* algebra/array2.spad.pamphlet (InnerTwoDimensionalArray): Rename

	from InnerIndexedTwoDimensionalArray.  Adjust users.

1 files changed, 47 insertions, 47 deletions

diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 79402788..9ae70ffb 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,5 +1,5 @@
 
-(1961236 . 3577300069)       
+(1961236 . 3577302777)       
 (-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 
@@ -239,7 +239,7 @@ NIL
 (-77) 
 ((|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."))) 
 ((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
-((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1089)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1065))) (|HasCategory| (-483) (QUOTE (-796 (-328)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1089)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1089)))) (|HasCategory| (-483) (QUOTE (-453 (-1089) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) 
+((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1089)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1065))) (|HasCategory| (-483) (QUOTE (-796 (-328)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1089)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1089)))) (|HasCategory| (-483) (QUOTE (-454 (-1089) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) 
 (-78) 
 ((|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| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) 
 NIL 
@@ -291,7 +291,7 @@ NIL
 (-90 |p|) 
 ((|constructor| (NIL "Stream-based implementation of 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}."))) 
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+((|HasCategory| (-89 |#1|) (QUOTE (-821))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-1089)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-472)))) (|HasCategory| (-89 |#1|) (QUOTE (-933))) (|HasCategory| (-89 |#1|) (QUOTE (-740))) (|HasCategory| (-89 |#1|) (QUOTE (-756))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-740))) (|HasCategory| (-89 |#1|) (QUOTE (-756)))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-1065))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-328)))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-89 |#1|) (QUOTE (-580 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-811 (-1089)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-809 (-1089)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -454) (QUOTE (-1089)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) 
 (-91 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" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
@@ -499,7 +499,7 @@ NIL
 (-142 R) 
 ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) 
 ((-3987 OR (|has| |#1| (-494)) (-12 (|has| |#1| (-258)) (|has| |#1| (-821)))) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3990 |has| |#1| (-6 -3990)) (-3993 |has| |#1| (-6 -3993)) (-1375 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
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 (-143 R S) 
 ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) 
 NIL 
@@ -615,7 +615,7 @@ NIL
 (-171) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|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."))) 
 ((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
-((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1089)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1065))) (|HasCategory| (-483) (QUOTE (-796 (-328)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1089)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1089)))) (|HasCategory| (-483) (QUOTE (-453 (-1089) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) 
+((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1089)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1065))) (|HasCategory| (-483) (QUOTE (-796 (-328)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1089)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1089)))) (|HasCategory| (-483) (QUOTE (-454 (-1089) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) 
 (-172) 
 ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
@@ -927,7 +927,7 @@ NIL
 (-249 S) 
 ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{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."))) 
 ((-3991 OR (|has| |#1| (-961)) (|has| |#1| (-411))) (-3988 |has| |#1| (-961)) (-3989 |has| |#1| (-961))) 
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+((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (OR (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-663)))) (|HasCategory| |#1| (QUOTE (-411))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1089)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-411)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-663)))) 
 (-250 S R) 
 ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) 
 NIL 
@@ -987,7 +987,7 @@ NIL
 (-264 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))}."))) 
 ((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
-((|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-472)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-933))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-756))) (OR (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-756)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-483)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-1065))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-328)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-483)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-580 (-483)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-811 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-809 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -453) (QUOTE (-1089)) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) 
+((|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-472)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-933))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-756))) (OR (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-756)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-483)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-1065))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-328)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-483)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-580 (-483)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-811 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-809 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -454) (QUOTE (-1089)) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) 
 (-265 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|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 
 ((-3991 OR (-12 (|has| |#1| (-494)) (OR (|has| |#1| (-961)) (|has| |#1| (-411)))) (|has| |#1| (-961)) (|has| |#1| (-411))) (-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) ((-3996 "*") |has| |#1| (-494)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-494)) (-3986 |has| |#1| (-494))) 
@@ -1079,7 +1079,7 @@ NIL
 (-287 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1089)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
 (-288 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
@@ -1315,7 +1315,7 @@ NIL
 (-346 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 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| #1="nil" #2="sqfr" #3="irred" #4="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| #1# #2# #3# #4#) $ (|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| #1# #2# #3# #4#)) (|:| |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| #1# #2# #3# #4#)) (|:| |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."))) 
 ((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
-((|HasCategory| |#1| (QUOTE (-453 (-1089) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-1133))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-390)))) 
+((|HasCategory| |#1| (QUOTE (-454 (-1089) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-1133))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-390)))) 
 (-347 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."))) 
 NIL 
@@ -1323,7 +1323,7 @@ NIL
 (-348 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 gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) 
 ((-3981 -12 (|has| |#1| (-6 -3992)) (|has| |#1| (-390)) (|has| |#1| (-6 -3981))) (-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-950 (-1089)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-796 (-328)))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-482))) (-12 (|HasAttribute| |#1| (QUOTE -3981)) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-390)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-950 (-1089)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-796 (-328)))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-482))) (-12 (|HasAttribute| |#1| (QUOTE -3981)) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-390)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
 (-349 A B) 
 ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) 
 NIL 
@@ -1631,7 +1631,7 @@ NIL
 (-425) 
 ((|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."))) 
 ((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
-((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1089)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1065))) (|HasCategory| (-483) (QUOTE (-796 (-328)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1089)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1089)))) (|HasCategory| (-483) (QUOTE (-453 (-1089) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) 
+((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1089)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1065))) (|HasCategory| (-483) (QUOTE (-796 (-328)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1089)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1089)))) (|HasCategory| (-483) (QUOTE (-454 (-1089) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) 
 (-426 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 
@@ -1668,102 +1668,102 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) 
 ((-3995 . T) (-3994 . T)) 
 ((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-435 K R UP) 
+(-435 R |Row| |Col|) 
+((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) 
+((-3994 . T) (-3995 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-436 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 
-(-436 R UP -3092) 
+(-437 R UP -3092) 
 ((|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{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\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{mi} is given by \\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{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{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 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 
-(-437 |mn|) 
+(-438 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data."))) 
 ((-3995 . T) (-3994 . T)) 
 ((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1013)))) (|HasCategory| (-85) (QUOTE (-553 (-472)))) (|HasCategory| (-85) (QUOTE (-756))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| (-85) (QUOTE (-1013))) (|HasCategory| (-85) (QUOTE (-552 (-772)))) (|HasCategory| (-85) (QUOTE (-72)))) 
-(-438 K R UP L) 
+(-439 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)}."))) 
 NIL 
 NIL 
-(-439) 
+(-440) 
 ((|constructor| (NIL "\\indented{1}{This domain implements a container of information} about the AXIOM library")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{\\spad{ic}}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of the information contained in \\axiom{\\spad{ic}}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,s)} selects a particular field from \\axiom{\\spad{ic}}. Valid fields are \\axiom{name,{} nargs,{} exposed,{} type,{} abbreviation,{} kind,{} origin,{} params,{} condition,{} doc}."))) 
 NIL 
 NIL 
-(-440 R Q A B) 
+(-441 R Q A B) 
 ((|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{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) 
 NIL 
 NIL 
-(-441 -3092 |Expon| |VarSet| |DPoly|) 
+(-442 -3092 |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| (QUOTE (-553 (-1089))))) 
-(-442 |vl| |nv|) 
+(-443 |vl| |nv|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) 
 NIL 
 NIL 
-(-443 T$) 
+(-444 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement idempotent operations."))) 
 (((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3056 (|f| |x| |x|) |x|))) . T)) 
 NIL 
-(-444) 
+(-445) 
 ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) 
 NIL 
 NIL 
-(-445 A S) 
+(-446 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
-(-446 A S) 
+(-447 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
-(-447 A S) 
+(-448 A S) 
 ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|IndexedProductTerm| |#1| |#2|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) 
 NIL 
 NIL 
-(-448 A S) 
+(-449 A S) 
 ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support.")) (|combineWithIf| (($ $ $ (|Mapping| |#1| |#1| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{combineWithIf(u,v,f,p)} returns the result of combining index-wise,{} coefficients of \\spad{u} and \\spad{u} if when satisfy the predicate \\spad{p}. Those pairs of coefficients which fail\\spad{p} are implicitly ignored."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
-(-449 A S) 
+(-450 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
-(-450 A S) 
+(-451 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
-(-451 A S) 
+(-452 A S) 
 ((|constructor| (NIL "An indexed product term is a utility domain used in the representation of indexed direct product objects.")) (|coefficient| ((|#1| $) "\\spad{coefficient t} returns the coefficient of the tern \\spad{t}.")) (|index| ((|#2| $) "\\spad{index t} returns the index of the term \\spad{t}.")) (|term| (($ |#2| |#1|) "\\spad{term(s,a)} constructs a term with index \\spad{s} and coefficient \\spad{a}."))) 
 NIL 
 NIL 
-(-452 S A B) 
+(-453 S A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-453 A B) 
+(-454 A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#1|) (|List| |#2|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#1| |#2|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-454 S E |un|) 
+(-455 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-716)))) 
-(-455 S |mn|) 
+(-456 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{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}"))) 
 ((-3995 . T) (-3994 . T)) 
 ((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-456) 
+(-457) 
 ((|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'."))) 
 NIL 
 NIL 
-(-457 |p| |n|) 
+(-458 |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}."))) 
 ((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 ((OR (|HasCategory| (-516 |#1|) (QUOTE (-118))) (|HasCategory| (-516 |#1|) (QUOTE (-318)))) (|HasCategory| (-516 |#1|) (QUOTE (-120))) (|HasCategory| (-516 |#1|) (QUOTE (-318))) (|HasCategory| (-516 |#1|) (QUOTE (-118)))) 
-(-458 R |Row| |Col|) 
-((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) 
-((-3994 . T) (-3995 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-459 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,{} m*h and 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 
@@ -2819,7 +2819,7 @@ NIL
 (-722 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}."))) 
 ((-3988 . T) (-3989 . T) (-3991 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-348 (-483)))))) (OR (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-348 (-483))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-348 (-483)))))) (OR (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-348 (-483))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) 
 (-723 OR R OS S) 
 ((|constructor| (NIL "\\spad{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}."))) 
 NIL 
@@ -3051,11 +3051,11 @@ NIL
 (-780 |p|) 
 ((|constructor| (NIL "Stream-based implementation of 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)."))) 
 ((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
-((|HasCategory| (-778 |#1|) (QUOTE (-821))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-1089)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-120))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-472)))) (|HasCategory| (-778 |#1|) (QUOTE (-933))) (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756))) (OR (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756)))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-1065))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-328)))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-778 |#1|) (QUOTE (-580 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-189))) (|HasCategory| (-778 |#1|) (QUOTE (-811 (-1089)))) (|HasCategory| (-778 |#1|) (QUOTE (-190))) (|HasCategory| (-778 |#1|) (QUOTE (-809 (-1089)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -453) (QUOTE (-1089)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -778) (|devaluate| |#1|)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (QUOTE (-258))) (|HasCategory| (-778 |#1|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))))) 
+((|HasCategory| (-778 |#1|) (QUOTE (-821))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-1089)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-120))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-472)))) (|HasCategory| (-778 |#1|) (QUOTE (-933))) (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756))) (OR (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756)))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-1065))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-328)))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-778 |#1|) (QUOTE (-580 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-189))) (|HasCategory| (-778 |#1|) (QUOTE (-811 (-1089)))) (|HasCategory| (-778 |#1|) (QUOTE (-190))) (|HasCategory| (-778 |#1|) (QUOTE (-809 (-1089)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -454) (QUOTE (-1089)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -778) (|devaluate| |#1|)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (QUOTE (-258))) (|HasCategory| (-778 |#1|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))))) 
 (-781 |p| PADIC) 
 ((|constructor| (NIL "This is the category of stream-based representations of 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)}."))) 
