" 2401108 NIL RF (NIL T) -7 NIL NIL NIL) (-1037 2398384 2398447 2398550 "RFFACTOR" 2398669 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1036 2398109 2398144 2398241 "RFFACT" 2398343 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1035 2396226 2396590 2396972 "RFDIST" 2397749 T RFDIST (NIL) -7 NIL NIL NIL) (-1034 2395679 2395771 2395934 "RETSOL" 2396128 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1033 2395315 2395395 2395438 "RETRACT" 2395571 NIL RETRACT (NIL T) -9 NIL 2395658 NIL) (-1032 2395164 2395189 2395276 "RETRACT-" 2395281 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1031 2394793 2394986 2395056 "RETAST" 2395116 T RETAST (NIL) -8 NIL NIL NIL) (-1030 2387647 2394446 2394573 "RESULT" 2394688 T RESULT (NIL) -8 NIL NIL NIL) (-1029 2386273 2386916 2387115 "RESRING" 2387550 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1028 2385909 2385958 2386056 "RESLATC" 2386210 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1027 2385615 2385649 2385756 "REPSQ" 2385868 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1026 2383037 2383617 2384219 "REP" 2385035 T REP (NIL) -7 NIL NIL NIL) (-1025 2382735 2382769 2382880 "REPDB" 2382996 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1024 2376645 2378024 2379247 "REP2" 2381547 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1023 2373022 2373703 2374511 "REP1" 2375872 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1022 2365748 2371163 2371619 "REGSET" 2372652 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1021 2364561 2364896 2365146 "REF" 2365533 NIL REF (NIL T) -8 NIL NIL NIL) (-1020 2363938 2364041 2364208 "REDORDER" 2364445 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1019 2359943 2363151 2363378 "RECLOS" 2363766 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1018 2358995 2359176 2359391 "REALSOLV" 2359750 T REALSOLV (NIL) -7 NIL NIL NIL) (-1017 2358841 2358882 2358912 "REAL" 2358917 T REAL (NIL) -9 NIL 2358952 NIL) (-1016 2355324 2356126 2357010 "REAL0Q" 2358006 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1015 2350925 2351913 2352974 "REAL0" 2354305 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1014 2350423 2350642 2350736 "RDUCEAST" 2350853 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1013 2349828 2349900 2350107 "RDIV" 2350345 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1012 2348896 2349070 2349283 "RDIST" 2349650 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1011 2347493 2347780 2348152 "RDETRS" 2348604 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1010 2345305 2345759 2346297 "RDETR" 2347035 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1009 2343916 2344194 2344598 "RDEEFS" 2345021 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1008 2342411 2342717 2343149 "RDEEF" 2343604 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1007 2336672 2339547 2339577 "RCFIELD" 2340872 T RCFIELD (NIL) -9 NIL 2341602 NIL) (-1006 2334736 2335240 2335936 "RCFIELD-" 2336011 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1005 2331052 2332837 2332880 "RCAGG" 2333964 NIL RCAGG (NIL T) -9 NIL 2334429 NIL) (-1004 2330680 2330774 2330937 "RCAGG-" 2330942 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1003 2330015 2330127 2330292 "RATRET" 2330564 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1002 2329568 2329635 2329756 "RATFACT" 2329943 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1001 2328876 2328996 2329148 "RANDSRC" 2329438 T RANDSRC (NIL) -7 NIL NIL NIL) (-1000 2328610 2328654 2328727 "RADUTIL" 2328825 T RADUTIL (NIL) -7 NIL NIL NIL) (-999 2321772 2327452 2327760 "RADIX" 2328334 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-998 2313429 2321616 2321744 "RADFF" 2321749 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-997 2313081 2313156 2313184 "RADCAT" 2313341 T RADCAT (NIL) -9 NIL NIL NIL) (-996 2312866 2312914 2313011 "RADCAT-" 2313016 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-995 2311017 2312641 2312730 "QUEUE" 2312810 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-994 2307593 2310954 2310999 "QUAT" 2311004 NIL QUAT (NIL T) -8 NIL NIL NIL) (-993 2307231 2307274 2307401 "QUATCT2" 2307544 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-992 2300978 2304280 2304320 "QUATCAT" 2305100 NIL QUATCAT (NIL T) -9 NIL 2305866 NIL) (-991 2297122 2298159 2299546 "QUATCAT-" 2299640 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-990 2294642 2296206 2296247 "QUAGG" 2296622 NIL QUAGG (NIL T) -9 NIL 2296797 NIL) (-989 2294274 2294467 2294535 "QQUTAST" 2294594 T QQUTAST (NIL) -8 NIL NIL NIL) (-988 2293199 2293672 2293844 "QFORM" 2294146 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-987 2284411 2289616 2289656 "QFCAT" 2290314 NIL QFCAT (NIL T) -9 NIL 2291315 NIL) (-986 2279983 2281184 2282775 "QFCAT-" 2282869 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-985 2279621 2279664 2279791 "QFCAT2" 2279934 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-984 2279081 2279191 2279321 "QEQUAT" 2279511 T QEQUAT (NIL) -8 NIL NIL NIL) (-983 2272229 2273300 2274484 "QCMPACK" 2278014 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-982 2269805 2270226 2270654 "QALGSET" 2271884 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-981 2269050 2269224 2269456 "QALGSET2" 2269625 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-980 2267741 2267964 2268281 "PWFFINTB" 2268823 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-979 2265923 2266091 2266445 "PUSHVAR" 2267555 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-978 2261841 2262895 2262936 "PTRANFN" 2264820 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-977 2260243 2260534 2260856 "PTPACK" 2261552 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-976 2259875 2259932 2260041 "PTFUNC2" 2260180 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-975 2254402 2258747 2258788 "PTCAT" 2259084 NIL PTCAT (NIL T) -9 NIL 2259237 NIL) (-974 2254060 2254095 2254219 "PSQFR" 2254361 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-973 2252655 2252953 2253287 "PSEUDLIN" 2253758 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-972 2239425 2241789 2244113 "PSETPK" 2250415 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-971 2232469 2235183 2235279 "PSETCAT" 2238300 NIL PSETCAT (NIL T T T T) -9 NIL 2239114 NIL) (-970 2230305 2230939 2231760 "PSETCAT-" 2231765 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-969 2229654 2229819 2229847 "PSCURVE" 2230115 T PSCURVE (NIL) -9 NIL 2230282 NIL) (-968 2226010 2227492 2227557 "PSCAT" 2228401 NIL PSCAT (NIL T T T) -9 NIL 2228641 NIL) (-967 2225073 2225289 2225689 "PSCAT-" 2225694 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-966 2223805 2224438 2224643 "PRTITION" 2224888 T PRTITION (NIL) -8 NIL NIL NIL) (-965 2223307 2223526 2223618 "PRTDAST" 2223733 T PRTDAST (NIL) -8 NIL NIL NIL) (-964 2212405 2214611 2216799 "PRS" 2221169 NIL PRS (NIL T T) -7 NIL NIL NIL) (-963 2210263 2211755 2211795 "PRQAGG" 2211978 NIL PRQAGG (NIL T) -9 NIL 2212080 NIL) (-962 2209649 2209878 2209906 "PROPLOG" 2210091 T PROPLOG (NIL) -9 NIL 2210213 NIL) (-961 2206819 2207463 2207927 "PROPFRML" 2209217 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-960 2206279 2206389 2206519 "PROPERTY" 2206709 T PROPERTY (NIL) -8 NIL NIL NIL) (-959 2200364 2204445 2205265 "PRODUCT" 2205505 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-958 2197677 2199822 2200056 "PR" 2200175 NIL PR (NIL T T) -8 NIL NIL NIL) (-957 2197473 2197505 2197564 "PRINT" 2197638 T PRINT (NIL) -7 NIL NIL NIL) (-956 2196813 2196930 2197082 "PRIMES" 2197353 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-955 2194878 2195279 2195745 "PRIMELT" 2196392 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-954 2194607 2194656 2194684 "PRIMCAT" 2194808 T PRIMCAT (NIL) -9 NIL NIL NIL) (-953 2190768 2194545 2194590 "PRIMARR" 2194595 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-952 2189775 2189953 2190181 "PRIMARR2" 2190586 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-951 2189418 2189474 2189585 "PREASSOC" 2189713 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-950 2188893 2189026 2189054 "PPCURVE" 2189259 T PPCURVE (NIL) -9 NIL 2189395 NIL) (-949 2188515 2188688 2188771 "PORTNUM" 2188830 T PORTNUM (NIL) -8 NIL NIL NIL) (-948 2185874 2186273 2186865 "POLYROOT" 2188096 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-947 2179819 2185478 2185638 "POLY" 2185747 NIL POLY (NIL T) -8 NIL NIL NIL) (-946 2179202 2179260 2179494 "POLYLIFT" 2179755 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-945 2175477 2175926 2176555 "POLYCATQ" 2178747 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-944 2162294 2167652 2167717 "POLYCAT" 2171231 NIL POLYCAT (NIL T T T) -9 NIL 2173159 NIL) (-943 2155744 2157605 2159989 "POLYCAT-" 2159994 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-942 2155331 2155399 2155519 "POLY2UP" 2155670 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-941 2154963 2155020 2155129 "POLY2" 2155268 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-940 2153648 2153887 2154163 "POLUTIL" 2154737 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-939 2152003 2152280 2152611 "POLTOPOL" 2153370 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-938 2147521 2151939 2151985 "POINT" 2151990 NIL POINT (NIL T) -8 NIL NIL NIL) (-937 2145708 2146065 2146440 "PNTHEORY" 2147166 T PNTHEORY (NIL) -7 NIL NIL NIL) (-936 2144127 2144424 2144836 "PMTOOLS" 2145406 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-935 2143720 2143798 2143915 "PMSYM" 2144043 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-934 2143230 2143299 2143473 "PMQFCAT" 2143645 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-933 2142585 2142695 2142851 "PMPRED" 2143107 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-932 2141981 2142067 2142228 "PMPREDFS" 2142486 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-931 2140624 2140832 2141217 "PMPLCAT" 2141743 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-930 2140156 2140235 2140387 "PMLSAGG" 2140539 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-929 2139631 2139707 2139888 "PMKERNEL" 2140074 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-928 2139248 2139323 2139436 "PMINS" 2139550 NIL PMINS (NIL T) -7 NIL NIL NIL) (-927 2138676 2138745 2138961 "PMFS" 2139173 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-926 2137904 2138022 2138227 "PMDOWN" 2138553 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-925 2137067 2137226 2137408 "PMASS" 2137742 T PMASS (NIL) -7 NIL NIL NIL) (-924 2136341 2136452 2136615 "PMASSFS" 2136953 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-923 2135996 2136064 2136158 "PLOTTOOL" 2136267 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-922 2130618 2131807 2132955 "PLOT" 2134868 T PLOT (NIL) -8 NIL NIL NIL) (-921 2126432 2127466 2128387 "PLOT3D" 2129717 T PLOT3D (NIL) -8 NIL NIL NIL) (-920 2125344 2125521 2125756 "PLOT1" 2126236 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-919 2100738 2105410 2110261 "PLEQN" 2120610 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-918 2100056 2100178 2100358 "PINTERP" 2100603 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-917 2099749 2099796 2099899 "PINTERPA" 2100003 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-916 2098997 2099518 2099605 "PI" 2099645 T PI (NIL) -8 NIL NIL 2099712) (-915 2097394 2098335 2098363 "PID" 2098545 T PID (NIL) -9 NIL 2098679 NIL) (-914 2097119 2097156 2097244 "PICOERCE" 2097351 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-913 2096439 2096578 2096754 "PGROEB" 2096975 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-912 2092026 2092840 2093745 "PGE" 2095554 T PGE (NIL) -7 NIL NIL NIL) (-911 2090150 2090396 2090762 "PGCD" 2091743 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-910 2089488 2089591 2089752 "PFRPAC" 2090034 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-909 2086168 2088036 2088389 "PFR" 2089167 NIL PFR (NIL T) -8 NIL NIL NIL) (-908 2084557 2084801 2085126 "PFOTOOLS" 2085915 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-907 2083090 2083329 2083680 "PFOQ" 2084314 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-906 2081563 2081775 2082138 "PFO" 2082874 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-905 2078151 2081452 2081521 "PF" 2081526 NIL PF (NIL NIL) -8 NIL NIL NIL) (-904 2075585 2076822 2076850 "PFECAT" 2077435 T PFECAT (NIL) -9 NIL 2077819 NIL) (-903 2075030 2075184 2075398 "PFECAT-" 2075403 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-902 2073634 2073885 2074186 "PFBRU" 2074779 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-901 2071501 2071852 2072284 "PFBR" 2073285 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-900 2067417 2068877 2069553 "PERM" 2070858 NIL PERM (NIL T) -8 NIL NIL NIL) (-899 2062683 2063624 2064494 "PERMGRP" 2066580 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-898 2060815 2061746 2061787 "PERMCAT" 2062233 NIL PERMCAT (NIL T) -9 NIL 2062538 NIL) (-897 2060468 2060509 2060633 "PERMAN" 2060768 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-896 2058004 2060133 2060255 "PENDTREE" 2060379 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-895 2056097 2056831 2056872 "PDRING" 2057529 NIL PDRING (NIL T) -9 NIL 2057815 NIL) (-894 2055200 2055418 2055780 "PDRING-" 2055785 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-893 2052442 2053193 2053861 "PDEPROB" 2054552 T PDEPROB (NIL) -8 NIL NIL NIL) (-892 2049989 2050491 2051046 "PDEPACK" 2051907 T PDEPACK (NIL) -7 NIL NIL NIL) (-891 2048901 2049091 2049342 "PDECOMP" 2049788 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-890 2046506 2047323 2047351 "PDECAT" 2048138 T PDECAT (NIL) -9 NIL 2048851 NIL) (-889 2046257 2046290 2046380 "PCOMP" 2046467 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-888 2044462 2045058 2045355 "PBWLB" 2045986 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-887 2036967 2038535 2039873 "PATTERN" 2043145 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-886 2036599 2036656 2036765 "PATTERN2" 2036904 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-885 2034356 2034744 2035201 "PATTERN1" 2036188 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-884 2031751 2032305 2032786 "PATRES" 2033921 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-883 2031315 2031382 2031514 "PATRES2" 2031678 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-882 2029198 2029603 2030010 "PATMATCH" 2030982 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-881 2028734 2028917 2028958 "PATMAB" 2029065 NIL PATMAB (NIL T) -9 NIL 2029148 NIL) (-880 2027279 2027588 2027846 "PATLRES" 2028539 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-879 2026825 2026948 2026989 "PATAB" 2026994 NIL PATAB (NIL T) -9 NIL 2027166 NIL) (-878 2024306 2024838 2025411 "PARTPERM" 2026272 T PARTPERM (NIL) -7 NIL NIL NIL) (-877 2023927 2023990 2024092 "PARSURF" 2024237 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-876 2023559 2023616 2023725 "PARSU2" 2023864 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-875 2023323 2023363 2023430 "PARSER" 2023512 T PARSER (NIL) -7 NIL NIL NIL) (-874 2022944 2023007 2023109 "PARSCURV" 2023254 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-873 2022576 2022633 2022742 "PARSC2" 2022881 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-872 2022215 2022273 2022370 "PARPCURV" 2022512 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-871 2021847 2021904 2022013 "PARPC2" 2022152 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-870 2021367 2021453 2021572 "PAN2EXPR" 2021748 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-869 2020173 2020488 2020716 "PALETTE" 2021159 T PALETTE (NIL) -8 NIL NIL NIL) (-868 2018641 2019178 2019538 "PAIR" 2019859 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-867 2012547 2017900 2018094 "PADICRC" 2018496 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-866 2005811 2011893 2012077 "PADICRAT" 2012395 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-865 2004161 2005748 2005793 "PADIC" 2005798 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-864 2001371 2002901 2002941 "PADICCT" 2003522 NIL PADICCT (NIL NIL) -9 NIL 2003804 NIL) (-863 2000328 2000528 2000796 "PADEPAC" 2001158 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-862 1999540 1999673 1999879 "PADE" 2000190 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-861 1997962 1998748 1999028 "OWP" 1999344 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-860 1997482 1997668 1997765 "OVERSET" 1997885 T OVERSET (NIL) -8 NIL NIL NIL) (-859 1996555 1997087 1997259 "OVAR" 1997350 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-858 1995819 1995940 1996101 "OUT" 1996414 T OUT (NIL) -7 NIL NIL NIL) (-857 1984726 1986928 1989128 "OUTFORM" 1993639 T OUTFORM (NIL) -8 NIL NIL NIL) (-856 1984062 1984323 1984450 "OUTBFILE" 1984619 T OUTBFILE (NIL) -8 NIL NIL NIL) (-855 1983369 1983534 1983562 "OUTBCON" 1983880 T OUTBCON (NIL) -9 NIL 1984046 NIL) (-854 1982970 1983082 1983239 "OUTBCON-" 1983244 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-853 1982378 1982699 1982788 "OSI" 1982901 T OSI (NIL) -8 NIL NIL NIL) (-852 1981934 1982246 1982274 "OSGROUP" 1982279 T OSGROUP (NIL) -9 NIL 1982301 NIL) (-851 1980679 1980906 1981191 "ORTHPOL" 1981681 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-850 1978265 1980514 1980635 "OREUP" 1980640 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-849 1975703 1977956 1978083 "ORESUP" 1978207 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-848 1973231 1973731 1974292 "OREPCTO" 1975192 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-847 1967055 1969222 1969263 "OREPCAT" 1971611 NIL OREPCAT (NIL T) -9 NIL 1972715 NIL) (-846 1964202 1964984 1966042 "OREPCAT-" 1966047 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-845 1963379 1963651 1963679 "ORDSET" 1963988 T ORDSET (NIL) -9 NIL 1964152 NIL) (-844 1962898 1963020 1963213 "ORDSET-" 1963218 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-843 1961532 1962289 1962317 "ORDRING" 1962519 T ORDRING (NIL) -9 NIL 1962644 NIL) (-842 1961177 1961271 1961415 "ORDRING-" 1961420 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-841 1960583 1961020 1961048 "ORDMON" 1961053 T ORDMON (NIL) -9 NIL 1961074 NIL) (-840 1959745 1959892 1960087 "ORDFUNS" 1960432 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-839 1959109 1959502 1959530 "ORDFIN" 1959595 T ORDFIN (NIL) -9 NIL 1959669 NIL) (-838 1955701 1957695 1958104 "ORDCOMP" 1958733 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-837 1954967 1955094 1955280 "ORDCOMP2" 1955561 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-836 1951575 1952458 1953272 "OPTPROB" 1954173 T OPTPROB (NIL) -8 NIL NIL NIL) (-835 1948377 1949016 1949720 "OPTPACK" 1950891 T OPTPACK (NIL) -7 NIL NIL NIL) (-834 1946090 1946830 1946858 "OPTCAT" 1947677 T OPTCAT (NIL) -9 NIL 1948327 NIL) (-833 1945533 1945767 1945872 "OPSIG" 1946005 T OPSIG (NIL) -8 NIL NIL NIL) (-832 1945301 1945340 1945406 "OPQUERY" 1945487 T OPQUERY (NIL) -7 NIL NIL NIL) (-831 1942467 1943612 1944116 "OP" 1944830 NIL OP (NIL T) -8 NIL NIL NIL) (-830 1942002 1942173 1942214 "OPERCAT" 1942349 NIL OPERCAT (NIL T) -9 NIL 1942417 NIL) (-829 1941848 1941875 1941961 "OPERCAT-" 1941966 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-828 1938693 1940645 1941014 "ONECOMP" 1941512 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-827 1937998 1938113 1938287 "ONECOMP2" 1938565 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-826 1937417 1937523 1937653 "OMSERVER" 1937888 T OMSERVER (NIL) -7 NIL NIL NIL) (-825 1934305 1936857 1936897 "OMSAGG" 1936958 NIL OMSAGG (NIL T) -9 NIL 1937022 NIL) (-824 1932928 1933191 1933473 "OMPKG" 1934043 T OMPKG (NIL) -7 NIL NIL NIL) (-823 1932358 1932461 1932489 "OM" 1932788 T OM (NIL) -9 NIL NIL NIL) (-822 1930940 1931907 1932076 "OMLO" 1932239 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-821 1929865 1930012 1930239 "OMEXPR" 1930766 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-820 1929183 1929411 1929547 "OMERR" 1929749 T OMERR (NIL) -8 NIL NIL NIL) (-819 1928361 1928604 1928764 "OMERRK" 1929043 T OMERRK (NIL) -8 NIL NIL NIL) (-818 1927839 1928038 1928146 "OMENC" 1928273 T OMENC (NIL) -8 NIL NIL NIL) (-817 1921734 1922919 1924090 "OMDEV" 1926688 T OMDEV (NIL) -8 NIL NIL NIL) (-816 1920803 1920974 1921168 "OMCONN" 1921560 T OMCONN (NIL) -8 NIL NIL NIL) (-815 1919424 1920366 1920394 "OINTDOM" 1920399 T OINTDOM (NIL) -9 NIL 1920420 NIL) (-814 1915230 1916414 1917130 "OFMONOID" 1918740 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-813 1914668 1915167 1915212 "ODVAR" 1915217 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-812 1912126 1914413 1914568 "ODR" 1914573 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-811 1904470 1911902 1912028 "ODPOL" 1912033 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-810 1898346 1904342 1904447 "ODP" 1904452 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-809 1897112 1897327 1897602 "ODETOOLS" 1898120 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-808 1894081 1894737 1895453 "ODESYS" 1896445 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-807 1888963 1889871 1890896 "ODERTRIC" 1893156 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-806 1888389 1888471 1888665 "ODERED" 1888875 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-805 1885277 1885825 1886502 "ODERAT" 1887812 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-804 1882237 1882701 1883298 "ODEPRRIC" 1884806 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-803 1880207 1880776 1881262 "ODEPROB" 1881771 T ODEPROB (NIL) -8 NIL NIL NIL) (-802 1876729 1877212 1877859 "ODEPRIM" 1879686 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-801 1875978 1876080 1876340 "ODEPAL" 1876621 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-800 1872140 1872931 1873795 "ODEPACK" 1875134 T ODEPACK (NIL) -7 NIL NIL NIL) (-799 1871173 1871280 1871509 "ODEINT" 1872029 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-798 1865274 1866699 1868146 "ODEIFTBL" 1869746 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-797 1860609 1861395 1862354 "ODEEF" 1864433 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-796 1859944 1860033 1860263 "ODECONST" 1860514 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-795 1858095 1858730 1858758 "ODECAT" 1859363 T ODECAT (NIL) -9 NIL 1859894 NIL) (-794 1855002 1857807 1857926 "OCT" 1858008 NIL OCT (NIL T) -8 NIL NIL NIL) (-793 1854640 1854683 1854810 "OCTCT2" 1854953 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-792 1849414 1851814 1851854 "OC" 1852951 NIL OC (NIL T) -9 NIL 1853809 NIL) (-791 1846641 1847389 1848379 "OC-" 1848473 NIL OC- (NIL T T) -8 NIL NIL NIL) (-790 1846019 1846461 1846489 "OCAMON" 1846494 T OCAMON (NIL) -9 NIL 1846515 NIL) (-789 1845576 1845891 1845919 "OASGP" 1845924 T OASGP (NIL) -9 NIL 1845944 NIL) (-788 1844863 1845326 1845354 "OAMONS" 1845394 T OAMONS (NIL) -9 NIL 1845437 NIL) (-787 1844303 1844710 1844738 "OAMON" 1844743 T OAMON (NIL) -9 NIL 1844763 NIL) (-786 1843607 1844099 1844127 "OAGROUP" 1844132 T OAGROUP (NIL) -9 NIL 1844152 NIL) (-785 1843297 1843347 1843435 "NUMTUBE" 1843551 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-784 1836870 1838388 1839924 "NUMQUAD" 1841781 T NUMQUAD (NIL) -7 NIL NIL NIL) (-783 1832626 1833614 1834639 "NUMODE" 1835865 T NUMODE (NIL) -7 NIL NIL NIL) (-782 1830007 1830861 1830889 "NUMINT" 1831812 T NUMINT (NIL) -9 NIL 1832576 NIL) (-781 1828955 1829152 1829370 "NUMFMT" 1829809 T NUMFMT (NIL) -7 NIL NIL NIL) (-780 1815314 1818259 1820791 "NUMERIC" 1826462 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-779 1809711 1814763 1814858 "NTSCAT" 1814863 NIL NTSCAT (NIL T T T T) -9 NIL 1814902 NIL) (-778 1808905 1809070 1809263 "NTPOLFN" 1809550 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-777 1796745 1805730 1806542 "NSUP" 1808126 NIL NSUP (NIL T) -8 NIL NIL NIL) (-776 1796377 1796434 1796543 "NSUP2" 1796682 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-775 1786374 1796151 1796284 "NSMP" 1796289 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-774 1784806 1785107 1785464 "NREP" 1786062 NIL NREP (NIL T) -7 NIL NIL NIL) (-773 1783397 1783649 1784007 "NPCOEF" 1784549 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-772 1782463 1782578 1782794 "NORMRETR" 1783278 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-771 1780504 1780794 1781203 "NORMPK" 1782171 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-770 1780189 1780217 1780341 "NORMMA" 1780470 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-769 1780016 1780146 1780175 "NONE" 1780180 T NONE (NIL) -8 NIL NIL NIL) (-768 1779805 1779834 1779903 "NONE1" 1779980 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-767 1779288 1779350 1779536 "NODE1" 1779737 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-766 1777559 1778382 1778637 "NNI" 1778984 T NNI (NIL) -8 NIL NIL 1779219) (-765 1775979 1776292 1776656 "NLINSOL" 1777227 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-764 1772247 1773215 1774114 "NIPROB" 1775100 T NIPROB (NIL) -8 NIL NIL NIL) (-763 1771004 1771238 1771540 "NFINTBAS" 1772009 