aboutsummaryrefslogtreecommitdiff
path: root/src/share/algebra/browse.daase
diff options
context:
space:
mode:
Diffstat (limited to 'src/share/algebra/browse.daase')
-rw-r--r--src/share/algebra/browse.daase176
1 files changed, 88 insertions, 88 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 7b9391eb..5f119975 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
-(1970276 . 3577897419)
+(1969262 . 3577905059)
(-18 A S)
((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result.")))
NIL
NIL
(-19 S)
((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-20 S)
((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}")))
@@ -74,7 +74,7 @@ NIL
NIL
(-36 |Key| |Entry|)
((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Maybe| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \\spad{nothing} if \\spad{u} has no key \\spad{k}.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
NIL
(-37 S R)
((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")))
@@ -110,8 +110,8 @@ NIL
((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496))))
(-45 |Key| |Entry|)
((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data.")))
-((-3997 . T) (-3998 . T))
-((OR (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))))
+((-3998 . T))
+((OR (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))))
(-46 S R E)
((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
NIL
@@ -158,11 +158,11 @@ NIL
NIL
(-57 R |Row| |Col|)
((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}'s")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-58 S)
((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))
(-59 A B)
((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")))
@@ -170,7 +170,7 @@ NIL
NIL
(-60 R)
((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-61 R L)
((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op, m)} returns \\spad{[w, eq, lw, lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,...,A_n]} such that if \\spad{y = [y_1,...,y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',y_j'',...,y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}'s.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op, m)} returns \\spad{[M,w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}.")))
@@ -178,7 +178,7 @@ NIL
((|HasCategory| |#1| (QUOTE (-312))))
(-62 S)
((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-63 S)
((|constructor| (NIL "This is the category of Spad abstract syntax trees.")))
@@ -222,7 +222,7 @@ NIL
NIL
(-73 S)
((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and pr. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} := \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-74 R UP M |Row| |Col|)
((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}.")))
@@ -254,7 +254,7 @@ NIL
NIL
(-81)
((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-1014))) (|HasCategory| $ (QUOTE (-318 (-85)))) (-12 (|HasCategory| $ (QUOTE (-318 (-85)))) (|HasCategory| (-85) (QUOTE (-72)))))
(-82 R S)
((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}")))
@@ -306,7 +306,7 @@ NIL
NIL
(-94 S)
((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-95 S)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")))
@@ -314,7 +314,7 @@ NIL
NIL
(-96)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-97 A S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")))
@@ -322,15 +322,15 @@ NIL
NIL
(-98 S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-99 S)
((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-100 S)
((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-101)
((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256.")))
@@ -338,7 +338,7 @@ NIL
NIL
(-102)
((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-757)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) (|HasCategory| (-101) (QUOTE (-553 (-773)))) (|HasCategory| (-101) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-101) (QUOTE (-757))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-1014))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014)))) (-12 (|HasCategory| $ (QUOTE (-318 (-101)))) (|HasCategory| (-101) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-101)))))
(-103)
((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host")))
@@ -386,7 +386,7 @@ NIL
NIL
(-114)
((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}.")))
-((-3997 . T) (-3987 . T) (-3998 . T))
+((-3987 . T) (-3998 . T))
((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-320)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (|HasCategory| (-117) (QUOTE (-320))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-1014))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| $ (QUOTE (-318 (-117)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72)))))
(-115 R Q A)
((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\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| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn.")))
@@ -634,7 +634,7 @@ NIL
NIL
(-176 S)
((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-177 |CoefRing| |listIndVar|)
((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}.")))
@@ -654,7 +654,7 @@ NIL
NIL
(-181 R)
((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3999 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))))
(-182 A S)
((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones.")))
@@ -714,11 +714,11 @@ NIL
((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasAttribute| |#3| (QUOTE -3994)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1014))))
(-196 -2623 R)
((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")))
-((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994)) (-3997 . T))
+((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994)))
NIL
(-197 -2623 R)
((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation.")))