 ((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-950 (-1089)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756)))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (QUOTE (-796 (-328)))) (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-482))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-950 (-1089)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756)))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (QUOTE (-796 (-328)))) (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1089)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-482))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
 (-782 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 `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#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 `s' and `t'."))) 
 NIL 
@@ -3567,7 +3567,7 @@ NIL
 (-909 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.}"))) 
 ((-3987 |has| |#1| (-246)) (-3988 . T) (-3989 . T) (-3991 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-482)))) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-482)))) 
 (-910 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
 NIL 
@@ -3599,7 +3599,7 @@ NIL
 (-917 |bb|) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|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."))) 
 ((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
-((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1089)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1065))) (|HasCategory| (-483) (QUOTE (-796 (-328)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1089)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1089)))) (|HasCategory| (-483) (QUOTE (-453 (-1089) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) 
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 (-918) 
 ((|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}."))) 
 NIL 
@@ -4255,7 +4255,7 @@ NIL
 (-1081 |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. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
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|#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-821)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-118))))) 
 (-1082 R -3092) 
 ((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) 
 NIL 
@@ -4483,7 +4483,7 @@ NIL
 (-1138 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} 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{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\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. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
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 (-1139 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) 
 NIL 
@@ -4503,7 +4503,7 @@ NIL
 (-1143 |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. This pair represents the Laurent series \\spad{x**n * f(x)}."))) 
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 (-1144 ZP) 
 ((|constructor| (NIL "Package for 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 
@@ -4780,4 +4780,4 @@ NIL
 NIL 
 NIL 
 NIL 
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"TABLBUMP.spad" 1737151 1737162 1740362 1740367) (-1099 "SYSTEM.spad" 1736379 1736388 1737141 1737146) (-1098 "SYSSOLP.spad" 1733862 1733873 1736369 1736374) (-1097 "SYSPTR.spad" 1733761 1733770 1733852 1733857) (-1096 "SYSNNI.spad" 1732984 1732995 1733751 1733756) (-1095 "SYSINT.spad" 1732388 1732399 1732974 1732979) (-1094 "SYNTAX.spad" 1728722 1728731 1732378 1732383) (-1093 "SYMTAB.spad" 1726790 1726799 1728712 1728717) (-1092 "SYMS.spad" 1722819 1722828 1726780 1726785) (-1091 "SYMPOLY.spad" 1721952 1721963 1722034 1722161) (-1090 "SYMFUNC.spad" 1721453 1721464 1721942 1721947) (-1089 "SYMBOL.spad" 1718948 1718957 1721443 1721448) (-1088 "SUTS.spad" 1716061 1716089 1717480 1717577) (-1087 "SUPXS.spad" 1713403 1713431 1714252 1714401) (-1086 "SUPFRACF.spad" 1712508 1712526 1713393 1713398) (-1085 "SUP2.spad" 1711900 1711913 1712498 1712503) (-1084 "SUP.spad" 1708984 1708995 1709757 1709910) (-1083 "SUMRF.spad" 1707958 1707969 1708974 1708979) (-1082 "SUMFS.spad" 1707587 1707604 1707948 1707953) (-1081 "SULS.spad" 1699840 1699868 1700798 1701221) (-1080 "syntax.spad" 1699609 1699618 1699830 1699835) (-1079 "SUCH.spad" 1699299 1699314 1699599 1699604) (-1078 "SUBSPACE.spad" 1691430 1691445 1699289 1699294) (-1077 "SUBRESP.spad" 1690600 1690614 1691386 1691391) (-1076 "STTFNC.spad" 1687068 1687084 1690590 1690595) (-1075 "STTF.spad" 1683167 1683183 1687058 1687063) (-1074 "STTAYLOR.spad" 1675844 1675855 1683074 1683079) (-1073 "STRTBL.spad" 1674231 1674248 1674380 1674407) (-1072 "STRING.spad" 1673099 1673108 1673484 1673511) (-1071 "STREAM3.spad" 1672672 1672687 1673089 1673094) (-1070 "STREAM2.spad" 1671800 1671813 1672662 1672667) (-1069 "STREAM1.spad" 1671506 1671517 1671790 1671795) (-1068 "STREAM.spad" 1668502 1668513 1671109 1671124) (-1067 "STINPROD.spad" 1667438 1667454 1668492 1668497) (-1066 "STEPAST.spad" 1666672 1666681 1667428 1667433) (-1065 "STEP.spad" 1665989 1665998 1666662 1666667) (-1064 "STBL.spad" 1664379 1664407 1664546 1664561) (-1063 "STAGG.spad" 1663078 1663089 1664369 1664374) (-1062 "STAGG.spad" 1661775 1661788 1663068 1663073) (-1061 "STACK.spad" 1661197 1661208 1661447 1661474) (-1060 "SRING.spad" 1660957 1660966 1661187 1661192) (-1059 "SREGSET.spad" 1658689 1658706 1660591 1660618) (-1058 "SRDCMPK.spad" 1657266 1657286 1658679 1658684) (-1057 "SRAGG.spad" 1652449 1652458 1657234 1657261) (-1056 "SRAGG.spad" 1647652 1647663 1652439 1652444) (-1055 "SQMATRIX.spad" 1645329 1645347 1646245 1646332) (-1054 "SPLTREE.spad" 1640071 1640084 1644867 1644894) (-1053 "SPLNODE.spad" 1636691 1636704 1640061 1640066) (-1052 "SPFCAT.spad" 1635500 1635509 1636681 1636686) (-1051 "SPECOUT.spad" 1634052 1634061 1635490 1635495) (-1050 "SPADXPT.spad" 1626143 1626152 1634042 1634047) (-1049 "spad-parser.spad" 1625608 1625617 1626133 1626138) (-1048 "SPADAST.spad" 1625309 1625318 1625598 1625603) (-1047 "SPACEC.spad" 1609524 1609535 1625299 1625304) (-1046 "SPACE3.spad" 1609300 1609311 1609514 1609519) (-1045 "SORTPAK.spad" 1608849 1608862 1609256 1609261) (-1044 "SOLVETRA.spad" 1606612 1606623 1608839 1608844) (-1043 "SOLVESER.spad" 1605068 1605079 1606602 1606607) (-1042 "SOLVERAD.spad" 1601094 1601105 1605058 1605063) (-1041 "SOLVEFOR.spad" 1599556 1599574 1601084 1601089) (-1040 "SNTSCAT.spad" 1599156 1599173 1599524 1599551) (-1039 "SMTS.spad" 1597473 1597499 1598750 1598847) (-1038 "SMP.spad" 1595281 1595301 1595671 1595798) (-1037 "SMITH.spad" 1594126 1594151 1595271 1595276) (-1036 "SMATCAT.spad" 1592244 1592274 1594070 1594121) (-1035 "SMATCAT.spad" 1590294 1590326 1592122 1592127) (-1034 "SKAGG.spad" 1589263 1589274 1590262 1590289) (-1033 "SINT.spad" 1588562 1588571 1589129 1589258) (-1032 "SIMPAN.spad" 1588290 1588299 1588552 1588557) (-1031 "SIGNRF.spad" 1587415 1587426 1588280 1588285) (-1030 "SIGNEF.spad" 1586701 1586718 1587405 1587410) (-1029 "syntax.spad" 1586118 1586127 1586691 1586696) (-1028 "SIG.spad" 1585480 1585489 1586108 1586113) (-1027 "SHP.spad" 1583424 1583439 1585436 1585441) (-1026 "SHDP.spad" 1572917 1572944 1573434 1573531) (-1025 "SGROUP.spad" 1572525 1572534 1572907 1572912) (-1024 "SGROUP.spad" 1572131 1572142 1572515 1572520) (-1023 "catdef.spad" 1571841 1571853 1571952 1572126) (-1022 "catdef.spad" 1571397 1571409 1571662 1571836) (-1021 "SGCF.spad" 1564536 1564545 1571387 1571392) (-1020 "SFRTCAT.spad" 1563482 1563499 1564504 1564531) (-1019 "SFRGCD.spad" 1562545 1562565 1563472 1563477) (-1018 "SFQCMPK.spad" 1557358 1557378 1562535 1562540) (-1017 "SEXOF.spad" 1557201 1557241 1557348 1557353) (-1016 "SEXCAT.spad" 1555029 1555069 1557191 1557196) (-1015 "SEX.spad" 1554921 1554930 1555019 1555024) (-1014 "SETMN.spad" 1553381 1553398 1554911 1554916) (-1013 "SETCAT.spad" 1552866 1552875 1553371 1553376) (-1012 "SETCAT.spad" 1552349 1552360 1552856 1552861) (-1011 "SETAGG.spad" 1548898 1548909 1552329 1552344) (-1010 "SETAGG.spad" 