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-762 1770178 1770654 1770695 "NETCLT" 1770867 NIL NETCLT (NIL T) -9 NIL 1770949 NIL) (-761 1768886 1769117 1769398 "NCODIV" 1769946 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-760 1768648 1768685 1768760 "NCNTFRAC" 1768843 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-759 1766828 1767192 1767612 "NCEP" 1768273 NIL NCEP (NIL T) -7 NIL NIL NIL) (-758 1765739 1766478 1766506 "NASRING" 1766616 T NASRING (NIL) -9 NIL 1766690 NIL) (-757 1765534 1765578 1765672 "NASRING-" 1765677 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-756 1764687 1765186 1765214 "NARNG" 1765331 T NARNG (NIL) -9 NIL 1765422 NIL) (-755 1764379 1764446 1764580 "NARNG-" 1764585 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-754 1763258 1763465 1763700 "NAGSP" 1764164 T NAGSP (NIL) -7 NIL NIL NIL) (-753 1754530 1756214 1757887 "NAGS" 1761605 T NAGS (NIL) -7 NIL NIL NIL) (-752 1753078 1753386 1753717 "NAGF07" 1754219 T NAGF07 (NIL) -7 NIL NIL NIL) (-751 1747616 1748907 1750214 "NAGF04" 1751791 T NAGF04 (NIL) -7 NIL NIL NIL) (-750 1740584 1742198 1743831 "NAGF02" 1746003 T NAGF02 (NIL) -7 NIL NIL NIL) (-749 1735808 1736908 1738025 "NAGF01" 1739487 T NAGF01 (NIL) -7 NIL NIL NIL) (-748 1729436 1731002 1732587 "NAGE04" 1734243 T NAGE04 (NIL) -7 NIL NIL NIL) (-747 1720605 1722726 1724856 "NAGE02" 1727326 T NAGE02 (NIL) -7 NIL NIL NIL) (-746 1716558 1717505 1718469 "NAGE01" 1719661 T NAGE01 (NIL) -7 NIL NIL NIL) (-745 1714353 1714887 1715445 "NAGD03" 1716020 T NAGD03 (NIL) -7 NIL NIL NIL) (-744 1706103 1708031 1709985 "NAGD02" 1712419 T NAGD02 (NIL) -7 NIL NIL NIL) (-743 1699914 1701339 1702779 "NAGD01" 1704683 T NAGD01 (NIL) -7 NIL NIL NIL) (-742 1696123 1696945 1697782 "NAGC06" 1699097 T NAGC06 (NIL) -7 NIL NIL NIL) (-741 1694588 1694920 1695276 "NAGC05" 1695787 T NAGC05 (NIL) -7 NIL NIL NIL) (-740 1693964 1694083 1694227 "NAGC02" 1694464 T NAGC02 (NIL) -7 NIL NIL NIL) (-739 1693024 1693581 1693621 "NAALG" 1693700 NIL NAALG (NIL T) -9 NIL 1693761 NIL) (-738 1692859 1692888 1692978 "NAALG-" 1692983 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-737 1686809 1687917 1689104 "MULTSQFR" 1691755 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-736 1686128 1686203 1686387 "MULTFACT" 1686721 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-735 1679221 1683091 1683144 "MTSCAT" 1684214 NIL MTSCAT (NIL T T) -9 NIL 1684728 NIL) (-734 1678933 1678987 1679079 "MTHING" 1679161 NIL MTHING (NIL T) -7 NIL NIL NIL) (-733 1678725 1678758 1678818 "MSYSCMD" 1678893 T MSYSCMD (NIL) -7 NIL NIL NIL) (-732 1674837 1677480 1677800 "MSET" 1678438 NIL MSET (NIL T) -8 NIL NIL NIL) (-731 1671932 1674398 1674439 "MSETAGG" 1674444 NIL MSETAGG (NIL T) -9 NIL 1674478 NIL) (-730 1667815 1669311 1670056 "MRING" 1671232 NIL MRING (NIL T T) -8 NIL NIL NIL) (-729 1667381 1667448 1667579 "MRF2" 1667742 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-728 1666999 1667034 1667178 "MRATFAC" 1667340 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-727 1664611 1664906 1665337 "MPRFF" 1666704 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-726 1658671 1664465 1664562 "MPOLY" 1664567 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-725 1658161 1658196 1658404 "MPCPF" 1658630 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-724 1657675 1657718 1657902 "MPC3" 1658112 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1656870 1656951 1657172 "MPC2" 1657590 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-722 1655171 1655508 1655898 "MONOTOOL" 1656530 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-721 1654422 1654713 1654741 "MONOID" 1654960 T MONOID (NIL) -9 NIL 1655107 NIL) (-720 1653968 1654087 1654268 "MONOID-" 1654273 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-719 1644827 1650735 1650794 "MONOGEN" 1651468 NIL MONOGEN (NIL T T) -9 NIL 1651924 NIL) (-718 1642045 1642780 1643780 "MONOGEN-" 1643899 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-717 1640904 1641324 1641352 "MONADWU" 1641744 T MONADWU (NIL) -9 NIL 1641982 NIL) (-716 1640276 1640435 1640683 "MONADWU-" 1640688 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-715 1639661 1639879 1639907 "MONAD" 1640114 T MONAD (NIL) -9 NIL 1640226 NIL) (-714 1639346 1639424 1639556 "MONAD-" 1639561 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-713 1637662 1638259 1638538 "MOEBIUS" 1639099 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-712 1637054 1637432 1637472 "MODULE" 1637477 NIL MODULE (NIL T) -9 NIL 1637503 NIL) (-711 1636622 1636718 1636908 "MODULE-" 1636913 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-710 1634337 1634986 1635313 "MODRING" 1636446 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-709 1631323 1632442 1632963 "MODOP" 1633866 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-708 1629938 1630390 1630667 "MODMONOM" 1631186 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-707 1619745 1628229 1628643 "MODMON" 1629575 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-706 1616936 1618589 1618865 "MODFIELD" 1619620 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-705 1615940 1616217 1616407 "MMLFORM" 1616766 T MMLFORM (NIL) -8 NIL NIL NIL) (-704 1615466 1615509 1615688 "MMAP" 1615891 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-703 1613683 1614416 1614457 "MLO" 1614880 NIL MLO (NIL T) -9 NIL 1615122 NIL) (-702 1611050 1611565 1612167 "MLIFT" 1613164 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-701 1610441 1610525 1610679 "MKUCFUNC" 1610961 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-700 1610040 1610110 1610233 "MKRECORD" 1610364 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-699 1609088 1609249 1609477 "MKFUNC" 1609851 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-698 1608476 1608580 1608736 "MKFLCFN" 1608971 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-697 1608019 1608386 1608445 "MKCHSET" 1608450 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-696 1607296 1607398 1607583 "MKBCFUNC" 1607912 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-695 1604038 1606850 1606986 "MINT" 1607180 T MINT (NIL) -8 NIL NIL NIL) (-694 1602850 1603093 1603370 "MHROWRED" 1603793 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-693 1598276 1601385 1601790 "MFLOAT" 1602465 T MFLOAT (NIL) -8 NIL NIL NIL) (-692 1597633 1597709 1597880 "MFINFACT" 1598188 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-691 1593948 1594796 1595680 "MESH" 1596769 T MESH (NIL) -7 NIL NIL NIL) (-690 1592338 1592650 1593003 "MDDFACT" 1593635 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-689 1589180 1591497 1591538 "MDAGG" 1591793 NIL MDAGG (NIL T) -9 NIL 1591936 NIL) (-688 1578958 1588473 1588680 "MCMPLX" 1588993 T MCMPLX (NIL) -8 NIL NIL NIL) (-687 1578099 1578245 1578445 "MCDEN" 1578807 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-686 1575989 1576259 1576639 "MCALCFN" 1577829 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-685 1574914 1575154 1575387 "MAYBE" 1575795 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-684 1572526 1573049 1573611 "MATSTOR" 1574385 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-683 1568532 1571898 1572146 "MATRIX" 1572311 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-682 1564301 1565005 1565741 "MATLIN" 1567889 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-681 1554455 1557593 1557670 "MATCAT" 1562550 NIL MATCAT (NIL T T T) -9 NIL 1563967 NIL) (-680 1550819 1551832 1553188 "MATCAT-" 1553193 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-679 1549413 1549566 1549899 "MATCAT2" 1550654 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-678 1547525 1547849 1548233 "MAPPKG3" 1549088 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-677 1546506 1546679 1546901 "MAPPKG2" 1547349 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-676 1545005 1545289 1545616 "MAPPKG1" 1546212 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-675 1544111 1544411 1544588 "MAPPAST" 1544848 T MAPPAST (NIL) -8 NIL NIL NIL) (-674 1543722 1543780 1543903 "MAPHACK3" 1544047 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-673 1543314 1543375 1543489 "MAPHACK2" 1543654 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-672 1542752 1542855 1542997 "MAPHACK1" 1543205 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-671 1540858 1541452 1541756 "MAGMA" 1542480 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-670 1540364 1540582 1540673 "MACROAST" 1540787 T MACROAST (NIL) -8 NIL NIL NIL) (-669 1536831 1538603 1539064 "M3D" 1539936 NIL M3D (NIL T) -8 NIL NIL NIL) (-668 1530985 1535200 1535241 "LZSTAGG" 1536023 NIL LZSTAGG (NIL T) -9 NIL 1536318 NIL) (-667 1526959 1528116 1529573 "LZSTAGG-" 1529578 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-666 1524073 1524850 1525337 "LWORD" 1526504 NIL LWORD (NIL T) -8 NIL NIL NIL) (-665 1523676 1523877 1523952 "LSTAST" 1524018 T LSTAST (NIL) -8 NIL NIL NIL) (-664 1516877 1523447 1523581 "LSQM" 1523586 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-663 1516101 1516240 1516468 "LSPP" 1516732 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-662 1513913 1514214 1514670 "LSMP" 1515790 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-661 1510692 1511366 1512096 "LSMP1" 1513215 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-660 1504617 1509859 1509900 "LSAGG" 1509962 NIL LSAGG (NIL T) -9 NIL 1510040 NIL) (-659 1501312 1502236 1503449 "LSAGG-" 1503454 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-658 1498938 1500456 1500705 "LPOLY" 1501107 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-657 1498520 1498605 1498728 "LPEFRAC" 1498847 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-656 1496867 1497614 1497867 "LO" 1498352 NIL LO (NIL T T T) -8 NIL NIL NIL) (-655 1496519 1496631 1496659 "LOGIC" 1496770 T LOGIC (NIL) -9 NIL 1496851 NIL) (-654 1496381 1496404 1496475 "LOGIC-" 1496480 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-653 1495574 1495714 1495907 "LODOOPS" 1496237 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-652 1493032 1495490 1495556 "LODO" 1495561 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-651 1491570 1491805 1492158 "LODOF" 1492779 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-650 1487926 1490323 1490364 "LODOCAT" 1490802 NIL LODOCAT (NIL T) -9 NIL 1491013 NIL) (-649 1487659 1487717 1487844 "LODOCAT-" 1487849 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-648 1485014 1487500 1487618 "LODO2" 1487623 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-647 1482484 1484951 1484996 "LODO1" 1485001 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-646 1481344 1481509 1481821 "LODEEF" 1482307 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-645 1476630 1479474 1479515 "LNAGG" 1480462 NIL LNAGG (NIL T) -9 NIL 1480906 NIL) (-644 1475777 1475991 1476333 "LNAGG-" 1476338 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-643 1471940 1472702 1473341 "LMOPS" 1475192 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-642 1471335 1471697 1471738 "LMODULE" 1471799 NIL LMODULE (NIL T) -9 NIL 1471841 NIL) (-641 1468581 1470980 1471103 "LMDICT" 1471245 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-640 1468307 1468489 1468549 "LITERAL" 1468554 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-639 1461534 1467253 1467551 "LIST" 1468042 NIL LIST (NIL T) -8 NIL NIL NIL) (-638 1461059 1461133 1461272 "LIST3" 1461454 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-637 1460066 1460244 1460472 "LIST2" 1460877 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-636 1458200 1458512 1458911 "LIST2MAP" 1459713 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-635 1456930 1457566 1457607 "LINEXP" 1457862 NIL LINEXP (NIL T) -9 NIL 1458011 NIL) (-634 1455577 1455837 1456134 "LINDEP" 1456682 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-633 1452344 1453063 1453840 "LIMITRF" 1454832 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-632 1450620 1450915 1451331 "LIMITPS" 1452039 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-631 1445075 1450131 1450359 "LIE" 1450441 NIL LIE (NIL T T) -8 NIL NIL NIL) (-630 1444124 1444567 1444607 "LIECAT" 1444747 NIL LIECAT (NIL T) -9 NIL 1444898 NIL) (-629 1443965 1443992 1444080 "LIECAT-" 1444085 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-628 1436577 1443414 1443579 "LIB" 1443820 T LIB (NIL) -8 NIL NIL NIL) (-627 1432214 1433095 1434030 "LGROBP" 1435694 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-626 1430080 1430354 1430716 "LF" 1431935 NIL LF (NIL T T) -7 NIL NIL NIL) (-625 1428920 1429612 1429640 "LFCAT" 1429847 T LFCAT (NIL) -9 NIL 1429986 NIL) (-624 1425824 1426452 1427140 "LEXTRIPK" 1428284 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-623 1422595 1423394 1423897 "LEXP" 1425404 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-622 1422098 1422316 1422408 "LETAST" 1422523 T LETAST (NIL) -8 NIL NIL NIL) (-621 1420496 1420809 1421210 "LEADCDET" 1421780 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-620 1419686 1419760 1419989 "LAZM3PK" 1420417 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-619 1414641 1417763 1418301 "LAUPOL" 1419198 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-618 1414206 1414250 1414418 "LAPLACE" 1414591 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-617 1412180 1413307 1413558 "LA" 1414039 NIL LA (NIL T T T) -8 NIL NIL NIL) (-616 1411261 1411811 1411852 "LALG" 1411914 NIL LALG (NIL T) -9 NIL 1411973 NIL) (-615 1410975 1411034 1411170 "LALG-" 1411175 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-614 1410810 1410834 1410875 "KVTFROM" 1410937 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-613 1409613 1410027 1410256 "KTVLOGIC" 1410601 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-612 1409448 1409472 1409513 "KRCFROM" 1409575 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-611 1408352 1408539 1408838 "KOVACIC" 1409248 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-610 1408187 1408211 1408252 "KONVERT" 1408314 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-609 1408022 1408046 1408087 "KOERCE" 1408149 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-608 1405756 1406516 1406909 "KERNEL" 1407661 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-607 1405258 1405339 1405469 "KERNEL2" 1405670 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-606 1399109 1403797 1403851 "KDAGG" 1404228 NIL KDAGG (NIL T T) -9 NIL 1404434 NIL) (-605 1398638 1398762 1398967 "KDAGG-" 1398972 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-604 1391813 1398299 1398454 "KAFILE" 1398516 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-603 1386268 1391324 1391552 "JORDAN" 1391634 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-602 1385674 1385917 1386038 "JOINAST" 1386167 T JOINAST (NIL) -8 NIL NIL NIL) (-601 1385520 1385579 1385634 "JAVACODE" 1385639 T JAVACODE (NIL) -8 NIL NIL NIL) (-600 1381819 1383725 1383779 "IXAGG" 1384708 NIL IXAGG (NIL T T) -9 NIL 1385167 NIL) (-599 1380738 1381044 1381463 "IXAGG-" 1381468 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-598 1376318 1380660 1380719 "IVECTOR" 1380724 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-597 1375084 1375321 1375587 "ITUPLE" 1376085 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-596 1373520 1373697 1374003 "ITRIGMNP" 1374906 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-595 1372265 1372469 1372752 "ITFUN3" 1373296 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-594 1371897 1371954 1372063 "ITFUN2" 1372202 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-593 1369734 1370759 1371058 "ITAYLOR" 1371631 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-592 1358717 1363871 1365034 "ISUPS" 1368604 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-591 1357821 1357961 1358197 "ISUMP" 1358564 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-590 1353085 1357622 1357701 "ISTRING" 1357774 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-589 1352588 1352806 1352898 "ISAST" 1353013 T ISAST (NIL) -8 NIL NIL NIL) (-588 1351798 1351879 1352095 "IRURPK" 1352502 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-587 1350734 1350935 1351175 "IRSN" 1351578 T IRSN (NIL) -7 NIL NIL NIL) (-586 1348763 1349118 1349554 "IRRF2F" 1350372 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-585 1348510 1348548 1348624 "IRREDFFX" 1348719 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-584 1347125 1347384 1347683 "IROOT" 1348243 NIL IROOT (NIL T) -7 NIL NIL NIL) (-583 1343757 1344809 1345501 "IR" 1346465 NIL IR (NIL T) -8 NIL NIL NIL) (-582 1341370 1341865 1342431 "IR2" 1343235 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-581 1340442 1340555 1340776 "IR2F" 1341253 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-580 1340233 1340267 1340327 "IPRNTPK" 1340402 T IPRNTPK (NIL) -7 NIL NIL NIL) (-579 1336852 1340122 1340191 "IPF" 1340196 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-578 1335215 1336777 1336834 "IPADIC" 1336839 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-577 1334555 1334775 1334905 "IP4ADDR" 1335105 T IP4ADDR (NIL) -8 NIL NIL NIL) (-576 1334055 1334259 1334369 "IOMODE" 1334465 T IOMODE (NIL) -8 NIL NIL NIL) (-575 1333128 1333652 1333779 "IOBFILE" 1333948 T IOBFILE (NIL) -8 NIL NIL NIL) (-574 1332616 1333032 1333060 "IOBCON" 1333065 T IOBCON (NIL) -9 NIL 1333086 NIL) (-573 1332113 1332171 1332361 "INVLAPLA" 1332552 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-572 1321762 1324115 1326501 "INTTR" 1329777 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-571 1318106 1318848 1319712 "INTTOOLS" 1320947 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-570 1317692 1317783 1317900 "INTSLPE" 1318009 T INTSLPE (NIL) -7 NIL NIL NIL) (-569 1315687 1317615 1317674 "INTRVL" 1317679 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-568 1313289 1313801 1314376 "INTRF" 1315172 NIL INTRF (NIL T) -7 NIL NIL NIL) (-567 1312700 1312797 1312939 "INTRET" 1313187 NIL INTRET (NIL T) -7 NIL NIL NIL) (-566 1310697 1311086 1311556 "INTRAT" 1312308 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-565 1307925 1308508 1309134 "INTPM" 1310182 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-564 1304628 1305227 1305972 "INTPAF" 1307311 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-563 1299807 1300769 1301820 "INTPACK" 1303597 T INTPACK (NIL) -7 NIL NIL NIL) (-562 1296719 1299536 1299663 "INT" 1299700 T INT (NIL) -8 NIL NIL NIL) (-561 1295971 1296123 1296331 "INTHERTR" 1296561 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-560 1295410 1295490 1295678 "INTHERAL" 1295885 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-559 1293256 1293699 1294156 "INTHEORY" 1294973 T INTHEORY (NIL) -7 NIL NIL NIL) (-558 1284564 1286185 1287964 "INTG0" 1291608 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-557 1265137 1269927 1274737 "INTFTBL" 1279774 T INTFTBL (NIL) -8 NIL NIL NIL) (-556 1264386 1264524 1264697 "INTFACT" 1264996 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-555 1261771 1262217 1262781 "INTEF" 1263940 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-554 1260238 1260943 1260971 "INTDOM" 1261272 T INTDOM (NIL) -9 NIL 1261479 NIL) (-553 1259607 1259781 1260023 "INTDOM-" 1260028 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-552 1256102 1257991 1258045 "INTCAT" 1258844 NIL INTCAT (NIL T) -9 NIL 1259164 NIL) (-551 1255575 1255677 1255805 "INTBIT" 1255994 T INTBIT (NIL) -7 NIL NIL NIL) (-550 1254246 1254400 1254714 "INTALG" 1255420 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-549 1253703 1253793 1253963 "INTAF" 1254150 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-548 1247157 1253513 1253653 "INTABL" 1253658 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-547 1246617 1247030 1247058 "INT8" 1247063 T INT8 (NIL) -8 NIL NIL 1247071) (-546 1246076 1246489 1246517 "INT32" 1246522 T INT32 (NIL) -8 NIL NIL 1246530) (-545 1245535 1245948 1245976 "INT16" 1245981 T INT16 (NIL) -8 NIL NIL 1245989) (-544 1240550 1243224 1243252 "INS" 1244186 T INS (NIL) -9 NIL 1244851 NIL) (-543 1237790 1238561 1239535 "INS-" 1239608 NIL INS- (NIL T) -8 NIL NIL NIL) (-542 1236565 1236792 1237090 "INPSIGN" 1237543 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-541 1235683 1235800 1235997 "INPRODPF" 1236445 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-540 1234577 1234694 1234931 "INPRODFF" 1235563 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-539 1233577 1233729 1233989 "INNMFACT" 1234413 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-538 1232774 1232871 1233059 "INMODGCD" 1233476 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-537 1231283 1231527 1231851 "INFSP" 1232519 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-536 1230467 1230584 1230767 "INFPROD0" 1231163 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-535 1227349 1228532 1229047 "INFORM" 1229960 T INFORM (NIL) -8 NIL NIL NIL) (-534 1226959 1227019 1227117 "INFORM1" 1227284 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-533 1226482 1226571 1226685 "INFINITY" 1226865 T INFINITY (NIL) -7 NIL NIL NIL) (-532 1225658 1226202 1226303 "INETCLTS" 1226401 T INETCLTS (NIL) -8 NIL NIL NIL) (-531 1224275 1224524 1224845 "INEP" 1225406 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-530 1223551 1224172 1224237 "INDE" 1224242 NIL INDE (NIL T) -8 NIL NIL NIL) (-529 1223115 1223183 1223300 "INCRMAPS" 1223478 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-528 1221933 1222384 1222590 "INBFILE" 1222929 T INBFILE (NIL) -8 NIL NIL NIL) (-527 1217244 1218169 1219113 "INBFF" 1221021 NIL INBFF (NIL T) -7 NIL NIL NIL) (-526 1216152 1216421 1216449 "INBCON" 1216962 T INBCON (NIL) -9 NIL 1217228 NIL) (-525 1215404 1215627 1215903 "INBCON-" 1215908 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-524 1214906 1215125 1215217 "INAST" 1215332 T INAST (NIL) -8 NIL NIL NIL) (-523 1214360 1214585 1214691 "IMPTAST" 1214820 T IMPTAST (NIL) -8 NIL NIL NIL) (-522 1210854 1214204 1214308 "IMATRIX" 1214313 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-521 1209566 1209689 1210004 "IMATQF" 1210710 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-520 1207786 1208013 1208350 "IMATLIN" 1209322 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-519 1202412 1207710 1207768 "ILIST" 1207773 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-518 1200365 1202272 1202385 "IIARRAY2" 1202390 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-517 1195798 1200276 1200340 "IFF" 1200345 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-516 1195172 1195415 1195531 "IFAST" 1195702 T IFAST (NIL) -8 NIL NIL NIL) (-515 1190215 1194464 1194652 "IFARRAY" 1195029 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-514 1189422 1190119 1190192 "IFAMON" 1190197 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-513 1189006 1189071 1189125 "IEVALAB" 1189332 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-512 1188681 1188749 1188909 "IEVALAB-" 1188914 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-511 1188339 1188595 1188658 "IDPO" 1188663 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-510 1187616 1188228 1188303 "IDPOAMS" 1188308 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-509 1186950 1187505 1187580 "IDPOAM" 1187585 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-508 1186035 1186285 1186338 "IDPC" 1186751 NIL IDPC (NIL T T) -9 NIL 1186900 NIL) (-507 1185531 1185927 1186000 "IDPAM" 1186005 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-506 1184934 1185423 1185496 "IDPAG" 1185501 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-505 1184702 1184849 1184899 "IDENT" 1184904 T IDENT (NIL) -8 NIL NIL NIL) (-504 1180957 1181805 1182700 "IDECOMP" 1183859 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-503 1173831 1174880 1175927 "IDEAL" 1179993 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-502 1172995 1173107 1173306 "ICDEN" 1173715 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-501 1172094 1172475 1172622 "ICARD" 1172868 T ICARD (NIL) -8 NIL NIL NIL) (-500 1170154 1170467 1170872 "IBPTOOLS" 1171771 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-499 1165788 1169774 1169887 "IBITS" 1170073 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-498 1162511 1163087 1163782 "IBATOOL" 1165205 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-497 1160291 1160752 1161285 "IBACHIN" 1162046 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-496 1158168 1160137 1160240 "IARRAY2" 1160245 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-495 1154321 1158094 1158151 "IARRAY1" 1158156 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-494 1148315 1152733 1153214 "IAN" 1153860 T IAN (NIL) -8 NIL NIL NIL) (-493 1147826 1147883 1148056 "IALGFACT" 1148252 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-492 1147354 1147467 1147495 "HYPCAT" 1147702 T HYPCAT (NIL) -9 NIL NIL NIL) (-491 1146892 1147009 1147195 "HYPCAT-" 1147200 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-490 1146514 1146687 1146770 "HOSTNAME" 1146829 T HOSTNAME (NIL) -8 NIL NIL NIL) (-489 1146359 1146396 1146437 "HOMOTOP" 1146442 NIL HOMOTOP (NIL T) -9 NIL 1146475 NIL) (-488 1143038 1144369 