-((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994)) (-3997 . T))
+((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994)))
((OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-718))) (OR (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-320))) (OR (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-962))))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-190))) (OR (|HasCategory| |#2| (QUOTE (-190))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-1014))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-1014))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-962))))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasAttribute| |#2| (QUOTE -3994)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))))
(-198 -2623 A B)
((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}.")))
@@ -742,7 +742,7 @@ NIL
NIL
(-203 S)
((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))))
(-204 M)
((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}")))
@@ -770,11 +770,11 @@ NIL
NIL
(-210 |n| R M S)
((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view.")))
-((-3994 OR (-2564 (|has| |#4| (-962)) (|has| |#4| (-190))) (|has| |#4| (-6 -3994)) (-2564 (|has| |#4| (-962)) (|has| |#4| (-810 (-1091))))) (-3991 |has| |#4| (-962)) (-3992 |has| |#4| (-962)) (-3997 . T))
+((-3994 OR (-2564 (|has| |#4| (-962)) (|has| |#4| (-190))) (|has| |#4| (-6 -3994)) (-2564 (|has| |#4| (-962)) (|has| |#4| (-810 (-1091))))) (-3991 |has| |#4| (-962)) (-3992 |has| |#4| (-962)))
((OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-320))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-664))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-718))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-757))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-810 (-1091)))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-962))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|))))) (|HasCategory| |#4| (QUOTE (-312))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-962)))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-312)))) (|HasCategory| |#4| (QUOTE (-962))) (|HasCategory| |#4| (QUOTE (-664))) (|HasCategory| |#4| (QUOTE (-718))) (OR (|HasCategory| |#4| (QUOTE (-718))) (|HasCategory| |#4| (QUOTE (-757)))) (|HasCategory| |#4| (QUOTE (-757))) (|HasCategory| |#4| (QUOTE (-320))) (OR (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-581 (-485)))) (|HasCategory| |#4| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#4| (QUOTE (-581 (-485)))) (|HasCategory| |#4| (QUOTE (-962))))) (|HasCategory| |#4| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-810 (-1091)))) (|HasCategory| |#4| (QUOTE (-962)))) (|HasCategory| |#4| (QUOTE (-190))) (OR (|HasCategory| |#4| (QUOTE (-190))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-812 (-1091)))) (|HasCategory| |#4| (QUOTE (-962)))) (|HasCategory| |#4| (QUOTE (-810 (-1091))))) (|HasCategory| |#4| (QUOTE (-1014))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#4| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#4| (QUOTE (-664))) (|HasCategory| |#4| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#4| (QUOTE (-718))) (|HasCategory| |#4| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#4| (QUOTE (-757))) (|HasCategory| |#4| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#4| (QUOTE (-810 (-1091)))) (|HasCategory| |#4| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#4| (QUOTE (-1014))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-718))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-757))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-810 (-1091)))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-485)))) (|HasCategory| |#4| (QUOTE (-1014)))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-664))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (|HasCategory| |#4| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-718))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-757))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-810 (-1091)))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-485)))) (|HasCategory| |#4| (QUOTE (-1014)))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-664))) (|HasCategory| |#4| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-485)))) (|HasCategory| |#4| (QUOTE (-962))))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (-12 (|HasCategory| |#4| (QUOTE (-581 (-485)))) (|HasCategory| |#4| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-810 (-1091)))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-812 (-1091)))) (|HasCategory| |#4| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-962))))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-485)))) (|HasCategory| |#4| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-951 (-485)))) (|HasCategory| |#4| (QUOTE (-1014)))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#4| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-810 (-1091)))) (|HasCategory| |#4| (QUOTE (-962)))) (|HasAttribute| |#4| (QUOTE -3994)) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-962))))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-812 (-1091)))) (|HasCategory| |#4| (QUOTE (-962)))) (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-23))) (|HasCategory| |#4| (QUOTE (-104))) (|HasCategory| |#4| (QUOTE (-25))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))))
(-211 |n| R S)
((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view.")))