1545455 1545468 1548888 1548893) (-1009 "SET.spad" 1543764 1543775 1544861 1544900) (-1008 "syntax.spad" 1543467 1543476 1543754 1543759) (-1007 "SEGXCAT.spad" 1542623 1542636 1543457 1543462) (-1006 "SEGCAT.spad" 1541548 1541559 1542613 1542618) (-1005 "SEGBIND2.spad" 1541246 1541259 1541538 1541543) (-1004 "SEGBIND.spad" 1541004 1541015 1541193 1541198) (-1003 "SEGAST.spad" 1540734 1540743 1540994 1540999) (-1002 "SEG2.spad" 1540169 1540182 1540690 1540695) (-1001 "SEG.spad" 1539982 1539993 1540088 1540093) (-1000 "SDVAR.spad" 1539258 1539269 1539972 1539977) (-999 "SDPOL.spad" 1536951 1536961 1537241 1537368) (-998 "SCPKG.spad" 1535041 1535051 1536941 1536946) (-997 "SCOPE.spad" 1534219 1534227 1535031 1535036) (-996 "SCACHE.spad" 1532916 1532926 1534209 1534214) (-995 "SASTCAT.spad" 1532826 1532834 1532906 1532911) (-994 "SAOS.spad" 1532699 1532707 1532816 1532821) (-993 "SAERFFC.spad" 1532413 1532432 1532689 1532694) (-992 "SAEFACT.spad" 1532115 1532134 1532403 1532408) (-991 "SAE.spad" 1529766 1529781 1530376 1530511) (-990 "RURPK.spad" 1527426 1527441 1529756 1529761) (-989 "RULESET.spad" 1526880 1526903 1527416 1527421) (-988 "RULECOLD.spad" 1526733 1526745 1526870 1526875) (-987 "RULE.spad" 1524982 1525005 1526723 1526728) (-986 "RTVALUE.spad" 1524718 1524726 1524972 1524977) (-985 "syntax.spad" 1524436 1524444 1524708 1524713) (-984 "RSETGCD.spad" 1520879 1520898 1524426 1524431) (-983 "RSETCAT.spad" 1510848 1510864 1520847 1520874) (-982 "RSETCAT.spad" 1500837 1500855 1510838 1510843) (-981 "RSDCMPK.spad" 1499338 1499357 1500827 1500832) (-980 "RRCC.spad" 1497723 1497752 1499328 1499333) (-979 "RRCC.spad" 1496106 1496137 1497713 1497718) (-978 "RPTAST.spad" 1495809 1495817 1496096 1496101) (-977 "RPOLCAT.spad" 1475314 1475328 1495677 1495804) (-976 "RPOLCAT.spad" 1454612 1454628 1474977 1474982) (-975 "ROMAN.spad" 1453941 1453949 1454478 1454607) (-974 "ROIRC.spad" 1453022 1453053 1453931 1453936) (-973 "RNS.spad" 1451999 1452007 1452924 1453017) (-972 "RNS.spad" 1451062 1451072 1451989 1451994) (-971 "RNGBIND.spad" 1450223 1450236 1451017 1451022) (-970 "RNG.spad" 1449832 1449840 1450213 1450218) (-969 "RNG.spad" 1449439 1449449 1449822 1449827) (-968 "RMODULE.spad" 1449221 1449231 1449429 1449434) (-967 "RMCAT2.spad" 1448642 1448698 1449211 1449216) (-966 "RMATRIX.spad" 1447452 1447470 1447794 1447833) (-965 "RMATCAT.spad" 1443032 1443062 1447408 1447447) (-964 "RMATCAT.spad" 1438502 1438534 1442880 1442885) (-963 "RLINSET.spad" 1438207 1438217 1438492 1438497) (-962 "RINTERP.spad" 1438096 1438115 1438197 1438202) (-961 "RING.spad" 1437567 1437575 1438076 1438091) (-960 "RING.spad" 1437046 1437056 1437557 1437562) (-959 "RIDIST.spad" 1436439 1436447 1437036 1437041) (-958 "RGCHAIN.spad" 1434994 1435009 1435887 1435914) (-957 "RGBCSPC.spad" 1434784 1434795 1434984 1434989) (-956 "RGBCMDL.spad" 1434347 1434358 1434774 1434779) (-955 "RFFACTOR.spad" 1433810 1433820 1434337 1434342) (-954 "RFFACT.spad" 1433546 1433557 1433800 1433805) (-953 "RFDIST.spad" 1432543 1432551 1433536 1433541) (-952 "RF.spad" 1430218 1430228 1432533 1432538) (-951 "RETSOL.spad" 1429638 1429650 1430208 1430213) (-950 "RETRACT.spad" 1429067 1429077 1429628 1429633) (-949 "RETRACT.spad" 1428494 1428506 1429057 1429062) (-948 "RETAST.spad" 1428307 1428315 1428484 1428489) (-947 "RESRING.spad" 1427655 1427701 1428245 1428302) (-946 "RESLATC.spad" 1426980 1426990 1427645 1427650) (-945 "REPSQ.spad" 1426712 1426722 1426970 1426975) (-944 "REPDB.spad" 1426420 1426430 1426702 1426707) (-943 "REP2.spad" 1416135 1416145 1426262 1426267) (-942 "REP1.spad" 1410356 1410366 1416085 1416090) (-941 "REP.spad" 1407911 1407919 1410346 1410351) (-940 "REGSET.spad" 1405737 1405753 1407545 1407572) (-939 "REF.spad" 1405256 1405266 1405727 1405732) (-938 "REDORDER.spad" 1404463 1404479 1405246 1405251) (-937 "RECLOS.spad" 1403360 1403379 1404063 1404156) (-936 "REALSOLV.spad" 1402501 1402509 1403350 1403355) (-935 "REAL0Q.spad" 1399800 1399814 1402491 1402496) (-934 "REAL0.spad" 1396645 1396659 1399790 1399795) (-933 "REAL.spad" 1396518 1396526 1396635 1396640) (-932 "RDUCEAST.spad" 1396240 1396248 1396508 1396513) (-931 "RDIV.spad" 1395896 1395920 1396230 1396235) (-930 "RDIST.spad" 1395464 1395474 1395886 1395891) (-929 "RDETRS.spad" 1394329 1394346 1395454 1395459) (-928 "RDETR.spad" 1392469 1392486 1394319 1394324) (-927 "RDEEFS.spad" 1391569 1391585 1392459 1392464) (-926 "RDEEF.spad" 1390580 1390596 1391559 1391564) (-925 "RCFIELD.spad" 1387799 1387807 1390482 1390575) (-924 "RCFIELD.spad" 1385104 1385114 1387789 1387794) (-923 "RCAGG.spad" 1383041 1383051 1385094 1385099) (-922 "RCAGG.spad" 1380905 1380917 1382960 1382965) (-921 "RATRET.spad" 1380266 1380276 1380895 1380900) (-920 "RATFACT.spad" 1379959 1379970 1380256 1380261) (-919 "RANDSRC.spad" 1379279 1379287 1379949 1379954) (-918 "RADUTIL.spad" 1379036 1379044 1379269 1379274) (-917 "RADIX.spad" 1376081 1376094 1377626 1377719) (-916 "RADFF.spad" 1373998 1374034 1374116 1374272) (-915 "RADCAT.spad" 1373594 1373602 1373988 1373993) (-914 "RADCAT.spad" 1373188 1373198 1373584 1373589) (-913 "QUEUE.spad" 1372602 1372612 1372860 1372887) (-912 "QUATCT2.spad" 1372223 1372241 1372592 1372597) (-911 "QUATCAT.spad" 1370394 1370404 1372153 1372218) (-910 "QUATCAT.spad" 1368330 1368342 1370091 1370096) (-909 "QUAT.spad" 1366937 1366947 1367279 1367344) (-908 "QUAGG.spad" 1365771 1365781 1366905 1366932) (-907 "QQUTAST.spad" 1365540 1365548 1365761 1365766) (-906 "QFORM.spad" 1365159 1365173 1365530 1365535) (-905 "QFCAT2.spad" 1364852 1364868 1365149 1365154) (-904 "QFCAT.spad" 1363555 1363565 1364754 1364847) (-903 "QFCAT.spad" 1361891 1361903 1363092 1363097) (-902 "QEQUAT.spad" 1361450 1361458 1361881 1361886) (-901 "QCMPACK.spad" 1356365 1356384 1361440 1361445) (-900 "QALGSET2.spad" 1354361 1354379 1356355 1356360) (-899 "QALGSET.spad" 1350466 1350498 1354275 1354280) (-898 "PWFFINTB.spad" 1347882 1347903 1350456 1350461) (-897 "PUSHVAR.spad" 1347221 1347240 1347872 1347877) (-896 "PTRANFN.spad" 1343357 1343367 1347211 1347216) (-895 "PTPACK.spad" 1340445 1340455 1343347 1343352) (-894 "PTFUNC2.spad" 1340268 1340282 1340435 1340440) (-893 "PTCAT.spad" 1339523 1339533 1340236 1340263) (-892 "PSQFR.spad" 1338838 1338862 1339513 1339518) (-891 "PSEUDLIN.spad" 1337724 1337734 1338828 1338833) (-890 "PSETPK.spad" 1324429 1324445 1337602 1337607) (-889 "PSETCAT.spad" 1318829 1318852 1324409 1324424) (-888 "PSETCAT.spad" 1313203 1313228 1318785 1318790) (-887 "PSCURVE.spad" 1312202 1312210 1313193 1313198) (-886 "PSCAT.spad" 1310985 1311014 1312100 1312197) (-885 "PSCAT.spad" 1309858 1309889 1310975 1310980) (-884 "PRTITION.spad" 1308556 1308564 1309848 1309853) (-883 "PRTDAST.spad" 1308275 1308283 1308546 1308551) (-882 "PRS.spad" 1297893 1297910 1308231 1308236) (-881 "PRQAGG.spad" 1297328 1297338 1297861 1297888) (-880 "PROPLOG.spad" 1296932 1296940 1297318 1297323) (-879 "PROPFUN2.spad" 1296555 1296568 1296922 1296927) (-878 "PROPFUN1.spad" 1295961 1295972 1296545 1296550) (-877 "PROPFRML.spad" 1294529 1294540 1295951 1295956) (-876 "PROPERTY.spad" 1294025 1294033 1294519 1294524) (-875 "PRODUCT.spad" 1291722 1291734 1292006 1292061) (-874 "PRINT.spad" 1291474 1291482 1291712 1291717) (-873 "PRIMES.spad" 1289735 1289745 1291464 1291469) (-872 "PRIMELT.spad" 1287856 1287870 1289725 1289730) (-871 "PRIMCAT.spad" 1287499 1287507 1287846 1287851) (-870 "PRIMARR2.spad" 1286266 1286278 1287489 1287494) (-869 "PRIMARR.spad" 1285321 1285331 1285491 1285518) (-868 "PREASSOC.spad" 1284703 1284715 1285311 1285316) (-867 "PR.spad" 1283221 1283233 1283920 1284047) (-866 "PPCURVE.spad" 1282358 1282366 1283211 1283216) (-865 "PORTNUM.spad" 1282149 1282157 1282348 1282353) (-864 "POLYROOT.spad" 1280998 1281020 1282105 1282110) (-863 "POLYLIFT.spad" 1280263 1280286 1280988 1280993) (-862 "POLYCATQ.spad" 1278389 1278411 1280253 1280258) (-861 "POLYCAT.spad" 1271891 1271912 1278257 1278384) (-860 "POLYCAT.spad" 1264913 1264936 1271281 1271286) (-859 "POLY2UP.spad" 