1144410 "HOAGG" 1145391 NIL HOAGG (NIL T) -9 NIL 1146070 NIL) (-487 1141632 1142031 1142557 "HOAGG-" 1142562 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-486 1135674 1141229 1141377 "HEXADEC" 1141504 T HEXADEC (NIL) -8 NIL NIL NIL) (-485 1134422 1134644 1134907 "HEUGCD" 1135451 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-484 1133525 1134259 1134389 "HELLFDIV" 1134394 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-483 1131753 1133302 1133390 "HEAP" 1133469 NIL HEAP (NIL T) -8 NIL NIL NIL) (-482 1131044 1131305 1131439 "HEADAST" 1131639 T HEADAST (NIL) -8 NIL NIL NIL) (-481 1124964 1130959 1131021 "HDP" 1131026 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-480 1118715 1124599 1124751 "HDMP" 1124865 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-479 1118040 1118179 1118343 "HB" 1118571 T HB (NIL) -7 NIL NIL NIL) (-478 1111537 1117886 1117990 "HASHTBL" 1117995 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-477 1111040 1111258 1111350 "HASAST" 1111465 T HASAST (NIL) -8 NIL NIL NIL) (-476 1108852 1110662 1110844 "HACKPI" 1110878 T HACKPI (NIL) -8 NIL NIL NIL) (-475 1104547 1108705 1108818 "GTSET" 1108823 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-474 1098073 1104425 1104523 "GSTBL" 1104528 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-473 1090386 1097104 1097369 "GSERIES" 1097864 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-472 1089553 1089944 1089972 "GROUP" 1090175 T GROUP (NIL) -9 NIL 1090309 NIL) (-471 1088919 1089078 1089329 "GROUP-" 1089334 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-470 1087288 1087607 1087994 "GROEBSOL" 1088596 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-469 1086228 1086490 1086541 "GRMOD" 1087070 NIL GRMOD (NIL T T) -9 NIL 1087238 NIL) (-468 1085996 1086032 1086160 "GRMOD-" 1086165 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-467 1081322 1082350 1083350 "GRIMAGE" 1085016 T GRIMAGE (NIL) -8 NIL NIL NIL) (-466 1079789 1080049 1080373 "GRDEF" 1081018 T GRDEF (NIL) -7 NIL NIL NIL) (-465 1079233 1079349 1079490 "GRAY" 1079668 T GRAY (NIL) -7 NIL NIL NIL) (-464 1078446 1078826 1078877 "GRALG" 1079030 NIL GRALG (NIL T T) -9 NIL 1079123 NIL) (-463 1078107 1078180 1078343 "GRALG-" 1078348 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-462 1074911 1077692 1077870 "GPOLSET" 1078014 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-461 1074265 1074322 1074580 "GOSPER" 1074848 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-460 1070024 1070703 1071229 "GMODPOL" 1073964 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-459 1069029 1069213 1069451 "GHENSEL" 1069836 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-458 1063080 1063923 1064950 "GENUPS" 1068113 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-457 1062777 1062828 1062917 "GENUFACT" 1063023 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-456 1062189 1062266 1062431 "GENPGCD" 1062695 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-455 1061663 1061698 1061911 "GENMFACT" 1062148 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-454 1060231 1060486 1060793 "GENEEZ" 1061406 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-453 1054144 1059842 1060004 "GDMP" 1060154 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-452 1043521 1047915 1049021 "GCNAALG" 1053127 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-451 1041948 1042776 1042804 "GCDDOM" 1043059 T GCDDOM (NIL) -9 NIL 1043216 NIL) (-450 1041418 1041545 1041760 "GCDDOM-" 1041765 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-449 1040090 1040275 1040579 "GB" 1041197 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-448 1028710 1031036 1033428 "GBINTERN" 1037781 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-447 1026547 1026839 1027260 "GBF" 1028385 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-446 1025328 1025493 1025760 "GBEUCLID" 1026363 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-445 1024677 1024802 1024951 "GAUSSFAC" 1025199 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-444 1023044 1023346 1023660 "GALUTIL" 1024396 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-443 1021352 1021626 1021950 "GALPOLYU" 1022771 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-442 1018717 1019007 1019414 "GALFACTU" 1021049 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-441 1010523 1012022 1013630 "GALFACT" 1017149 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-440 1007911 1008569 1008597 "FVFUN" 1009753 T FVFUN (NIL) -9 NIL 1010473 NIL) (-439 1007177 1007359 1007387 "FVC" 1007678 T FVC (NIL) -9 NIL 1007861 NIL) (-438 1006847 1007002 1007070 "FUNDESC" 1007129 T FUNDESC (NIL) -8 NIL NIL NIL) (-437 1006489 1006644 1006725 "FUNCTION" 1006799 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1004260 1004811 1005277 "FT" 1006043 T FT (NIL) -8 NIL NIL NIL) (-435 1003078 1003561 1003764 "FTEM" 1004077 T FTEM (NIL) -8 NIL NIL NIL) (-434 1001334 1001623 1002027 "FSUPFACT" 1002769 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999731 1000020 1000352 "FST" 1001022 T FST (NIL) -8 NIL NIL NIL) (-432 998902 999008 999203 "FSRED" 999613 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 997581 997836 998190 "FSPRMELT" 998617 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994666 995104 995603 "FSPECF" 997144 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976726 985169 985209 "FS" 989057 NIL FS (NIL T) -9 NIL 991346 NIL) (-428 965376 968366 972422 "FS-" 972719 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964890 964944 965121 "FSINT" 965317 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 963217 963883 964186 "FSERIES" 964669 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 962231 962347 962578 "FSCINT" 963097 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 958465 961175 961216 "FSAGG" 961586 NIL FSAGG (NIL T) -9 NIL 961845 NIL) (-423 956227 956828 957624 "FSAGG-" 957719 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 955269 955412 955639 "FSAGG2" 956080 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952924 953203 953757 "FS2UPS" 954987 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 952506 952549 952704 "FS2" 952875 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 951363 951534 951843 "FS2EXPXP" 952331 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950789 950904 951056 "FRUTIL" 951243 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 942244 946284 947642 "FR" 949463 NIL FR (NIL T) -8 NIL NIL NIL) (-416 937319 939962 940002 "FRNAALG" 941398 NIL FRNAALG (NIL T) -9 NIL 942005 NIL) (-415 932997 934068 935343 "FRNAALG-" 936093 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 932635 932678 932805 "FRNAAF2" 932948 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 931042 931489 931784 "FRMOD" 932447 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928821 929425 929742 "FRIDEAL" 930833 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 928016 928103 928392 "FRIDEAL2" 928728 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 927149 927563 927604 "FRETRCT" 927609 NIL FRETRCT (NIL T) -9 NIL 927785 NIL) (-409 926261 926492 926843 "FRETRCT-" 926848 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 923473 924649 924708 "FRAMALG" 925590 NIL FRAMALG (NIL T T) -9 NIL 925882 NIL) (-407 921607 922062 922692 "FRAMALG-" 922915 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 915565 921082 921358 "FRAC" 921363 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 915201 915258 915365 "FRAC2" 915502 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914837 914894 915001 "FR2" 915138 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 909510 912362 912390 "FPS" 913509 T FPS (NIL) -9 NIL 914066 NIL) (-402 908959 909068 909232 "FPS-" 909378 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 906413 908048 908076 "FPC" 908301 T FPC (NIL) -9 NIL 908443 NIL) (-400 906206 906246 906343 "FPC-" 906348 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 905084 905694 905735 "FPATMAB" 905740 NIL FPATMAB (NIL T) -9 NIL 905892 NIL) (-398 902784 903260 903686 "FPARFRAC" 904721 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 898178 898676 899358 "FORTRAN" 902216 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895894 896394 896933 "FORT" 897659 T FORT (NIL) -7 NIL NIL NIL) (-395 893570 894132 894160 "FORTFN" 895220 T FORTFN (NIL) -9 NIL 895844 NIL) (-394 893334 893384 893412 "FORTCAT" 893471 T FORTCAT (NIL) -9 NIL 893533 NIL) (-393 891467 891950 892340 "FORMULA" 892964 T FORMULA (NIL) -8 NIL NIL NIL) (-392 891255 891285 891354 "FORMULA1" 891431 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890778 890830 891003 "FORDER" 891197 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889874 890038 890231 "FOP" 890605 T FOP (NIL) -7 NIL NIL NIL) (-389 888482 889154 889328 "FNLA" 889756 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 887237 887626 887654 "FNCAT" 888114 T FNCAT (NIL) -9 NIL 888374 NIL) (-387 886803 887196 887224 "FNAME" 887229 T FNAME (NIL) -8 NIL NIL NIL) (-386 885466 886395 886423 "FMTC" 886428 T FMTC (NIL) -9 NIL 886464 NIL) (-385 881828 882989 883618 "FMONOID" 884870 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 881047 881570 881719 "FM" 881724 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 878471 879117 879145 "FMFUN" 880289 T FMFUN (NIL) -9 NIL 880997 NIL) (-382 877740 877921 877949 "FMC" 878239 T FMC (NIL) -9 NIL 878421 NIL) (-381 874934 875768 875822 "FMCAT" 877017 NIL FMCAT (NIL T T) -9 NIL 877512 NIL) (-380 873827 874700 874800 "FM1" 874879 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 871601 872017 872511 "FLOATRP" 873378 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 865225 869330 869951 "FLOAT" 871000 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862663 863163 863741 "FLOATCP" 864692 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 861472 862276 862317 "FLINEXP" 862322 NIL FLINEXP (NIL T) -9 NIL 862415 NIL) (-375 860626 860861 861189 "FLINEXP-" 861194 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859702 859846 860070 "FLASORT" 860478 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856919 857761 857813 "FLALG" 859040 NIL FLALG (NIL T T) -9 NIL 859507 NIL) (-372 850703 854405 854446 "FLAGG" 855708 NIL FLAGG (NIL T) -9 NIL 856360 NIL) (-371 849429 849768 850258 "FLAGG-" 850263 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 848471 848614 848841 "FLAGG2" 849282 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 845446 846420 846479 "FINRALG" 847607 NIL FINRALG (NIL T T) -9 NIL 848115 NIL) (-368 844606 844835 845174 "FINRALG-" 845179 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 844012 844225 844253 "FINITE" 844449 T FINITE (NIL) -9 NIL 844556 NIL) (-366 836470 838631 838671 "FINAALG" 842338 NIL FINAALG (NIL T) -9 NIL 843791 NIL) (-365 831811 832852 833996 "FINAALG-" 835375 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 831206 831566 831669 "FILE" 831741 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829890 830202 830256 "FILECAT" 830940 NIL FILECAT (NIL T T) -9 NIL 831156 NIL) (-362 827758 829252 829280 "FIELD" 829320 T FIELD (NIL) -9 NIL 829400 NIL) (-361 826378 826763 827274 "FIELD-" 827279 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 824256 825013 825360 "FGROUP" 826064 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 823346 823510 823730 "FGLMICPK" 824088 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 819213 823271 823328 "FFX" 823333 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818814 818875 819010 "FFSLPE" 819146 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814807 815586 816382 "FFPOLY" 818050 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 814311 814347 814556 "FFPOLY2" 814765 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 810197 814230 814293 "FFP" 814298 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 805630 810108 810172 "FF" 810177 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800791 804973 805163 "FFNBX" 805484 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795765 799926 800184 "FFNBP" 800645 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 790433 795049 795260 "FFNB" 795598 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 789265 789463 789778 "FFINTBAS" 790230 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 785493 787672 787700 "FFIELDC" 788320 T FFIELDC (NIL) -9 NIL 788696 NIL) (-347 784156 784526 785023 "FFIELDC-" 785028 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783726 783771 783895 "FFHOM" 784098 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 781424 781908 782425 "FFF" 783241 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 777077 781166 781267 "FFCGX" 781367 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772744 776809 776916 "FFCGP" 777020 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767962 772471 772579 "FFCG" 772680 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749795 758833 758919 "FFCAT" 764084 NIL FFCAT (NIL T T T) -9 NIL 765535 NIL) (-340 744993 746040 747354 "FFCAT-" 748584 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 744404 744447 744682 "FFCAT2" 744944 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 733616 737376 738596 "FEXPR" 743256 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 732616 733051 733092 "FEVALAB" 733176 NIL FEVALAB (NIL T) -9 NIL 733437 NIL) (-336 731775 731985 732323 "FEVALAB-" 732328 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 730368 731158 731361 "FDIV" 731674 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 727434 728149 728264 "FDIVCAT" 729832 NIL FDIVCAT (NIL T T T T) -9 NIL 730269 NIL) (-333 727196 727223 727393 "FDIVCAT-" 727398 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 726416 726503 726780 "FDIV2" 727103 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 725102 725361 725650 "FCPAK1" 726147 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 724230 724602 724743 "FCOMP" 724993 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707967 711380 714918 "FC" 720712 T FC (NIL) -8 NIL NIL NIL) (-328 700546 704531 704571 "FAXF" 706373 NIL FAXF (NIL T) -9 NIL 707065 NIL) (-327 697825 698480 699305 "FAXF-" 699770 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692925 697201 697377 "FARRAY" 697682 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 688178 690210 690263 "FAMR" 691286 NIL FAMR (NIL T T) -9 NIL 691746 NIL) (-324 687068 687370 687805 "FAMR-" 687810 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 686264 686990 687043 "FAMONOID" 687048 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 684076 684760 684813 "FAMONC" 685754 NIL FAMONC (NIL T T) -9 NIL 686140 NIL) (-321 682768 683830 683967 "FAGROUP" 683972 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 680563 680882 681285 "FACUTIL" 682449 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679662 679847 680069 "FACTFUNC" 680373 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 672067 678913 679125 "EXPUPXS" 679518 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 669550 670090 670676 "EXPRTUBE" 671501 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665744 666336 667073 "EXPRODE" 668889 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 651118 664399 664827 "EXPR" 665348 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 645525 646112 646925 "EXPR2UPS" 650416 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 645161 645218 645325 "EXPR2" 645462 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 636566 644293 644590 "EXPEXPAN" 644998 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 636393 636523 636552 "EXIT" 636557 T EXIT (NIL) -8 NIL NIL NIL) (-310 635900 636117 636208 "EXITAST" 636322 T EXITAST (NIL) -8 NIL NIL NIL) (-309 635527 635589 635702 "EVALCYC" 635832 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 635068 635186 635227 "EVALAB" 635397 NIL EVALAB (NIL T) -9 NIL 635501 NIL) (-307 634549 634671 634892 "EVALAB-" 634897 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 632017 633285 633313 "EUCDOM" 633868 T EUCDOM (NIL) -9 NIL 634218 NIL) (-305 630422 630864 631454 "EUCDOM-" 631459 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617962 620720 623470 "ESTOOLS" 627692 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 617594 617651 617760 "ESTOOLS2" 617899 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 617345 617387 617467 "ESTOOLS1" 617546 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 611250 612978 613006 "ES" 615774 T ES (NIL) -9 NIL 617183 NIL) (-300 606198 607484 609301 "ES-" 609465 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 602573 603333 604113 "ESCONT" 605438 T ESCONT (NIL) -7 NIL NIL NIL) (-298 602318 602350 602432 "ESCONT1" 602535 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601993 602043 602143 "ES2" 602262 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 601623 601681 601790 "ES1" 601929 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600839 600968 601144 "ERROR" 601467 T ERROR (NIL) -7 NIL NIL NIL) (-294 594342 600698 600789 "EQTBL" 600794 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586899 589656 591105 "EQ" 592926 NIL -3310 (NIL T) -8 NIL NIL NIL) (-292 586531 586588 586697 "EQ2" 586836 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581823 582869 583962 "EP" 585470 NIL EP (NIL T) -7 NIL NIL NIL) (-290 580405 580706 581023 "ENV" 581526 T ENV (NIL) -8 NIL NIL NIL) (-289 579584 580104 580132 "ENTIRER" 580137 T ENTIRER (NIL) -9 NIL 580183 NIL) (-288 576086 577539 577909 "EMR" 579383 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 575230 575415 575469 "ELTAGG" 575849 NIL ELTAGG (NIL T T) -9 NIL 576060 NIL) (-286 574949 575011 575152 "ELTAGG-" 575157 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574738 574767 574821 "ELTAB" 574905 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573864 574010 574209 "ELFUTS" 574589 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 573606 573662 573690 "ELEMFUN" 573795 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 573476 573497 573565 "ELEMFUN-" 573570 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 568367 571576 571617 "ELAGG" 572557 NIL ELAGG (NIL T) -9 NIL 573020 NIL) (-280 566652 567086 567749 "ELAGG-" 567754 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 565309 565589 565884 "ELABEXPR" 566377 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 558175 559976 560803 "EFUPXS" 564585 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 551625 553426 554236 "EFULS" 557451 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 549047 549405 549884 "EFSTRUC" 551257 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 538119 539684 541244 "EF" 547562 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 537220 537604 537753 "EAB" 537990 T EAB (NIL) -8 NIL NIL NIL) (-273 536429 537179 537207 "E04UCFA" 537212 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 535638 536388 536416 "E04NAFA" 536421 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534847 535597 535625 "E04MBFA" 535630 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 534056 534806 534834 "E04JAFA" 534839 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 533267 534015 534043 "E04GCFA" 534048 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 532478 533226 533254 "E04FDFA" 533259 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531687 532437 532465 "E04DGFA" 532470 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525865 527212 528576 "E04AGNT" 530343 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 524571 525051 525091 "DVARCAT" 525566 NIL DVARCAT (NIL T) -9 NIL 525765 NIL) (-264 523775 523987 524301 "DVARCAT-" 524306 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516675 523574 523703 "DSMP" 523708 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 511485 512620 513688 "DROPT" 515627 T DROPT (NIL) -8 NIL NIL NIL) (-261 511150 511209 511307 "DROPT1" 511420 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 506265 507391 508528 "DROPT0" 510033 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 504610 504935 505321 "DRAWPT" 505899 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 499197 500120 501199 "DRAW" 503584 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498830 498883 499001 "DRAWHACK" 499138 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 497561 497830 498121 "DRAWCX" 498559 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 497077 497145 497296 "DRAWCURV" 497487 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 487548 489507 491622 "DRAWCFUN" 494982 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 484361 486243 486284 "DQAGG" 486913 NIL DQAGG (NIL T) -9 NIL 487186 NIL) (-252 472640 479339 479422 "DPOLCAT" 481274 NIL DPOLCAT (NIL T T T T) -9 NIL 481819 NIL) (-251 467479 468825 470783 "DPOLCAT-" 470788 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 460634 467340 467438 "DPMO" 467443 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453692 460414 460581 "DPMM" 460586 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 453324 453611 453659 "DOMCTOR" 453664 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452619 452846 452983 "DOMAIN" 453207 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 446370 452254 452406 "DMP" 452520 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445970 446026 446170 "DLP" 446308 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439840 445297 445487 "DLIST" 445812 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436684 438693 438734 "DLAGG" 439284 NIL DLAGG (NIL T) -9 NIL 439514 NIL) (-242 435497 436127 436155 "DIVRING" 436247 T DIVRING (NIL) -9 NIL 436330 NIL) (-241 434734 434924 435224 "DIVRING-" 435229 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432836 433193 433599 "DISPLAY" 434348 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426778 432750 432813 "DIRPROD" 432818 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425626 425829 426094 "DIRPROD2" 426571 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414889 420841 420894 "DIRPCAT" 421304 NIL DIRPCAT (NIL NIL T) -9 NIL 422144 NIL) (-236 412215 412857 413738 "DIRPCAT-" 414075 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 411502 411662 411848 "DIOSP" 412049 T DIOSP (NIL) -7 NIL NIL NIL) (-234 408204 410414 410455 "DIOPS" 410889 NIL DIOPS (NIL T) -9 NIL 411118 NIL) (-233 407753 407867 408058 "DIOPS-" 408063 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406645 407239 407267 "DIFRING" 407454 T DIFRING (NIL) -9 NIL 407564 NIL) (-231 406291 406368 406520 "DIFRING-" 406525 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 404096 405334 405375 "DIFEXT" 405738 NIL DIFEXT (NIL T) -9 NIL 406032 NIL) (-229 402381 402809 403475 "DIFEXT-" 403480 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399703 401913 401954 "DIAGG" 401959 NIL DIAGG (NIL T) -9 NIL 401979 NIL) (-227 399087 399244 399496 "DIAGG-" 399501 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 394552 398046 398323 "DHMATRIX" 398856 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 390164 391073 392083 "DFSFUN" 393562 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 385280 389095 389407 "DFLOAT" 389872 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 383508 383789 384185 "DFINTTLS" 384988 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 380573 381529 381929 "DERHAM" 383174 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 378422 380348 380437 "DEQUEUE" 380517 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377637 377770 377966 "DEGRED" 378284 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 374032 374777 375630 "DEFINTRF" 376865 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 371559 372028 372627 "DEFINTEF" 373551 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370936 371179 371294 "DEFAST" 371464 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364978 370533 370681 "DECIMAL" 370808 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 362490 362948 363454 "DDFACT" 364522 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 362086 362129 362280 "DBLRESP" 362441 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359985 360319 360679 "DBASE" 361853 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 359254 359465 359611 "DATAARY" 359884 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 358387 359213 359241 "D03FAFA" 359246 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 357521 358346 358374 "D03EEFA" 358379 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 355471 355937 356426 "D03AGNT" 357052 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354787 355430 355458 "D02EJFA" 355463 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 354103 354746 354774 "D02CJFA" 354779 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 353419 354062 354090 "D02BHFA" 354095 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352735 353378 353406 "D02BBFA" 353411 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345933 347521 349127 "D02AGNT" 351149 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343702 344224 344770 "D01WGTS" 345407 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342797 343661 343689 "D01TRNS" 343694 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341892 