-((-3994 OR (-2564 (|has| |#3| (-962)) (|has| |#3| (-190))) (|has| |#3| (-6 -3994)) (-2564 (|has| |#3| (-962)) (|has| |#3| (-810 (-1091))))) (-3991 |has| |#3| (-962)) (-3992 |has| |#3| (-962)) (-3997 . T))
+((-3994 OR (-2564 (|has| |#3| (-962)) (|has| |#3| (-190))) (|has| |#3| (-6 -3994)) (-2564 (|has| |#3| (-962)) (|has| |#3| (-810 (-1091))))) (-3991 |has| |#3| (-962)) (-3992 |has| |#3| (-962)))
((OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-312))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-718))) (OR (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757)))) (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-320))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-190))) (OR (|HasCategory| |#3| (QUOTE (-190))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-810 (-1091))))) (|HasCategory| |#3| (QUOTE (-1014))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasAttribute| |#3| (QUOTE -3994)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-553 (-773)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#3|)))))
(-212 A R S V E)
((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.")))
@@ -786,7 +786,7 @@ NIL
NIL
(-214 S)
((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
NIL
(-215 |Ex|)
((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")))
@@ -934,7 +934,7 @@ NIL
NIL
(-251 |Key| |Entry|)
((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))))
(-252)
((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates.")))
@@ -1042,7 +1042,7 @@ NIL
NIL
(-278 S)
((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))
(-279 S -3094)
((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace.")))
@@ -1202,7 +1202,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-72))))
(-318 S)
((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\spad{reduce(f,u,x)},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\spad{reduce(f,u,x)} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the starting value,{} usually the identity operation of \\spad{f}. Same as \\spad{reduce(f,u)} if \\spad{u} has 2 or more elements. Returns \\spad{f(x,y)} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\spad{reduce(+,u,0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\spad{[x,y,...,z]} then \\spad{reduce(f,u)} returns \\spad{f(..f(f(x,y),...),z)}. Note: if \\spad{u} has one element \\spad{x},{} \\spad{reduce(f,u)} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{members([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. For collections,{}} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) holds for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\spad{p(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})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}.")))
-((-3997 . T))
+NIL
NIL
(-319 S)
((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set.")))
@@ -1226,7 +1226,7 @@ NIL
((|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))))
(-324 S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
-((-3997 . T))
+NIL
NIL
(-325 S A R B)
((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain.")))
@@ -1406,7 +1406,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-320))))
(-369 S)
((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}.")))
-((-3997 . T) (-3987 . T) (-3998 . T))
+((-3987 . T) (-3998 . T))
NIL
(-370 S A R B)
((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain.")))
@@ -1542,7 +1542,7 @@ NIL
NIL
(-403 R E |VarSet| P)
((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|))))
(-404 S R E)
((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}.")))
@@ -1590,11 +1590,11 @@ NIL
((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|)))))))
(-415 |Key| |Entry| |Tbl| |dent|)
((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))))
(-416 R E V P)
((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|))))
(-417)
((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}.")))
@@ -1606,7 +1606,7 @@ NIL
NIL
(-419 |Key| |Entry| |hashfn|)
((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))))
(-420)
((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre's book Lie Groups -- Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight <= \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2")))
@@ -1618,7 +1618,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118)))))
(-422 -2623 S)
((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}.")))
-((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994)) (-3997 . T))
+((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994)))
((OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-718))) (OR (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-320))) (OR (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-962))))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-190))) (OR (|HasCategory| |#2| (QUOTE (-190))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-1014))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-1014))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-962))))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasAttribute| |#2| (QUOTE -3994)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))))
(-423)
((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header.")))
@@ -1626,7 +1626,7 @@ NIL
NIL
(-424 S)
((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-425 -3094 UP UPUP R)
((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree.")))
@@ -1674,11 +1674,11 @@ NIL
((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485)))))
(-436 S |mn|)
((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))
(-437 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.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-438 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")))
@@ -1690,7 +1690,7 @@ NIL
NIL
(-440 |mn|)
((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-1014))) (|HasCategory| $ (QUOTE (-318 (-85)))) (-12 (|HasCategory| $ (QUOTE (-318 (-85)))) (|HasCategory| (-85) (QUOTE (-72)))))
(-441 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)}.")))