1264365 1264379 1264903 1264908) (-858 "POLY2.spad" 1263962 1263974 1264355 1264360) (-857 "POLY.spad" 1261630 1261640 1262145 1262272) (-856 "POLUTIL.spad" 1260595 1260624 1261586 1261591) (-855 "POLTOPOL.spad" 1259343 1259358 1260585 1260590) (-854 "POINT.spad" 1258226 1258236 1258313 1258340) (-853 "PNTHEORY.spad" 1254928 1254936 1258216 1258221) (-852 "PMTOOLS.spad" 1253703 1253717 1254918 1254923) (-851 "PMSYM.spad" 1253252 1253262 1253693 1253698) (-850 "PMQFCAT.spad" 1252843 1252857 1253242 1253247) (-849 "PMPREDFS.spad" 1252305 1252327 1252833 1252838) (-848 "PMPRED.spad" 1251792 1251806 1252295 1252300) (-847 "PMPLCAT.spad" 1250869 1250887 1251721 1251726) (-846 "PMLSAGG.spad" 1250454 1250468 1250859 1250864) (-845 "PMKERNEL.spad" 1250033 1250045 1250444 1250449) (-844 "PMINS.spad" 1249613 1249623 1250023 1250028) (-843 "PMFS.spad" 1249190 1249208 1249603 1249608) (-842 "PMDOWN.spad" 1248480 1248494 1249180 1249185) (-841 "PMASSFS.spad" 1247455 1247471 1248470 1248475) (-840 "PMASS.spad" 1246473 1246481 1247445 1247450) (-839 "PLOTTOOL.spad" 1246253 1246261 1246463 1246468) (-838 "PLOT3D.spad" 1242717 1242725 1246243 1246248) (-837 "PLOT1.spad" 1241890 1241900 1242707 1242712) (-836 "PLOT.spad" 1236813 1236821 1241880 1241885) (-835 "PLEQN.spad" 1224215 1224242 1236803 1236808) (-834 "PINTERPA.spad" 1223999 1224015 1224205 1224210) (-833 "PINTERP.spad" 1223621 1223640 1223989 1223994) (-832 "PID.spad" 1222595 1222603 1223547 1223616) (-831 "PICOERCE.spad" 1222252 1222262 1222585 1222590) (-830 "PI.spad" 1221869 1221877 1222226 1222247) (-829 "PGROEB.spad" 1220478 1220492 1221859 1221864) (-828 "PGE.spad" 1212151 1212159 1220468 1220473) (-827 "PGCD.spad" 1211105 1211122 1212141 1212146) (-826 "PFRPAC.spad" 1210254 1210264 1211095 1211100) (-825 "PFR.spad" 1206957 1206967 1210156 1210249) (-824 "PFOTOOLS.spad" 1206215 1206231 1206947 1206952) (-823 "PFOQ.spad" 1205585 1205603 1206205 1206210) (-822 "PFO.spad" 1205004 1205031 1205575 1205580) (-821 "PFECAT.spad" 1202714 1202722 1204930 1204999) (-820 "PFECAT.spad" 1200452 1200462 1202670 1202675) (-819 "PFBRU.spad" 1198340 1198352 1200442 1200447) (-818 "PFBR.spad" 1195900 1195923 1198330 1198335) (-817 "PF.spad" 1195474 1195486 1195705 1195798) (-816 "PERMGRP.spad" 1190244 1190254 1195464 1195469) (-815 "PERMCAT.spad" 1188905 1188915 1190224 1190239) (-814 "PERMAN.spad" 1187461 1187475 1188895 1188900) (-813 "PERM.spad" 1183271 1183281 1187294 1187309) (-812 "PENDTREE.spad" 1182685 1182695 1182965 1182970) (-811 "PDSPC.spad" 1181498 1181508 1182675 1182680) (-810 "PDSPC.spad" 1180309 1180321 1181488 1181493) (-809 "PDRING.spad" 1180151 1180161 1180289 1180304) (-808 "PDMOD.spad" 1179967 1179979 1180119 1180146) (-807 "PDECOMP.spad" 1179437 1179454 1179957 1179962) (-806 "PDDOM.spad" 1178875 1178888 1179427 1179432) (-805 "PDDOM.spad" 1178311 1178326 1178865 1178870) (-804 "PCOMP.spad" 1178164 1178177 1178301 1178306) (-803 "PBWLB.spad" 1176762 1176779 1178154 1178159) (-802 "PATTERN2.spad" 1176500 1176512 1176752 1176757) (-801 "PATTERN1.spad" 1174844 1174860 1176490 1176495) (-800 "PATTERN.spad" 1169419 1169429 1174834 1174839) (-799 "PATRES2.spad" 1169091 1169105 1169409 1169414) (-798 "PATRES.spad" 1166674 1166686 1169081 1169086) (-797 "PATMATCH.spad" 1164915 1164946 1166426 1166431) (-796 "PATMAB.spad" 1164344 1164354 1164905 1164910) (-795 "PATLRES.spad" 1163430 1163444 1164334 1164339) (-794 "PATAB.spad" 1163194 1163204 1163420 1163425) (-793 "PARTPERM.spad" 1161250 1161258 1163184 1163189) (-792 "PARSURF.spad" 1160684 1160712 1161240 1161245) (-791 "PARSU2.spad" 1160481 1160497 1160674 1160679) (-790 "script-parser.spad" 1160001 1160009 1160471 1160476) (-789 "PARSCURV.spad" 1159435 1159463 1159991 1159996) (-788 "PARSC2.spad" 1159226 1159242 1159425 1159430) (-787 "PARPCURV.spad" 1158688 1158716 1159216 1159221) (-786 "PARPC2.spad" 1158479 1158495 1158678 1158683) (-785 "PARAMAST.spad" 1157607 1157615 1158469 1158474) (-784 "PAN2EXPR.spad" 1157019 1157027 1157597 1157602) (-783 "PALETTE.spad" 1156133 1156141 1157009 1157014) (-782 "PAIR.spad" 1155207 1155220 1155776 1155781) (-781 "PADICRC.spad" 1152612 1152630 1153775 1153868) (-780 "PADICRAT.spad" 1150672 1150684 1150885 1150978) (-779 "PADICCT.spad" 1149221 1149233 1150598 1150667) (-778 "PADIC.spad" 1148924 1148936 1149147 1149216) (-777 "PADEPAC.spad" 1147613 1147632 1148914 1148919) (-776 "PADE.spad" 1146365 1146381 1147603 1147608) (-775 "OWP.spad" 1145613 1145643 1146223 1146290) (-774 "OVERSET.spad" 1145186 1145194 1145603 1145608) (-773 "OVAR.spad" 1144967 1144990 1145176 1145181) (-772 "OUTFORM.spad" 1134375 1134383 1144957 1144962) (-771 "OUTBFILE.spad" 1133809 1133817 1134365 1134370) (-770 "OUTBCON.spad" 1132879 1132887 1133799 1133804) (-769 "OUTBCON.spad" 1131947 1131957 1132869 1132874) (-768 "OUT.spad" 1131065 1131073 1131937 1131942) (-767 "OSI.spad" 1130540 1130548 1131055 1131060) (-766 "OSGROUP.spad" 1130458 1130466 1130530 1130535) (-765 "ORTHPOL.spad" 1128969 1128979 1130401 1130406) (-764 "OREUP.spad" 1128463 1128491 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"CTORCALL.spad" 169430 169440 169831 169836) (-157 "CTOR.spad" 169121 169129 169420 169425) (-156 "CSTTOOLS.spad" 168366 168379 169111 169116) (-155 "CRFP.spad" 162138 162151 168356 168361) (-154 "CRCEAST.spad" 161858 161866 162128 162133) (-153 "CRAPACK.spad" 160925 160935 161848 161853) (-152 "CPMATCH.spad" 160426 160441 160847 160852) (-151 "CPIMA.spad" 160131 160150 160416 160421) (-150 "COORDSYS.spad" 155140 155150 160121 160126) (-149 "CONTOUR.spad" 154567 154575 155130 155135) (-148 "CONTFRAC.spad" 150317 150327 154469 154562) (-147 "CONDUIT.spad" 150075 150083 150307 150312) (-146 "COMRING.spad" 149749 149757 150013 150070) (-145 "COMPPROP.spad" 149267 149275 149739 149744) (-144 "COMPLPAT.spad" 149034 149049 149257 149262) (-143 "COMPLEX2.spad" 148749 148761 149024 149029) (-142 "COMPLEX.spad" 144455 144465 144699 144957) (-141 "COMPILER.spad" 144004 144012 144445 144450) (-140 "COMPFACT.spad" 143606 143620 143994 143999) (-139 "COMPCAT.spad" 141681 141691 143343 143601) (-138 "COMPCAT.spad" 139497 139509 141161 141166) (-137 "COMMUPC.spad" 139245 139263 139487 139492) (-136 "COMMONOP.spad" 138778 138786 139235 139240) (-135 "COMMAAST.spad" 138541 138549 138768 138773) (-134 "COMM.spad" 138352 138360 138531 138536) (-133 "COMBOPC.spad" 137275 137283 138342 138347) (-132 "COMBINAT.spad" 136042 136052 137265 137270) (-131 "COMBF.spad" 133464 133480 136032 136037) (-130 "COLOR.spad" 132301 132309 133454 133459) (-129 "COLONAST.spad" 131967 131975 132291 132296) (-128 "CMPLXRT.spad" 131678 131695 131957 131962) (-127 "CLLCTAST.spad" 131340 131348 131668 131673) (-126 "CLIP.spad" 127448 127456 131330 131335) (-125 "CLIF.spad" 126103 126119 127404 127443) (-124 "CLAGG.spad" 122640 122650 126093 126098) (-123 "CLAGG.spad" 119061 119073 122516 122521) (-122 "CINTSLPE.spad" 118416 118429 119051 119056) (-121 "CHVAR.spad" 116554 116576 118406 118411) (-120 "CHARZ.spad" 116469 116477 116534 116549) (-119 "CHARPOL.spad" 115995 116005 116459 116464) (-118 "CHARNZ.spad" 115757 115765 115975 115990) (-117 "CHAR.spad" 113125 113133 115747 115752) (-116 "CFCAT.spad" 112453 112461 113115 113120) (-115 "CDEN.spad" 111673 111687 112443 112448) (-114 "CCLASS.spad" 109853 109861 111115 111154) (-113 "CATEGORY.spad" 108927 108935 109843 109848) (-112 "CATCTOR.spad" 108818 108826 108917 108922) (-111 "CATAST.spad" 108444 108452 108808 108813) (-110 "CASEAST.spad" 108158 108166 108434 108439) (-109 "CARTEN2.spad" 107548 107575 108148 108153) (-108 "CARTEN.spad" 103300 103324 107538 107543) (-107 "CARD.spad" 100595 100603 103274 103295) (-106 "CAPSLAST.spad" 100377 100385 100585 100590) (-105 "CACHSET.spad" 100001 100009 100367 100372) (-104 "CABMON.spad" 99556 99564 99991 99996) (-103 "BYTEORD.spad" 99231 99239 99546 99551) (-102 "BYTEBUF.spad" 97198 97206 98484 98511) (-101 "BYTE.spad" 96673 96681 97188 97193) (-100 "BTREE.spad" 95811 95821 96345 96372) (-99 "BTOURN.spad" 94882 94891 95483 95510) (-98 "BTCAT.spad" 94275 94284 94850 94877) (-97 "BTCAT.spad" 93688 93699 94265 94270) (-96 "BTAGG.spad" 93155 93162 93656 93683) (-95 "BTAGG.spad" 92642 92651 93145 93150) (-94 "BSTREE.spad" 91449 91458 92314 92341) (-93 "BRILL.spad" 89655 89665 91439 91444) (-92 "BRAGG.spad" 88612 88621 89645 89650) (-91 "BRAGG.spad" 87533 87544 88568 88573) (-90 "BPADICRT.spad" 85593 85604 85839 85932) (-89 "BPADIC.spad" 85266 85277 85519 85588) (-88 "BOUNDZRO.spad" 84923 84939 85256 85261) (-87 "BOP1.spad" 82382 82391 84913 84918) (-86 "BOP.spad" 77525 77532 82372 82377) (-85 "BOOLEAN.spad" 77074 77081 77515 77520) (-84 "BOOLE.spad" 76725 76732 77064 77069) (-83 "BOOLE.spad" 76374 76383 76715 76720) (-82 "BMODULE.spad" 76087 76098 76342 76369) (-81 "BITS.spad" 75519 75526 75733 75760) (-80 "catdef.spad" 75402 75412 75509 75514) (-79 "catdef.spad" 75153 75163 75392 75397) (-78 "BINDING.spad" 74575 74582 75143 75148) (-77 "BINARY.spad" 72810 72817 73165 73258) (-76 "BGAGG.spad" 72016 72025 72790 72805) (-75 "BGAGG.spad" 71230 71241 72006 72011) (-74 "BEZOUT.spad" 70371 70397 71180 71185) (-73 "BBTREE.spad" 67314 67323 70043 70070) (-72 "BASTYPE.spad" 66814 66821 67304 67309) (-71 "BASTYPE.spad" 66312 66321 66804 66809) (-70 "BALFACT.spad" 65772 65784 66302 66307) (-69 "AUTOMOR.spad" 65223 65232 65752 65767) (-68 "ATTREG.spad" 61946 61953 64975 65218) (-67 "ATTRAST.spad" 61663 61670 61936 61941) (-66 "ATRIG.spad" 61133 61140 61653 61658) (-65 "ATRIG.spad" 60601 60610 61123 61128) (-64 "ASTCAT.spad" 60505 60512 60591 60596) (-63 "ASTCAT.spad" 60407 60416 60495 60500) (-62 "ASTACK.spad" 59811 59820 60079 60106) (-61 "ASSOCEQ.spad" 58645 58656 59767 59772) (-60 "ARRAY2.spad" 58078 58087 58317 58344) (-59 "ARRAY12.spad" 56791 56802 58068 58073) (-58 "ARRAY1.spad" 55670 55679 56016 56043) (-57 "ARR2CAT.spad" 51452 51473 55638 55665) (-56 "ARR2CAT.spad" 47254 47277 51442 51447) (-55 "ARITY.spad" 46626 46633 47244 47249) (-54 "APPRULE.spad" 45910 45932 46616 46621) (-53 "APPLYORE.spad" 45529 45542 45900 45905) (-52 "ANY1.spad" 44600 44609 45519 45524) (-51 "ANY.spad" 43451 43458 44590 44595) (-50 "ANTISYM.spad" 41896 41912 43431 43446) (-49 "ANON.spad" 41605 41612 41886 41891) (-48 "AN.spad" 40073 40080 41436 41529) (-47 "AMR.spad" 38258 38269 39971 40068) (-46 "AMR.spad" 36306 36319 38021 38026) (-45 "ALIST.spad" 33544 33565 33894 33921) (-44 "ALGSC.spad" 32679 32705 33416 33469) (-43 "ALGPKG.spad" 28462 28473 32635 32640) (-42 "ALGMFACT.spad" 27655 27669 28452 28457) (-41 "ALGMANIP.spad" 25156 25171 27499 27504) (-40 "ALGFF.spad" 22974 23001 23191 23347) (-39 "ALGFACT.spad" 22093 22103 22964 22969) (-38 "ALGEBRA.spad" 21926 21935 22049 22088) (-37 "ALGEBRA.spad" 21791 21802 21916 21921) (-36 "ALAGG.spad" 21303 21324 21759 21786) (-35 "AHYP.spad" 20684 20691 21293 21298) (-34 "AGG.spad" 19393 19400 20674 20679) (-33 "AGG.spad" 18066 18075 19349 19354) (-32 "AF.spad" 16511 16526 18015 18020) (-31 "ADDAST.spad" 16197 16204 16501 16506) (-30 "ACPLOT.spad" 15074 15081 16187 16192) (-29 "ACFS.spad" 12931 12940 14976 15069) (-28 "ACFS.spad" 10874 10885 12921 12926) (-27 "ACF.spad" 7628 7635 10776 10869) (-26 "ACF.spad" 4468 4477 7618 7623) (-25 "ABELSG.spad" 4009 4016 4458 4463) (-24 "ABELSG.spad" 3548 3557 3999 4004) (-23 "ABELMON.spad" 2976 2983 3538 3543) (-22 "ABELMON.spad" 2402 2411 2966 2971) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
\ No newline at end of file
+((-3 NIL 1961216 1961221 1961226 1961231) (-2 NIL 1961196 1961201 1961206 1961211) (-1 NIL 1961176 1961181 1961186 1961191) (0 NIL 1961156 1961161 1961166 1961171) (-1208 "ZMOD.spad" 1960965 1960978 1961094 1961151) (-1207 "ZLINDEP.spad" 1960063 1960074 1960955 1960960) (-1206 "ZDSOLVE.spad" 1950024 1950046 1960053 1960058) (-1205 "YSTREAM.spad" 1949519 1949530 1950014 1950019) (-1204 "YDIAGRAM.spad" 1949153 1949162 1949509 1949514) (-1203 "XRPOLY.spad" 1948373 1948393 1949009 1949078) (-1202 "XPR.spad" 1946168 1946181 1948091 1948190) (-1201 "XPOLYC.spad" 1945487 1945503 1946094 1946163) (-1200 "XPOLY.spad" 1945042 1945053 1945343 1945412) (-1199 "XPBWPOLY.spad" 1943513 1943533 1944848 1944917) (-1198 "XFALG.spad" 1940561 1940577 1943439 1943508) (-1197 "XF.spad" 1939024 1939039 1940463 1940556) (-1196 "XF.spad" 1937467 1937484 1938908 1938913) (-1195 "XEXPPKG.spad" 1936726 1936752 1937457 1937462) (-1194 "XDPOLY.spad" 1936340 1936356 1936582 1936651) (-1193 "XALG.spad" 1936008 1936019 1936296 1936335) (-1192 "WUTSET.spad" 1932011 1932028 1935642 1935669) (-1191 "WP.spad" 1931218 1931262 1931869 1931936) (-1190 "WHILEAST.spad" 1931016 1931025 1931208 1931213) (-1189 "WHEREAST.spad" 1930687 1930696 1931006 1931011) (-1188 "WFFINTBS.spad" 1928350 1928372 1930677 1930682) (-1187 "WEIER.spad" 1926572 1926583 1928340 1928345) (-1186 "VSPACE.spad" 1926245 1926256 1926540 1926567) (-1185 "VSPACE.spad" 1925938 1925951 1926235 1926240) (-1184 "VOID.spad" 1925615 1925624 1925928 1925933) (-1183 "VIEWDEF.spad" 1920816 1920825 1925605 1925610) (-1182 "VIEW3D.spad" 1904777 1904786 1920806 1920811) (-1181 "VIEW2D.spad" 1892676 1892685 1904767 1904772) (-1180 "VIEW.spad" 1890396 1890405 1892666 1892671) (-1179 "VECTOR2.spad" 1889035 1889048 1890386 1890391) (-1178 "VECTOR.spad" 1887754 1887765 1888005 1888032) (-1177 "VECTCAT.spad" 1885666 1885677 1887722 1887749) (-1176 "VECTCAT.spad" 1883387 1883400 1885445 1885450) (-1175 "VARIABLE.spad" 1883167 1883182 1883377 1883382) (-1174 "UTYPE.spad" 1882811 1882820 1883157 1883162) (-1173 "UTSODETL.spad" 1882106 1882130 1882767 1882772) (-1172 "UTSODE.spad" 1880322 1880342 1882096 1882101) (-1171 "UTSCAT.spad" 1877801 1877817 1880220 1880317) (-1170 "UTSCAT.spad" 1874948 1874966 1877369 1877374) (-1169 "UTS2.spad" 1874543 1874578 1874938 1874943) (-1168 "UTS.spad" 1869555 1869583 1873075 1873172) (-1167 "URAGG.spad" 1864276 1864287 1869545 1869550) (-1166 "URAGG.spad" 1858961 1858974 1864232 1864237) (-1165 "UPXSSING.spad" 1856729 1856755 1858165 1858298) (-1164 "UPXSCONS.spad" 1854547 1854567 1854920 1855069) (-1163 "UPXSCCA.spad" 1853118 1853138 1854393 1854542) (-1162 "UPXSCCA.spad" 1851831 1851853 1853108 1853113) (-1161 "UPXSCAT.spad" 1850420 1850436 1851677 1851826) (-1160 "UPXS2.spad" 1849963 1850016 1850410 1850415) (-1159 "UPXS.spad" 1847318 1847346 1848154 1848303) (-1158 "UPSQFREE.spad" 1845733 1845747 1847308 1847313) (-1157 "UPSCAT.spad" 1843528 1843552 1845631 1845728) (-1156 "UPSCAT.spad" 1841024 1841050 1843129 1843134) (-1155 "UPOLYC2.spad" 1840495 1840514 1841014 1841019) (-1154 "UPOLYC.spad" 1835575 1835586 1840337 1840490) (-1153 "UPOLYC.spad" 1830573 1830586 1835337 1835342) (-1152 "UPMP.spad" 1829505 1829518 1830563 1830568) (-1151 "UPDIVP.spad" 1829070 1829084 1829495 1829500) (-1150 "UPDECOMP.spad" 1827331 1827345 1829060 1829065) (-1149 "UPCDEN.spad" 1826548 1826564 1827321 1827326) (-1148 "UP2.spad" 1825912 1825933 1826538 1826543) (-1147 "UP.spad" 1823382 1823397 1823769 1823922) (-1146 "UNISEG2.spad" 1822879 1822892 1823338 1823343) (-1145 "UNISEG.spad" 1822232 1822243 1822798 1822803) (-1144 "UNIFACT.spad" 1821335 1821347 1822222 1822227) (-1143 "ULSCONS.spad" 1815378 1815398 1815748 1815897) (-1142 "ULSCCAT.spad" 1813115 1813135 1815224 1815373) (-1141 "ULSCCAT.spad" 1810960 1810982 1813071 1813076) (-1140 "ULSCAT.spad" 1809200 1809216 1810806 1810955) (-1139 "ULS2.spad" 1808714 1808767 1809190 1809195) (-1138 "ULS.spad" 1800980 1801008 1801925 1802348) (-1137 "UINT8.spad" 1800857 1800866 1800970 1800975) (-1136 "UINT64.spad" 1800733 1800742 1800847 1800852) (-1135 "UINT32.spad" 1800609 1800618 1800723 1800728) (-1134 "UINT16.spad" 1800485 1800494 1800599 1800604) (-1133 "UFD.spad" 1799550 1799559 1800411 1800480) (-1132 "UFD.spad" 1798677 1798688 1799540 1799545) (-1131 "UDVO.spad" 1797558 1797567 1798667 1798672) (-1130 "UDPO.spad" 1795139 1795150 1797514 1797519) (-1129 "TYPEAST.spad" 1795058 1795067 1795129 1795134) (-1128 "TYPE.spad" 1794990 1794999 1795048 1795053) (-1127 "TWOFACT.spad" 1793642 1793657 