342756 342784 "D01GBFA" 342789 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340987 341851 341879 "D01FCFA" 341884 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 340082 340946 340974 "D01ASFA" 340979 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 339177 340041 340069 "D01AQFA" 340074 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 338272 339136 339164 "D01APFA" 339169 T D01APFA (NIL) -8 NIL NIL NIL) (-196 337367 338231 338259 "D01ANFA" 338264 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 336462 337326 337354 "D01AMFA" 337359 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 335557 336421 336449 "D01ALFA" 336454 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334652 335516 335544 "D01AKFA" 335549 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333747 334611 334639 "D01AJFA" 334644 T D01AJFA (NIL) -8 NIL NIL NIL) (-191 327044 328595 330156 "D01AGNT" 332206 T D01AGNT (NIL) -7 NIL NIL NIL) (-190 326381 326509 326661 "CYCLOTOM" 326912 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-189 323116 323829 324556 "CYCLES" 325674 T CYCLES (NIL) -7 NIL NIL NIL) (-188 322428 322562 322733 "CVMP" 322977 NIL CVMP (NIL T) -7 NIL NIL NIL) (-187 320199 320457 320833 "CTRIGMNP" 322156 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-186 319690 319990 320064 "CTOR" 320145 T CTOR (NIL) -8 NIL NIL NIL) (-185 319226 319421 319522 "CTORKIND" 319609 T CTORKIND (NIL) -8 NIL NIL NIL) (-184 318574 318833 318861 "CTORCAT" 319043 T CTORCAT (NIL) -9 NIL 319156 NIL) (-183 318172 318283 318442 "CTORCAT-" 318447 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-182 317688 317875 317973 "CTORCALL" 318094 T CTORCALL (NIL) -8 NIL NIL NIL) (-181 317062 317161 317314 "CSTTOOLS" 317585 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-180 312861 313518 314276 "CRFP" 316374 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-179 312363 312582 312674 "CRCEAST" 312789 T CRCEAST (NIL) -8 NIL NIL NIL) (-178 311410 311595 311823 "CRAPACK" 312167 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-177 310794 310895 311099 "CPMATCH" 311286 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-176 310519 310547 310653 "CPIMA" 310760 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-175 306883 307555 308273 "COORDSYS" 309854 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-174 306267 306396 306546 "CONTOUR" 306753 T CONTOUR (NIL) -8 NIL NIL NIL) (-173 302193 304270 304762 "CONTFRAC" 305807 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-172 302073 302094 302122 "CONDUIT" 302159 T CONDUIT (NIL) -9 NIL NIL NIL) (-171 301246 301766 301794 "COMRING" 301799 T COMRING (NIL) -9 NIL 301851 NIL) (-170 300327 300604 300788 "COMPPROP" 301082 T COMPPROP (NIL) -8 NIL NIL NIL) (-169 299988 300023 300151 "COMPLPAT" 300286 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-168 290045 299797 299906 "COMPLEX" 299911 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289681 289738 289845 "COMPLEX2" 289982 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-166 289399 289434 289532 "COMPFACT" 289640 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-165 273572 283792 283832 "COMPCAT" 284836 NIL COMPCAT (NIL T) -9 NIL 286221 NIL) (-164 263088 266011 269638 "COMPCAT-" 269994 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-163 262817 262845 262948 "COMMUPC" 263054 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-162 262612 262645 262704 "COMMONOP" 262778 T COMMONOP (NIL) -7 NIL NIL NIL) (-161 262195 262363 262450 "COMM" 262545 T COMM (NIL) -8 NIL NIL NIL) (-160 261799 261999 262074 "COMMAAST" 262140 T COMMAAST (NIL) -8 NIL NIL NIL) (-159 261048 261242 261270 "COMBOPC" 261608 T COMBOPC (NIL) -9 NIL 261783 NIL) (-158 259944 260154 260396 "COMBINAT" 260838 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-157 256142 256715 257355 "COMBF" 259366 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-156 254928 255258 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(-143 235232 235933 236268 "CHAR" 236928 T CHAR (NIL) -8 NIL NIL NIL) (-142 234958 235019 235047 "CFCAT" 235158 T CFCAT (NIL) -9 NIL NIL NIL) (-141 234203 234314 234496 "CDEN" 234842 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-140 230195 233356 233636 "CCLASS" 233943 T CCLASS (NIL) -8 NIL NIL NIL) (-139 229502 229645 229808 "CATEGORY" 230052 T -10 (NIL) -8 NIL NIL NIL) (-138 229134 229421 229469 "CATCTOR" 229474 T CATCTOR (NIL) -8 NIL NIL NIL) (-137 228608 228834 228933 "CATAST" 229055 T CATAST (NIL) -8 NIL NIL NIL) (-136 228111 228329 228421 "CASEAST" 228536 T CASEAST (NIL) -8 NIL NIL NIL) (-135 223163 224140 224893 "CARTEN" 227414 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 222271 222419 222640 "CARTEN2" 223010 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-133 220613 221421 221678 "CARD" 222034 T CARD (NIL) -8 NIL NIL NIL) (-132 220216 220417 220492 "CAPSLAST" 220558 T CAPSLAST (NIL) -8 NIL NIL NIL) (-131 219588 219916 219944 "CACHSET" 220076 T CACHSET (NIL) -9 NIL 220153 NIL) 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\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 59a15a90..cc1eb45f 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,75 +1,72 @@ -(735570 . 3442535949) +(735629 . 3442698066) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |xinit| (-224)) (|:| |xend| (-224)) - (|:| |fn| (-1256 (-315 (-224)))) (|:| |yinit| (-639 (-224))) - (|:| |intvals| (-639 (-224))) (|:| |g| (-315 (-224))) - (|:| |abserr| (-224)) (|:| |relerr| (-224)))) - (-5 *2 (-378)) (-5 *1 (-204))))) -(((*1 *2) - (-12 (-4 *3 (-554)) (-5 *2 (-639 (-683 *3))) (-5 *1 (-43 *3 *4)) - (-4 *4 (-416 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1256 *4)) (-4 *4 (-348)) (-5 *2 (-1164 *4)) - (-5 *1 (-527 *4))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-1005 *3)) (-4 *3 (-1207)) (-4 *3 (-1092)) - (-5 *2 (-112))))) + (-12 (-5 *3 (-947 (-562))) (-5 *2 (-639 *1)) (-4 *1 (-1007)))) + ((*1 *2 *3) + (-12 (-5 *3 (-947 (-406 (-562)))) (-5 *2 (-639 *1)) (-4 *1 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(-12 (-4 *5 (-13 (-610 *2) (-171))) (-5 *2 (-887 *4)) (-5 *1 (-169 *4 *5 *3)) (-4 *4 (-1092)) (-4 *3 (-165 *5)))) @@ -1097,7 +1008,7 @@ ((*1 *1 *2) (-4037 (-12 (-5 *2 (-947 (-562))) (-4 *1 (-1058 *3 *4 *5)) - (-12 (-2236 (-4 *3 (-38 (-406 (-562))))) (-4 *3 (-38 (-562))) + (-12 (-2234 (-4 *3 (-38 (-406 (-562))))) (-4 *3 (-38 (-562))) (-4 *5 (-610 (-1168)))) (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *5 (-845))) (-12 (-5 *2 (-947 (-562))) (-4 *1 (-1058 *3 *4 *5)) @@ -1108,12 +1019,12 @@ (-4 *3 (-38 (-406 (-562)))) (-4 *5 (-610 (-1168))) (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *5 (-845)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-639 *7)) (|:| -1495 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-639 *7)) (|:| -1501 *8))) (-4 *7 (-1058 *4 *5 *6)) (-4 *8 (-1064 *4 *5 *6 *7)) (-4 *4 (-451)) (-4 *5 (-788)) (-4 *6 (-845)) (-5 *2 (-1150)) (-5 *1 (-1062 *4 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-639 *7)) (|:| -1495 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-639 *7)) (|:| -1501 *8))) (-4 *7 (-1058 *4 *5 *6)) (-4 *8 (-1101 *4 *5 *6 *7)) (-4 *4 (-451)) (-4 *5 (-788)) (-4 *6 (-845)) (-5 *2 (-1150)) (-5 *1 (-1137 *4 *5 *6 *7 *8)))) @@ -1145,6 +1056,8 @@ (-4 *4 (-13 (-843) (-306) (-146) (-1017))) (-14 *6 (-639 (-1168))) (-5 *2 (-639 (-775 *4 (-859 *6)))) (-5 *1 (-1282 *4 *5 *6)) (-14 *5 (-639 (-1168)))))) +(((*1 *2 *1) + (-12 (-5 *2 (-639 (-1193 *3))) (-5 *1 (-1193 *3)) (-4 *3 (-1092))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) (-4 *2 (-13 (-429 *3) (-997))))) @@ -1164,56 +1077,61 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) -(((*1 *2 *3 *2) (-12 (-5 *3 (-766)) (-5 *1 (-851 *2)) (-4 *2 (-171)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1164 (-562))) (-5 *1 (-937)) (-5 *3 (-562))))) -(((*1 *2 *3) (-12 (-5 *3 (-639 (-562))) (-5 *2 (-766)) (-5 *1 (-587))))) -(((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-817))))) (((*1 *2 *1 *1) - (|partial| -12 (-4 *1 (-328 *3)) (-4 *3 (-362)) (-4 *3 (-367)) - (-5 *2 (-1164 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-328 *3)) (-4 *3 (-362)) (-4 *3 (-367)) - (-5 *2 (-1164 *3))))) -(((*1 *2 *3 *3) - (-12 (|has| *2 (-6 (-4404 "*"))) (-4 *5 (-372 *2)) (-4 *6 (-372 *2)) - (-4 *2 (-1044)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1232 *2)) - (-4 *4 (-681 *2 *5 *6))))) -(((*1 *1 *1) - (-12 (-5 *1 (-592 *2)) (-4 *2 (-38 (-406 (-562)))) (-4 *2 (-1044))))) + (-12 (-4 *3 (-554)) (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *5 (-845)) + (-5 *2 (-639 *1)) (-4 *1 (-1058 *3 *4 *5))))) +(((*1 *2 *3 *3 *4) + (-12 (-4 *5 (-451)) (-4 *6 (-788)) (-4 *7 (-845)) + (-4 *3 (-1058 *5 *6 *7)) + (-5 *2 (-639 (-2 (|:| |val| *3) (|:| -1501 *4)))) + (-5 *1 (-1100 *5 *6 *7 *3 *4)) (-4 *4 (-1064 *5 *6 *7 *3))))) +(((*1 *2 *3 *2 *4) + (-12 (-5 *3 (-114)) (-5 *4 (-766)) (-4 *5 (-451)) (-4 *5 (-845)) + (-4 *5 (-1033 (-562))) (-4 *5 (-554)) (-5 *1 (-41 *5 *2)) + (-4 *2 (-429 *5)) + (-4 *2 + (-13 (-362) (-301) + (-10 -8 (-15 -4063 ((-1117 *5 (-608 $)) $)) + (-15 -4079 ((-1117 *5 (-608 $)) $)) + (-15 -4053 ($ (-1117 *5 (-608 $)))))))))) 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(-224)))) (-5 *4 (-1086 (-378))) @@ -1268,17 +1186,22 @@ (-12 (-5 *3 (-877 *5)) (-5 *4 (-1084 (-378))) (-4 *5 (-13 (-610 (-535)) (-1092))) (-5 *2 (-1125 (-224))) (-5 *1 (-258 *5))))) -(((*1 *2 *3 *4 *5 *6 *3 *3 *3 *3 *6 *3 *7 *8) - (-12 (-5 *3 (-562)) (-5 *4 (-683 (-224))) (-5 *5 (-112)) - (-5 *6 (-224)) (-5 *7 (-3 (|:| |fn| (-387)) (|:| |fp| (-68 APROD)))) - (-5 *8 (-3 (|:| |fn| (-387)) (|:| |fp| (-73 MSOLVE)))) - (-5 *2 (-1030)) (-5 *1 (-751))))) -(((*1 *2 *1) - (-12 (-4 *1 (-600 *2 *3)) (-4 *3 (-1207)) (-4 *2 (-1092)) - (-4 *2 (-845))))) +(((*1 *1 *1) (-4 *1 (-625))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-626 *3 *2)) + (-4 *2 (-13 (-429 *3) (-997) (-1192)))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 (-938 *3) (-938 *3))) (-5 *1 (-175 *3)) + (-4 *3 (-13 (-362) (-1192) (-997)))))) (((*1 *2 *1) - (-12 (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *5 (-845)) (-5 *2 (-639 *1)) - (-4 *1 (-1058 *3 *4 *5))))) + (-12 (-4 *1 (-322 *3 *4)) (-4 *3 (-1092)) (-4 *4 (-130)) + (-5 *2 (-639 (-2 (|:| |gen| *3) (|:| -3430 *4)))))) + ((*1 *2 *1) + (-12 (-5 *2 (-639 (-2 (|:| -4221 *3) (|:| -3044 *4)))) + (-5 *1 (-730 *3 *4)) (-4 *3 (-1044)) (-4 *4 (-721)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1234 *3 *4)) (-4 *3 (-1044)) (-4 *4 (-787)) + (-5 *2 (-1148 (-2 (|:| |k| *4) (|:| |c| *3))))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) @@ -1295,50 +1218,62 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) -(((*1 *2) (-12 (-5 *2 (-766)) (-5 *1 (-444 *3)) (-4 *3 (-1044))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-1 *5 *5)) (-4 *5 (-1232 *4)) (-4 *4 (-1211)) - (-4 *6 (-1232 (-406 *5))) - (-5 *2 - (-2 (|:| |num| *1) (|:| |den| *5) (|:| |derivden| *5) - (|:| |gd| *5))) - (-4 *1 (-341 *4 *5 *6))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1094 (-1094 *3))) (-5 *1 (-899 *3)) (-4 *3 (-1092))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-639 (-562))) (-5 *1 (-135 *3 *4 *5)) (-14 *3 (-562)) + (-14 *4 (-766)) (-4 *5 (-171))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-639 (-2 (|:| |val| (-639 *8)) (|:| -1495 *9)))) + (-12 (-5 *3 (-639 (-2 (|:| |val| (-639 *8)) (|:| -1501 *9)))) (-5 *4 (-766)) (-4 *8 (-1058 *5 *6 *7)) (-4 *9 (-1064 *5 *6 *7 *8)) (-4 *5 (-451)) (-4 *6 (-788)) (-4 *7 (-845)) (-5 *2 (-1261)) (-5 *1 (-1062 *5 *6 *7 *8 *9)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-639 (-2 (|:| |val| (-639 *8)) (|:| -1495 *9)))) + (-12 (-5 *3 (-639 (-2 (|:| |val| (-639 *8)) (|:| -1501 *9)))) (-5 *4 (-766)) (-4 *8 (-1058 *5 *6 *7)) (-4 *9 (-1101 *5 *6 *7 *8)) (-4 *5 (-451)) (-4 *6 (-788)) (-4 *7 (-845)) (-5 *2 (-1261)) (-5 *1 (-1137 *5 *6 *7 *8 *9))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1126 *3)) (-4 *3 (-1044)) - (-5 *2 (-639 (-639 (-639 (-766)))))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1150)) (-5 *2 (-1261)) (-5 *1 (-1257)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-1150)) (-5 *2 (-1261)) (-5 *1 (-1258))))) -(((*1 *2 *3 *4 *3 *3 *3 *3 *4 *3) - (-12 (-5 *3 (-562)) (-5 *4 (-683 (-168 (-224)))) (-5 *2 (-1030)) - (-5 *1 (-751))))) -(((*1 *2 *1) (-12 (-5 *2 (-817)) (-5 *1 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*1) (|:| -1441 *1))) (-4 *1 (-847 *3)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-99 *5)) (-4 *5 (-362)) (-4 *5 (-1044)) + (-5 *2 (-2 (|:| -3380 *3) (|:| -1441 *3))) (-5 *1 (-848 *5 *3)) + (-4 *3 (-847 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1164 *5)) (-4 *5 (-362)) (-5 *2 (-639 *6)) + (-5 *1 (-531 *5 *6 *4)) (-4 *6 (-362)) (-4 *4 (-13 (-362) (-843)))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1005 *3)) (-4 *3 (-1207)) (-4 *3 (-1092)) + (-5 *2 (-112))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-562)) (-5 *4 (-417 *2)) (-4 *2 (-944 *7 *5 *6)) + (-5 *1 (-737 *5 *6 *7 *2)) (-4 *5 (-788)) (-4 *6 (-845)) + (-4 *7 (-306))))) +(((*1 *2 *3) + (|partial| -12 + (-5 *3 + (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) + (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) + (|:| |relerr| (-224)))) + (-5 *2 (-2 (|:| -2429 (-114)) (|:| |w| (-224)))) (-5 *1 (-203))))) +(((*1 *2) (-12 (-5 *2 (-916)) (-5 *1 (-1259)))) + ((*1 *2 *2) (-12 (-5 *2 (-916)) (-5 *1 (-1259))))) (((*1 *1 *2) (-12 (-5 *2 (-1150)) (-5 *1 (-143)))) ((*1 *1 *2) (-12 (-5 *2 (-766)) (-5 *1 (-143))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1150)) (-5 *2 (-562)) (-5 *1 (-1189 *4)) - (-4 *4 (-1044))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) @@ -1355,27 +1290,26 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) -(((*1 *2 *2 *3 *2) - (-12 (-5 *3 (-766)) (-4 *4 (-348)) (-5 *1 (-215 *4 *2)) - (-4 *2 (-1232 *4))))) -(((*1 *2 *3) (-12 (-5 *3 (-378)) (-5 *2 (-1150)) (-5 *1 (-304))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-143))))) -(((*1 *2 *2) (-12 (-5 *2 (-224)) (-5 *1 (-256))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-237 *3 *2)) (-4 *2 (-1207)) (-4 *2 (-1044)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-766)) (-5 *1 (-857)))) - ((*1 *1 *1) (-5 *1 (-857))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-938 (-224))) (-5 *2 (-224)) (-5 *1 (-1203)))) - ((*1 *2 *1 *1) - (-12 (-4 *1 (-1254 *2)) (-4 *2 (-1207)) (-4 *2 (-1044))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *3 (-1 *6 *6)) (-4 *6 (-1232 *5)) - (-4 *5 (-13 (-27) (-429 *4))) - (-4 *4 (-13 (-845) (-554) (-1033 (-562)))) - (-4 *7 (-1232 (-406 *6))) (-5 *1 (-550 *4 *5 *6 *7 *2)) - (-4 *2 (-341 *5 *6 *7))))) -(((*1 *2 *3) (-12 (-5 *3 (-1150)) (-5 *2 (-52)) (-5 *1 (-1185))))) +(((*1 *1 *1) (-12 (-5 *1 (-887 *2)) (-4 *2 (-1092))))) +(((*1 *2) (-12 (-5 *2 (-1261)) (-5 *1 (-97))))) +(((*1 *2 *3 *3 *4 *5) + (-12 (-5 *3 (-639 (-947 *6))) (-5 *4 (-639 (-1168))) (-4 *6 (-451)) + (-5 *2 (-639 (-639 *7))) (-5 *1 (-537 *6 *7 *5)) (-4 *7 (-362)) + (-4 *5 (-13 (-362) (-843)))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) + (-4 *2 (-13 (-429 *3) (-997)))))) +(((*1 *2 *3) + (|partial| -12 (-5 *2 (-562)) (-5 *1 (-567 *3)) (-4 *3 (-1033 *2))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1200 *3 *4 *5 *6)) (-4 *3 (-554)) (-4 *4 (-788)) + (-4 *5 (-845)) (-4 *6 (-1058 *3 *4 *5)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1200 *4 *5 *6 *3)) (-4 *4 (-554)) (-4 *5 (-788)) + (-4 *6 (-845)) (-4 *3 (-1058 *4 *5 *6)) (-5 *2 (-112))))) +(((*1 *1 *2) + (-12 (-5 *2 (-639 (-916))) (-5 *1 (-1093 *3 *4)) (-14 *3 (-916)) + (-14 *4 (-916))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) @@ -1392,35 +1326,98 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-562)) (-4 *1 (-322 *4 *2)) (-4 *4 (-1092)) - (-4 *2 (-130))))) -(((*1 *2 *1) (-12 (-4 *1 (-1126 *3)) (-4 *3 (-1044)) (-5 *2 (-766))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-608 *2)) (-4 *2 (-13 (-27) (-1192) (-429 *4))) - (-4 *4 (-13 (-554) (-845) (-1033 (-562)) (-635 (-562)))) - (-5 *1 (-276 *4 *2))))) -(((*1 *2 *1) - (-12 (-4 *1 (-971 *3 *4 *5 *6)) (-4 *3 (-1044)) (-4 *4 (-788)) - (-4 *5 (-845)) (-4 *6 (-1058 *3 *4 *5)) (-5 *2 (-112))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1150)) (-5 *2 (-112)) (-5 *1 (-114))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-1164 *3)) (-4 *3 (-348)) (-5 *1 (-356 *3))))) -(((*1 *1) (-5 *1 (-140)))) -(((*1 *2 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(-1090 *2)) (-4 *2 (-1092))))) +(((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-1 (-112) *9)) (-5 *5 (-1 (-112) *9 *9)) + (-4 *9 (-1058 *6 *7 *8)) (-4 *6 (-554)) (-4 *7 (-788)) + (-4 *8 (-845)) (-5 *2 (-2 (|:| |bas| *1) (|:| -2774 (-639 *9)))) + (-5 *3 (-639 *9)) (-4 *1 (-1200 *6 *7 *8 *9)))) + ((*1 *2 *3 *4) + (|partial| -12 (-5 *4 (-1 (-112) *8 *8)) (-4 *8 (-1058 *5 *6 *7)) + (-4 *5 (-554)) (-4 *6 (-788)) (-4 *7 (-845)) + (-5 *2 (-2 (|:| |bas| *1) (|:| -2774 (-639 *8)))) + (-5 *3 (-639 *8)) (-4 *1 (-1200 *5 *6 *7 *8))))) +(((*1 *2 *3) + (-12 (-5 *3 (-315 (-378))) (-5 *2 (-315 (-224))) (-5 *1 (-304))))) +(((*1 *1 *1 *1) (-4 *1 (-962)))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-224))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) @@ -1441,6 +1438,8 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) +(((*1 *1) (-5 *1 (-818)))) +(((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-817))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-639 *8)) (-5 *4 (-135 *5 *6 *7)) (-14 *5 (-562)) (-14 *6 (-766)) (-4 *7 (-171)) (-4 *8 (-171)) @@ -1450,55 +1449,19 @@ (-4 *8 (-1044)) (-4 *2 (-944 *9 *7 *5)) (-5 *1 (-723 *5 *6 *7 *8 *9 *4 *2)) (-4 *7 (-788)) (-4 *4 (-944 *8 *6 *5))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) - (|:| -1590 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) - (|:| |relerr| (-224)))) - (-5 *2 (-1148 (-224))) (-5 *1 (-191)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-315 (-224))) (-5 *4 (-639 (-1168))) - (-5 *5 (-1086 (-838 (-224)))) (-5 *2 (-1148 (-224))) (-5 *1 (-299)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1256 (-315 (-224)))) (-5 *4 (-639 (-1168))) - (-5 *5 (-1086 (-838 (-224)))) (-5 *2 (-1148 (-224))) (-5 *1 (-299))))) -(((*1 *2 *3) - (-12 (-5 *2 (-112)) (-5 *1 (-120 *3)) (-4 *3 (-1232 (-562))))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-120 *3)) (-4 *3 (-1232 (-562)))))) -(((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5) - (-12 (-5 *3 (-916)) (-5 *4 (-224)) (-5 *5 (-562)) (-5 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*1) - (-12 (-5 *2 (-639 (-1156 *3 *4))) (-5 *1 (-1156 *3 *4)) - (-14 *3 (-916)) (-4 *4 (-1044)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-451)) (-4 *3 (-1044)) - (-5 *2 (-2 (|:| |primePart| *1) (|:| |commonPart| *1))) - (-4 *1 (-1232 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1 (-112) *2)) (-4 *2 (-131)) (-5 *1 (-1076 *2)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1 (-562) *2 *2)) (-4 *2 (-131)) (-5 *1 (-1076 *2))))) + (-12 (-4 *1 (-1200 *3 *4 *5 *6)) (-4 *3 (-554)) (-4 *4 (-788)) + (-4 *5 (-845)) (-4 *6 (-1058 *3 *4 *5)) (-4 *5 (-367)) + (-5 *2 (-766))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-788)) (-4 *4 (-845)) (-4 *6 (-306)) (-5 *2 (-417 *3)) + (-5 *1 (-737 *5 *4 *6 *3)) (-4 *3 (-944 *6 *5 *4))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 (-224) (-224))) (-5 *4 (-1086 (-378))) (-5 *5 (-639 (-262))) (-5 *2 (-1257)) (-5 *1 (-254)))) @@ -1629,8 +1592,8 @@ (-12 (-14 *3 (-639 (-1168))) (-4 *4 (-171)) (-4 *6 (-237 (-3492 *3) (-766))) (-14 *7 - (-1 (-112) (-2 (|:| -2466 *5) (|:| -1960 *6)) - (-2 (|:| -2466 *5) (|:| -1960 *6)))) + (-1 (-112) (-2 (|:| -2464 *5) (|:| -1300 *6)) + (-2 (|:| -2464 *5) (|:| -1300 *6)))) (-5 *1 (-460 *3 *4 *5 *6 *7 *2)) (-4 *5 (-845)) (-4 *2 (-944 *4 *6 (-859 *3))))) ((*1 *1 *1 *2) @@ -1709,7 +1672,8 @@ (-12 (-4 *1 (-1273 *3 *2)) (-4 *3 (-845)) (-4 *2 (-1044)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-1279 *2 *3)) (-4 *2 (-1044)) (-4 *3 (-841))))) -(((*1 *2 *1) (-12 (-4 *1 (-366 *2)) (-4 *2 (-171))))) +(((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-315 *3)) (-4 *3 (-554)) (-4 *3 (-845))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1044)) (-4 *4 (-787)))) @@ -1817,9 +1781,9 @@ (-4 *6 (-362)) (-5 *2 (-583 *6)) (-5 *1 (-582 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -3860 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -2929 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-362)) (-4 *6 (-362)) - (-5 *2 (-2 (|:| -3860 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -2929 *6) (|:| |coeff| *6))) (-5 *1 (-582 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -1938,7 +1902,7 @@ (-4 *8 (-1044)) (-4 *6 (-788)) (-4 *2 (-13 (-1092) - (-10 -8 (-15 -1835 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-766)))))) + (-10 -8 (-15 -1836 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-766)))))) (-5 *1 (-946 *6 *7 *8 *5 *2)) (-4 *5 (-944 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-953 *5)) (-4 *5 (-1207)) @@ -1952,7 +1916,7 @@ (-4 *6 (-13 (-845) (-10 -8 (-15 -4208 ((-1168) $)) - (-15 -2444 ((-3 $ "failed") (-1168)))))) + (-15 -2443 ((-3 $ "failed") (-1168)))))) (-5 *1 (-979 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-554)) (-4 *6 (-554)) @@ -2059,63 +2023,46 @@ (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) (((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-639 (-1164 *5))) (-5 *3 (-1164 *5)) - (-4 *5 (-165 *4)) (-4 *4 (-544)) (-5 *1 (-148 *4 *5)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-639 *3)) (-4 *3 (-1232 *5)) - (-4 *5 (-1232 *4)) (-4 *4 (-348)) (-5 *1 (-357 *4 *5 *3)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-639 (-1164 (-562)))) (-5 *3 (-1164 (-562))) - (-5 *1 (-570)))) + (-12 (-5 *2 (-683 *4)) (-5 *3 (-916)) (-4 *4 (-1044)) + (-5 *1 (-1023 *4)))) ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-639 (-1164 *1))) (-5 *3 (-1164 *1)) - (-4 *1 (-904))))) + (-12 (-5 *2 (-639 (-683 *4))) (-5 *3 (-916)) (-4 *4 (-1044)) + (-5 *1 (-1023 *4))))) (((*1 *2 *3) - (|partial| -12 (-5 *3 (-916)) - (-5 *2 (-1256 (-639 (-2 (|:| -2534 *4) (|:| -2466 (-1112)))))) - (-5 *1 (-345 *4)) (-4 *4 (-348))))) + (-12 (-5 *3 (-1168)) (-5 *2 (-1 *6 *5)) (-5 *1 (-701 *4 *5 *6)) + (-4 *4 (-610 (-535))) (-4 *5 (-1207)) (-4 *6 (-1207))))) (((*1 *2 *1) (-12 (-5 *2 (-639 *5)) (-5 *1 (-135 *3 *4 *5)) (-14 *3 (-562)) (-14 *4 (-766)) (-4 *5 (-171))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-34)) (-5 *3 (-766)) (-5 *2 (-112)))) + ((*1 *2 *3 *3) + (|partial| -12 (-5 *2 (-112)) (-5 *1 (-1208 *3)) (-4 *3 (-1092)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-1 (-112) *3 *3)) (-4 *3 (-1092)) (-5 *2 (-112)) + (-5 *1 (-1208 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-224)) (-5 *4 (-562)) (-5 *2 (-1030)) (-5 *1 (-753))))) +(((*1 *1 *1) (-4 *1 (-1136)))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-845) (-451))) (-5 *1 (-1198 *3 *2)) - (-4 *2 (-13 (-429 *3) (-1192)))))) -(((*1 *1 *1 *2) - (|partial| -12 (-5 *2 (-916)) (-5 *1 (-1093 *3 *4)) (-14 *3 *2) - (-14 *4 *2)))) -(((*1 *1 *2 *3 *3 *3 *3) - (-12 (-5 *2 (-1 (-938 (-224)) (-224))) (-5 *3 (-1086 (-224))) - (-5 *1 (-921)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1 (-938 (-224)) (-224))) (-5 *3 (-1086 (-224))) - (-5 *1 (-921)))) - ((*1 *1 *2 *3 *3 *3) - (-12 (-5 *2 (-1 (-938 (-224)) (-224))) (-5 *3 (-1086 (-224))) - (-5 *1 (-922)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1 (-938 (-224)) (-224))) (-5 *3 (-1086 (-224))) - (-5 *1 (-922))))) -(((*1 *2 *3) (-12 (-5 *3 (-766)) (-5 *2 (-378)) (-5 *1 (-1035))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *5 *5)) (-4 *5 (-1247 *4)) - (-4 *4 (-38 (-406 (-562)))) (-5 *2 (-1 (-1148 *4) (-1148 *4))) - (-5 *1 (-1249 *4 *5))))) -(((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4403)) (-4 *1 (-243 *2)) (-4 *2 (-1207)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-281 *2)) (-4 *2 (-1207)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-281 *2)) (-4 *2 (-1207)))) + (-12 (-4 *3 (-348)) (-4 *4 (-328 *3)) (-4 *5 (-1232 *4)) + (-5 *1 (-772 *3 *4 *5 *2 *6)) (-4 *2 (-1232 *5)) (-14 *6 (-916)))) ((*1 *1 *1 *2) - (-12 (|has| *1 (-6 -4403)) (-4 *1 (-1244 *2)) (-4 *2 (-1207)))) - ((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4403)) (-4 *1 (-1244 *2)) (-4 *2 (-1207))))) + (-12 (-5 *2 (-766)) (-4 *1 (-1275 *3)) (-4 *3 (-362)) (-4 *3 (-367)))) + ((*1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-362)) (-4 *2 (-367))))) +(((*1 *1 *2) (-12 (-5 *2 (-639 *3)) (-4 *3 (-1092)) (-5 *1 (-900 *3))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5) + (-12 (-5 *3 (-1 (-378) (-378))) (-5 *4 (-378)) + (-5 *2 + (-2 (|:| -2533 *4) (|:| -3964 *4) (|:| |totalpts| (-562)) + (|:| |success| (-112)))) + (-5 *1 (-784)) (-5 *5 (-562))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-114)) (-5 *3 (-639 *1)) (-4 *1 (-301)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-301)) (-5 *2 (-114)))) ((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-608 *3)) (-4 *3 (-845)))) ((*1 *1 *2 *3 *4) (-12 (-5 *2 (-114)) (-5 *3 (-639 *5)) (-5 *4 (-766)) (-4 *5 (-845)) (-5 *1 (-608 *5))))) -(((*1 *2 *2) (-12 (-5 *2 (-916)) (-5 *1 (-356 *3)) (-4 *3 (-348))))) -(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1208 *3)) (-4 *3 (-1092))))) +(((*1 *2 *1) (-12 (-4 *1 (-388)) (-5 *2 (-112))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) @@ -2135,39 +2082,21 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) +(((*1 *1 *2) (-12 (-5 *2 (-639 (-857))) (-5 *1 (-857)))) + ((*1 *1 *1) (-5 *1 (-857)))) (((*1 *1 *1) (-4 *1 (-544)))) +(((*1 *1 *2) + (-12 (-5 *2 (-315 *3)) (-4 *3 (-13 (-1044) (-845))) + (-5 *1 (-222 *3 *4)) (-14 *4 (-639 (-1168)))))) +(((*1 *1 *2) (-12 (-5 *2 (-869)) (-5 *1 (-262)))) + ((*1 *1 *2) (-12 (-5 *2 (-378)) (-5 *1 (-262))))) (((*1 *2 *3) - (-12 (-5 *3 (-1256 *1)) (-4 *1 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(-901 *5 *6 *7 *8)) (-5 *4 (-1164 *8)))) - ((*1 *2 *3) - (-12 (-4 *4 (-904)) (-4 *5 (-1232 *4)) (-5 *2 (-417 (-1164 *5))) - (-5 *1 (-902 *4 *5)) (-5 *3 (-1164 *5))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-362)) (-5 *1 (-761 *2 *3)) (-4 *2 (-703 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-847 *2)) (-4 *2 (-1044)) (-4 *2 (-362))))) -(((*1 *1 *2) (-12 (-5 *2 (-1112)) (-5 *1 (-329))))) + (-12 (-4 *4 (-451)) (-4 *5 (-788)) (-4 *6 (-845)) (-5 *2 (-766)) + (-5 *1 (-448 *4 *5 *6 *3)) (-4 *3 (-944 *4 *5 *6))))) +(((*1 *2 *3) + (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-562))) (-5 *1 (-1042))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-528))))) +(((*1 *1 *2) (-12 (-5 *2 (-639 *3)) (-4 *3 (-1207)) (-4 *1 (-107 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) (-4 *2 (-13 (-429 *3) (-997))))) @@ -2184,46 +2113,52 @@ (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3)))) ((*1 *1 *1) (-4 *1 (-1195)))) -(((*1 *2 *3 *3 *4) - (-12 (-4 *5 (-451)) (-4 *6 (-788)) (-4 *7 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(-845)) (-5 *2 (-112)) (-5 *1 (-972 *5 *6 *7 *8))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-971 *4 *5 *6 *3)) (-4 *4 (-1044)) (-4 *5 (-788)) + (-4 *6 (-845)) (-4 *3 (-1058 *4 *5 *6)) (-4 *4 (-554)) + (-5 *2 (-2 (|:| |num| *3) (|:| |den| *4)))))) +(((*1 *1) (-5 *1 (-557)))) +(((*1 *2 *3) + (-12 (-5 *3 (-639 *4)) (-4 *4 (-1092)) (-5 *2 (-1261)) + (-5 *1 (-1208 *4)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-639 *4)) (-4 *4 (-1092)) (-5 *2 (-1261)) + (-5 *1 (-1208 *4))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) (-4 *2 (-13 (-429 *3) (-997))))) @@ -2240,29 +2175,35 @@ (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3)))) ((*1 *1 *1) (-4 *1 (-1195)))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-562)) (-5 *1 (-690 *2)) (-4 *2 (-1232 *3))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-608 *4)) (-4 *4 (-845)) (-4 *2 (-845)) - (-5 *1 (-607 *2 *4))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) - (-4 *2 (-13 (-429 *3) (-997)))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *2 (-1256 (-562))) (-5 *3 (-562)) (-5 *1 (-1102)))) - ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-1256 (-562))) (-5 *3 (-639 (-562))) (-5 *4 (-562)) - (-5 *1 (-1102))))) -(((*1 *2) - (-12 (-4 *4 (-171)) (-5 *2 (-112)) (-5 *1 (-365 *3 *4)) - (-4 *3 (-366 *4)))) - ((*1 *2) (-12 (-4 *1 (-366 *3)) (-4 *3 (-171)) (-5 *2 (-112))))) +(((*1 *2 *1) + (-12 (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *5 (-845)) (-5 *2 (-639 *1)) + (-4 *1 (-1058 *3 *4 *5))))) +(((*1 *1 *2) (-12 (-5 *2 (-156)) (-5 *1 (-869))))) +(((*1 *1 *2) + (|partial| -12 (-5 *2 (-814 *3)) (-4 *3 (-845)) (-5 *1 (-666 *3))))) +(((*1 *1) (-5 *1 (-140)))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-112)) (-4 *5 (-13 (-362) (-843))) + (-5 *2 (-639 (-2 (|:| -2656 (-639 *3)) (|:| -3964 *5)))) + (-5 *1 (-180 *5 *3)) (-4 *3 (-1232 (-168 *5))))) + ((*1 *2 *3 *3) + (-12 (-4 *4 (-13 (-362) (-843))) + (-5 *2 (-639 (-2 (|:| -2656 (-639 *3)) (|:| -3964 *4)))) + (-5 *1 (-180 *4 *3)) (-4 *3 (-1232 (-168 *4)))))) +(((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-817))))) (((*1 *2) (-12 (-5 *2 (-828 (-562))) (-5 *1 (-533)))) ((*1 *1) (-12 (-5 *1 (-828 *2)) (-4 *2 (-1092))))) -(((*1 *1 *2 *2) (-12 (-4 *1 (-552 *2)) (-4 *2 (-13 (-403) (-1192)))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-133))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-224)) (-5 *4 (-562)) (-5 *2 (-1030)) (-5 *1 (-753))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-869)) (-5 *3 (-639 (-262))) (-5 *1 (-260))))) +(((*1 *1 *1) (-12 (-5 *1 (-173 *2)) (-4 *2 (-306))))) +(((*1 *2 *3 *4 *4 *4) + (-12 (-5 *3 (-639 *8)) (-5 *4 (-112)) (-4 *8 (-1058 *5 *6 *7)) + (-4 *5 (-451)) (-4 *6 (-788)) (-4 *7 (-845)) + (-5 *2 (-639 (-1022 *5 *6 *7 *8))) (-5 *1 (-1022 *5 *6 *7 *8)))) + ((*1 *2 *3 *4 *4 *4) + (-12 (-5 *3 (-639 *8)) (-5 *4 (-112)) (-4 *8 (-1058 *5 *6 *7)) + (-4 *5 (-451)) (-4 *6 (-788)) (-4 *7 (-845)) + (-5 *2 (-639 (-1138 *5 *6 *7 *8))) (-5 *1 (-1138 *5 *6 *7 *8))))) (((*1 *1 *2) (-12 (-5 *2 (-1112)) (-5 *1 (-329))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) @@ -2280,35 +2221,32 @@ (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3)))) ((*1 *1 *1) (-4 *1 (-1195)))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1207)) (-5 *1 (-1124 *4 *2)) - (-4 *2 (-13 (-600 (-562) *4) (-10 -7 (-6 -4402) (-6 -4403)))))) - ((*1 *2 *2) - (-12 (-4 *3 (-845)) (-4 *3 (-1207)) (-5 *1 (-1124 *3 *2)) - (-4 *2 (-13 (-600 (-562) *3) (-10 -7 (-6 -4402) (-6 -4403))))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-224)) (-5 *4 (-562)) (-5 *2 (-1030)) (-5 *1 (-753))))) -(((*1 *1 *2 *3) - (-12 (-5 *1 (-643 *2 *3 *4)) (-4 *2 (-1092)) (-4 *3 (-23)) - (-14 *4 *3)))) -(((*1 *2 *3) - (-12 (-14 *4 (-639 (-1168))) (-14 *5 (-766)) - (-5 *2 - (-639 - (-503 (-406 (-562)) (-239 *5 (-766)) (-859 *4) - (-246 *4 (-406 (-562)))))) - (-5 *1 (-504 *4 *5)) - (-5 *3 - (-503 (-406 (-562)) (-239 *5 (-766)) (-859 *4) - (-246 *4 (-406 (-562)))))))) -(((*1 *1 *1) (-4 *1 (-1053)))) -(((*1 *2 *1 *1 *1) - (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1))) - (-4 *1 (-306)))) - ((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -3148 *1))) - (-4 *1 (-306))))) -(((*1 *2 *1) (-12 (-5 *2 (-1150)) (-5 *1 (-1188))))) +(((*1 *2 *3) (-12 (-5 *3 (-938 *2)) (-5 *1 (-977 *2)) (-4 *2 (-1044))))) +(((*1 *2 *3) (-12 (-5 *3 (-857)) (-5 *2 (-1150)) (-5 *1 (-705))))) +(((*1 *2 *2 *3 *4) + (|partial| -12 + (-5 *3 + (-1 (-3 (-2 (|:| -2929 *4) (|:| |coeff| *4)) "failed") *4)) + (-4 *4 (-362)) (-5 *1 (-572 *4 *2)) (-4 *2 (-1232 *4))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) + (-4 *2 (-13 (-429 *3) (-997)))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-372 *2)) (-4 *2 (-1207)) (-4 *2 (-845)))) + ((*1 *1 *2 *1 *1) + (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-372 *3)) (-4 *3 (-1207)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-963 *2)) (-4 *2 (-845)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-1126 *2)) (-4 *2 (-1044)))) + ((*1 *1 *2) + (-12 (-5 *2 (-639 *1)) (-4 *1 (-1126 *3)) (-4 *3 (-1044)))) + ((*1 *1 *2) + (-12 (-5 *2 (-639 (-1156 *3 *4))) (-5 *1 (-1156 *3 *4)) + (-14 *3 (-916)) (-4 *4 (-1044)))) + ((*1 *1 *1 *1) + (-12 (-5 *1 (-1156 *2 *3)) (-14 *2 (-916)) (-4 *3 (-1044))))) +(((*1 *2 *1) (-12 (-4 *1 (-554)) (-5 *2 (-112))))) +(((*1 *1 *1) + (|partial| -12 (-5 *1 (-1133 *2 *3)) (-4 *2 (-13 (-1092) (-34))) + (-4 *3 (-13 (-1092) (-34)))))) (((*1 *2) (-12 (-4 *2 (-13 (-429 *3) (-997))) (-5 *1 (-275 *3 *2)) (-4 *3 (-13 (-845) (-554))))) @@ -2316,12 +2254,9 @@ (-12 (-5 *1 (-338 *2 *3 *4)) (-14 *2 (-639 (-1168))) (-14 *3 (-639 (-1168))) (-4 *4 (-386)))) ((*1 *1) (-5 *1 (-476))) ((*1 *1) (-4 *1 (-1192)))) -(((*1 *2 *3 *4 *5 *5) - (-12 (-5 *5 (-766)) (-4 *6 (-1092)) (-4 *7 (-895 *6)) - (-5 *2 (-683 *7)) (-5 *1 (-686 *6 *7 *3 *4)) (-4 *3 (-372 *7)) - (-4 *4 (-13 (-372 *6) (-10 -7 (-6 -4402))))))) (((*1 *2 *1) - (-12 (-4 *1 (-1239 *3 *2)) (-4 *3 (-1044)) (-4 *2 (-1216 *3))))) + (-12 (-5 *2 (-639 (-2 (|:| |integrand| *3) (|:| |intvar| *3)))) + (-5 *1 (-583 *3)) (-4 *3 (-362))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) (-4 *2 (-13 (-429 *3) (-997))))) @@ -2341,65 +2276,48 @@ (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3)))) ((*1 *1 *1) (-4 *1 (-1195)))) -(((*1 *2 *3) - (-12 (-4 *4 (-554)) (-4 *5 (-987 *4)) - (-5 *2 (-2 (|:| |num| *3) (|:| |den| *4))) (-5 *1 (-141 *4 *5 *3)) - (-4 *3 (-372 *5)))) - ((*1 *2 *3) - (-12 (-4 *4 (-554)) (-4 *5 (-987 *4)) - (-5 *2 (-2 (|:| |num| *6) (|:| |den| *4))) - (-5 *1 (-502 *4 *5 *6 *3)) (-4 *6 (-372 *4)) (-4 *3 (-372 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-683 *5)) (-4 *5 (-987 *4)) (-4 *4 (-554)) - (-5 *2 (-2 (|:| |num| (-683 *4)) (|:| |den| *4))) - (-5 *1 (-687 *4 *5)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-13 (-362) (-146) (-1033 (-406 (-562))))) - (-4 *6 (-1232 *5)) - (-5 *2 (-2 (|:| -3342 *7) (|:| |rh| (-639 (-406 *6))))) - (-5 *1 (-802 *5 *6 *7 *3)) (-5 *4 (-639 (-406 *6))) - (-4 *7 (-650 *6)) (-4 *3 (-650 (-406 *6))))) - ((*1 *2 *3) - (-12 (-4 *4 (-554)) (-4 *5 (-987 *4)) - (-5 *2 (-2 (|:| |num| *3) (|:| |den| *4))) (-5 *1 (-1225 *4 *5 *3)) - (-4 *3 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+(((*1 *2 *3 *4 *4 *5) + (-12 (-5 *4 (-608 *3)) (-5 *5 (-1 (-1164 *3) (-1164 *3))) + (-4 *3 (-13 (-27) (-429 *6))) (-4 *6 (-13 (-845) (-554))) + (-5 *2 (-583 *3)) (-5 *1 (-549 *6 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) (-4 *2 (-13 (-429 *3) (-997))))) @@ -2420,47 +2338,23 @@ (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3)))) ((*1 *1 *1) (-4 *1 (-1195)))) -(((*1 *2 *2) - (-12 (-5 *2 (-1148 *3)) (-4 *3 (-1044)) (-5 *1 (-1152 *3))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-639 *6)) (-4 *6 (-1058 *3 *4 *5)) (-4 *3 (-554)) - (-4 *4 (-788)) (-4 *5 (-845)) (-5 *1 (-972 *3 *4 *5 *6)))) - ((*1 *2 *2 *2 *3) - (-12 (-5 *2 (-639 *7)) (-5 *3 (-112)) (-4 *7 (-1058 *4 *5 *6)) - (-4 *4 (-554)) (-4 *5 (-788)) (-4 *6 (-845)) +(((*1 *2 *3) + (-12 (-5 *3 (-639 *7)) (-4 *7 (-1058 *4 *5 *6)) (-4 *4 (-554)) + (-4 *5 (-788)) (-4 *6 (-845)) (-5 *2 (-112)) (-5 *1 (-972 *4 *5 *6 *7))))) +(((*1 *1 *1 *1) (-5 *1 (-857)))) (((*1 *2 *1) (-12 (-5 *2 (-1206)) (-5 *1 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*2 *3) - (-12 (-5 *2 (-639 (-639 (-562)))) (-5 *1 (-966)) - (-5 *3 (-639 (-562)))))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-224)) (-5 *4 (-562)) (-5 *2 (-1030)) (-5 *1 (-753))))) (((*1 *2 *3) - (-12 (-5 *3 (-639 (-2 (|:| |den| (-562)) (|:| |gcdnum| (-562))))) - (-4 *4 (-1232 (-406 *2))) (-5 *2 (-562)) (-5 *1 (-908 *4 *5)) - (-4 *5 (-1232 (-406 *4)))))) + (-12 (-5 *3 (-639 (-480 *4 *5))) (-14 *4 (-639 (-1168))) + (-4 *5 (-451)) (-5 *2 (-639 (-246 *4 *5))) (-5 *1 (-627 *4 *5))))) +(((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-494))))) +(((*1 *2 *1) (-12 (-5 *2 (-562)) (-5 *1 (-966))))) (((*1 *2 *1) (-12 (-5 *2 (-1117 (-562) (-608 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-987 *2)) (-4 *4 (-1232 *3)) (-4 *2 (-306)) @@ -2476,9 +2370,19 @@ (-12 (-4 *4 (-171)) (-4 *2 (|SubsetCategory| (-721) *4)) (-5 *1 (-656 *3 *4 *2)) (-4 *3 (-712 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-987 *2)) (-4 *2 (-554))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) + (-12 (-5 *3 (-1150)) (-5 *4 (-562)) (-5 *5 (-683 (-168 (-224)))) + (-5 *2 (-1030)) (-5 *1 (-749))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-451)) (-4 *3 (-788)) (-4 *5 (-845)) (-5 *2 (-112)) - (-5 *1 (-448 *4 *3 *5 *6)) (-4 *6 (-944 *4 *3 *5))))) + (-12 (-5 *3 (-639 *7)) (-4 *7 (-1058 *4 *5 *6)) (-4 *4 (-451)) + (-4 *5 (-788)) (-4 *6 (-845)) (-5 *2 (-112)) + (-5 *1 (-983 *4 *5 *6 *7 *8)) (-4 *8 (-1064 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-639 *7)) (-4 *7 (-1058 *4 *5 *6)) (-4 *4 (-451)) + (-4 *5 (-788)) (-4 *6 (-845)) (-5 *2 (-112)) + (-5 *1 (-1099 *4 *5 *6 *7 *8)) (-4 *8 (-1064 *4 *5 *6 *7))))) +(((*1 *1) (-12 (-4 *1 (-424 *2)) (-4 *2 (-367)) (-4 *2 (-1092))))) +(((*1 *2 *1) (-12 (-5 *2 (-639 (-109))) (-5 *1 (-174))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) (-4 *2 (-13 (-429 *3) (-997))))) @@ -2499,66 +2403,49 @@ (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3)))) ((*1 *1 *1) (-4 *1 (-1195)))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1229 *5 *4)) (-4 *4 (-815)) (-14 *5 (-1168)) - (-5 *2 (-639 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*4)) (-4 *2 (-845)) (-4 *3 (-1092)) (-14 *4 - (-1 (-112) (-2 (|:| -2466 *2) (|:| -1960 *3)) - (-2 (|:| -2466 *2) (|:| -1960 *3)))))) + (-1 (-112) (-2 (|:| -2464 *2) (|:| -1300 *3)) + (-2 (|:| -2464 *2) (|:| -1300 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-505)) (-5 *3 (-1110)) (-5 *1 (-833)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-868 *2 *3)) (-4 *2 (-1207)) (-4 *3 (-1207)))) ((*1 *1 *2) - (-12 (-5 *2 (-639 (-2 (|:| -2320 (-1168)) (|:| -2694 *4)))) + (-12 (-5 *2 (-639 (-2 (|:| -2319 (-1168)) (|:| -2693 *4)))) (-4 *4 (-1092)) (-5 *1 (-884 *3 *4)) (-4 *3 (-1092)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-639 *5)) (-4 *5 (-13 (-1092) (-34))) (-5 *2 (-639 (-1132 *3 *5))) (-5 *1 (-1132 *3 *5)) (-4 *3 (-13 (-1092) (-34))))) ((*1 *2 *3) - (-12 (-5 *3 (-639 (-2 (|:| |val| *4) (|:| -1495 *5)))) + (-12 (-5 *3 (-639 (-2 (|:| |val| *4) (|:| -1501 *5)))) (-4 *4 (-13 (-1092) (-34))) (-4 *5 (-13 (-1092) (-34))) (-5 *2 (-639 (-1132 *4 *5))) (-5 *1 (-1132 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -1495 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -1501 *4))) (-4 *3 (-13 (-1092) (-34))) (-4 *4 (-13 (-1092) (-34))) (-5 *1 (-1132 *3 *4)))) ((*1 *1 *2 *3) @@ -2634,98 +2521,107 @@ (-12 (-4 *3 (-171)) (-4 *2 (-712 *3)) (-5 *1 (-656 *2 *3 *4)) (-4 *4 (|SubsetCategory| (-721) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-987 *2)) (-4 *2 (-554))))) -(((*1 *2) - (-12 (-4 *3 (-1044)) (-5 *2 (-953 (-707 *3 *4))) (-5 *1 (-707 *3 *4)) - (-4 *4 (-1232 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-315 (-224))) (-5 *2 (-315 (-406 (-562)))) - (-5 *1 (-304))))) -(((*1 *2 *3 *2) (-12 (-5 *2 (-1150)) (-5 *3 (-562)) (-5 *1 (-240))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-433)) +(((*1 *2 *1) (-12 (-4 *1 (-388)) (-5 *2 (-112))))) +(((*1 *2 *2 *3 *4) + (-12 (-5 *2 (-639 *8)) (-5 *3 (-1 (-112) *8 *8)) + (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1058 *5 *6 *7)) (-4 *5 (-554)) + (-4 *6 (-788)) (-4 *7 (-845)) (-5 *1 (-972 *5 *6 *7 *8))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1164 *9)) (-5 *4 (-639 *7)) (-5 *5 (-639 (-639 *8))) + (-4 *7 (-845)) (-4 *8 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(-4064 'X) (-4064 '-3171) (-693)))) (-5 *1 (-86 *3)) (-14 *3 (-1168)))) ((*1 *1 *2) - (-12 (-5 *2 (-683 (-338 (-4066 'XL 'XR 'ELAM) (-4066) (-693)))) + (-12 (-5 *2 (-683 (-338 (-4064 'XL 'XR 'ELAM) (-4064) (-693)))) (-5 *1 (-87 *3)) (-14 *3 (-1168)))) ((*1 *1 *2) - (-12 (-5 *2 (-338 (-4066 'X) (-4066 '-3172) (-693))) (-5 *1 (-89 *3)) + (-12 (-5 *2 (-338 (-4064 'X) (-4064 '-3171) (-693))) (-5 *1 (-89 *3)) (-14 *3 (-1168)))) ((*1 *1 *2) (-12 (-5 *2 (-639 (-135 *3 *4 *5))) (-5 *1 (-135 *3 *4 *5)) @@ -2796,65 +2692,65 @@ ((*1 *1 *2) (-12 (-5 *2 (-639 (-329))) (-4 *1 (-395)))) ((*1 *1 *2) (-12 (-5 *2 (-293 (-315 (-168 (-378))))) (-5 *1 (-397 *3 *4 *5 *6)) - (-14 *3 (-1168)) (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2650 "void"))) + (-14 *3 (-1168)) (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2649 "void"))) (-14 *5 (-639 (-1168))) (-14 *6 (-1172)))) ((*1 *1 *2) (-12 (-5 *2 (-293 (-315 (-378)))) (-5 *1 (-397 *3 *4 *5 *6)) - (-14 *3 (-1168)) (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2650 "void"))) + (-14 *3 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|fst| (-433)) (|:| -2650 "void"))) + (-14 *3 (-1168)) (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2649 "void"))) (-14 *5 (-639 (-1168))) (-14 *6 (-1172)))) ((*1 *1 *2) (-12 (-5 *2 (-315 (-693))) (-5 *1 (-397 *3 *4 *5 *6)) - (-14 *3 (-1168)) (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2650 "void"))) + (-14 *3 (-1168)) (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2649 "void"))) (-14 *5 (-639 (-1168))) (-14 *6 (-1172)))) ((*1 *1 *2) (-12 (-5 *2 (-315 (-695))) (-5 *1 (-397 *3 *4 *5 *6)) - (-14 *3 (-1168)) (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2650 "void"))) + (-14 *3 (-1168)) (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2649 "void"))) (-14 *5 (-639 (-1168))) (-14 *6 (-1172)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |localSymbols| (-1172)) (|:| -3473 (-639 (-329))))) (-5 *1 (-397 *3 *4 *5 *6)) (-14 *3 (-1168)) - (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2650 "void"))) + (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2649 "void"))) (-14 *5 (-639 (-1168))) (-14 *6 (-1172)))) ((*1 *1 *2) (-12 (-5 *2 (-639 (-329))) (-5 *1 (-397 *3 *4 *5 *6)) - (-14 *3 (-1168)) (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2650 "void"))) + (-14 *3 (-1168)) (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2649 "void"))) (-14 *5 (-639 (-1168))) (-14 *6 (-1172)))) ((*1 *1 *2) (-12 (-5 *2 (-329)) (-5 *1 (-397 *3 *4 *5 *6)) (-14 *3 (-1168)) - (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2650 "void"))) + (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2649 "void"))) (-14 *5 (-639 (-1168))) (-14 *6 (-1172)))) ((*1 *1 *2) (-12 (-5 *2 (-330 *4)) (-4 *4 (-13 (-845) (-21))) @@ -2957,7 +2853,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-639 (-2 (|:| -4221 *3) (|:| -3045 *4)))) + (-12 (-5 *2 (-639 (-2 (|:| -4221 *3) (|:| -3044 *4)))) (-4 *3 (-1044)) (-4 *4 (-721)) (-5 *1 (-730 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-562)) (-4 *1 (-758)))) ((*1 *1 *2) @@ -2966,25 +2862,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) - (|:| -1590 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) + (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (|:| |mdnia| (-2 (|:| |fn| (-315 (-224))) - (|:| -1590 (-639 (-1086 (-838 (-224))))) + (|:| -2147 (-639 (-1086 (-838 (-224))))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))))) (-5 *1 (-764)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-315 (-224))) - (|:| -1590 (-639 (-1086 (-838 (-224))))) (|:| |abserr| (-224)) + (|:| -2147 (-639 (-1086 (-838 (-224))))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (-5 *1 (-764)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) - (|:| -1590 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) + (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (-5 *1 (-764)))) ((*1 *2 *3) (-12 (-5 *2 (-769)) (-5 *1 (-768 *3)) (-4 *3 (-1207)))) @@ -3002,23 +2898,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-315 (-224))) (|:| -3729 (-639 (-224))) + (-2 (|:| |fn| (-315 (-224))) (|:| -3730 (-639 (-224))) (|:| |lb| (-639 (-838 (-224)))) (|:| |cf| (-639 (-315 (-224)))) (|:| |ub| (-639 (-838 (-224)))))) (|:| |lsa| (-2 (|:| |lfn| (-639 (-315 (-224)))) - (|:| -3729 (-639 (-224))))))) + (|:| -3730 (-639 (-224))))))) (-5 *1 (-836)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-639 (-315 (-224)))) (|:| -3729 (-639 (-224))))) + (-2 (|:| |lfn| (-639 (-315 (-224)))) (|:| -3730 (-639 (-224))))) (-5 *1 (-836)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-315 (-224))) (|:| -3729 (-639 (-224))) + (-2 (|:| |fn| (-315 (-224))) (|:| -3730 (-639 (-224))) (|:| |lb| (-639 (-838 (-224)))) (|:| |cf| (-639 (-315 (-224)))) (|:| |ub| (-639 (-838 (-224)))))) (-5 *1 (-836)))) @@ -3121,23 +3017,24 @@ ((*1 *1 *2) (-12 (-5 *2 (-658 *3 *4)) (-4 *3 (-845)) (-4 *4 (-171)) (-5 *1 (-1276 *3 *4))))) -(((*1 *2 *3 *3 *4 *5 *3 *6) - (-12 (-5 *3 (-562)) (-5 *4 (-683 (-224))) (-5 *5 (-224)) - (-5 *6 (-3 (|:| |fn| (-387)) (|:| |fp| (-81 FCN)))) (-5 *2 (-1030)) - (-5 *1 (-741))))) -(((*1 *2 *1 *1) - (-12 (-4 *3 (-554)) (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *5 (-845)) - (-5 *2 (-639 *1)) (-4 *1 (-1058 *3 *4 *5))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-639 (-562))) (-5 *1 (-135 *3 *4 *5)) (-14 *3 (-562)) - (-14 *4 (-766)) (-4 *5 (-171))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-490)) (-5 *4 (-949)) (-5 *2 (-685 (-532))) + (-5 *1 (-532)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-949)) (-4 *3 (-1092)) (-5 *2 (-685 *1)) + (-4 *1 (-762 *3))))) +(((*1 *2 *3 *4 *5 *6) + (-12 (-5 *6 (-916)) (-4 *5 (-306)) (-4 *3 (-1232 *5)) + (-5 *2 (-2 (|:| |plist| (-639 *3)) (|:| |modulo| *5))) + (-5 *1 (-459 *5 *3)) (-5 *4 (-639 *3))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-315 (-562))) (|:| -3197 (-315 (-378))) + (-3 (|:| I (-315 (-562))) (|:| -3196 (-315 (-378))) (|:| CF (-315 (-168 (-378)))) (|:| |switch| (-1167)))) (-5 *1 (-1167))))) -(((*1 *2) (-12 (-5 *2 (-1261)) (-5 *1 (-97))))) +(((*1 *2 *3) + (-12 (-5 *3 (-639 (-315 (-224)))) (-5 *2 (-112)) (-5 *1 (-266))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1207)))) ((*1 *1 *2) @@ -3215,24 +3112,24 @@ ((*1 *1 *2) (|partial| -4037 (-12 (-5 *2 (-947 *3)) - (-12 (-2236 (-4 *3 (-38 (-406 (-562))))) - (-2236 (-4 *3 (-38 (-562)))) (-4 *5 (-610 (-1168)))) + (-12 (-2234 (-4 *3 (-38 (-406 (-562))))) + (-2234 (-4 *3 (-38 (-562)))) (-4 *5 (-610 (-1168)))) (-4 *3 (-1044)) (-4 *1 (-1058 *3 *4 *5)) (-4 *4 (-788)) (-4 *5 (-845))) (-12 (-5 *2 (-947 *3)) - (-12 (-2236 (-4 *3 (-544))) (-2236 (-4 *3 (-38 (-406 (-562))))) + (-12 (-2234 (-4 *3 (-544))) (-2234 (-4 *3 (-38 (-406 (-562))))) (-4 *3 (-38 (-562))) (-4 *5 (-610 (-1168)))) (-4 *3 (-1044)) (-4 *1 (-1058 *3 *4 *5)) (-4 *4 (-788)) (-4 *5 (-845))) (-12 (-5 *2 (-947 *3)) - (-12 (-2236 (-4 *3 (-987 (-562)))) (-4 *3 (-38 (-406 (-562)))) + (-12 (-2234 (-4 *3 (-987 (-562)))) (-4 *3 (-38 (-406 (-562)))) (-4 *5 (-610 (-1168)))) (-4 *3 (-1044)) (-4 *1 (-1058 *3 *4 *5)) (-4 *4 (-788)) (-4 *5 (-845))))) ((*1 *1 *2) (|partial| -4037 (-12 (-5 *2 (-947 (-562))) (-4 *1 (-1058 *3 *4 *5)) - (-12 (-2236 (-4 *3 (-38 (-406 (-562))))) (-4 *3 (-38 (-562))) + (-12 (-2234 (-4 *3 (-38 (-406 (-562))))) (-4 *3 (-38 (-562))) (-4 *5 (-610 (-1168)))) (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *5 (-845))) (-12 (-5 *2 (-947 (-562))) (-4 *1 (-1058 *3 *4 *5)) @@ -3242,50 +3139,9 @@ (|partial| -12 (-5 *2 (-947 (-406 (-562)))) (-4 *1 (-1058 *3 *4 *5)) (-4 *3 (-38 (-406 (-562)))) (-4 *5 (-610 (-1168))) (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *5 (-845))))) -(((*1 *2 *3 *3 *4) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1232 *5)) - (-4 *5 (-13 (-362) (-146) (-1033 (-562)))) - (-5 *2 - (-2 (|:| |a| *6) (|:| |b| (-406 *6)) (|:| |c| (-406 *6)) - (|:| -3355 *6))) - (-5 *1 (-1010 *5 *6)) (-5 *3 (-406 *6))))) -(((*1 *1) (-5 *1 (-818)))) -(((*1 *2 *3) - (-12 (-5 *3 (-1168)) (-5 *2 (-1 *6 *5)) (-5 *1 (-701 *4 *5 *6)) - (-4 *4 (-610 (-535))) (-4 *5 (-1207)) (-4 *6 (-1207))))) -(((*1 *1 *2) - (-12 (-5 *2 (-315 *3)) (-4 *3 (-13 (-1044) (-845))) - (-5 *1 (-222 *3 *4)) (-14 *4 (-639 (-1168)))))) -(((*1 *1 *1) - (-12 (-5 *1 (-592 *2)) (-4 *2 (-38 (-406 (-562)))) (-4 *2 (-1044))))) -(((*1 *1 *2) - (|partial| -12 (-5 *2 (-814 *3)) (-4 *3 (-845)) (-5 *1 (-666 *3))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-112)))) - ((*1 *1 *1 *1) (-5 *1 (-857)))) -(((*1 *2 *3) (-12 (-5 *3 (-938 *2)) (-5 *1 (-977 *2)) (-4 *2 (-1044))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-168 (-224))) (-5 *4 (-562)) (-5 *2 (-1030)) - (-5 *1 (-753))))) (((*1 *2 *3) - (-12 (-5 *3 (-639 (-480 *4 *5))) (-14 *4 (-639 (-1168))) - (-4 *5 (-451)) (-5 *2 (-639 (-246 *4 *5))) (-5 *1 (-627 *4 *5))))) -(((*1 *1 *2 *2) - (-12 - (-5 *2 - (-3 (|:| I (-315 (-562))) (|:| -3197 (-315 (-378))) - (|:| CF (-315 (-168 (-378)))) (|:| |switch| (-1167)))) - (-5 *1 (-1167))))) -(((*1 *2 *1) (-12 (-5 *2 (-639 (-1206))) (-5 *1 (-602))))) -(((*1 *2 *2) (-12 (-5 *2 (-562)) (-5 *1 (-551))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1164 *9)) (-5 *4 (-639 *7)) (-5 *5 (-639 (-639 *8))) - (-4 *7 (-845)) (-4 *8 (-306)) (-4 *9 (-944 *8 *6 *7)) (-4 *6 (-788)) - (-5 *2 - (-2 (|:| |upol| (-1164 *8)) (|:| |Lval| (-639 *8)) - (|:| |Lfact| - (-639 (-2 (|:| -1635 (-1164 *8)) (|:| -1960 (-562))))) - (|:| |ctpol| *8))) - (-5 *1 (-737 *6 *7 *8 *9))))) + (-12 (-5 *3 (-916)) (-5 *2 (-1164 *4)) (-5 *1 (-585 *4)) + (-4 *4 (-348))))) (((*1 *2 *3 *4 *4 *2 *2 *2 *2) (-12 (-5 *2 (-562)) (-5 *3 @@ -3293,15 +3149,59 @@ (|:| |polj| *4))) (-4 *6 (-788)) (-4 *4 (-944 *5 *6 *7)) (-4 *5 (-451)) (-4 *7 (-845)) (-5 *1 (-448 *5 *6 *7 *4))))) +(((*1 *1 *1) (-12 (-5 *1 (-592 *2)) (-4 *2 (-1044))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) + (-4 *2 (-13 (-429 *3) (-997)))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) + (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) + (|:| |relerr| (-224)))) + (-5 *2 + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| "There are singularities at both end points") + (|:| |notEvaluated| "End point continuity not yet evaluated"))) + (-5 *1 (-191))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-562)) (-5 *1 (-479))))) +(((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-112)))) + ((*1 *1 *1 *1) (-5 *1 (-857)))) +(((*1 *2 *1) (-12 (-4 *1 (-668 *3)) (-4 *3 (-1207)) (-5 *2 (-112))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-650 *2)) (-4 *2 (-1044)) (-4 *2 (-362)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-1 *4 *4)) (-4 *4 (-362)) (-5 *1 (-653 *4 *2)) + (-4 *2 (-650 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-639 (-1206))) (-5 *1 (-602))))) +(((*1 *1 *2 *2) + (-12 + (-5 *2 + (-3 (|:| I (-315 (-562))) (|:| -3196 (-315 (-378))) + (|:| CF (-315 (-168 (-378)))) (|:| |switch| (-1167)))) + (-5 *1 (-1167))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1256 *4)) (-5 *3 (-766)) (-4 *4 (-348)) + (-5 *1 (-527 *4))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) + (-4 *2 (-13 (-429 *3) (-997)))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1232 *5)) (-4 *5 (-362)) (-5 *2 (-2 (|:| |answer| *3) (|:| |polypart| *3))) (-5 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- (-12 (-5 *3 (-647 (-406 *6))) (-5 *4 (-406 *6)) (-4 *6 (-1232 *5)) - (-4 *5 (-13 (-362) (-146) (-1033 (-562)) (-1033 (-406 (-562))))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -3928 (-639 *4)))) - (-5 *1 (-805 *5 *6)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-647 (-406 *6))) (-4 *6 (-1232 *5)) - (-4 *5 (-13 (-362) (-146) (-1033 (-562)) (-1033 (-406 (-562))))) - (-5 *2 (-2 (|:| -3928 (-639 (-406 *6))) (|:| -1545 (-683 *5)))) - (-5 *1 (-805 *5 *6)) (-5 *4 (-639 (-406 *6))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-648 *6 (-406 *6))) (-5 *4 (-406 *6)) (-4 *6 (-1232 *5)) - (-4 *5 (-13 (-362) (-146) (-1033 (-562)) (-1033 (-406 (-562))))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -3928 (-639 *4)))) - (-5 *1 (-805 *5 *6)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-648 *6 (-406 *6))) (-4 *6 (-1232 *5)) - (-4 *5 (-13 (-362) (-146) (-1033 (-562)) (-1033 (-406 (-562))))) - (-5 *2 (-2 (|:| -3928 (-639 (-406 *6))) (|:| -1545 (-683 *5)))) - (-5 *1 (-805 *5 *6)) (-5 *4 (-639 (-406 *6)))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-451)) (-4 *4 (-845)) (-4 *5 (-788)) (-5 *2 (-112)) (-5 *1 (-982 *3 *4 *5 *6)) @@ -3563,11 +3460,16 @@ ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1132 *3 *4)) (-4 *3 (-13 (-1092) (-34))) (-4 *4 (-13 (-1092) (-34)))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1170 (-406 (-562)))) (-5 *1 (-189)) (-5 *3 (-562))))) -(((*1 *2 *1) - (-12 (-5 *2 (-639 (-562))) (-5 *1 (-999 *3)) (-14 *3 (-562))))) -(((*1 *1) (-5 *1 (-224))) ((*1 *1) (-5 *1 (-378)))) +(((*1 *2 *1) (-12 (-5 *2 (-766)) (-5 *1 (-143))))) +(((*1 *2 *1) (-12 (-4 *1 (-1085 *2)) (-4 *2 (-1207))))) +(((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *7)) (-5 *4 (-1164 *7)) + (-4 *5 (-1044)) (-4 *7 (-1044)) (-4 *2 (-1232 *5)) + (-5 *1 (-500 *5 *2 *6 *7)) (-4 *6 (-1232 *2))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-451)) (-4 *6 (-788)) (-4 *7 (-845)) + (-4 *3 (-1058 *5 *6 *7)) (-5 *2 (-639 *4)) + (-5 *1 (-1100 *5 *6 *7 *3 *4)) (-4 *4 (-1064 *5 *6 *7 *3))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1150)) (-5 *1 (-114)))) ((*1 *2 *2 *3) (-12 (-5 *3 (-1150)) (-4 *4 (-845)) (-5 *1 (-924 *4 *2)) @@ -3575,72 +3477,51 @@ ((*1 *2 *3 *4) (-12 (-5 *3 (-1168)) (-5 *4 (-1150)) (-5 *2 (-315 (-562))) (-5 *1 (-925))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1148 (-639 (-562)))) (-5 *3 (-639 (-562))) - (-5 *1 (-878))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1150)) (-5 *2 (-112)) (-5 *1 (-824))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) - (-12 (-5 *3 (-1 (-378) (-378))) (-5 *4 (-378)) - (-5 *2 - (-2 (|:| -2534 *4) (|:| -3964 *4) (|:| |totalpts| (-562)) - (|:| |success| (-112)))) - (-5 *1 (-784)) (-5 *5 (-562))))) -(((*1 *2 *3 *4 *4 *5 *4 *6 *4 *5) - (-12 (-5 *3 (-1150)) (-5 *5 (-683 (-224))) (-5 *6 (-683 (-562))) - (-5 *4 (-562)) (-5 *2 (-1030)) (-5 *1 (-752))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-639 *6)) (-5 *4 (-1168)) (-4 *6 (-429 *5)) - (-4 *5 (-845)) (-5 *2 (-639 (-608 *6))) (-5 *1 (-571 *5 *6))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-766)) (-5 *1 (-114)))) + ((*1 *2 *1) (-12 (-4 *1 (-830 *3)) (-4 *3 (-1092)) (-5 *2 (-55))))) +(((*1 *2 *3 *1) + (|partial| -12 (-5 *3 (-887 *4)) (-4 *4 (-1092)) (-4 *2 (-1092)) + (-5 *1 (-884 *4 *2))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-133)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-828 *3)) (-4 *3 (-1092)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-838 *3)) (-4 *3 (-1092))))) (((*1 *2 *1) - (-12 (-4 *1 (-341 *3 *4 *5)) (-4 *3 (-1211)) (-4 *4 (-1232 *3)) - (-4 *5 (-1232 (-406 *4))) - (-5 *2 (-2 (|:| |num| (-1256 *4)) (|:| |den| *4)))))) -(((*1 *1 *1) (-5 *1 (-857)))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-1092)) (-4 *3 (-895 *5)) (-5 *2 (-1256 *3)) - (-5 *1 (-686 *5 *3 *6 *4)) (-4 *6 (-372 *3)) - (-4 *4 (-13 (-372 *5) (-10 -7 (-6 -4402))))))) -(((*1 *2 *3 *4 *3 *4 *5 *3 *4 *3 *3 *3 *3) - (-12 (-5 *4 (-683 (-224))) (-5 *5 (-683 (-562))) (-5 *3 (-562)) - (-5 *2 (-1030)) (-5 *1 (-751))))) -(((*1 *1 *2) + (-12 (-5 *2 (-868 (-961 *3) (-961 *3))) (-5 *1 (-961 *3)) + (-4 *3 (-962))))) +(((*1 *2 *1) (-12 (-5 *2 (-1148 *3)) (-5 *1 (-173 *3)) (-4 *3 (-306))))) +(((*1 *2 *3) (-12 (-5 *3 (-938 *2)) (-5 *1 (-977 *2)) (-4 *2 (-1044))))) +(((*1 *2 *1) + (-12 (-4 *1 (-325 *3 *4)) (-4 *3 (-1044)) (-4 *4 (-787)) + (-5 *2 (-639 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-381 *3 *4)) (-4 *3 (-1044)) (-4 *4 (-1092)) + (-5 *2 (-639 *3)))) + ((*1 *2 *1) + (-12 (-5 *2 (-1148 *3)) (-5 *1 (-593 *3)) (-4 *3 (-1044)))) + ((*1 *2 *1) + (-12 (-5 *2 (-639 *3)) (-5 *1 (-730 *3 *4)) (-4 *3 (-1044)) + (-4 *4 (-721)))) + ((*1 *2 *1) (-12 (-4 *1 (-847 *3)) (-4 *3 (-1044)) (-5 *2 (-639 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1247 *3)) (-4 *3 (-1044)) (-5 *2 (-1148 *3))))) +(((*1 *2 *3 *3 *4) + (-12 (-4 *5 (-451)) (-4 *6 (-788)) (-4 *7 (-845)) + (-4 *3 (-1058 *5 *6 *7)) + (-5 *2 (-639 (-2 (|:| |val| *3) (|:| -1501 *4)))) + (-5 *1 (-1100 *5 *6 *7 *3 *4)) (-4 *4 (-1064 *5 *6 *7 *3))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-639 - (-2 - (|:| -2320 - (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) - (|:| -1590 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) - (|:| |relerr| (-224)))) - (|:| -2694 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1148 (-224))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -1590 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated")))))))) - (-5 *1 (-557))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-855)) (-5 *2 (-685 (-129))) (-5 *3 (-129))))) + (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-766)) (|:| |poli| *6) + (|:| |polj| *6)))) + (-4 *4 (-788)) (-4 *6 (-944 *3 *4 *5)) (-4 *3 (-451)) (-4 *5 (-845)) + (-5 *1 (-448 *3 *4 *5 *6))))) +(((*1 *2 *1) (-12 (-4 *1 (-792 *2)) (-4 *2 (-171)))) + ((*1 *2 *1) (-12 (-4 *1 (-992 *2)) (-4 *2 (-171))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-224)) (-5 *4 (-562)) (-5 *2 (-1030)) (-5 *1 (-753))))) + (-12 (-5 *3 (-916)) (-5 *4 (-417 *6)) (-4 *6 (-1232 *5)) + (-4 *5 (-1044)) (-5 *2 (-639 *6)) (-5 *1 (-443 *5 *6))))) (((*1 *2 *3) (-12 (-5 *3 (-1150)) (-5 *2 (-311)) (-5 *1 (-295)))) ((*1 *2 *3) (-12 (-5 *3 (-639 (-1150))) (-5 *2 (-311)) (-5 *1 (-295)))) @@ -3648,15 +3529,20 @@ ((*1 *2 *3 *4) (-12 (-5 *4 (-639 (-1150))) (-5 *3 (-1150)) (-5 *2 (-311)) (-5 *1 (-295))))) -(((*1 *2 *2) - (-12 (-5 *2 (-639 (-2 (|:| |val| (-639 *6)) (|:| -1495 *7)))) - (-4 *6 (-1058 *3 *4 *5)) (-4 *7 (-1064 *3 *4 *5 *6)) (-4 *3 (-451)) - (-4 *4 (-788)) (-4 *5 (-845)) (-5 *1 (-983 *3 *4 *5 *6 *7)))) - ((*1 *2 *2) - (-12 (-5 *2 (-639 (-2 (|:| |val| (-639 *6)) (|:| -1495 *7)))) - (-4 *6 (-1058 *3 *4 *5)) (-4 *7 (-1064 *3 *4 *5 *6)) (-4 *3 (-451)) - (-4 *4 (-788)) (-4 *5 (-845)) (-5 *1 (-1099 *3 *4 *5 *6 *7))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-978 *2)) (-4 *2 (-1192))))) (((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-817))))) +(((*1 *2 *1) + (|partial| -12 + (-4 *3 (-13 (-845) (-1033 (-562)) (-635 (-562)) (-451))) + (-5 *2 (-838 *4)) (-5 *1 (-312 *3 *4 *5 *6)) + (-4 *4 (-13 (-27) (-1192) (-429 *3))) (-14 *5 (-1168)) + (-14 *6 *4))) + ((*1 *2 *1) + (|partial| -12 + (-4 *3 (-13 (-845) (-1033 (-562)) (-635 (-562)) (-451))) + (-5 *2 (-838 *4)) (-5 *1 (-1242 *3 *4 *5 *6)) + (-4 *4 (-13 (-27) (-1192) (-429 *3))) (-14 *5 (-1168)) + (-14 *6 *4)))) (((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1207)))) ((*1 *1 *2) (-12 (-5 *2 (-947 (-378))) (-5 *1 (-338 *3 *4 *5)) @@ -3712,11 +3598,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) - (|:| -1590 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) + (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (|:| |mdnia| (-2 (|:| |fn| (-315 (-224))) - (|:| -1590 (-639 (-1086 (-838 (-224))))) + (|:| -2147 (-639 (-1086 (-838 (-224))))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))))) (-5 *1 (-764)))) ((*1 *2 *1) @@ -3732,13 +3618,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-315 (-224))) (|:| -3729 (-639 (-224))) + (-2 (|:| |fn| (-315 (-224))) (|:| -3730 (-639 (-224))) (|:| |lb| (-639 (-838 (-224)))) (|:| |cf| (-639 (-315 (-224)))) (|:| |ub| (-639 (-838 (-224)))))) (|:| |lsa| (-2 (|:| |lfn| (-639 (-315 (-224)))) - (|:| -3729 (-639 (-224))))))) + (|:| -3730 (-639 (-224))))))) (-5 *1 (-836)))) ((*1 *2 *1) (-12 @@ -3759,24 +3645,24 @@ ((*1 *1 *2) (-4037 (-12 (-5 *2 (-947 *3)) - (-12 (-2236 (-4 *3 (-38 (-406 (-562))))) - (-2236 (-4 *3 (-38 (-562)))) (-4 *5 (-610 (-1168)))) + (-12 (-2234 (-4 *3 (-38 (-406 (-562))))) + (-2234 (-4 *3 (-38 (-562)))) (-4 *5 (-610 (-1168)))) (-4 *3 (-1044)) (-4 *1 (-1058 *3 *4 *5)) (-4 *4 (-788)) (-4 *5 (-845))) (-12 (-5 *2 (-947 *3)) - (-12 (-2236 (-4 *3 (-544))) (-2236 (-4 *3 (-38 (-406 (-562))))) + (-12 (-2234 (-4 *3 (-544))) (-2234 (-4 *3 (-38 (-406 (-562))))) (-4 *3 (-38 (-562))) (-4 *5 (-610 (-1168)))) (-4 *3 (-1044)) (-4 *1 (-1058 *3 *4 *5)) (-4 *4 (-788)) (-4 *5 (-845))) (-12 (-5 *2 (-947 *3)) - (-12 (-2236 (-4 *3 (-987 (-562)))) (-4 *3 (-38 (-406 (-562)))) + (-12 (-2234 (-4 *3 (-987 (-562)))) (-4 *3 (-38 (-406 (-562)))) (-4 *5 (-610 (-1168)))) (-4 *3 (-1044)) (-4 *1 (-1058 *3 *4 *5)) (-4 *4 (-788)) (-4 *5 (-845))))) ((*1 *1 *2) (-4037 (-12 (-5 *2 (-947 (-562))) (-4 *1 (-1058 *3 *4 *5)) - (-12 (-2236 (-4 *3 (-38 (-406 (-562))))) (-4 *3 (-38 (-562))) + (-12 (-2234 (-4 *3 (-38 (-406 (-562))))) (-4 *3 (-38 (-562))) (-4 *5 (-610 (-1168)))) (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *5 (-845))) (-12 (-5 *2 (-947 (-562))) (-4 *1 (-1058 *3 *4 *5)) @@ -3786,842 +3672,955 @@ (-12 (-5 *2 (-947 (-406 (-562)))) (-4 *1 (-1058 *3 *4 *5)) (-4 *3 (-38 (-406 (-562)))) (-4 *5 (-610 (-1168))) (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *5 (-845))))) -(((*1 *2 *3 *4 *4 *5 *3 *3 *4 *3 *3 *3) - (-12 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FCN)))) - (-5 *9 (-3 (|:| |fn| (-387)) (|:| |fp| (-88 OUTPUT)))) - (-5 *3 (-224)) (-5 *2 (-1030)) (-5 *1 (-744))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) - (-4 *2 (-13 (-429 *3) (-997)))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-554)) - (-5 *2 - (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-964 *4 *3)) (-4 *3 (-1232 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-819)) (-5 *1 (-820))))) +(((*1 *2) (-12 (-5 *2 (-378)) (-5 *1 (-1035))))) +(((*1 *2 *1) (-12 (-5 *2 (-857)) (-5 *1 (-52))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1273 *3 *4)) (-4 *3 (-845)) (-4 *4 (-1044)) + (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1279 *3 *4)) (-4 *3 (-1044)) + (-4 *4 (-841))))) +(((*1 *2 *3 *4 *3) + (-12 (-5 *3 (-562)) (-5 *4 (-683 (-224))) (-5 *2 (-1030)) + (-5 *1 (-742))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) @@ -8060,55 +8187,24 @@ (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-503 (-406 (-562)) (-239 *5 (-766)) (-859 *4) - (-246 *4 (-406 (-562))))) - (-14 *4 (-639 (-1168))) (-14 *5 (-766)) (-5 *2 (-112)) - (-5 *1 (-504 *4 *5))))) -(((*1 *2) (-12 (-5 *2 (-1261)) (-5 *1 (-1209))))) -(((*1 *2 *1 *3 *3) - (-12 (|has| *1 (-6 -4403)) (-4 *1 (-600 *3 *4)) (-4 *3 (-1092)) - (-4 *4 (-1207)) (-5 *2 (-1261))))) -(((*1 *2 *3) - (-12 (-5 *3 (-246 *4 *5)) (-14 *4 (-639 (-1168))) (-4 *5 (-1044)) - (-5 *2 (-947 *5)) (-5 *1 (-939 *4 *5))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1168)) - (-4 *5 (-13 (-554) (-845) (-1033 (-562)) (-635 (-562)))) - (-5 *2 - (-2 (|:| |func| *3) (|:| |kers| (-639 (-608 *3))) - (|:| |vals| (-639 *3)))) - (-5 *1 (-276 *5 *3)) (-4 *3 (-13 (-27) (-1192) (-429 *5)))))) -(((*1 *2 *2 *1) - (-12 (-4 *1 (-1200 *3 *4 *5 *2)) (-4 *3 (-554)) (-4 *4 (-788)) - (-4 *5 (-845)) (-4 *2 (-1058 *3 *4 *5))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-114)) (-5 *4 (-639 *2)) (-5 *1 (-113 *2)) - (-4 *2 (-1092)))) - ((*1 *2 *2 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(-1152 *4)) (-4 *4 (-1044)) + (-5 *3 (-562))))) +(((*1 *2 *3 *2) (-12 (-5 *2 (-1150)) (-5 *3 (-562)) (-5 *1 (-240))))) +(((*1 *1) (-12 (-5 *1 (-226 *2)) (-4 *2 (-13 (-362) (-1192)))))) +(((*1 *1) (-5 *1 (-140)))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1150)) (-5 *2 (-1261)) (-5 *1 (-1258))))) +(((*1 *2 *2) (-12 (-5 *2 (-562)) (-5 *1 (-921))))) +(((*1 *2 *3 *3 *3 *4 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-224)) (-5 *4 (-562)) + (-5 *5 (-3 (|:| |fn| (-387)) (|:| |fp| (-64 G)))) (-5 *2 (-1030)) + (-5 *1 (-743))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1207)) (-5 *1 (-374 *4 *2)) + (-4 *2 (-13 (-372 *4) (-10 -7 (-6 -4404))))))) (((*1 *1 *2 *3) (-12 (-4 *1 (-381 *3 *2)) (-4 *3 (-1044)) (-4 *2 (-1092)))) ((*1 *2 *3 *4) @@ -8117,6 +8213,25 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-814 *4)) (-4 *4 (-845)) (-4 *1 (-1273 *4 *3)) (-4 *3 (-1044))))) +(((*1 *2 *2) + (-12 (-5 *2 (-1148 *3)) (-4 *3 (-1044)) (-5 *1 (-1152 *3)))) + ((*1 *1 *1) + (-12 (-5 *1 (-1248 *2 *3 *4)) (-4 *2 (-1044)) (-14 *3 (-1168)) + (-14 *4 *2)))) +(((*1 *2 *3) + (-12 (-5 *3 (-683 *2)) (-4 *4 (-1232 *2)) + (-4 *2 (-13 (-306) (-10 -8 (-15 -3788 ((-417 $) $))))) + (-5 *1 (-498 *2 *4 *5)) (-4 *5 (-408 *2 *4)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1115 *3 *2 *4 *5)) (-4 *4 (-237 *3 *2)) + (-4 *5 (-237 *3 *2)) (-4 *2 (-1044))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-433)) + (-5 *2 + (-639 + (-3 (|:| -3253 (-1168)) + (|:| -1852 (-639 (-3 (|:| S (-1168)) (|:| P (-947 (-562))))))))) + (-5 *1 (-1172))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) @@ -8133,45 +8248,19 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) -(((*1 *2 *1 *1 *3 *4) - (-12 (-5 *3 (-1 (-112) *5 *5)) (-5 *4 (-1 (-112) *6 *6)) - (-4 *5 (-13 (-1092) (-34))) (-4 *6 (-13 (-1092) (-34))) - (-5 *2 (-112)) (-5 *1 (-1132 *5 *6))))) -(((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-817))))) -(((*1 *1 *1 *1) - (|partial| -12 (-4 *1 (-847 *2)) (-4 *2 (-1044)) (-4 *2 (-362))))) -(((*1 *2 *3 *3 *4 *5) - (-12 (-5 *3 (-1150)) (-4 *6 (-451)) (-4 *7 (-788)) (-4 *8 (-845)) - (-4 *4 (-1058 *6 *7 *8)) (-5 *2 (-1261)) - (-5 *1 (-771 *6 *7 *8 *4 *5)) (-4 *5 (-1064 *6 *7 *8 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-583 *3)) (-4 *3 (-362))))) -(((*1 *2 *1) (-12 (-4 *1 (-668 *2)) (-4 *2 (-1207))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1164 (-406 (-947 *3)))) (-5 *1 (-452 *3 *4 *5 *6)) - (-4 *3 (-554)) (-4 *3 (-171)) (-14 *4 (-916)) - (-14 *5 (-639 (-1168))) (-14 *6 (-1256 (-683 *3)))))) +(((*1 *2 *3) (-12 (-5 *3 (-1150)) (-5 *2 (-916)) (-5 *1 (-781))))) +(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *4 *5 *3 *3 *3 *6 *4 *3) + (-12 (-5 *4 (-683 (-224))) (-5 *5 (-683 (-562))) (-5 *6 (-224)) + (-5 *3 (-562)) (-5 *2 (-1030)) (-5 *1 (-747))))) +(((*1 *2 *3 *4 *4 *3) + (-12 (-5 *3 (-562)) (-5 *4 (-683 (-224))) (-5 *2 (-1030)) + (-5 *1 (-746))))) +(((*1 *1) + (-12 (-5 *1 (-643 *2 *3 *4)) (-4 *2 (-1092)) (-4 *3 (-23)) + (-14 *4 *3)))) (((*1 *2 *2 *2) - (-12 (-4 *3 (-1044)) (-5 *1 (-889 *2 *3)) (-4 *2 (-1232 *3)))) - ((*1 *2 *2 *2) - (-12 (-5 *2 (-1148 *3)) (-4 *3 (-1044)) (-5 *1 (-1152 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-165 *3)) (-4 *3 (-171)) (-4 *3 (-544)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-417 *3)) (-4 *3 (-544)) (-4 *3 (-554)))) - ((*1 *2 *1) (-12 (-4 *1 (-544)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-4 *1 (-792 *3)) (-4 *3 (-171)) (-4 *3 (-544)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-828 *3)) (-4 *3 (-544)) (-4 *3 (-1092)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-838 *3)) (-4 *3 (-544)) (-4 *3 (-1092)))) - ((*1 *2 *1) - (-12 (-4 *1 (-992 *3)) (-4 *3 (-171)) (-4 *3 (-544)) (-5 *2 (-112)))) - ((*1 *2 *3) - (-12 (-5 *2 (-112)) (-5 *1 (-1003 *3)) (-4 *3 (-1033 (-406 (-562))))))) -(((*1 *2 *1) - (-12 (-5 *2 (-766)) (-5 *1 (-1156 *3 *4)) (-14 *3 (-916)) - (-4 *4 (-1044))))) + (-12 (-4 *3 (-1044)) (-5 *1 (-1228 *3 *2)) (-4 *2 (-1232 *3))))) +(((*1 *2 *3) (-12 (-5 *2 (-639 (-562))) (-5 *1 (-445)) (-5 *3 (-562))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) @@ -8188,37 +8277,35 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-845) (-451))) (-5 *1 (-1198 *3 *2)) - (-4 *2 (-13 (-429 *3) (-1192)))))) -(((*1 *2) - (-12 (-5 *2 (-1261)) (-5 *1 (-1184 *3 *4)) (-4 *3 (-1092)) - (-4 *4 (-1092))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1095 *3 *4 *5 *6 *7)) (-4 *3 (-1092)) (-4 *4 (-1092)) + (-4 *5 (-1092)) (-4 *6 (-1092)) (-4 *7 (-1092)) (-5 *2 (-112))))) +(((*1 *1) (-5 *1 (-818)))) +(((*1 *1 *1) + (-12 (-5 *1 (-592 *2)) (-4 *2 (-38 (-406 (-562)))) (-4 *2 (-1044))))) +(((*1 *2) (-12 (-5 *2 (-1150)) (-5 *1 (-240))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-554)) (-5 *2 (-639 (-766))) (-5 *1 (-964 *4 *3)) - (-4 *3 (-1232 *4))))) -(((*1 *2 *3 *4 *4 *4 *5 *4 *5 *5 *3) - (-12 (-5 *3 (-562)) (-5 *4 (-683 (-224))) (-5 *5 (-224)) - (-5 *2 (-1030)) (-5 *1 (-746))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-766)) (-4 *1 (-1232 *3)) (-4 *3 (-1044))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-1090 *3)) (-4 *3 (-1092)) (-5 *2 (-112))))) + (-12 (-4 *4 (-13 (-451) (-146))) (-5 *2 (-417 *3)) + (-5 *1 (-100 *4 *3)) (-4 *3 (-1232 *4)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-639 *3)) (-4 *3 (-1232 *5)) (-4 *5 (-13 (-451) (-146))) + (-5 *2 (-417 *3)) (-5 *1 (-100 *5 *3))))) (((*1 *2 *3) - (-12 (-5 *2 (-417 (-1164 *1))) (-5 *1 (-315 *4)) (-5 *3 (-1164 *1)) - (-4 *4 (-451)) (-4 *4 (-554)) (-4 *4 (-845)))) - ((*1 *2 *3) - (-12 (-4 *1 (-904)) (-5 *2 (-417 (-1164 *1))) (-5 *3 (-1164 *1))))) + (|partial| -12 (-5 *3 (-1256 *4)) (-4 *4 (-635 (-562))) + (-5 *2 (-1256 (-562))) (-5 *1 (-1283 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-1256 *1)) (-4 *1 (-366 *4)) (-4 *4 (-171)) - (-5 *2 (-683 *4)))) - ((*1 *2) - (-12 (-4 *4 (-171)) (-5 *2 (-683 *4)) (-5 *1 (-415 *3 *4)) - (-4 *3 (-416 *4)))) - ((*1 *2) (-12 (-4 *1 (-416 *3)) (-4 *3 (-171)) (-5 *2 (-683 *3))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1247 *4)) (-5 *1 (-1249 *4 *2)) - (-4 *4 (-38 (-406 (-562))))))) + (-12 (-5 *3 (-647 (-406 *2))) (-4 *2 (-1232 *4)) (-5 *1 (-805 *4 *2)) + (-4 *4 (-13 (-362) (-146) (-1033 (-562)) (-1033 (-406 (-562))))))) + ((*1 *2 *3) + (-12 (-5 *3 (-648 *2 (-406 *2))) (-4 *2 (-1232 *4)) + (-5 *1 (-805 *4 *2)) + (-4 *4 (-13 (-362) (-146) (-1033 (-562)) (-1033 (-406 (-562)))))))) +(((*1 *2 *3 *3 *3 *4 *4 *3) + (-12 (-5 *3 (-562)) (-5 *4 (-683 (-224))) (-5 *2 (-1030)) + (-5 *1 (-750))))) +(((*1 *1) (-5 *1 (-436)))) +(((*1 *1 *1) + (-12 (-5 *1 (-1156 *2 *3)) (-14 *2 (-916)) (-4 *3 (-1044))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) (-4 *2 (-13 (-429 *3) (-997))))) @@ -8235,59 +8322,33 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-978 *2)) (-4 *2 (-1192))))) (((*1 *2 *3) - (-12 (-5 *3 (-1164 (-562))) (-5 *2 (-562)) (-5 *1 (-937))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-683 *8)) (-5 *4 (-766)) (-4 *8 (-944 *5 *7 *6)) - (-4 *5 (-13 (-306) (-146))) (-4 *6 (-13 (-845) (-610 (-1168)))) - (-4 *7 (-788)) - (-5 *2 - (-639 - (-2 (|:| |det| *8) (|:| |rows| (-639 (-562))) - (|:| |cols| (-639 (-562)))))) - (-5 *1 (-919 *5 *6 *7 *8))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-335 *5 *6 *7 *8)) (-4 *5 (-429 *4)) - (-4 *6 (-1232 *5)) (-4 *7 (-1232 (-406 *6))) - (-4 *8 (-341 *5 *6 *7)) - (-4 *4 (-13 (-845) (-554) (-1033 (-562)))) - (-5 *2 (-2 (|:| -1900 (-766)) (|:| -1407 *8))) - (-5 *1 (-906 *4 *5 *6 *7 *8)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-335 (-406 (-562)) *4 *5 *6)) - (-4 *4 (-1232 (-406 (-562)))) (-4 *5 (-1232 (-406 *4))) - (-4 *6 (-341 (-406 (-562)) *4 *5)) - (-5 *2 (-2 (|:| -1900 (-766)) (|:| -1407 *6))) - (-5 *1 (-907 *4 *5 *6))))) -(((*1 *2 *1) - (-12 (-5 *2 (-868 (-961 *3) (-961 *3))) (-5 *1 (-961 *3)) - (-4 *3 (-962))))) -(((*1 *1 *2) - (|partial| -12 (-5 *2 (-639 *6)) (-4 *6 (-1058 *3 *4 *5)) - (-4 *3 (-554)) (-4 *4 (-788)) (-4 *5 (-845)) - (-5 *1 (-1269 *3 *4 *5 *6)))) - ((*1 *1 *2 *3 *4) - (|partial| -12 (-5 *2 (-639 *8)) (-5 *3 (-1 (-112) *8 *8)) - (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1058 *5 *6 *7)) (-4 *5 (-554)) - (-4 *6 (-788)) (-4 *7 (-845)) (-5 *1 (-1269 *5 *6 *7 *8))))) + (-12 (-5 *3 (-838 (-378))) (-5 *2 (-838 (-224))) (-5 *1 (-304))))) (((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-441 *3)) (-4 *3 (-1232 (-562)))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-916)) (-5 *3 (-639 (-262))) (-5 *1 (-260)))) - ((*1 *1 *2) (-12 (-5 *2 (-916)) (-5 *1 (-262))))) + (-12 (-5 *2 (-1261)) (-5 *1 (-1184 *3 *4)) (-4 *3 (-1092)) + (-4 *4 (-1092))))) +(((*1 *2 *2) (-12 (-5 *2 (-224)) (-5 *1 (-225)))) + ((*1 *2 *2) (-12 (-5 *2 (-168 (-224))) (-5 *1 (-225))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) - (|:| -1590 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) - (|:| |relerr| (-224)))) - (-5 *2 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))) - (-5 *1 (-191))))) + (-12 (-5 *3 (-1256 *4)) (-4 *4 (-1044)) (-4 *2 (-1232 *4)) + (-5 *1 (-443 *4 *2)))) + ((*1 *2 *3 *2 *4) + (-12 (-5 *2 (-406 (-1164 (-315 *5)))) (-5 *3 (-1256 (-315 *5))) + (-5 *4 (-562)) (-4 *5 (-13 (-554) (-845))) (-5 *1 (-1122 *5))))) +(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-466)))) + ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-466))))) +(((*1 *2 *1 *1) + (-12 (-5 *2 (-2 (|:| -1606 (-777 *3)) (|:| |coef1| (-777 *3)))) + (-5 *1 (-777 *3)) (-4 *3 (-554)) (-4 *3 (-1044)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-554)) (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *5 (-845)) + (-5 *2 (-2 (|:| -1606 *1) (|:| |coef1| *1))) + (-4 *1 (-1058 *3 *4 *5))))) +(((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) + (-12 (-4 *1 (-792 *2)) (-4 *2 (-171)))) + ((*1 *1 *2 *2) + (-12 (-5 *2 (-994 *3)) (-4 *3 (-171)) (-5 *1 (-794 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) (-4 *2 (-13 (-429 *3) (-997))))) @@ -8304,55 +8365,56 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) -(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *5 *6 *5 *4 *7 *3) - (-12 (-5 *4 (-683 (-562))) (-5 *5 (-112)) (-5 *7 (-683 (-224))) - (-5 *3 (-562)) (-5 *6 (-224)) (-5 *2 (-1030)) (-5 *1 (-749))))) -(((*1 *1 *1 *2 *1) - (-12 (-5 *2 (-562)) (-5 *1 (-1148 *3)) (-4 *3 (-1207)))) - ((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4403)) (-4 *1 (-1244 *2)) (-4 *2 (-1207))))) -(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-562)) (-5 *3 (-916)) (-5 *1 (-693)))) - ((*1 *2 *2 *2 *3 *4) - (-12 (-5 *2 (-683 *5)) (-5 *3 (-99 *5)) (-5 *4 (-1 *5 *5)) - (-4 *5 (-362)) (-5 *1 (-973 *5))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1168)) (-5 *5 (-1086 (-224))) (-5 *2 (-922)) + (-5 *1 (-920 *3)) (-4 *3 (-610 (-535))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1168)) (-5 *2 (-922)) (-5 *1 (-920 *3)) + (-4 *3 (-610 (-535))))) + ((*1 *1 *2) (-12 (-5 *2 (-1 (-224) (-224))) (-5 *1 (-922)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1 (-224) 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*2 *3) (-12 (-5 *3 (-1150)) (-5 *2 (-562)) (-5 *1 (-240)))) + ((*1 *2 *3) + (-12 (-5 *3 (-639 (-1150))) (-5 *2 (-562)) (-5 *1 (-240))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-683 *3)) + (-4 *3 (-13 (-306) (-10 -8 (-15 -3788 ((-417 $) $))))) + (-4 *4 (-1232 *3)) (-5 *1 (-498 *3 *4 *5)) (-4 *5 (-408 *3 *4)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *2 (-683 *3)) + (-4 *3 (-13 (-306) (-10 -8 (-15 -3788 ((-417 $) $))))) + (-4 *4 (-1232 *3)) (-5 *1 (-498 *3 *4 *5)) (-4 *5 (-408 *3 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-1 *5 *5)) (-4 *1 (-341 *4 *5 *6)) (-4 *4 (-1211)) - (-4 *5 (-1232 *4)) (-4 *6 (-1232 (-406 *5))) - (-5 *2 (-2 (|:| |num| (-683 *5)) (|:| |den| *5)))))) + (-12 (-5 *2 (-1 (-938 *3) (-938 *3))) (-5 *1 (-175 *3)) + (-4 *3 (-13 (-362) (-1192) (-997)))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) (-4 *2 (-13 (-429 *3) (-997))))) @@ -8481,62 +8540,62 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 *3 (-38 (-406 (-562)))) (-5 *1 (-1154 *3))))) -(((*1 *1 *1) (-4 *1 (-864 *2)))) 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(-5 *1 (-662 *5 *6 *4 *3)) (-4 *3 (-681 *5 *6 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-681 *3 *4 *5)) (-4 *3 (-1044)) (-4 *4 (-372 *3)) @@ -12463,134 +12445,26 @@ (-12 (-4 *1 (-1047 *3 *4 *5 *6 *7)) (-4 *5 (-1044)) (-4 *6 (-237 *4 *5)) (-4 *7 (-237 *3 *5)) (-4 *5 (-554)) (-5 *2 (-766))))) -(((*1 *2 *3) - (-12 (-5 *3 (-764)) - (-5 *2 - (-2 (|:| -2172 (-378)) (|:| -3254 (-1150)) - (|:| |explanations| (-639 (-1150))) (|:| |extra| (-1030)))) - (-5 *1 (-563)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-764)) (-5 *4 (-1056)) - (-5 *2 - (-2 (|:| -2172 (-378)) (|:| -3254 (-1150)) - (|:| |explanations| (-639 (-1150))) (|:| |extra| (-1030)))) - (-5 *1 (-563)))) - ((*1 *2 *3 *4) - (-12 (-4 *1 (-782)) (-5 *3 (-1056)) - (-5 *4 - (-2 (|:| |fn| (-315 (-224))) - (|:| -1590 (-639 (-1086 (-838 (-224))))) (|:| |abserr| (-224)) - (|:| |relerr| (-224)))) - (-5 *2 - (-2 (|:| -2172 (-378)) (|:| |explanations| (-1150)) - (|:| |extra| (-1030)))))) - ((*1 *2 *3 *4) - (-12 (-4 *1 (-782)) (-5 *3 (-1056)) - (-5 *4 - (-2 (|:| |var| 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(-1035))))) +(((*1 *2 *1) + (-12 (-5 *2 (-639 (-562))) (-5 *1 (-999 *3)) (-14 *3 (-562))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-562)) (-5 *4 (-683 (-224))) (-5 *2 (-1030)) + (-5 *1 (-750))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) - (|:| -1590 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) + (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (-5 *2 (-2 @@ -14833,7 +14838,7 @@ (-3 (|:| |str| (-1148 (-224))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1590 + (|:| -2147 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -14841,146 +14846,202 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-557))))) +(((*1 *2 *3 *4 *5 *6) + (-12 (-5 *5 (-639 (-639 (-3 (|:| |array| *6) (|:| |scalar| *3))))) + (-5 *4 (-639 (-3 (|:| |array| (-639 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(-386)))) @@ -15149,42 +15188,31 @@ ((*1 *1 *2) (-12 (-5 *2 (-406 (-562))) (-4 *1 (-1007)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1007)) (-5 *2 (-916)))) ((*1 *1 *1) (-4 *1 (-1007)))) -(((*1 *2 *2) (-12 (-5 *2 (-315 (-224))) (-5 *1 (-266))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) - (|:| -1590 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) - (|:| |relerr| (-224)))) - (-5 *2 (-378)) (-5 *1 (-191))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-554)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -2835 *4))) - (-5 *1 (-964 *4 *3)) (-4 *3 (-1232 *4))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-362)) (-5 *1 (-761 *2 *3)) (-4 *2 (-703 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-847 *2)) (-4 *2 (-1044)) (-4 *2 (-362))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1148 *3)) (-4 *3 (-1044)) (-5 *1 (-1152 *3)))) - ((*1 *1 *1) - (-12 (-5 *1 (-1248 *2 *3 *4)) (-4 *2 (-1044)) (-14 *3 (-1168)) - (-14 *4 *2)))) -(((*1 *2 *3 *4 *5 *3) - (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 (-1 (-3 (-2 (|:| -3860 *6) (|:| |coeff| *6)) 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(-262))))) (((*1 *2 *3) - (|partial| -12 (-5 *2 (-562)) (-5 *1 (-1189 *3)) (-4 *3 (-1044))))) + (-12 (-5 *3 (-562)) (-4 *4 (-788)) (-4 *5 (-845)) (-4 *2 (-1044)) + (-5 *1 (-320 *4 *5 *2 *6)) (-4 *6 (-944 *2 *4 *5))))) (((*1 *1 *1) (-12 (-4 *1 (-119 *2)) (-4 *2 (-1207)))) ((*1 *1 *1) (-12 (-5 *1 (-666 *2)) (-4 *2 (-845)))) ((*1 *1 *1) (-12 (-5 *1 (-671 *2)) (-4 *2 (-845)))) @@ -15682,89 +15643,177 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-843) (-362))) (-5 *1 (-1054 *2 *3)) (-4 *3 (-1232 *2))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1148 (-639 (-562)))) (-5 *1 (-878)) (-5 *3 (-562))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-639 + (-2 + (|:| -2319 + (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) + (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) + (|:| |relerr| (-224)))) + (|:| -2693 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1148 (-224))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2147 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-557))))) +(((*1 *2 *1) (-12 (-4 *1 (-843)) (-5 *2 (-562)))) + ((*1 *2 *1) (-12 (-5 *2 (-562)) (-5 *1 (-900 *3)) (-4 *3 (-1092)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1061 *4 *3)) (-4 *4 (-13 (-843) (-362))) + (-4 *3 (-1232 *4)) (-5 *2 (-562)))) + ((*1 *2 *3) + (|partial| -12 + (-4 *4 (-13 (-554) (-845) (-1033 *2) (-635 *2) (-451))) + (-5 *2 (-562)) (-5 *1 (-1108 *4 *3)) + (-4 *3 (-13 (-27) (-1192) (-429 *4))))) + ((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-1168)) (-5 *5 (-838 *3)) + (-4 *3 (-13 (-27) (-1192) (-429 *6))) + (-4 *6 (-13 (-554) (-845) (-1033 *2) (-635 *2) (-451))) + (-5 *2 (-562)) (-5 *1 (-1108 *6 *3)))) + ((*1 *2 *3 *4 *3 *5) + (|partial| -12 (-5 *4 (-1168)) (-5 *5 (-1150)) + (-4 *6 (-13 (-554) (-845) (-1033 *2) (-635 *2) (-451))) + (-5 *2 (-562)) (-5 *1 (-1108 *6 *3)) + (-4 *3 (-13 (-27) (-1192) (-429 *6))))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-406 (-947 *4))) (-4 *4 (-451)) (-5 *2 (-562)) + (-5 *1 (-1109 *4)))) + ((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-1168)) (-5 *5 (-838 (-406 (-947 *6)))) + (-5 *3 (-406 (-947 *6))) (-4 *6 (-451)) (-5 *2 (-562)) + (-5 *1 (-1109 *6)))) + ((*1 *2 *3 *4 *3 *5) + (|partial| -12 (-5 *3 (-406 (-947 *6))) (-5 *4 (-1168)) + (-5 *5 (-1150)) (-4 *6 (-451)) (-5 *2 (-562)) (-5 *1 (-1109 *6)))) + ((*1 *2 *3) + (|partial| -12 (-5 *2 (-562)) (-5 *1 (-1189 *3)) (-4 *3 (-1044))))) +(((*1 *2 *2) + (-12 (-5 *2 (-639 *7)) (-4 *7 (-1064 *3 *4 *5 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(|:| -2466 *5) (|:| -1960 *2)))) - (-4 *2 (-237 (-3492 *3) (-766))) (-5 *1 (-460 *3 *4 *5 *2 *6 *7)) - (-4 *5 (-845)) (-4 *7 (-944 *4 *2 (-859 *3)))))) +(((*1 *2 *3 *4 *5 *6) + (-12 (-5 *4 (-112)) (-5 *5 (-1094 (-766))) (-5 *6 (-766)) + (-5 *2 + (-2 (|:| |contp| (-562)) + (|:| -2656 (-639 (-2 (|:| |irr| *3) (|:| -2794 (-562))))))) + (-5 *1 (-441 *3)) (-4 *3 (-1232 (-562)))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1256 *1)) (-4 *1 (-366 *4)) (-4 *4 (-171)) + (-5 *2 (-683 *4)))) + ((*1 *2 *1) (-12 (-4 *1 (-416 *3)) (-4 *3 (-171)) (-5 *2 (-683 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-639 (-608 *1))) (-4 *1 (-301))))) -(((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-1 *3 *3 *3 *3 *3)) (-4 *3 (-1092)) (-5 *1 (-103 *3)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-1 *2 *2 *2)) (-5 *1 (-103 *2)) (-4 *2 (-1092))))) -(((*1 *1 *2) +(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1207)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-121 *2)) (-4 *2 (-845)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-126 *2)) (-4 *2 (-845)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-562)) (-4 *1 (-281 *3)) (-4 *3 (-1207)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-562)) (-4 *1 (-281 *2)) (-4 *2 (-1207)))) + ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |mval| (-683 *3)) (|:| |invmval| (-683 *3)) - (|:| |genIdeal| (-503 *3 *4 *5 *6)))) - (-4 *3 (-362)) (-4 *4 (-788)) (-4 *5 (-845)) - (-5 *1 (-503 *3 *4 *5 *6)) (-4 *6 (-944 *3 *4 *5))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-1164 *1)) (-4 *1 (-1007))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-306) (-146))) (-4 *5 (-788)) (-4 *6 (-845)) - (-4 *7 (-944 *4 *5 *6)) (-5 *2 (-639 (-639 *7))) - (-5 *1 (-447 *4 *5 *6 *7)) (-5 *3 (-639 *7)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-13 (-306) (-146))) (-4 *6 (-788)) - (-4 *7 (-845)) (-4 *8 (-944 *5 *6 *7)) (-5 *2 (-639 (-639 *8))) - (-5 *1 (-447 *5 *6 *7 *8)) (-5 *3 (-639 *8))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-362) (-146) (-1033 (-406 (-562))))) - (-4 *5 (-1232 *4)) (-5 *2 (-639 (-2 (|:| -2328 *5) (|:| -3680 *5)))) - (-5 *1 (-802 *4 *5 *3 *6)) (-4 *3 (-650 *5)) - (-4 *6 (-650 (-406 *5))))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-13 (-362) (-146) (-1033 (-406 (-562))))) - (-4 *4 (-1232 *5)) (-5 *2 (-639 (-2 (|:| -2328 *4) (|:| -3680 *4)))) - (-5 *1 (-802 *5 *4 *3 *6)) (-4 *3 (-650 *4)) - (-4 *6 (-650 (-406 *4))))) - ((*1 *2 *3) - (-12 (-4 *4 (-13 (-362) (-146) (-1033 (-406 (-562))))) - (-4 *5 (-1232 *4)) (-5 *2 (-639 (-2 (|:| -2328 *5) (|:| -3680 *5)))) - (-5 *1 (-802 *4 *5 *6 *3)) (-4 *6 (-650 *5)) - (-4 *3 (-650 (-406 *5))))) + (-2 + (|:| -2319 + (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) + (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) + (|:| |relerr| (-224)))) + (|:| -2693 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1148 (-224))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2147 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))))) + (-5 *1 (-557)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-766)) (-4 *1 (-689 *2)) (-4 *2 (-1092)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -2319 + (-2 (|:| |xinit| (-224)) (|:| |xend| (-224)) + (|:| |fn| (-1256 (-315 (-224)))) (|:| |yinit| (-639 (-224))) + (|:| |intvals| (-639 (-224))) (|:| |g| (-315 (-224))) + (|:| |abserr| (-224)) (|:| |relerr| (-224)))) + (|:| -2693 + (-2 (|:| |stiffness| (-378)) (|:| |stability| (-378)) + (|:| |expense| (-378)) (|:| |accuracy| (-378)) + (|:| |intermediateResults| (-378)))))) + (-5 *1 (-798)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-13 (-362) (-146) (-1033 (-406 (-562))))) - (-4 *4 (-1232 *5)) (-5 *2 (-639 (-2 (|:| -2328 *4) (|:| -3680 *4)))) - (-5 *1 (-802 *5 *4 *6 *3)) (-4 *6 (-650 *4)) - (-4 *3 (-650 (-406 *4)))))) -(((*1 *2 *1) (-12 (-4 *1 (-306)) (-5 *2 (-766))))) -(((*1 *1) (-5 *1 (-140))) ((*1 *1 *1) (-5 *1 (-143))) - ((*1 *1 *1) (-4 *1 (-1136)))) + (-12 (-5 *2 (-1261)) (-5 *1 (-1184 *3 *4)) (-4 *3 (-1092)) + (-4 *4 (-1092))))) +(((*1 *1 *1) (-12 (-4 *1 (-429 *2)) (-4 *2 (-845)) (-4 *2 (-554)))) + ((*1 *1 *1) (-12 (-4 *1 (-987 *2)) (-4 *2 (-554))))) +(((*1 *2) + (-12 (-4 *4 (-171)) (-5 *2 (-112)) (-5 *1 (-365 *3 *4)) + (-4 *3 (-366 *4)))) + ((*1 *2) (-12 (-4 *1 (-366 *3)) (-4 *3 (-171)) (-5 *2 (-112))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-639 *6)) (-4 *1 (-944 *4 *5 *6)) (-4 *4 (-1044)) + (-4 *5 (-788)) (-4 *6 (-845)) (-5 *2 (-766)))) + ((*1 *2 *1) + (-12 (-4 *1 (-944 *3 *4 *5)) (-4 *3 (-1044)) (-4 *4 (-788)) + (-4 *5 (-845)) (-5 *2 (-766))))) +(((*1 *2) + (-12 (-4 *3 (-554)) (-5 *2 (-639 *4)) (-5 *1 (-43 *3 *4)) + (-4 *4 (-416 *3))))) +(((*1 *1 *1) + (-12 (-5 *1 (-1132 *2 *3)) (-4 *2 (-13 (-1092) (-34))) + (-4 *3 (-13 (-1092) (-34)))))) (((*1 *2 *1) (-12 (-4 *3 (-1092)) (-4 *4 (-13 (-1044) (-881 *3) (-845) (-610 (-887 *3)))) (-5 *2 (-639 (-1068 *3 *4 *5))) (-5 *1 (-1069 *3 *4 *5)) (-4 *5 (-13 (-429 *4) (-881 *3) (-610 (-887 *3))))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1148 *3)) (-4 *3 (-1044)) (-5 *1 (-1152 *3)))) - ((*1 *1 *1) - (-12 (-5 *1 (-1248 *2 *3 *4)) (-4 *2 (-1044)) (-14 *3 (-1168)) - (-14 *4 *2)))) +(((*1 *2 *1) (-12 (-5 *2 (-1127)) (-5 *1 (-1266))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-787)) (-4 *2 (-1044)))) ((*1 *2 *1) (-12 (-4 *2 (-1044)) (-5 *1 (-50 *2 *3)) (-14 *3 (-639 (-1168))))) @@ -15776,8 +15825,8 @@ ((*1 *2 *1) (-12 (-14 *3 (-639 (-1168))) (-4 *5 (-237 (-3492 *3) (-766))) (-14 *6 - (-1 (-112) (-2 (|:| -2466 *4) (|:| -1960 *5)) - (-2 (|:| -2466 *4) (|:| -1960 *5)))) + (-1 (-112) (-2 (|:| -2464 *4) (|:| -1300 *5)) + (-2 (|:| -2464 *4) (|:| -1300 *5)))) (-4 *2 (-171)) (-5 *1 (-460 *3 *2 *4 *5 *6 *7)) (-4 *4 (-845)) (-4 *7 (-944 *2 *5 (-859 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-508 *2 *3)) (-4 *3 (-845)) (-4 *2 (-1092)))) @@ -15794,34 +15843,47 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1058 *3 *4 *2)) (-4 *3 (-1044)) (-4 *4 (-788)) (-4 *2 (-845))))) -(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1030))))) -(((*1 *2) (-12 (-5 *2 (-562)) (-5 *1 (-693)))) - ((*1 *2 *2) (-12 (-5 *2 (-562)) (-5 *1 (-693))))) (((*1 *2 *3 *1) - (-12 (-4 *1 (-600 *3 *4)) (-4 *3 (-1092)) (-4 *4 (-1207)) - (-5 *2 (-112))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1256 *5)) (-4 *5 (-635 *4)) (-4 *4 (-554)) - (-5 *2 (-112)) (-5 *1 (-634 *4 *5))))) -(((*1 *1 *1 *2) - (-12 (-4 *1 (-971 *3 *4 *2 *5)) (-4 *3 (-1044)) (-4 *4 (-788)) - (-4 *2 (-845)) (-4 *5 (-1058 *3 *4 *2))))) + (-12 (|has| *1 (-6 -4403)) (-4 *1 (-488 *3)) (-4 *3 (-1207)) + (-4 *3 (-1092)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-900 *4)) (-4 *4 (-1092)) (-5 *2 (-112)) + (-5 *1 (-899 *4)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-916)) (-5 *2 (-112)) (-5 *1 (-1093 *4 *5)) (-14 *4 *3) + (-14 *5 *3)))) +(((*1 *2 *1 *3) + (-12 (-4 *1 (-855)) (-5 *2 (-685 (-129))) (-5 *3 (-129))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-639 (-947 *5))) (-5 *4 (-639 (-1168))) (-4 *5 (-554)) - (-5 *2 (-639 (-639 (-293 (-406 (-947 *5)))))) (-5 *1 (-765 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-639 (-947 *4))) (-4 *4 (-554)) - (-5 *2 (-639 (-639 (-293 (-406 (-947 *4)))))) (-5 *1 (-765 *4)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-683 *7)) - (-5 *5 - (-1 (-2 (|:| |particular| (-3 *6 "failed")) (|:| -3928 (-639 *6))) - *7 *6)) - (-4 *6 (-362)) (-4 *7 (-650 *6)) + (-12 (-4 *5 (-362)) (-4 *5 (-554)) (-5 *2 - (-2 (|:| |particular| (-3 (-1256 *6) "failed")) - (|:| -3928 (-639 (-1256 *6))))) - (-5 *1 (-808 *6 *7)) (-5 *4 (-1256 *6))))) + (-2 (|:| |minor| (-639 (-916))) (|:| -3339 *3) + (|:| |minors| (-639 (-639 (-916)))) (|:| |ops| (-639 *3)))) + (-5 *1 (-90 *5 *3)) (-5 *4 (-916)) (-4 *3 (-650 *5))))) +(((*1 *1) (-5 *1 (-1077)))) +(((*1 *2) + (-12 (-4 *4 (-171)) (-5 *2 (-766)) (-5 *1 (-164 *3 *4)) + (-4 *3 (-165 *4)))) + ((*1 *2) + (-12 (-14 *4 *2) (-4 *5 (-1207)) (-5 *2 (-766)) + (-5 *1 (-236 *3 *4 *5)) (-4 *3 (-237 *4 *5)))) + ((*1 *2) + (-12 (-4 *4 (-845)) (-5 *2 (-766)) (-5 *1 (-428 *3 *4)) + (-4 *3 (-429 *4)))) + ((*1 *2) (-12 (-5 *2 (-766)) (-5 *1 (-543 *3)) (-4 *3 (-544)))) + ((*1 *2) (-12 (-4 *1 (-758)) (-5 *2 (-766)))) + ((*1 *2) + (-12 (-4 *4 (-171)) (-5 *2 (-766)) (-5 *1 (-791 *3 *4)) + (-4 *3 (-792 *4)))) + ((*1 *2) + (-12 (-4 *4 (-554)) (-5 *2 (-766)) (-5 *1 (-986 *3 *4)) + (-4 *3 (-987 *4)))) + ((*1 *2) + (-12 (-4 *4 (-171)) (-5 *2 (-766)) (-5 *1 (-991 *3 *4)) + (-4 *3 (-992 *4)))) + ((*1 *2) (-12 (-5 *2 (-766)) (-5 *1 (-1006 *3)) (-4 *3 (-1007)))) + ((*1 *2) (-12 (-4 *1 (-1044)) (-5 *2 (-766)))) + ((*1 *2) (-12 (-5 *2 (-766)) (-5 *1 (-1052 *3)) (-4 *3 (-1053))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *2)) @@ -15838,31 +15900,26 @@ ((*1 *2 *2) (-12 (-5 *2 (-1148 *3)) (-4 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(-5 *2 - (-2 (|:| |mainpart| *3) - (|:| |limitedlogs| - (-639 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) - (-5 *1 (-568 *6))))) -(((*1 *2) (-12 (-5 *2 (-639 (-1150))) (-5 *1 (-1259)))) - ((*1 *2 *2) (-12 (-5 *2 (-639 (-1150))) (-5 *1 (-1259))))) + (-12 (-5 *2 (-1223 (-562))) (-4 *1 (-281 *3)) (-4 *3 (-1207)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-562)) (-4 *1 (-281 *3)) (-4 *3 (-1207))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-378)) (-5 *2 (-1261)) (-5 *1 (-1258))))) (((*1 *1 *1) (-4 *1 (-242))) ((*1 *1 *1) (-12 (-4 *2 (-171)) (-5 *1 (-288 *2 *3 *4 *5 *6 *7)) @@ -16109,18 +16141,23 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *1) (-12 (-4 *1 (-792 *2)) (-4 *2 (-171)) (-4 *2 (-362))))) -(((*1 *2 *2 *2 *2) - (-12 (-5 *2 (-683 *3)) (-4 *3 (-1044)) (-5 *1 (-684 *3))))) -(((*1 *1) (-5 *1 (-436)))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-554)) (-4 *3 (-1044)) + (-5 *2 (-2 (|:| -3380 *1) (|:| -1441 *1))) (-4 *1 (-847 *3)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-99 *5)) (-4 *5 (-554)) (-4 *5 (-1044)) + (-5 *2 (-2 (|:| -3380 *3) (|:| -1441 *3))) (-5 *1 (-848 *5 *3)) + (-4 *3 (-847 *5))))) +(((*1 *2 *3) + (-12 (-5 *3 (-916)) (-5 *2 (-1164 *4)) (-5 *1 (-356 *4)) + (-4 *4 (-348))))) (((*1 *2 *1) (-12 (-5 *2 (-639 (-1150))) (-5 *1 (-1187))))) -(((*1 *2 *2 *2 *2 *3) - (-12 (-4 *3 (-554)) (-5 *1 (-964 *3 *2)) (-4 *2 (-1232 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-639 (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224))) - (|:| -1590 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) + (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224)) (|:| |relerr| (-224))))) (-5 *1 (-557)))) ((*1 *2 *1) @@ -16135,61 +16172,56 @@ (|:| |intvals| (-639 (-224))) (|:| |g| (-315 (-224))) (|:| |abserr| (-224)) (|:| |relerr| (-224))))) (-5 *1 (-798))))) -(((*1 *2 *3 *3 *2) - (-12 (-5 *2 (-683 (-562))) (-5 *3 (-639 (-562))) (-5 *1 (-1102))))) -(((*1 *2 *1) - (-12 (-5 *2 (-406 (-947 *3))) (-5 *1 (-452 *3 *4 *5 *6)) - (-4 *3 (-554)) (-4 *3 (-171)) (-14 *4 (-916)) - (-14 *5 (-639 (-1168))) (-14 *6 (-1256 (-683 *3)))))) +(((*1 *1 *2) (-12 (-5 *1 (-685 *2)) (-4 *2 (-609 (-857)))))) +(((*1 *1 *1) (-12 (-5 *1 (-961 *2)) (-4 *2 (-962))))) +(((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-817))))) +(((*1 *2) + (-12 (-4 *4 (-171)) (-5 *2 (-112)) (-5 *1 (-365 *3 *4)) + (-4 *3 (-366 *4)))) + ((*1 *2) (-12 (-4 *1 (-366 *3)) (-4 *3 (-171)) (-5 *2 (-112))))) (((*1 *2 *3) - (-12 (-4 *4 (-451)) - (-5 *2 - (-639 - (-2 (|:| |eigval| (-3 (-406 (-947 *4)) (-1157 (-1168) (-947 *4)))) - (|:| |geneigvec| (-639 (-683 (-406 (-947 *4)))))))) - (-5 *1 (-291 *4)) (-5 *3 (-683 (-406 (-947 *4))))))) -(((*1 *1 *2 *3) - (-12 (-5 *3 (-1148 *2)) (-4 *2 (-306)) (-5 *1 (-173 *2))))) + (-12 (-5 *3 (-1086 (-838 (-224)))) (-5 *2 (-224)) (-5 *1 (-191)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1086 (-838 (-224)))) (-5 *2 (-224)) (-5 *1 (-299)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1086 (-838 (-224)))) (-5 *2 (-224)) (-5 *1 (-304))))) (((*1 *2 *3 *1) (|partial| -12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1092)) (-4 *4 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*1) (-12 (-5 *2 (-1127)) (-5 *1 (-1088)))) ((*1 *2 *1) @@ -16269,41 +16301,35 @@ ((*1 *1 *2) (-12 (-5 *2 (-1148 (-2 (|:| |k| (-766)) (|:| |c| *3)))) (-4 *3 (-1044)) (-4 *1 (-1247 *3))))) -(((*1 *1 *2 *3) (-12 (-5 *2 (-1164 *1)) (-5 *3 (-1168)) (-4 *1 (-27)))) - ((*1 *1 *2) (-12 (-5 *2 (-1164 *1)) (-4 *1 (-27)))) - ((*1 *1 *2) (-12 (-5 *2 (-947 *1)) (-4 *1 (-27)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-1168)) (-4 *1 (-29 *3)) (-4 *3 (-13 (-845) (-554))))) - ((*1 *1 *1) (-12 (-4 *1 (-29 *2)) (-4 *2 (-13 (-845) (-554))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1164 *2)) (-5 *4 (-1168)) (-4 *2 (-429 *5)) - (-5 *1 (-32 *5 *2)) (-4 *5 (-13 (-845) (-554))))) - ((*1 *1 *2 *3) - (|partial| -12 (-5 *2 (-1164 *1)) (-5 *3 (-916)) (-4 *1 (-1007)))) - ((*1 *1 *2 *3 *4) - (|partial| -12 (-5 *2 (-1164 *1)) (-5 *3 (-916)) (-5 *4 (-857)) - (-4 *1 (-1007)))) - ((*1 *1 *2 *3) - (|partial| -12 (-5 *3 (-916)) (-4 *4 (-13 (-843) (-362))) - (-4 *1 (-1061 *4 *2)) (-4 *2 (-1232 *4))))) -(((*1 *2 *3 *4 *5 *6 *5 *3 *7) - (-12 (-5 *4 (-562)) - (-5 *6 - (-2 (|:| |try| (-378)) (|:| |did| (-378)) (|:| -4335 (-378)))) - (-5 *7 (-1 (-1261) (-1256 *5) (-1256 *5) (-378))) - (-5 *3 (-1256 (-378))) (-5 *5 (-378)) (-5 *2 (-1261)) - (-5 *1 (-783)))) - ((*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3) - (-12 (-5 *4 (-562)) - (-5 *6 - (-2 (|:| |try| (-378)) (|:| |did| (-378)) (|:| -4335 (-378)))) - (-5 *7 (-1 (-1261) (-1256 *5) (-1256 *5) (-378))) - (-5 *3 (-1256 (-378))) (-5 *5 (-378)) (-5 *2 (-1261)) - (-5 *1 (-783))))) -(((*1 *2) - (-12 - (-5 *2 (-2 (|:| -3712 (-639 (-1168))) (|:| -2010 (-639 (-1168))))) - (-5 *1 (-1209))))) +(((*1 *2 *2) + (-12 (-5 *2 (-114)) (-4 *3 (-13 (-845) (-554))) (-5 *1 (-32 *3 *4)) + (-4 *4 (-429 *3)))) + ((*1 *1 *2 *3) (-12 (-5 *2 (-1168)) (-5 *3 (-766)) (-5 *1 (-114)))) + ((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-114)))) + ((*1 *2 *2) + (-12 (-5 *2 (-114)) (-4 *3 (-13 (-845) (-554))) (-5 *1 (-157 *3 *4)) + (-4 *4 (-429 *3)))) + ((*1 *2 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-114)) (-5 *1 (-162)))) + ((*1 *2 *2) + (-12 (-5 *2 (-114)) (-4 *3 (-13 (-845) (-554))) (-5 *1 (-275 *3 *4)) + (-4 *4 (-13 (-429 *3) (-997))))) + ((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-300 *3)) (-4 *3 (-301)))) + ((*1 *2 *2) (-12 (-4 *1 (-301)) (-5 *2 (-114)))) + ((*1 *2 *2) + (-12 (-5 *2 (-114)) (-4 *4 (-845)) (-5 *1 (-428 *3 *4)) + (-4 *3 (-429 *4)))) + ((*1 *2 *2) + (-12 (-5 *2 (-114)) (-4 *3 (-13 (-845) (-554))) (-5 *1 (-430 *3 *4)) + (-4 *4 (-429 *3)))) + ((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-608 *3)) (-4 *3 (-845)))) + ((*1 *2 *2) + (-12 (-5 *2 (-114)) (-4 *3 (-13 (-845) (-554))) (-5 *1 (-626 *3 *4)) + (-4 *4 (-13 (-429 *3) (-997) (-1192))))) + ((*1 *2 *1) (-12 (-5 *2 (-1127)) (-5 *1 (-1014))))) +(((*1 *2 *1) (-12 (-5 *2 (-639 (-608 *1))) (-4 *1 (-301))))) +(((*1 *2 *2) + (-12 (-4 *3 (-306)) (-4 *4 (-372 *3)) (-4 *5 (-372 *3)) + (-5 *1 (-1116 *3 *4 *5 *2)) (-4 *2 (-681 *3 *4 *5))))) (((*1 *2 *3) (-12 (-5 *3 (-1168)) (-4 *4 (-13 (-451) (-845) (-1033 (-562)) (-635 (-562)))) @@ -16341,22 +16367,9 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-406 (-562))) (-4 *4 (-1044)) (-4 *1 (-1239 *4 *3)) (-4 *3 (-1216 *4))))) -(((*1 *1 *1) - (-12 (-4 *1 (-325 *2 *3)) (-4 *2 (-1044)) (-4 *3 (-787)) - (-4 *2 (-451)))) - ((*1 *1 *1) - (-12 (-4 *1 (-341 *2 *3 *4)) (-4 *2 (-1211)) (-4 *3 (-1232 *2)) - (-4 *4 (-1232 (-406 *3))))) - ((*1 *1 *1) (-12 (-4 *1 (-847 *2)) (-4 *2 (-1044)) (-4 *2 (-451)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-944 *3 *4 *2)) (-4 *3 (-1044)) (-4 *4 (-788)) - (-4 *2 (-845)) (-4 *3 (-451)))) - ((*1 *1 *1) - (-12 (-4 *1 (-944 *2 *3 *4)) (-4 *2 (-1044)) (-4 *3 (-788)) - (-4 *4 (-845)) (-4 *2 (-451)))) - ((*1 *2 *2 *3) - (-12 (-4 *3 (-306)) (-4 *3 (-554)) (-5 *1 (-1155 *3 *2)) - (-4 *2 (-1232 *3))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1095 *3 *4 *5 *6 *7)) (-4 *3 (-1092)) (-4 *4 (-1092)) + (-4 *5 (-1092)) (-4 *6 (-1092)) (-4 *7 (-1092)) (-5 *2 (-112))))) (((*1 *2 *3) (-12 (-5 *3 (-1 *5)) (-4 *5 (-1092)) (-5 *2 (-1 *5 *4)) (-5 *1 (-677 *4 *5)) (-4 *4 (-1092)))) @@ -16368,40 +16381,36 @@ (-12 (-4 *1 (-1273 *3 *2)) (-4 *3 (-845)) (-4 *2 (-1044)))) ((*1 *2 *1) (-12 (-4 *2 (-1044)) (-5 *1 (-1279 *2 *3)) (-4 *3 (-841))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1164 *2)) (-4 *2 (-944 (-406 (-947 *6)) *5 *4)) - (-5 *1 (-727 *5 *4 *6 *2)) (-4 *5 (-788)) - (-4 *4 (-13 (-845) (-10 -8 (-15 -4208 ((-1168) $))))) - (-4 *6 (-554))))) -(((*1 *2 *1) (-12 (-5 *2 (-639 (-608 *1))) (-4 *1 (-301))))) -(((*1 *2 *3 *4) - (-12 (-4 *6 (-554)) (-4 *2 (-944 *3 *5 *4)) - (-5 *1 (-727 *5 *4 *6 *2)) (-5 *3 (-406 (-947 *6))) (-4 *5 (-788)) - (-4 *4 (-13 (-845) (-10 -8 (-15 -4208 ((-1168) $)))))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-562)) (-4 *1 (-1216 *4)) (-4 *4 (-1044)) (-4 *4 (-554)) - (-5 *2 (-406 (-947 *4))))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-562)) (-4 *1 (-1216 *4)) (-4 *4 (-1044)) (-4 *4 (-554)) - (-5 *2 (-406 (-947 *4)))))) -(((*1 *2 *2 *3 *4) - (-12 (-5 *2 (-1256 *5)) (-5 *3 (-766)) (-5 *4 (-1112)) (-4 *5 (-348)) - (-5 *1 (-527 *5))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-639 (-608 *5))) (-5 *3 (-1168)) (-4 *5 (-429 *4)) - (-4 *4 (-845)) (-5 *1 (-571 *4 *5))))) +(((*1 *2 *2) (-12 (-5 *2 (-1112)) (-5 *1 (-329))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-406 (-562))) + (-4 *4 (-13 (-554) (-845) (-1033 (-562)) (-635 (-562)))) + (-5 *1 (-276 *4 *2)) (-4 *2 (-13 (-27) (-1192) (-429 *4)))))) +(((*1 *1 *1) (-12 (-4 *1 (-668 *2)) (-4 *2 (-1207))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-639 *1)) (-4 *1 (-1058 *4 *5 *6)) (-4 *4 (-1044)) + (-4 *5 (-788)) (-4 *6 (-845)) (-5 *2 (-112)))) + ((*1 *2 *1 *1) + (-12 (-4 *1 (-1058 *3 *4 *5)) (-4 *3 (-1044)) (-4 *4 (-788)) + (-4 *5 (-845)) (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1200 *3 *4 *5 *6)) (-4 *3 (-554)) (-4 *4 (-788)) + (-4 *5 (-845)) (-4 *6 (-1058 *3 *4 *5)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1200 *4 *5 *6 *3)) (-4 *4 (-554)) (-4 *5 (-788)) + (-4 *6 (-845)) (-4 *3 (-1058 *4 *5 *6)) (-5 *2 (-112))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-916)) (-4 *1 (-739 *3)) (-4 *3 (-171))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1207)) (-4 *4 (-372 *3)) (-4 *5 (-372 *3)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4403)) (-4 *1 (-488 *3)) + (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4404)) (-4 *1 (-488 *3)) (-4 *3 (-1207))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-916)) (-5 *2 (-467)) (-5 *1 (-1257))))) -(((*1 *1 *2) (-12 (-5 *2 (-639 (-329))) (-5 *1 (-329))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1179 (-639 *4))) (-4 *4 (-845)) - (-5 *2 (-639 (-639 *4))) (-5 *1 (-1178 *4))))) -(((*1 *2 *2) (-12 (-5 *2 (-562)) (-5 *1 (-921))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-766)) (-5 *1 (-103 *3)) (-4 *3 (-1092))))) +(((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-817))))) +(((*1 *2 *1) + (-12 (-4 *1 (-334 *3 *4 *5 *6)) (-4 *3 (-362)) (-4 *4 (-1232 *3)) + (-4 *5 (-1232 (-406 *4))) (-4 *6 (-341 *3 *4 *5)) (-5 *2 (-112))))) (((*1 *2 *3) (-12 (-5 *3 (-1168)) (-4 *4 (-13 (-451) (-845) (-1033 (-562)) (-635 (-562)))) @@ -16438,21 +16447,41 @@ (-4 *3 (-1247 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1239 *3 *2)) (-4 *3 (-1044)) (-4 *2 (-1216 *3))))) -(((*1 *2 *2) (-12 (-5 *2 (-1150)) (-5 *1 (-857))))) +(((*1 *2 *3 *4 *5 *3) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 + (-1 (-2 (|:| |ans| *6) (|:| -1603 *6) (|:| |sol?