@@ -1762,7 +1762,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-717))))
(-458 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}")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))
(-459)
((|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'.")))
@@ -1890,7 +1890,7 @@ NIL
NIL
(-490 |Key| |Entry| |addDom|)
((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))))
(-491 R -3094)
((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}.")))
@@ -2122,7 +2122,7 @@ NIL
NIL
(-548 |Entry|)
((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))))
(-549 S |Key| |Entry|)
((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}.")))
@@ -2218,7 +2218,7 @@ NIL
NIL
(-572)
((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-51) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-554 (-474)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014))) (-12 (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (-12 (|HasCategory| $ (QUOTE (-318 (-51)))) (|HasCategory| (-51) (QUOTE (-72)))))
(-573 R A)
((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A).")))
@@ -2266,7 +2266,7 @@ NIL
NIL
(-584 S)
((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))))
(-585 A B)
((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}.")))
@@ -2290,7 +2290,7 @@ NIL
NIL
(-590 S)
((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))
(-591 R)
((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline")))
@@ -2366,7 +2366,7 @@ NIL
NIL
(-609 S)
((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-610 -3094 |Row| |Col| M)
((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.")))
@@ -2382,7 +2382,7 @@ NIL
NIL
(-613 |n| R)
((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication.")))
-((-3994 . T) (-3997 . T) (-3991 . T) (-3992 . T))
+((-3994 . T) (-3991 . T) (-3992 . T))
((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3999 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496))) (OR (|HasAttribute| |#2| (QUOTE (-3999 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146))))
(-614)
((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'.")))
@@ -2442,7 +2442,7 @@ NIL
((|HasAttribute| |#2| (QUOTE (-3999 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496))))
(-628 R |Row| |Col|)
((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-629 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.")))
@@ -2454,7 +2454,7 @@ NIL
((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))))
(-631 R)
((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3999 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))))
(-632 R)
((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} ** \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")))
@@ -2634,7 +2634,7 @@ NIL
((-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-757))))
(-676 S)
((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|unique| (((|List| |#1|) $) "\\spad{unique ms} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{members}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}.")))
-((-3997 . T) (-3987 . T) (-3998 . T))
+((-3987 . T) (-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))
(-677 S)
((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements.")))
@@ -2762,7 +2762,7 @@ NIL
((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))))
(-708 R E V P)
((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-709 S)
((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.")))
@@ -2874,7 +2874,7 @@ NIL
NIL
(-736 -2623 S |f|)
((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}.")))
-((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994)) (-3997 . T))
+((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994)))
((OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-718))) (OR (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-320))) (OR (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-962))))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-190))) (OR (|HasCategory| |#2| (QUOTE (-190))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-1014))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-1014))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-962))))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasAttribute| |#2| (QUOTE -3994)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))))
(-737 R)
((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline")))
@@ -2902,7 +2902,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190))))
(-743 S)
((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}.")))
-((-3997 . T) (-3987 . T) (-3998 . T))
+((-3987 . T) (-3998 . T))
NIL
(-744 R)
((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity.")))
@@ -3350,7 +3350,7 @@ NIL
NIL
(-855 R)
((|constructor| (NIL "This domain implements points in coordinate space")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))
(-856 |lv| R)
((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}.")))
@@ -3410,7 +3410,7 @@ NIL
NIL
(-870 S)
((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))
(-871 A B)
((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")))
@@ -3458,7 +3458,7 @@ NIL
NIL
(-882 S)
((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
NIL
(-883 R |polR|)
((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean2}}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.fr}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{S_{\\spad{e}-1}} where \\axiom{\\spad{P} ~ S_d,{} \\spad{Q} = S_{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)**(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{gcd(\\spad{P},{} \\spad{Q})} returns the gcd of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the gcd of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")))
@@ -3490,7 +3490,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-496))))
(-890 R E |VarSet| P)
((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned.")))