1794980 1794985) (-1126 "TUPLE.spad" 1793149 1793160 1793554 1793559) (-1125 "TUBETOOL.spad" 1790016 1790025 1793139 1793144) (-1124 "TUBE.spad" 1788663 1788680 1790006 1790011) (-1123 "TSETCAT.spad" 1776734 1776751 1788631 1788658) (-1122 "TSETCAT.spad" 1764791 1764810 1776690 1776695) (-1121 "TS.spad" 1763419 1763435 1764385 1764482) (-1120 "TRMANIP.spad" 1757783 1757800 1763107 1763112) (-1119 "TRIMAT.spad" 1756746 1756771 1757773 1757778) (-1118 "TRIGMNIP.spad" 1755273 1755290 1756736 1756741) (-1117 "TRIGCAT.spad" 1754785 1754794 1755263 1755268) (-1116 "TRIGCAT.spad" 1754295 1754306 1754775 1754780) (-1115 "TREE.spad" 1752935 1752946 1753967 1753994) (-1114 "TRANFUN.spad" 1752774 1752783 1752925 1752930) (-1113 "TRANFUN.spad" 1752611 1752622 1752764 1752769) (-1112 "TOPSP.spad" 1752285 1752294 1752601 1752606) (-1111 "TOOLSIGN.spad" 1751948 1751959 1752275 1752280) (-1110 "TEXTFILE.spad" 1750509 1750518 1751938 1751943) (-1109 "TEX1.spad" 1750065 1750076 1750499 1750504) (-1108 "TEX.spad" 1747259 1747268 1750055 1750060) (-1107 "TBCMPPK.spad" 1745360 1745383 1747249 1747254) (-1106 "TBAGG.spad" 1744418 1744441 1745340 1745355) (-1105 "TBAGG.spad" 1743484 1743509 1744408 1744413) (-1104 "TANEXP.spad" 1742892 1742903 1743474 1743479) (-1103 "TALGOP.spad" 1742616 1742627 1742882 1742887) (-1102 "TABLEAU.spad" 1742097 1742108 1742606 1742611) (-1101 "TABLE.spad" 1740372 1740395 1740642 1740669) (-1100 "TABLBUMP.spad" 1737151 1737162 1740362 1740367) (-1099 "SYSTEM.spad" 1736379 1736388 1737141 1737146) (-1098 "SYSSOLP.spad" 1733862 1733873 1736369 1736374) (-1097 "SYSPTR.spad" 1733761 1733770 1733852 1733857) (-1096 "SYSNNI.spad" 1732984 1732995 1733751 1733756) (-1095 "SYSINT.spad" 1732388 1732399 1732974 1732979) (-1094 "SYNTAX.spad" 1728722 1728731 1732378 1732383) (-1093 "SYMTAB.spad" 1726790 1726799 1728712 1728717) (-1092 "SYMS.spad" 1722819 1722828 1726780 1726785) (-1091 "SYMPOLY.spad" 1721952 1721963 1722034 1722161) (-1090 "SYMFUNC.spad" 1721453 1721464 1721942 1721947) (-1089 "SYMBOL.spad" 1718948 1718957 1721443 1721448) (-1088 "SUTS.spad" 1716061 1716089 1717480 1717577) (-1087 "SUPXS.spad" 1713403 1713431 1714252 1714401) (-1086 "SUPFRACF.spad" 1712508 1712526 1713393 1713398) (-1085 "SUP2.spad" 1711900 1711913 1712498 1712503) (-1084 "SUP.spad" 1708984 1708995 1709757 1709910) (-1083 "SUMRF.spad" 1707958 1707969 1708974 1708979) (-1082 "SUMFS.spad" 1707587 1707604 1707948 1707953) (-1081 "SULS.spad" 1699840 1699868 1700798 1701221) (-1080 "syntax.spad" 1699609 1699618 1699830 1699835) (-1079 "SUCH.spad" 1699299 1699314 1699599 1699604) (-1078 "SUBSPACE.spad" 1691430 1691445 1699289 1699294) (-1077 "SUBRESP.spad" 1690600 1690614 1691386 1691391) (-1076 "STTFNC.spad" 1687068 1687084 1690590 1690595) (-1075 "STTF.spad" 1683167 1683183 1687058 1687063) (-1074 "STTAYLOR.spad" 1675844 1675855 1683074 1683079) (-1073 "STRTBL.spad" 1674231 1674248 1674380 1674407) (-1072 "STRING.spad" 1673099 1673108 1673484 1673511) (-1071 "STREAM3.spad" 1672672 1672687 1673089 1673094) (-1070 "STREAM2.spad" 1671800 1671813 1672662 1672667) (-1069 "STREAM1.spad" 1671506 1671517 1671790 1671795) (-1068 "STREAM.spad" 1668502 1668513 1671109 1671124) (-1067 "STINPROD.spad" 1667438 1667454 1668492 1668497) (-1066 "STEPAST.spad" 1666672 1666681 1667428 1667433) (-1065 "STEP.spad" 1665989 1665998 1666662 1666667) (-1064 "STBL.spad" 1664379 1664407 1664546 1664561) (-1063 "STAGG.spad" 1663078 1663089 1664369 1664374) (-1062 "STAGG.spad" 1661775 1661788 1663068 1663073) (-1061 "STACK.spad" 1661197 1661208 1661447 1661474) (-1060 "SRING.spad" 1660957 1660966 1661187 1661192) (-1059 "SREGSET.spad" 1658689 1658706 1660591 1660618) (-1058 "SRDCMPK.spad" 1657266 1657286 1658679 1658684) (-1057 "SRAGG.spad" 1652449 1652458 1657234 1657261) (-1056 "SRAGG.spad" 1647652 1647663 1652439 1652444) (-1055 "SQMATRIX.spad" 1645329 1645347 1646245 1646332) (-1054 "SPLTREE.spad" 1640071 1640084 1644867 1644894) (-1053 "SPLNODE.spad" 1636691 1636704 1640061 1640066) (-1052 "SPFCAT.spad" 1635500 1635509 1636681 1636686) (-1051 "SPECOUT.spad" 1634052 1634061 1635490 1635495) (-1050 "SPADXPT.spad" 1626143 1626152 1634042 1634047) (-1049 "spad-parser.spad" 1625608 1625617 1626133 1626138) (-1048 "SPADAST.spad" 1625309 1625318 1625598 1625603) (-1047 "SPACEC.spad" 1609524 1609535 1625299 1625304) (-1046 "SPACE3.spad" 1609300 1609311 1609514 1609519) (-1045 "SORTPAK.spad" 1608849 1608862 1609256 1609261) (-1044 "SOLVETRA.spad" 1606612 1606623 1608839 1608844) (-1043 "SOLVESER.spad" 1605068 1605079 1606602 1606607) (-1042 "SOLVERAD.spad" 1601094 1601105 1605058 1605063) (-1041 "SOLVEFOR.spad" 1599556 1599574 1601084 1601089) (-1040 "SNTSCAT.spad" 1599156 1599173 1599524 1599551) (-1039 "SMTS.spad" 1597473 1597499 1598750 1598847) (-1038 "SMP.spad" 1595281 1595301 1595671 1595798) (-1037 "SMITH.spad" 1594126 1594151 1595271 1595276) (-1036 "SMATCAT.spad" 1592244 1592274 1594070 1594121) (-1035 "SMATCAT.spad" 1590294 1590326 1592122 1592127) (-1034 "SKAGG.spad" 1589263 1589274 1590262 1590289) (-1033 "SINT.spad" 1588562 1588571 1589129 1589258) (-1032 "SIMPAN.spad" 1588290 1588299 1588552 1588557) (-1031 "SIGNRF.spad" 1587415 1587426 1588280 1588285) (-1030 "SIGNEF.spad" 1586701 1586718 1587405 1587410) (-1029 "syntax.spad" 1586118 1586127 1586691 1586696) (-1028 "SIG.spad" 1585480 1585489 1586108 1586113) (-1027 "SHP.spad" 1583424 1583439 1585436 1585441) (-1026 "SHDP.spad" 1572917 1572944 1573434 1573531) (-1025 "SGROUP.spad" 1572525 1572534 1572907 1572912) (-1024 "SGROUP.spad" 1572131 1572142 1572515 1572520) (-1023 "catdef.spad" 1571841 1571853 1571952 1572126) (-1022 "catdef.spad" 1571397 1571409 1571662 1571836) (-1021 "SGCF.spad" 1564536 1564545 1571387 1571392) (-1020 "SFRTCAT.spad" 1563482 1563499 1564504 1564531) (-1019 "SFRGCD.spad" 1562545 1562565 1563472 1563477) (-1018 "SFQCMPK.spad" 1557358 1557378 1562535 1562540) (-1017 "SEXOF.spad" 1557201 1557241 1557348 1557353) (-1016 "SEXCAT.spad" 1555029 1555069 1557191 1557196) (-1015 "SEX.spad" 1554921 1554930 1555019 1555024) (-1014 "SETMN.spad" 1553381 1553398 1554911 1554916) (-1013 "SETCAT.spad" 1552866 1552875 1553371 1553376) (-1012 "SETCAT.spad" 1552349 1552360 1552856 1552861) (-1011 "SETAGG.spad" 1548898 1548909 1552329 1552344) (-1010 "SETAGG.spad" 1545455 1545468 1548888 1548893) (-1009 "SET.spad" 1543764 1543775 1544861 1544900) (-1008 "syntax.spad" 1543467 1543476 1543754 1543759) (-1007 "SEGXCAT.spad" 1542623 1542636 1543457 1543462) (-1006 "SEGCAT.spad" 1541548 1541559 1542613 1542618) (-1005 "SEGBIND2.spad" 1541246 1541259 1541538 1541543) (-1004 "SEGBIND.spad" 1541004 1541015 1541193 1541198) (-1003 "SEGAST.spad" 1540734 1540743 1540994 1540999) (-1002 "SEG2.spad" 1540169 1540182 1540690 1540695) (-1001 "SEG.spad" 1539982 1539993 1540088 1540093) (-1000 "SDVAR.spad" 1539258 1539269 1539972 1539977) (-999 "SDPOL.spad" 1536951 1536961 1537241 1537368) (-998 "SCPKG.spad" 1535041 1535051 1536941 1536946) (-997 "SCOPE.spad" 1534219 1534227 1535031 1535036) (-996 "SCACHE.spad" 1532916 1532926 1534209 1534214) (-995 "SASTCAT.spad" 1532826 1532834 1532906 1532911) (-994 "SAOS.spad" 1532699 1532707 1532816 1532821) (-993 "SAERFFC.spad" 1532413 1532432 1532689 1532694) (-992 "SAEFACT.spad" 1532115 1532134 1532403 1532408) (-991 "SAE.spad" 1529766 1529781 1530376 1530511) (-990 "RURPK.spad" 1527426 1527441 1529756 1529761) (-989 "RULESET.spad" 1526880 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(-913 "QUEUE.spad" 1372602 1372612 1372860 1372887) (-912 "QUATCT2.spad" 1372223 1372241 1372592 1372597) (-911 "QUATCAT.spad" 1370394 1370404 1372153 1372218) (-910 "QUATCAT.spad" 1368330 1368342 1370091 1370096) (-909 "QUAT.spad" 1366937 1366947 1367279 1367344) (-908 "QUAGG.spad" 1365771 1365781 1366905 1366932) (-907 "QQUTAST.spad" 1365540 1365548 1365761 1365766) (-906 "QFORM.spad" 1365159 1365173 1365530 1365535) (-905 "QFCAT2.spad" 1364852 1364868 1365149 1365154) (-904 "QFCAT.spad" 1363555 1363565 1364754 1364847) (-903 "QFCAT.spad" 