| (-112))) (-562) + *6)) + (-4 *6 (-362)) (-4 *7 (-1232 *6)) + (-5 *2 + (-3 (-2 (|:| |answer| (-406 *7)) (|:| |a0| *6)) + (-2 (|:| -2929 (-406 *7)) (|:| |coeff| (-406 *7))) "failed")) + (-5 *1 (-572 *6 *7)) (-5 *3 (-406 *7))))) +(((*1 *2 *2 *2) + (|partial| -12 (-4 *3 (-13 (-554) (-146))) (-5 *1 (-1226 *3 *2)) + (-4 *2 (-1232 *3))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-766)) (|:| |poli| *7) + (|:| |polj| *7))) + (-4 *5 (-788)) (-4 *7 (-944 *4 *5 *6)) (-4 *4 (-451)) (-4 *6 (-845)) + (-5 *2 (-112)) (-5 *1 (-448 *4 *5 *6 *7))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-562)) (-4 *1 (-1085 *3)) (-4 *3 (-1207))))) (((*1 *1 *1 *2) (-12 (-5 *2 - (-2 (|:| -3562 (-639 (-857))) (|:| -3659 (-639 (-857))) - (|:| |presup| (-639 (-857))) (|:| -2074 (-639 (-857))) + (-2 (|:| -1923 (-639 (-857))) (|:| -1593 (-639 (-857))) + (|:| |presup| (-639 (-857))) (|:| -3142 (-639 (-857))) (|:| |args| (-639 (-857))))) (-5 *1 (-1168)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-639 (-639 (-857)))) (-5 *1 (-1168))))) (((*1 *2) (-12 (-5 *2 (-639 *3)) (-5 *1 (-1076 *3)) (-4 *3 (-131))))) -(((*1 *2 *2) - (-12 (-5 *2 (-938 *3)) (-4 *3 (-13 (-362) (-1192) (-997))) - (-5 *1 (-175 *3))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-766)) (-4 *5 (-554)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) + (-5 *1 (-964 *5 *3)) (-4 *3 (-1232 *5))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-857) (-857))) (-5 *1 (-114)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-857) (-639 (-857)))) (-5 *1 (-114)))) ((*1 *2 *1) @@ -16462,7 +16491,7 @@ (-4 *3 (-13 (-845) (-10 -8 (-15 -2343 ((-1150) $ (-1168))) (-15 -1479 (*2 $)) - (-15 -1966 (*2 $))))))) + (-15 -1359 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-393)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-562)) (-5 *2 (-1261)) (-5 *1 (-393)))) ((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-501)))) @@ -16470,13 +16499,27 @@ ((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-1187)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-562)) (-5 *2 (-1261)) (-5 *1 (-1187))))) (((*1 *2 *1) (-12 (-4 *1 (-969)) (-5 *2 (-1086 (-224)))))) -(((*1 *2 *1 *3) (-12 (-4 *1 (-526)) (-5 *3 (-128)) (-5 *2 (-766))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-1096)) (-5 *1 (-279))))) +(((*1 *2 *1) + (-12 (-5 *2 (-173 (-406 (-562)))) (-5 *1 (-117 *3)) (-14 *3 (-562)))) + ((*1 *1 *2 *3 *3) + (-12 (-5 *3 (-1148 *2)) (-4 *2 (-306)) (-5 *1 (-173 *2)))) + ((*1 *1 *2) (-12 (-5 *2 (-406 *3)) (-4 *3 (-306)) (-5 *1 (-173 *3)))) + ((*1 *2 *3) + (-12 (-5 *2 (-173 (-562))) (-5 *1 (-760 *3)) (-4 *3 (-403)))) + ((*1 *2 *1) + (-12 (-5 *2 (-173 (-406 (-562)))) (-5 *1 (-866 *3)) (-14 *3 (-562)))) + ((*1 *2 *1) + (-12 (-14 *3 (-562)) (-5 *2 (-173 (-406 (-562)))) + (-5 *1 (-867 *3 *4)) (-4 *4 (-864 *3))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-766)) (-4 *6 (-1092)) (-4 *3 (-895 *6)) + (-5 *2 (-683 *3)) (-5 *1 (-686 *6 *3 *7 *4)) (-4 *7 (-372 *3)) + (-4 *4 (-13 (-372 *6) (-10 -7 (-6 -4403))))))) (((*1 *1 *2 *1) - (-12 (|has| *1 (-6 -4402)) (-4 *1 (-150 *2)) (-4 *2 (-1207)) + (-12 (|has| *1 (-6 -4403)) (-4 *1 (-150 *2)) (-4 *2 (-1207)) (-4 *2 (-1092)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4402)) (-4 *1 (-150 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4403)) (-4 *1 (-150 *3)) (-4 *3 (-1207)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-668 *3)) (-4 *3 (-1207)))) @@ -16488,29 +16531,18 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1132 *3 *4)) (-4 *3 (-13 (-1092) (-34))) (-4 *4 (-13 (-1092) (-34))) (-5 *1 (-1133 *3 *4))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1170 (-406 (-562)))) (-5 *1 (-189))))) -(((*1 *2 *3 *3 *4) - (-12 (-4 *5 (-451)) (-4 *6 (-788)) (-4 *7 (-845)) - (-4 *3 (-1058 *5 *6 *7)) - (-5 *2 (-639 (-2 (|:| |val| (-639 *3)) (|:| -1495 *4)))) - (-5 *1 (-1065 *5 *6 *7 *3 *4)) (-4 *4 (-1064 *5 *6 *7 *3))))) +(((*1 *1 *1) (-5 *1 (-224))) ((*1 *1 *1) (-5 *1 (-378))) + ((*1 *1) (-5 *1 (-378)))) +(((*1 *2 *3) + (-12 (-5 *3 (-639 (-2 (|:| -1635 (-1164 *6)) (|:| -1300 (-562))))) + (-4 *6 (-306)) (-4 *4 (-788)) (-4 *5 (-845)) (-5 *2 (-562)) + (-5 *1 (-737 *4 *5 *6 *7)) (-4 *7 (-944 *6 *4 *5))))) (((*1 *2 *3 *1) (|partial| -12 (-4 *1 (-606 *3 *2)) (-4 *3 (-1092)) (-4 *2 (-1092))))) -(((*1 *2 *2) - (-12 (-4 *3 (-554)) (-4 *4 (-987 *3)) (-5 *1 (-141 *3 *4 *2)) - (-4 *2 (-372 *4)))) - ((*1 *2 *3) - (-12 (-4 *4 (-554)) (-4 *5 (-987 *4)) (-4 *2 (-372 *4)) - (-5 *1 (-502 *4 *5 *2 *3)) (-4 *3 (-372 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-683 *5)) (-4 *5 (-987 *4)) (-4 *4 (-554)) - (-5 *2 (-683 *4)) (-5 *1 (-687 *4 *5)))) - ((*1 *2 *2) - (-12 (-4 *3 (-554)) (-4 *4 (-987 *3)) (-5 *1 (-1225 *3 *4 *2)) - (-4 *2 (-1232 *4))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-845) (-451))) (-5 *1 (-1198 *3 *2)) - (-4 *2 (-13 (-429 *3) (-1192)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1200 *3 *4 *5 *6)) (-4 *3 (-554)) (-4 *4 (-788)) + (-4 *5 (-845)) (-4 *6 (-1058 *3 *4 *5)) + (-5 *2 (-2 (|:| -1449 (-639 *6)) (|:| -3315 (-639 *6))))))) (((*1 *2 *3) (-12 (-5 *3 (-1168)) (-4 *4 (-13 (-451) (-845) (-1033 (-562)) (-635 (-562)))) @@ -16556,29 +16588,39 @@ (-5 *2 (-52)) (-5 *1 (-458 *7 *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1218 *3 *2)) (-4 *3 (-1044)) (-4 *2 (-1247 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-381 *3 *4)) (-4 *3 (-1044)) (-4 *4 (-1092)) - (-5 *2 (-2 (|:| |k| *4) (|:| |c| *3)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1256 (-639 (-2 (|:| -2534 *4) (|:| -2466 (-1112)))))) - (-4 *4 (-348)) (-5 *2 (-683 *4)) (-5 *1 (-345 *4))))) +(((*1 *2) + (|partial| -12 (-4 *3 (-554)) (-4 *3 (-171)) + (-5 *2 (-2 (|:| |particular| *1) (|:| -4291 (-639 *1)))) + (-4 *1 (-366 *3)))) + ((*1 *2) + (|partial| -12 + (-5 *2 + (-2 (|:| |particular| (-452 *3 *4 *5 *6)) + (|:| -4291 (-639 (-452 *3 *4 *5 *6))))) + (-5 *1 (-452 *3 *4 *5 *6)) (-4 *3 (-171)) (-14 *4 (-916)) + (-14 *5 (-639 (-1168))) (-14 *6 (-1256 (-683 *3)))))) +(((*1 *2) + (-12 (-5 *2 (-916)) (-5 *1 (-441 *3)) (-4 *3 (-1232 (-562))))) + ((*1 *2 *2) + (-12 (-5 *2 (-916)) (-5 *1 (-441 *3)) (-4 *3 (-1232 (-562)))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-112)) (-4 *5 (-348)) + (-5 *2 + (-2 (|:| |cont| *5) + (|:| -2656 (-639 (-2 (|:| |irr| *3) (|:| -2794 (-562))))))) + (-5 *1 (-215 *5 *3)) (-4 *3 (-1232 *5))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |xinit| (-224)) (|:| |xend| (-224)) - (|:| |fn| (-1256 (-315 (-224)))) (|:| |yinit| (-639 (-224))) - (|:| |intvals| (-639 (-224))) (|:| |g| (-315 (-224))) - (|:| |abserr| (-224)) (|:| |relerr| (-224)))) - (-5 *2 (-378)) (-5 *1 (-204))))) + (-12 (-5 *2 (-112)) (-5 *1 (-441 *3)) (-4 *3 (-1232 (-562)))))) (((*1 *2 *1) (-12 (-5 *2 (-769)) (-5 *1 (-52))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-916)) (-5 *4 (-1150)) (-5 *2 (-1261)) (-5 *1 (-1257))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-845) (-451))) (-5 *1 (-1198 *3 *2)) - (-4 *2 (-13 (-429 *3) (-1192)))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-766)) (-4 *1 (-978 *2)) (-4 *2 (-1192))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-554)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -2355 *4))) + (-5 *1 (-964 *4 *3)) (-4 *3 (-1232 *4))))) (((*1 *2 *1) (-12 (-4 *1 (-950)) (-5 *2 (-1086 (-224))))) ((*1 *2 *1) (-12 (-4 *1 (-969)) (-5 *2 (-1086 (-224)))))) -(((*1 *2 *3) (-12 (-5 *3 (-947 (-224))) (-5 *2 (-224)) (-5 *1 (-304))))) +(((*1 *2 *3) + (-12 (-5 *3 (-639 *2)) (-5 *1 (-485 *2)) (-4 *2 (-1232 (-562)))))) (((*1 *2 *1 *3 *4) (-12 (-5 *3 (-938 (-224))) (-5 *4 (-869)) (-5 *2 (-1261)) (-5 *1 (-467)))) @@ -16596,7 +16638,7 @@ ((*1 *2 *3 *3 *3 *3) (-12 (-5 *2 (-938 (-224))) (-5 *1 (-1203)) (-5 *3 (-224))))) (((*1 *1 *1) - (-12 (|has| *1 (-6 -4402)) (-4 *1 (-150 *2)) (-4 *2 (-1207)) + (-12 (|has| *1 (-6 -4403)) (-4 *1 (-150 *2)) (-4 *2 (-1207)) (-4 *2 (-1092))))) (((*1 *1 *2 *2 *3) (-12 (-5 *2 (-766)) (-4 *3 (-1207)) (-4 *1 (-57 *3 *4 *5)) @@ -16615,24 +16657,10 @@ ((*1 *1) (-12 (-5 *1 (-1156 *2 *3)) (-14 *2 (-916)) (-4 *3 (-1044)))) ((*1 *1 *1) (-5 *1 (-1168))) ((*1 *1) (-5 *1 (-1168))) ((*1 *1) (-5 *1 (-1187)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-224)) (-5 *4 (-562)) (-5 *2 (-1030)) (-5 *1 (-753))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-112)) (-4 *6 (-451)) (-4 *7 (-788)) (-4 *8 (-845)) - (-4 *3 (-1058 *6 *7 *8)) - (-5 *2 - (-2 (|:| |done| (-639 *4)) - (|:| |todo| (-639 (-2 (|:| |val| (-639 *3)) (|:| -1495 *4)))))) - (-5 *1 (-1062 *6 *7 *8 *3 *4)) (-4 *4 (-1064 *6 *7 *8 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-451)) (-4 *6 (-788)) (-4 *7 (-845)) - (-4 *3 (-1058 *5 *6 *7)) - (-5 *2 - (-2 (|:| |done| (-639 *4)) - (|:| |todo| (-639 (-2 (|:| |val| (-639 *3)) (|:| -1495 *4)))))) - (-5 *1 (-1137 *5 *6 *7 *3 *4)) (-4 *4 (-1101 *5 *6 *7 *3))))) -(((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-639 (-562))) (-5 *2 (-683 (-562))) (-5 *1 (-1102))))) +(((*1 *2 *3) + (-12 (-5 *3 (-947 *5)) (-4 *5 (-1044)) (-5 *2 (-480 *4 *5)) + (-5 *1 (-939 *4 *5)) (-14 *4 (-639 (-1168)))))) +(((*1 *2 *3) (-12 (-5 *3 (-938 *2)) (-5 *1 (-977 *2)) (-4 *2 (-1044))))) (((*1 *2 *1 *3 *3) (-12 (-5 *3 (-766)) (-4 *1 (-735 *4 *5)) (-4 *4 (-1044)) (-4 *5 (-845)) (-5 *2 (-947 *4)))) @@ -16646,17 +16674,22 @@ (-12 (-5 *3 (-766)) (-4 *1 (-1247 *4)) (-4 *4 (-1044)) (-5 *2 (-947 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-639 (-947 *4))) (-4 *4 (-451)) (-5 *2 (-112)) - (-5 *1 (-359 *4 *5)) (-14 *5 (-639 (-1168))))) - ((*1 *2 *3) - (-12 (-5 *3 (-639 (-775 *4 (-859 *5)))) (-4 *4 (-451)) - (-14 *5 (-639 (-1168))) (-5 *2 (-112)) (-5 *1 (-624 *4 *5))))) -(((*1 *2 *2) - (-12 (-5 *2 (-938 *3)) (-4 *3 (-13 (-362) (-1192) (-997))) - (-5 *1 (-175 *3))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1150)) (-5 *2 (-1261)) (-5 *1 (-1184 *4 *5)) - (-4 *4 (-1092)) (-4 *5 (-1092))))) + (-12 (-4 *4 (-27)) + (-4 *4 (-13 (-362) (-146) (-1033 (-562)) (-1033 (-406 (-562))))) + (-4 *5 (-1232 *4)) (-5 *2 (-639 (-647 (-406 *5)))) + (-5 *1 (-651 *4 *5)) (-5 *3 (-647 (-406 *5)))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-639 *6)) (-4 *6 (-845)) (-4 *4 (-362)) (-4 *5 (-788)) + (-5 *1 (-503 *4 *5 *6 *2)) (-4 *2 (-944 *4 *5 *6)))) + ((*1 *1 *1 *2) + (-12 (-4 *3 (-362)) (-4 *4 (-788)) (-4 *5 (-845)) + (-5 *1 (-503 *3 *4 *5 *2)) (-4 *2 (-944 *3 *4 *5))))) +(((*1 *2 *1 *1) (-12 (-4 *1 (-34)) (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-362) (-843))) + (-5 *2 (-2 (|:| |start| *3) (|:| -2656 (-417 *3)))) + (-5 *1 (-180 *4 *3)) (-4 *3 (-1232 (-168 *4)))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-1150)) (-5 *3 (-818)) (-5 *1 (-817))))) (((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-170)))) ((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-1257)))) ((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-1258))))) @@ -16680,46 +16713,34 @@ (-4 *4 (-1092)))) ((*1 *1) (-12 (-4 *1 (-987 *2)) (-4 *2 (-544)) (-4 *2 (-554))))) (((*1 *1 *2 *2 *1) (-12 (-5 *1 (-641 *2)) (-4 *2 (-1092))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-639 (-293 *4))) (-5 *1 (-623 *3 *4 *5)) (-4 *3 (-845)) - (-4 *4 (-13 (-171) (-712 (-406 (-562))))) (-14 *5 (-916))))) -(((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -3931 *1) (|:| -4389 *1) (|:| |associate| *1))) - (-4 *1 (-554))))) -(((*1 *2 *1) (-12 (-5 *2 (-1127)) (-5 *1 (-516))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-112) (-114) (-114))) (-5 *1 (-114))))) +(((*1 *2 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(-12 (-4 *4 (-554)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -1606 *3))) - (-5 *1 (-964 *4 *3)) (-4 *3 (-1232 *4))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1232 *5)) (-4 *5 (-362)) - (-4 *7 (-1232 (-406 *6))) - (-5 *2 (-2 (|:| |answer| *3) (|:| -3288 *3))) - (-5 *1 (-560 *5 *6 *7 *3)) (-4 *3 (-341 *5 *6 *7)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1232 *5)) (-4 *5 (-362)) - (-5 *2 - (-2 (|:| |answer| (-406 *6)) (|:| -3288 (-406 *6)) - (|:| |specpart| (-406 *6)) (|:| |polypart| *6))) - (-5 *1 (-561 *5 *6)) (-5 *3 (-406 *6))))) + (-12 (-5 *3 (-1 *6 *5 *4)) (-4 *5 (-1092)) (-4 *4 (-1092)) + (-4 *6 (-1092)) (-5 *2 (-1 *6 *5)) (-5 *1 (-678 *5 *4 *6))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-971 *4 *5 *6 *3)) (-4 *4 (-1044)) (-4 *5 (-788)) + (-4 *6 (-845)) (-4 *3 (-1058 *4 *5 *6)) (-4 *4 (-554)) + (-5 *2 (-2 (|:| |rnum| *4) (|:| |polnum| *3) (|:| |den| *4)))))) +(((*1 *1 *1) (-12 (-5 *1 (-293 *2)) (-4 *2 (-21)) (-4 *2 (-1207))))) +(((*1 *2 *3) (-12 (-5 *3 (-938 *2)) (-5 *1 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(-562))) (-5 *1 (-912))))) (((*1 *2 *1) (-12 (-4 *1 (-600 *3 *2)) (-4 *3 (-1092)) (-4 *3 (-845)) (-4 *2 (-1207)))) @@ -16896,54 +16936,37 @@ ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-562)) (-4 *1 (-1047 *4 *5 *2 *6 *7)) (-4 *6 (-237 *5 *2)) (-4 *7 (-237 *4 *2)) (-4 *2 (-1044))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-554)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2835 *4))) - (-5 *1 (-964 *4 *3)) (-4 *3 (-1232 *4))))) +(((*1 *2) (-12 (-5 *2 (-639 (-1150))) (-5 *1 (-1259))))) (((*1 *1 *2 *2) (-12 (-4 *1 (-165 *2)) (-4 *2 (-171))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-639 (-887 *3))) (-5 *1 (-887 *3)) - (-4 *3 (-1092))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1239 *3 *4)) (-4 *3 (-1044)) (-4 *4 (-1216 *3)) + (-5 *2 (-406 (-562)))))) (((*1 *2 *2) (-12 (-5 *1 (-676 *2)) (-4 *2 (-1092))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-777 *2)) (-4 *2 (-1044)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1058 *2 *3 *4)) (-4 *2 (-1044)) (-4 *3 (-788)) - (-4 *4 (-845))))) -(((*1 *2 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *3 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(-4 *6 (-1092)) + (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-678 *4 *5 *6)) (-4 *4 (-1092))))) +(((*1 *2 *3 *4 *4 *4 *4) + (-12 (-5 *4 (-224)) (-5 *2 - (-2 (|:| -1960 (-766)) (|:| -4221 *3) (|:| |radicand| (-639 *3)))) - (-5 *1 (-948 *5 *6 *7 *3 *8)) (-5 *4 (-766)) - (-4 *8 - (-13 (-362) - (-10 -8 (-15 -4054 ($ *3)) (-15 -4065 (*3 $)) (-15 -4076 (*3 $)))))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1164 *1)) (-5 *4 (-1168)) (-4 *1 (-27)) - (-5 *2 (-639 *1)))) - ((*1 *2 *3) (-12 (-5 *3 (-1164 *1)) (-4 *1 (-27)) (-5 *2 (-639 *1)))) - ((*1 *2 *3) (-12 (-5 *3 (-947 *1)) (-4 *1 (-27)) (-5 *2 (-639 *1)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-1168)) (-4 *4 (-13 (-845) (-554))) (-5 *2 (-639 *1)) - (-4 *1 (-29 *4)))) - ((*1 *2 *1) - (-12 (-4 *3 (-13 (-845) (-554))) (-5 *2 (-639 *1)) (-4 *1 (-29 *3)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-315 (-224))) (-5 *4 (-639 (-1168))) - (-5 *5 (-1086 (-838 (-224)))) (-5 *2 (-1148 (-224))) (-5 *1 (-299))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-766)) (-4 *5 (-1044)) (-4 *2 (-1232 *5)) - (-5 *1 (-1250 *5 *2 *6 *3)) (-4 *6 (-650 *2)) (-4 *3 (-1247 *5))))) + (-2 (|:| |brans| (-639 (-639 (-938 *4)))) + (|:| |xValues| (-1086 *4)) (|:| |yValues| (-1086 *4)))) + (-5 *1 (-152)) (-5 *3 (-639 (-639 (-938 *4))))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-766)) (-4 *1 (-1273 *3 *4)) (-4 *3 (-845)) + (-4 *4 (-1044)) (-4 *4 (-171)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1273 *2 *3)) (-4 *2 (-845)) (-4 *3 (-1044)) + (-4 *3 (-171))))) +(((*1 *2 *1) (-12 (-4 *1 (-792 *2)) (-4 *2 (-171)))) + ((*1 *2 *1) (-12 (-4 *1 (-992 *2)) (-4 *2 (-171))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-639 (-315 (-224)))) (|:| -3729 (-639 (-224))))) + (-2 (|:| |lfn| (-639 (-315 (-224)))) (|:| -3730 (-639 (-224))))) (-5 *2 (-639 (-1168))) (-5 *1 (-266)))) ((*1 *2 *3) (-12 (-5 *3 (-1164 *7)) (-4 *7 (-944 *6 *4 *5)) (-4 *4 (-788)) @@ -17023,7 +17038,7 @@ (-5 *1 (-945 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-362) - (-10 -8 (-15 -4054 ($ *7)) (-15 -4065 (*7 $)) (-15 -4076 (*7 $))))))) + (-10 -8 (-15 -4053 ($ *7)) (-15 -4063 (*7 $)) (-15 -4079 (*7 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1094 (-1168))) (-5 *1 (-961 *3)) (-4 *3 (-962)))) ((*1 *2 *1) @@ -17035,42 +17050,32 @@ ((*1 *2 *3) (-12 (-5 *3 (-406 (-947 *4))) (-4 *4 (-554)) (-5 *2 (-639 (-1168))) (-5 *1 (-1038 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-766)) (-5 *2 (-683 (-947 *4))) (-5 *1 (-1023 *4)) - (-4 *4 (-1044))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1256 *4)) (-4 *4 (-635 *5)) (-4 *5 (-362)) - (-4 *5 (-554)) (-5 *2 (-1256 *5)) (-5 *1 (-634 *5 *4)))) - ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1256 *4)) (-4 *4 (-635 *5)) - (-2236 (-4 *5 (-362))) (-4 *5 (-554)) (-5 *2 (-1256 (-406 *5))) - (-5 *1 (-634 *5 *4))))) -(((*1 *2 *1) - (-12 (-4 *1 (-372 *3)) (-4 *3 (-1207)) (-4 *3 (-845)) (-5 *2 (-112)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *1 (-372 *4)) (-4 *4 (-1207)) - (-5 *2 (-112))))) -(((*1 *2 *1) (-12 (-5 *2 (-1261)) (-5 *1 (-816))))) -(((*1 *1 *1 *1) - (-12 (-5 *1 (-135 *2 *3 *4)) (-14 *2 (-562)) (-14 *3 (-766)) - (-4 *4 (-171)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1168)) (-4 *4 (-13 (-845) (-554))) (-5 *1 (-157 *4 *2)) - (-4 *2 (-429 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1084 *2)) (-4 *2 (-429 *4)) (-4 *4 (-13 (-845) (-554))) - (-5 *1 (-157 *4 *2)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1084 *1)) (-4 *1 (-159)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-159)) (-5 *2 (-1168)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-464 *2 *3)) (-4 *2 (-171)) (-4 *3 (-23)))) - ((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-766)) (-5 *1 (-1276 *3 *4)) (-4 *3 (-845)) - (-4 *4 (-171))))) -(((*1 *2) - (-12 (-4 *4 (-171)) (-5 *2 (-112)) (-5 *1 (-365 *3 *4)) - (-4 *3 (-366 *4)))) - ((*1 *2) (-12 (-4 *1 (-366 *3)) (-4 *3 (-171)) (-5 *2 (-112))))) +(((*1 *2 *3 *3 *3) + (|partial| -12 (-4 *4 (-13 (-362) (-146) (-1033 (-562)))) + (-4 *5 (-1232 *4)) (-5 *2 (-639 (-406 *5))) (-5 *1 (-1011 *4 *5)) + (-5 *3 (-406 *5))))) +(((*1 *2 *2) + (-12 (-4 *3 (-451)) (-4 *3 (-845)) (-4 *3 (-1033 (-562))) + (-4 *3 (-554)) (-5 *1 (-41 *3 *2)) (-4 *2 (-429 *3)) + (-4 *2 + (-13 (-362) (-301) + (-10 -8 (-15 -4063 ((-1117 *3 (-608 $)) $)) + (-15 -4079 ((-1117 *3 (-608 $)) $)) + (-15 -4053 ($ (-1117 *3 (-608 $)))))))))) +(((*1 *2 *3 *3 *3) + (|partial| -12 + (-4 *4 (-13 (-146) (-27) (-1033 (-562)) (-1033 (-406 (-562))))) + (-4 *5 (-1232 *4)) (-5 *2 (-1164 (-406 *5))) (-5 *1 (-611 *4 *5)) + (-5 *3 (-406 *5)))) + ((*1 *2 *3 *3 *3 *4) + (|partial| -12 (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1232 *5)) + (-4 *5 (-13 (-146) (-27) (-1033 (-562)) (-1033 (-406 (-562))))) + (-5 *2 (-1164 (-406 *6))) (-5 *1 (-611 *5 *6)) (-5 *3 (-406 *6))))) +(((*1 *2) (-12 (-5 *2 (-916)) (-5 *1 (-1259)))) + ((*1 *2 *2) (-12 (-5 *2 (-916)) (-5 *1 (-1259))))) +(((*1 *2 *2) + (-12 (-5 *2 (-938 *3)) (-4 *3 (-13 (-362) (-1192) (-997))) + (-5 *1 (-175 *3))))) (((*1 *1 *1) (-12 (-4 *1 (-372 *2)) (-4 *2 (-1207)) (-4 *2 (-845)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-372 *3)) (-4 *3 (-1207)))) @@ -17079,26 +17084,29 @@ ((*1 *2 *1 *3) (-12 (-4 *4 (-1044)) (-4 *5 (-788)) (-4 *3 (-845)) (-4 *6 (-1058 *4 *5 *3)) - (-5 *2 (-2 (|:| |under| *1) (|:| -4014 *1) (|:| |upper| *1))) + (-5 *2 (-2 (|:| |under| *1) (|:| -3870 *1) (|:| |upper| *1))) (-4 *1 (-971 *4 *5 *3 *6))))) -(((*1 *1 *1 *1) (-5 *1 (-857)))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-306)) (-4 *6 (-372 *5)) (-4 *4 (-372 *5)) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -3928 (-639 *4)))) - (-5 *1 (-1116 *5 *6 *4 *3)) (-4 *3 (-681 *5 *6 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-335 *5 *6 *7 *8)) (-4 *5 (-429 *4)) (-4 *6 (-1232 *5)) - (-4 *7 (-1232 (-406 *6))) (-4 *8 (-341 *5 *6 *7)) - (-4 *4 (-13 (-845) (-554) (-1033 (-562)))) (-5 *2 (-112)) - (-5 *1 (-906 *4 *5 *6 *7 *8)))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-562)) (-5 *1 (-909 *3)) (-4 *3 (-306))))) +(((*1 *2 *1 *2) + (-12 (|has| *1 (-6 -4404)) (-4 *1 (-1244 *2)) (-4 *2 (-1207))))) +(((*1 *2 *2) (|partial| -12 (-5 *1 (-584 *2)) (-4 *2 (-544))))) +(((*1 *2 *3 *4 *5 *5) + (-12 (-5 *4 (-112)) (-5 *5 (-562)) (-4 *6 (-362)) (-4 *6 (-367)) + (-4 *6 (-1044)) (-5 *2 (-639 (-639 (-683 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*3) + (|:| |limitedlogs| + (-639 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-564 *6 *3 *7)) (-4 *7 (-1092))))) (((*1 *2) (-12 (-14 *4 *2) (-4 *5 (-1207)) (-5 *2 (-766)) (-5 *1 (-236 *3 *4 *5)) (-4 *3 (-237 *4 *5)))) @@ -17171,13 +17195,16 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-843) (-362))) (-5 *1 (-1054 *2 *3)) (-4 *3 (-1232 *2))))) -(((*1 *2 *2 *1) (-12 (-4 *1 (-253 *2)) (-4 *2 (-1207))))) -(((*1 *2 *3 *3 *3 *3 *4 *5 *5 *6 *7 *8 *8 *3) - (-12 (-5 *6 (-639 (-112))) (-5 *7 (-683 (-224))) - (-5 *8 (-683 (-562))) (-5 *3 (-562)) (-5 *4 (-224)) (-5 *5 (-112)) - (-5 *2 (-1030)) (-5 *1 (-749))))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-715)) (-5 *2 (-916)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-717)) (-5 *2 (-766))))) +(((*1 *2 *3 *4 *5 *3 *6 *3) + (-12 (-5 *3 (-562)) (-5 *5 (-168 (-224))) (-5 *6 (-1150)) + (-5 *4 (-224)) (-5 *2 (-1030)) (-5 *1 (-753))))) +(((*1 *1 *1) (-4 *1 (-172))) + ((*1 *1 *1) + (-12 (-4 *1 (-363 *2 *3)) (-4 *2 (-1092)) (-4 *3 (-1092))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-1168)) (-5 *1 (-279))))) +(((*1 *1 *1 *1 *1 *2) + (-12 (-5 *2 (-766)) (-4 *1 (-1058 *3 *4 *5)) (-4 *3 (-1044)) + (-4 *4 (-788)) (-4 *5 (-845)) (-4 *3 (-554))))) (((*1 *1 *2 *3) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1044)) (-4 *3 (-787)))) ((*1 *1 *2 *3) @@ -17187,8 +17214,8 @@ (-12 (-5 *3 (-708 *5 *6 *7)) (-4 *5 (-845)) (-4 *6 (-237 (-3492 *4) (-766))) (-14 *7 - (-1 (-112) (-2 (|:| -2466 *5) (|:| -1960 *6)) - (-2 (|:| -2466 *5) (|:| -1960 *6)))) + (-1 (-112) (-2 (|:| -2464 *5) (|:| -1300 *6)) + (-2 (|:| -2464 *5) (|:| -1300 *6)))) (-14 *4 (-639 (-1168))) (-4 *2 (-171)) (-5 *1 (-460 *4 *2 *5 *6 *7 *8)) (-4 *8 (-944 *2 *6 (-859 *4))))) ((*1 *1 *2 *3) @@ -17218,54 +17245,66 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-968 *4 *3 *2)) (-4 *4 (-1044)) (-4 *3 (-787)) (-4 *2 (-845))))) +(((*1 *2 *2) + (-12 (-5 *2 (-1148 *3)) (-4 *3 (-1044)) (-5 *1 (-1152 *3)))) + ((*1 *1 *1) + (-12 (-5 *1 (-1248 *2 *3 *4)) (-4 *2 (-1044)) (-14 *3 (-1168)) + (-14 *4 *2)))) +(((*1 *2 *2) (-12 (-5 *2 (-378)) (-5 *1 (-97))))) (((*1 *2 *3) - (-12 (-5 *2 (-608 *4)) (-5 *1 (-607 *3 *4)) (-4 *3 (-845)) - (-4 *4 (-845))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-554)) (-5 *2 (-639 *3)) (-5 *1 (-964 *4 *3)) - (-4 *3 (-1232 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-639 (-833))) (-5 *1 (-139))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1202 *3)) (-4 *3 (-969))))) -(((*1 *2 *3 *3 *3 *3 *3 *3 *3 *3 *4 *5 *5 *5 *5 *5 *5 *6 *6 *6 *3 *3 *5 - *7 *3 *8) - (-12 (-5 *5 (-683 (-224))) (-5 *6 (-112)) (-5 *7 (-683 (-562))) - (-5 *8 (-3 (|:| |fn| (-387)) (|:| |fp| (-65 QPHESS)))) - (-5 *3 (-562)) (-5 *4 (-224)) (-5 *2 (-1030)) (-5 *1 (-748))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1148 (-406 *3))) (-5 *1 (-173 *3)) (-4 *3 (-306))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-143))))) + (-12 (-5 *3 (-1256 (-315 (-224)))) + (-5 *2 + (-2 (|:| |additions| (-562)) (|:| |multiplications| (-562)) + (|:| |exponentiations| (-562)) (|:| |functionCalls| (-562)))) + (-5 *1 (-304))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-845) (-451))) (-5 *1 (-1198 *3 *2)) + (-4 *2 (-13 (-429 *3) (-1192)))))) +(((*1 *2 *3 *4 *4 *5 *3 *3 *3 *3 *3) + (-12 (-5 *3 (-562)) (-5 *5 (-683 (-224))) (-5 *4 (-224)) + (-5 *2 (-1030)) (-5 *1 (-747))))) +(((*1 *2 *3 *3 *4 *3 *3 *3 *3 *3 *3 *3 *5 *3 *6 *7) + (-12 (-5 *3 (-562)) (-5 *5 (-683 (-224))) + (-5 *6 (-3 (|:| |fn| (-387)) (|:| |fp| (-67 DOT)))) + (-5 *7 (-3 (|:| |fn| (-387)) (|:| |fp| (-68 IMAGE)))) (-5 *4 (-224)) + (-5 *2 (-1030)) (-5 *1 (-750)))) + ((*1 *2 *3 *3 *4 *3 *3 *3 *3 *3 *3 *3 *5 *3 *6 *7 *8) + (-12 (-5 *3 (-562)) (-5 *5 (-683 (-224))) + (-5 *6 (-3 (|:| |fn| (-387)) (|:| |fp| (-67 DOT)))) + (-5 *7 (-3 (|:| |fn| (-387)) (|:| |fp| (-68 IMAGE)))) (-5 *8 (-387)) + (-5 *4 (-224)) (-5 *2 (-1030)) (-5 *1 (-750))))) (((*1 *1) (-12 (-5 *1 (-639 *2)) (-4 *2 (-1207))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-643 *3 *4 *5)) (-4 *3 (-1092)) - (-4 *4 (-23)) (-14 *5 *4)))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-562) (-562))) (-5 *1 (-360 *3)) (-4 *3 (-1092)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-766) (-766))) (-5 *1 (-385 *3)) (-4 *3 (-1092)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-23)) (-14 *5 *4) + (-5 *1 (-643 *3 *4 *5)) (-4 *3 (-1092))))) (((*1 *1) (-5 *1 (-290)))) -(((*1 *2 *3 *3 *3) - (|partial| -12 (-4 *4 (-13 (-362) (-146) (-1033 (-562)))) - (-4 *5 (-1232 *4)) (-5 *2 (-639 (-406 *5))) (-5 *1 (-1011 *4 *5)) - (-5 *3 (-406 *5))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *4 (-562)) (-5 *6 (-1 (-1261) (-1256 *5) (-1256 *5) (-378))) + (-5 *3 (-1256 (-378))) (-5 *5 (-378)) (-5 *2 (-1261)) + (-5 *1 (-783)))) + ((*1 *2 *3 *4 *5 *5 *6 *3 *3 *3 *3) + (-12 (-5 *4 (-562)) (-5 *6 (-1 (-1261) (-1256 *5) (-1256 *5) (-378))) + (-5 *3 (-1256 (-378))) (-5 *5 (-378)) (-5 *2 (-1261)) + (-5 *1 (-783))))) +(((*1 *1 *1) + (-12 (-4 *2 (-348)) (-4 *2 (-1044)) (-5 *1 (-707 *2 *3)) + (-4 *3 (-1232 *2))))) (((*1 *2 *1) - (-12 (-4 *1 (-334 *3 *4 *5 *6)) (-4 *3 (-362)) (-4 *4 (-1232 *3)) - (-4 *5 (-1232 (-406 *4))) (-4 *6 (-341 *3 *4 *5)) - (-5 *2 (-412 *4 (-406 *4) *5 *6)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1256 *6)) (-4 *6 (-13 (-408 *4 *5) (-1033 *4))) - (-4 *4 (-987 *3)) (-4 *5 (-1232 *4)) (-4 *3 (-306)) - (-5 *1 (-412 *3 *4 *5 *6)))) - ((*1 *1 *2) - (-12 (-5 *2 (-639 *6)) (-4 *6 (-944 *3 *4 *5)) (-4 *3 (-362)) - (-4 *4 (-788)) (-4 *5 (-845)) (-5 *1 (-503 *3 *4 *5 *6))))) -(((*1 *2 *1) (-12 (-4 *1 (-792 *2)) (-4 *2 (-171))))) -(((*1 *2) - (-12 (-4 *3 (-554)) (-5 *2 (-639 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-416 *3))))) -(((*1 *1 *2) (-12 (-5 *2 (-562)) (-5 *1 (-857))))) -(((*1 *2) (-12 (-5 *2 (-869)) (-5 *1 (-1259)))) - ((*1 *2 *2) (-12 (-5 *2 (-869)) (-5 *1 (-1259))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *8)) - (-5 *4 (-683 (-1164 *8))) (-4 *5 (-1044)) (-4 *8 (-1044)) - (-4 *6 (-1232 *5)) (-5 *2 (-683 *6)) (-5 *1 (-500 *5 *6 *7 *8)) - (-4 *7 (-1232 *6))))) + (-12 (-5 *2 (-639 (-52))) (-5 *1 (-887 *3)) (-4 *3 (-1092))))) +(((*1 *2 *1) (-12 (-5 *2 (-1148 *3)) (-5 *1 (-173 *3)) (-4 *3 (-306))))) +(((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-683 *3)) (-4 *3 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