-((-3997 . T))
+NIL
NIL
(-891 R E V P)
((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(lp)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{lp} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{lq} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{bps} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in lp,{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(lp)} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{lp} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{lp} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor.")))
@@ -3506,7 +3506,7 @@ NIL
NIL
(-894 R)
((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-895 R1 R2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented")))
@@ -3566,7 +3566,7 @@ NIL
NIL
(-909 S)
((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\#q}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
NIL
(-910 R)
((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}")))
@@ -3586,7 +3586,7 @@ NIL
NIL
(-914 S)
((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,y,...,z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-915 S)
((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}.")))
@@ -3694,7 +3694,7 @@ NIL
NIL
(-941 R E V P)
((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|))))
(-942)
((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals.")))
@@ -3766,7 +3766,7 @@ NIL
NIL
(-959 R |ls|)
((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a Gcd-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| (-704 |#1| (-774 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-554 (-474)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-774 |#2|) (QUOTE (-320))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|))))))
(-960)
((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented")))
@@ -3794,11 +3794,11 @@ NIL
((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-146))))
(-966 |m| |n| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")))
-((-3997 . T) (-3992 . T) (-3991 . T))
+((-3992 . T) (-3991 . T))
NIL
(-967 |m| |n| R)
((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}.")))
-((-3997 . T) (-3992 . T) (-3991 . T))
+((-3992 . T) (-3991 . T))
((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-496))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-553 (-773)))))
(-968 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.")))
@@ -3866,7 +3866,7 @@ NIL
NIL
(-984 R E V P)
((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-985 R E V P TS)
((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts,{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")))
@@ -3970,7 +3970,7 @@ NIL
NIL
(-1010 S)
((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the members function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}")))
-((-3997 . T) (-3987 . T) (-3998 . T))
+((-3987 . T) (-3998 . T))
((OR (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))
(-1011 A S)
((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}.")))
@@ -4014,7 +4014,7 @@ NIL
NIL
(-1021 R E V P)
((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(ts,{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-1022)
((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber.")))
@@ -4038,7 +4038,7 @@ NIL
NIL
(-1027 |dimtot| |dim1| S)
((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}.")))
-((-3991 |has| |#3| (-962)) (-3992 |has| |#3| (-962)) (-3994 |has| |#3| (-6 -3994)) (-3997 . T))
+((-3991 |has| |#3| (-962)) (-3992 |has| |#3| (-962)) (-3994 |has| |#3| (-6 -3994)))
((OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-553 (-773)))) (|HasCategory| |#3| (QUOTE (-312))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-718))) (OR (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757)))) (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-320))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-190))) (OR (|HasCategory| |#3| (QUOTE (-190))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-810 (-1091))))) (|HasCategory| |#3| (QUOTE (-1014))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasAttribute| |#3| (QUOTE -3994)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#3|)))))
(-1028 R |x|)
((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}")))
@@ -4070,7 +4070,7 @@ NIL
NIL
(-1035 S)
((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\#s}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
NIL
(-1036 S)
((|constructor| (NIL "This category describes the class of homogeneous aggregates that support in place mutation that do not change their general shapes.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\spad{f(x)}")))
@@ -4082,7 +4082,7 @@ NIL
((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3999 "*"))) (|HasCategory| |#3| (QUOTE (-146))))
(-1038 |ndim| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")))
-((-3997 . T) (-3991 . T) (-3992 . T) (-3994 . T))
+((-3991 . T) (-3992 . T) (-3994 . T))
NIL
(-1039 R |Row| |Col| M)
((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}.")))
@@ -4098,7 +4098,7 @@ NIL
((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312))))
(-1042 R E V P)
((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-1043 UP -3094)
((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,g,h,i,k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,g,h,j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,g,h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,g,h,i,j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,g,h,i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,g,h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented")))
@@ -4154,11 +4154,11 @@ NIL
NIL
(-1056 V C)
((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in ls]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}lt)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}ls)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| (-1055 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014))) (OR (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-553 (-773)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72))))
(-1057 |ndim| R)
((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}.")))