1361891 1361903 1363092 1363097) (-902 "QEQUAT.spad" 1361450 1361458 1361881 1361886) (-901 "QCMPACK.spad" 1356365 1356384 1361440 1361445) (-900 "QALGSET2.spad" 1354361 1354379 1356355 1356360) (-899 "QALGSET.spad" 1350466 1350498 1354275 1354280) (-898 "PWFFINTB.spad" 1347882 1347903 1350456 1350461) (-897 "PUSHVAR.spad" 1347221 1347240 1347872 1347877) (-896 "PTRANFN.spad" 1343357 1343367 1347211 1347216) (-895 "PTPACK.spad" 1340445 1340455 1343347 1343352) (-894 "PTFUNC2.spad" 1340268 1340282 1340435 1340440) (-893 "PTCAT.spad" 1339523 1339533 1340236 1340263) (-892 "PSQFR.spad" 1338838 1338862 1339513 1339518) (-891 "PSEUDLIN.spad" 1337724 1337734 1338828 1338833) (-890 "PSETPK.spad" 1324429 1324445 1337602 1337607) (-889 "PSETCAT.spad" 1318829 1318852 1324409 1324424) (-888 "PSETCAT.spad" 1313203 1313228 1318785 1318790) (-887 "PSCURVE.spad" 1312202 1312210 1313193 1313198) (-886 "PSCAT.spad" 1310985 1311014 1312100 1312197) (-885 "PSCAT.spad" 1309858 1309889 1310975 1310980) (-884 "PRTITION.spad" 1308556 1308564 1309848 1309853) (-883 "PRTDAST.spad" 1308275 1308283 1308546 1308551) (-882 "PRS.spad" 1297893 1297910 1308231 1308236) (-881 "PRQAGG.spad" 1297328 1297338 1297861 1297888) (-880 "PROPLOG.spad" 1296932 1296940 1297318 1297323) (-879 "PROPFUN2.spad" 1296555 1296568 1296922 1296927) (-878 "PROPFUN1.spad" 1295961 1295972 1296545 1296550) (-877 "PROPFRML.spad" 1294529 1294540 1295951 1295956) (-876 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1174860 1176490 1176495) (-800 "PATTERN.spad" 1169419 1169429 1174834 1174839) (-799 "PATRES2.spad" 1169091 1169105 1169409 1169414) (-798 "PATRES.spad" 1166674 1166686 1169081 1169086) (-797 "PATMATCH.spad" 1164915 1164946 1166426 1166431) (-796 "PATMAB.spad" 1164344 1164354 1164905 1164910) (-795 "PATLRES.spad" 1163430 1163444 1164334 1164339) (-794 "PATAB.spad" 1163194 1163204 1163420 1163425) (-793 "PARTPERM.spad" 1161250 1161258 1163184 1163189) (-792 "PARSURF.spad" 1160684 1160712 1161240 1161245) (-791 "PARSU2.spad" 1160481 1160497 1160674 1160679) (-790 "script-parser.spad" 1160001 1160009 1160471 1160476) (-789 "PARSCURV.spad" 1159435 1159463 1159991 1159996) (-788 "PARSC2.spad" 1159226 1159242 1159425 1159430) (-787 "PARPCURV.spad" 1158688 1158716 1159216 1159221) (-786 "PARPC2.spad" 1158479 1158495 1158678 1158683) (-785 "PARAMAST.spad" 1157607 1157615 1158469 1158474) (-784 "PAN2EXPR.spad" 1157019 1157027 1157597 1157602) (-783 "PALETTE.spad" 1156133 1156141 1157009 1157014) (-782 "PAIR.spad" 1155207 1155220 1155776 1155781) (-781 "PADICRC.spad" 1152612 1152630 1153775 1153868) (-780 "PADICRAT.spad" 1150672 1150684 1150885 1150978) (-779 "PADICCT.spad" 1149221 1149233 1150598 1150667) (-778 "PADIC.spad" 1148924 1148936 1149147 1149216) (-777 "PADEPAC.spad" 1147613 1147632 1148914 1148919) (-776 "PADE.spad" 1146365 1146381 1147603 1147608) (-775 "OWP.spad" 1145613 1145643 1146223 1146290) (-774 "OVERSET.spad" 1145186 1145194 1145603 1145608) (-773 "OVAR.spad" 1144967 1144990 1145176 1145181) (-772 "OUTFORM.spad" 1134375 1134383 1144957 1144962) (-771 "OUTBFILE.spad" 1133809 1133817 1134365 1134370) (-770 "OUTBCON.spad" 1132879 1132887 1133799 1133804) (-769 "OUTBCON.spad" 1131947 1131957 1132869 1132874) (-768 "OUT.spad" 1131065 1131073 1131937 1131942) (-767 "OSI.spad" 1130540 1130548 1131055 1131060) (-766 "OSGROUP.spad" 1130458 1130466 1130530 1130535) (-765 "ORTHPOL.spad" 1128969 1128979 1130401 1130406) (-764 "OREUP.spad" 1128463 1128491 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978727 978860 978865) (-667 "MPC2.spad" 978341 978374 978677 978682) (-666 "MONOTOOL.spad" 976692 976709 978331 978336) (-665 "catdef.spad" 976125 976136 976346 976687) (-664 "catdef.spad" 975523 975534 975779 976120) (-663 "MONOID.spad" 974844 974852 975513 975518) (-662 "MONOID.spad" 974163 974173 974834 974839) (-661 "MONOGEN.spad" 972911 972924 974023 974158) (-660 "MONOGEN.spad" 971681 971696 972795 972800) (-659 "MONADWU.spad" 969761 969769 971671 971676) (-658 "MONADWU.spad" 967839 967849 969751 969756) (-657 "MONAD.spad" 966999 967007 967829 967834) (-656 "MONAD.spad" 966157 966167 966989 966994) (-655 "MOEBIUS.spad" 964893 964907 966137 966152) (-654 "MODULE.spad" 964763 964773 964861 964888) (-653 "MODULE.spad" 964653 964665 964753 964758) (-652 "MODRING.spad" 963988 964027 964633 964648) (-651 "MODOP.spad" 962645 962657 963810 963877) (-650 "MODMONOM.spad" 962376 962394 962635 962640) (-649 "MODMON.spad" 959446 959458 960161 960314) (-648 "MODFIELD.spad" 958808 958847 959348 959441) (-647 "MMLFORM.spad" 957668 957676 958798 958803) (-646 "MMAP.spad" 957410 957444 957658 957663) (-645 "MLO.spad" 955869 955879 957366 957405) (-644 "MLIFT.spad" 954481 954498 955859 955864) (-643 "MKUCFUNC.spad" 954016 954034 954471 954476) (-642 "MKRECORD.spad" 953604 953617 954006 954011) (-641 "MKFUNC.spad" 953011 953021 953594 953599) (-640 "MKFLCFN.spad" 951979 951989 953001 953006) (-639 "MKBCFUNC.spad" 951474 951492 951969 951974) (-638 "MHROWRED.spad" 949985 949995 951464 951469) (-637 "MFINFACT.spad" 949385 949407 949975 949980) (-636 "MESH.spad" 947180 947188 949375 949380) (-635 "MDDFACT.spad" 945399 945409 947170 947175) (-634 "MDAGG.spad" 944690 944700 945379 945394) (-633 "MCDEN.spad" 943900 943912 944680 944685) (-632 "MAYBE.spad" 943200 943211 943890 943895) (-631 "MATSTOR.spad" 940516 940526 943190 943195) (-630 "MATRIX.spad" 939295 939305 939779 939806) (-629 "MATLIN.spad" 936663 936687 939179 939184) (-628 "MATCAT2.spad" 935945 935993 936653 936658) (-627 "MATCAT.spad" 927507 927529 935913 935940) (-626 "MATCAT.spad" 918941 918965 927349 927354) (-625 "MAPPKG3.spad" 917856 917870 918931 918936) (-624 "MAPPKG2.spad" 917194 917206 917846 917851) (-623 "MAPPKG1.spad" 916022 916032 917184 917189) (-622 "MAPPAST.spad" 915361 915369 916012 916017) (-621 "MAPHACK3.spad" 915173 915187 915351 915356) (-620 "MAPHACK2.spad" 914942 914954 915163 915168) (-619 "MAPHACK1.spad" 914586 914596 914932 914937) (-618 "MAGMA.spad" 912392 912409 914576 914581) (-617 "MACROAST.spad" 911987 911995 912382 912387) (-616 "LZSTAGG.spad" 909241 909251 911977 911982) (-615 "LZSTAGG.spad" 906493 906505 909231 909236) (-614 "LWORD.spad" 903238 903255 906483 906488) (-613 "LSTAST.spad" 903022 903030 903228 903233) (-612 "LSQM.spad" 901300 901314 901694 901745) (-611 "LSPP.spad" 900835 900852 901290 901295) (-610 "LSMP1.spad" 898678 898692 900825 900830) (-609 "LSMP.spad" 897535 897563 898668 898673) (-608 "LSAGG.spad" 897204 897214 897503 897530) (-607 "LSAGG.spad" 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(-586 "LIST3.spad" 873212 873226 873891 873896) (-585 "LIST2MAP.spad" 870139 870151 873202 873207) (-584 "LIST2.spad" 868841 868853 870129 870134) (-583 "LIST.spad" 866723 866733 868066 868093) (-582 "LINSET.spad" 866502 866512 866713 866718) (-581 "LINFORM.spad" 865965 865977 866470 866497) (-580 "LINEXP.spad" 864708 864718 865955 865960) (-579 "LINELT.spad" 864079 864091 864591 864618) (-578 "LINDEP.spad" 862928 862940 863991 863996) (-577 "LINBASIS.spad" 862564 862579 862918 862923) (-576 "LIMITRF.spad" 860511 860521 862554 862559) (-575 "LIMITPS.spad" 859421 859434 860501 860506) (-574 "LIECAT.spad" 858905 858915 859347 859416) (-573 "LIECAT.spad" 858417 858429 858861 858866) (-572 "LIE.spad" 856421 856433 857695 857837) (-571 "LIB.spad" 854592 854600 855038 855053) (-570 "LGROBP.spad" 851945 851964 854582 854587) (-569 "LFCAT.spad" 851004 851012 851935 851940) (-568 "LF.spad" 849959 849975 850994 850999) (-567 "LEXTRIPK.spad" 845582 845597 849949 849954) (-566 "LEXP.spad" 843601 843628 845562 845577) (-565 "LETAST.spad" 843300 843308 843591 843596) (-564 "LEADCDET.spad" 841706 841723 843290 843295) (-563 "LAZM3PK.spad" 840450 840472 841696 841701) (-562 "LAUPOL.spad" 839117 839130 840017 840086) (-561 "LAPLACE.spad" 838700 838716 839107 839112) (-560 "LALG.spad" 838476 838486 838680 838695) (-559 "LALG.spad" 838260 838272 838466 838471) (-558 "LA.spad" 837700 837714 838182 838221) (-557 "KVTFROM.spad" 