-((-3994 . T) (-3986 |has| |#2| (-6 (-3999 "*"))) (-3997 . T) (-3991 . T) (-3992 . T))
+((-3994 . T) (-3986 |has| |#2| (-6 (-3999 "*"))) (-3991 . T) (-3992 . T))
((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3999 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3999 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146))))
(-1058 S)
((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case.")))
@@ -4166,7 +4166,7 @@ NIL
NIL
(-1059)
((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-1060 R E V P TS)
((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")))
@@ -4174,7 +4174,7 @@ NIL
NIL
(-1061 R E V P)
((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|))))
(-1062)
((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:")))
@@ -4182,7 +4182,7 @@ NIL
NIL
(-1063 S)
((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,y,...,z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-1064 A S)
((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}.")))
@@ -4194,7 +4194,7 @@ NIL
NIL
(-1066 |Key| |Ent| |dent|)
((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))))
(-1067)
((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For non-fiinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping.")))
@@ -4226,11 +4226,11 @@ NIL
NIL
(-1074)
((|constructor| (NIL "This is the domain of character strings.")) (|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-757)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-117) (QUOTE (-757))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-1014))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-117)))))
(-1075 |Entry|)
((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))))
(-1076 A)
((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by r: \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}")))
@@ -4342,7 +4342,7 @@ NIL
NIL
(-1103 |Key| |Entry|)
((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))))
(-1104 S)
((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau.")))
@@ -4362,7 +4362,7 @@ NIL
NIL
(-1108 |Key| |Entry|)
((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")))
-((-3997 . T) (-3998 . T))
+((-3998 . T))
NIL
(-1109 |Key| |Entry|)
((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table.")))
@@ -4398,7 +4398,7 @@ NIL
NIL
(-1117 S)
((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-1118 S)
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
@@ -4430,7 +4430,7 @@ NIL
((|HasCategory| |#4| (QUOTE (-320))))
(-1125 R E V P)
((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-1126 |Curve|)
((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}.")))
@@ -4646,11 +4646,11 @@ NIL
((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))))
(-1179 R)
((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
NIL
(-1180 R)
((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))
(-1181 A B)
((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}.")))
@@ -4706,7 +4706,7 @@ NIL
((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))))
(-1194 R E V P)
((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}.")))
-((-3998 . T) (-3997 . T))
+((-3998 . T))
((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|))))
(-1195 R)
((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.fr)")))
@@ -4788,4 +4788,4 @@ NIL
NIL
NIL
NIL