837443 837453 837690 837695) (-556 "KTVLOGIC.spad" 836987 836995 837433 837438) (-555 "KRCFROM.spad" 836733 836743 836977 836982) (-554 "KOVACIC.spad" 835464 835481 836723 836728) (-553 "KONVERT.spad" 835186 835196 835454 835459) (-552 "KOERCE.spad" 834923 834933 835176 835181) (-551 "KERNEL2.spad" 834626 834638 834913 834918) (-550 "KERNEL.spad" 833346 833356 834475 834480) (-549 "KDAGG.spad" 832455 832477 833326 833341) (-548 "KDAGG.spad" 831572 831596 832445 832450) (-547 "KAFILE.spad" 830462 830478 830697 830724) (-546 "JVMOP.spad" 830375 830383 830452 830457) (-545 "JVMMDACC.spad" 829429 829437 830365 830370) (-544 "JVMFDACC.spad" 828745 828753 829419 829424) (-543 "JVMCSTTG.spad" 827474 827482 828735 828740) (-542 "JVMCFACC.spad" 826920 826928 827464 827469) (-541 "JVMBCODE.spad" 826831 826839 826910 826915) (-540 "JORDAN.spad" 824648 824660 826109 826251) (-539 "JOINAST.spad" 824350 824358 824638 824643) (-538 "IXAGG.spad" 822483 822507 824340 824345) (-537 "IXAGG.spad" 820471 820497 822330 822335) (-536 "IVECTOR.spad" 819286 819301 819441 819468) (-535 "ITUPLE.spad" 818462 818472 819276 819281) (-534 "ITRIGMNP.spad" 817309 817328 818452 818457) (-533 "ITFUN3.spad" 816815 816829 817299 817304) (-532 "ITFUN2.spad" 816559 816571 816805 816810) (-531 "ITFORM.spad" 815914 815922 816549 816554) (-530 "ITAYLOR.spad" 813908 813923 815778 815875) (-529 "ISUPS.spad" 806357 806372 812894 812991) (-528 "ISUMP.spad" 805858 805874 806347 806352) (-527 "ISAST.spad" 805577 805585 805848 805853) (-526 "IRURPK.spad" 804294 804313 805567 805572) (-525 "IRSN.spad" 802298 802306 804284 804289) (-524 "IRRF2F.spad" 800791 800801 802254 802259) (-523 "IRREDFFX.spad" 800392 800403 800781 800786) (-522 "IROOT.spad" 798731 798741 800382 800387) (-521 "IRFORM.spad" 798055 798063 798721 798726) (-520 "IR2F.spad" 797269 797285 798045 798050) (-519 "IR2.spad" 796297 796313 797259 797264) (-518 "IR.spad" 794133 794147 796179 796206) (-517 "IPRNTPK.spad" 793893 793901 794123 794128) (-516 "IPF.spad" 793458 793470 793698 793791) (-515 "IPADIC.spad" 793227 793253 793384 793453) (-514 "IP4ADDR.spad" 792784 792792 793217 793222) (-513 "IOMODE.spad" 792306 792314 792774 792779) (-512 "IOBFILE.spad" 791691 791699 792296 792301) (-511 "IOBCON.spad" 791556 791564 791681 791686) (-510 "INVLAPLA.spad" 791205 791221 791546 791551) (-509 "INTTR.spad" 784599 784616 791195 791200) (-508 "INTTOOLS.spad" 782407 782423 784226 784231) (-507 "INTSLPE.spad" 781735 781743 782397 782402) (-506 "INTRVL.spad" 781301 781311 781649 781730) (-505 "INTRF.spad" 779733 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(-484 "INT16.spad" 752533 752541 752644 752649) (-483 "INT.spad" 752059 752067 752399 752528) (-482 "INS.spad" 749562 749570 751961 752054) (-481 "INS.spad" 747151 747161 749552 749557) (-480 "INPSIGN.spad" 746621 746634 747141 747146) (-479 "INPRODPF.spad" 745717 745736 746611 746616) (-478 "INPRODFF.spad" 744805 744829 745707 745712) (-477 "INNMFACT.spad" 743780 743797 744795 744800) (-476 "INMODGCD.spad" 743284 743314 743770 743775) (-475 "INFSP.spad" 741581 741603 743274 743279) (-474 "INFPROD0.spad" 740661 740680 741571 741576) (-473 "INFORM1.spad" 740286 740296 740651 740656) (-472 "INFORM.spad" 737497 737505 740276 740281) (-471 "INFINITY.spad" 737049 737057 737487 737492) (-470 "INETCLTS.spad" 737026 737034 737039 737044) (-469 "INEP.spad" 735572 735594 737016 737021) (-468 "INDE.spad" 735221 735238 735482 735487) (-467 "INCRMAPS.spad" 734658 734668 735211 735216) (-466 "INBFILE.spad" 733754 733762 734648 734653) (-465 "INBFF.spad" 729604 729615 733744 733749) (-464 "INBCON.spad" 727870 727878 729594 729599) (-463 "INBCON.spad" 726134 726144 727860 727865) (-462 "INAST.spad" 725795 725803 726124 726129) (-461 "IMPTAST.spad" 725503 725511 725785 725790) (-460 "IMATQF.spad" 724597 724641 725459 725464) (-459 "IMATLIN.spad" 723218 723242 724553 724558) (-458 "IFF.spad" 722631 722647 722902 722995) (-457 "IFAST.spad" 722245 722253 722621 722626) (-456 "IFARRAY.spad" 719772 719787 721470 721497) (-455 "IFAMON.spad" 719634 719651 719728 719733) (-454 "IEVALAB.spad" 719047 719059 719624 719629) (-453 "IEVALAB.spad" 718458 718472 719037 719042) (-452 "indexedp.spad" 718014 718026 718448 718453) (-451 "IDPOAMS.spad" 717692 717704 717926 717931) (-450 "IDPOAM.spad" 717334 717346 717604 717609) (-449 "IDPO.spad" 716748 716760 717246 717251) (-448 "IDPC.spad" 715463 715475 716738 716743) (-447 "IDPAM.spad" 715130 715142 715375 715380) (-446 "IDPAG.spad" 714799 714811 715042 715047) (-445 "IDENT.spad" 714451 714459 714789 714794) (-444 "catdef.spad" 714222 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93688 93699 94265 94270) (-96 "BTAGG.spad" 93155 93162 93656 93683) (-95 "BTAGG.spad" 92642 92651 93145 93150) (-94 "BSTREE.spad" 91449 91458 92314 92341) (-93 "BRILL.spad" 89655 89665 91439 91444) (-92 "BRAGG.spad" 88612 88621 89645 89650) (-91 "BRAGG.spad" 87533 87544 88568 88573) (-90 "BPADICRT.spad" 85593 85604 85839 85932) (-89 "BPADIC.spad" 85266 85277 85519 85588) (-88 "BOUNDZRO.spad" 84923 84939 85256 85261) (-87 "BOP1.spad" 82382 82391 84913 84918) (-86 "BOP.spad" 77525 77532 82372 82377) (-85 "BOOLEAN.spad" 77074 77081 77515 77520) (-84 "BOOLE.spad" 76725 76732 77064 77069) (-83 "BOOLE.spad" 76374 76383 76715 76720) (-82 "BMODULE.spad" 76087 76098 76342 76369) (-81 "BITS.spad" 75519 75526 75733 75760) (-80 "catdef.spad" 75402 75412 75509 75514) (-79 "catdef.spad" 75153 75163 75392 75397) (-78 "BINDING.spad" 74575 74582 75143 75148) (-77 "BINARY.spad" 72810 72817 73165 73258) (-76 "BGAGG.spad" 72016 72025 72790 72805) (-75 "BGAGG.spad" 71230 71241 72006 72011) (-74 "BEZOUT.spad" 70371 70397 71180 71185) (-73 "BBTREE.spad" 67314 67323 70043 70070) (-72 "BASTYPE.spad" 66814 66821 67304 67309) (-71 "BASTYPE.spad" 66312 66321 66804 66809) (-70 "BALFACT.spad" 65772 65784 66302 66307) (-69 "AUTOMOR.spad" 65223 65232 65752 65767) (-68 "ATTREG.spad" 61946 61953 64975 65218) (-67 "ATTRAST.spad" 61663 61670 61936 61941) (-66 "ATRIG.spad" 61133 61140 61653 61658) (-65 "ATRIG.spad" 60601 60610 61123 61128) (-64 "ASTCAT.spad" 60505 60512 60591 60596) (-63 "ASTCAT.spad" 60407 60416 60495 60500) (-62 "ASTACK.spad" 59811 59820 60079 60106) (-61 "ASSOCEQ.spad" 58645 58656 59767 59772) (-60 "ARRAY2.spad" 58078 58087 58317 58344) (-59 "ARRAY12.spad" 56791 56802 58068 58073) (-58 "ARRAY1.spad" 55670 55679 56016 56043) (-57 "ARR2CAT.spad" 51452 51473 55638 55665) (-56 "ARR2CAT.spad" 47254 47277 51442 51447) (-55 "ARITY.spad" 46626 46633 47244 47249) (-54 "APPRULE.spad" 45910 45932 46616 46621) (-53 "APPLYORE.spad" 45529 45542 45900 45905) (-52 "ANY1.spad" 44600 44609 45519 45524) (-51 "ANY.spad" 43451 43458 44590 44595) (-50 "ANTISYM.spad" 41896 41912 43431 43446) (-49 "ANON.spad" 41605 41612 41886 41891) (-48 "AN.spad" 40073 40080 41436 41529) (-47 "AMR.spad" 38258 38269 39971 40068) (-46 "AMR.spad" 36306 36319 38021 38026) (-45 "ALIST.spad" 33544 33565 33894 33921) (-44 "ALGSC.spad" 32679 32705 33416 33469) (-43 "ALGPKG.spad" 28462 28473 32635 32640) (-42 "ALGMFACT.spad" 27655 27669 28452 28457) (-41 "ALGMANIP.spad" 25156 25171 27499 27504) (-40 "ALGFF.spad" 22974 23001 23191 23347) (-39 "ALGFACT.spad" 22093 22103 22964 22969) (-38 "ALGEBRA.spad" 21926 21935 22049 22088) (-37 "ALGEBRA.spad" 21791 21802 21916 21921) (-36 "ALAGG.spad" 21303 21324 21759 21786) (-35 "AHYP.spad" 20684 20691 21293 21298) (-34 "AGG.spad" 19393 19400 20674 20679) (-33 "AGG.spad" 18066 18075 19349 19354) (-32 "AF.spad" 16511 16526 18015 18020) (-31 "ADDAST.spad" 16197 16204 16501 16506) (-30 "ACPLOT.spad" 15074 15081 16187 16192) (-29 "ACFS.spad" 12931 12940 14976 15069) (-28 "ACFS.spad" 10874 10885 12921 12926) (-27 "ACF.spad" 7628 7635 10776 10869) (-26 "ACF.spad" 4468 4477 7618 7623) (-25 "ABELSG.spad" 4009 4016 4458 4463) (-24 "ABELSG.spad" 3548 3557 3999 4004) (-23 "ABELMON.spad" 2976 2983 3538 3543) (-22 "ABELMON.spad" 2402 2411 2966 2971) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
\ No newline at end of file