-((-3 NIL 1970256 1970261 1970266 1970271) (-2 NIL 1970236 1970241 1970246 1970251) (-1 NIL 1970216 1970221 1970226 1970231) (0 NIL 1970196 1970201 1970206 1970211) (-1210 "ZMOD.spad" 1970005 1970018 1970134 1970191) (-1209 "ZLINDEP.spad" 1969103 1969114 1969995 1970000) (-1208 "ZDSOLVE.spad" 1959064 1959086 1969093 1969098) (-1207 "YSTREAM.spad" 1958559 1958570 1959054 1959059) (-1206 "YDIAGRAM.spad" 1958193 1958202 1958549 1958554) (-1205 "XRPOLY.spad" 1957413 1957433 1958049 1958118) (-1204 "XPR.spad" 1955208 1955221 1957131 1957230) (-1203 "XPOLYC.spad" 1954527 1954543 1955134 1955203) (-1202 "XPOLY.spad" 1954082 1954093 1954383 1954452) (-1201 "XPBWPOLY.spad" 1952553 1952573 1953888 1953957) (-1200 "XFALG.spad" 1949601 1949617 1952479 1952548) (-1199 "XF.spad" 1948064 1948079 1949503 1949596) (-1198 "XF.spad" 1946507 1946524 1947948 1947953) (-1197 "XEXPPKG.spad" 1945766 1945792 1946497 1946502) (-1196 "XDPOLY.spad" 1945380 1945396 1945622 1945691) (-1195 "XALG.spad" 1945048 1945059 1945336 1945375) (-1194 "WUTSET.spad" 1940890 1940907 1944521 1944548) (-1193 "WP.spad" 1940097 1940141 1940748 1940815) (-1192 "WHILEAST.spad" 1939895 1939904 1940087 1940092) (-1191 "WHEREAST.spad" 1939566 1939575 1939885 1939890) (-1190 "WFFINTBS.spad" 1937229 1937251 1939556 1939561) (-1189 "WEIER.spad" 1935451 1935462 1937219 1937224) (-1188 "VSPACE.spad" 1935124 1935135 1935419 1935446) (-1187 "VSPACE.spad" 1934817 1934830 1935114 1935119) (-1186 "VOID.spad" 1934494 1934503 1934807 1934812) (-1185 "VIEWDEF.spad" 1929695 1929704 1934484 1934489) (-1184 "VIEW3D.spad" 1913656 1913665 1929685 1929690) (-1183 "VIEW2D.spad" 1901555 1901564 1913646 1913651) (-1182 "VIEW.spad" 1899275 1899284 1901545 1901550) (-1181 "VECTOR2.spad" 1897914 1897927 1899265 1899270) (-1180 "VECTOR.spad" 1896472 1896483 1896723 1896750) (-1179 "VECTCAT.spad" 1894384 1894395 1896440 1896467) (-1178 "VECTCAT.spad" 1892105 1892118 1894163 1894168) (-1177 "VARIABLE.spad" 1891885 1891900 1892095 1892100) (-1176 "UTYPE.spad" 1891529 1891538 1891875 1891880) (-1175 "UTSODETL.spad" 1890824 1890848 1891485 1891490) (-1174 "UTSODE.spad" 1889040 1889060 1890814 1890819) (-1173 "UTSCAT.spad" 1886519 1886535 1888938 1889035) (-1172 "UTSCAT.spad" 1883666 1883684 1886087 1886092) (-1171 "UTS2.spad" 1883261 1883296 1883656 1883661) (-1170 "UTS.spad" 1878273 1878301 1881793 1881890) (-1169 "URAGG.spad" 1872994 1873005 1878263 1878268) (-1168 "URAGG.spad" 1867679 1867692 1872950 1872955) (-1167 "UPXSSING.spad" 1865447 1865473 1866883 1867016) (-1166 "UPXSCONS.spad" 1863265 1863285 1863638 1863787) (-1165 "UPXSCCA.spad" 1861836 1861856 1863111 1863260) (-1164 "UPXSCCA.spad" 1860549 1860571 1861826 1861831) (-1163 "UPXSCAT.spad" 1859138 1859154 1860395 1860544) (-1162 "UPXS2.spad" 1858681 1858734 1859128 1859133) (-1161 "UPXS.spad" 1856036 1856064 1856872 1857021) (-1160 "UPSQFREE.spad" 1854451 1854465 1856026 1856031) (-1159 "UPSCAT.spad" 1852246 1852270 1854349 1854446) (-1158 "UPSCAT.spad" 1849742 1849768 1851847 1851852) (-1157 "UPOLYC2.spad" 1849213 1849232 1849732 1849737) (-1156 "UPOLYC.spad" 1844293 1844304 1849055 1849208) (-1155 "UPOLYC.spad" 1839291 1839304 1844055 1844060) (-1154 "UPMP.spad" 1838223 1838236 1839281 1839286) (-1153 "UPDIVP.spad" 1837788 1837802 1838213 1838218) (-1152 "UPDECOMP.spad" 1836049 1836063 1837778 1837783) (-1151 "UPCDEN.spad" 1835266 1835282 1836039 1836044) (-1150 "UP2.spad" 1834630 1834651 1835256 1835261) (-1149 "UP.spad" 1832100 1832115 1832487 1832640) (-1148 "UNISEG2.spad" 1831597 1831610 1832056 1832061) (-1147 "UNISEG.spad" 1830950 1830961 1831516 1831521) (-1146 "UNIFACT.spad" 1830053 1830065 1830940 1830945) (-1145 "ULSCONS.spad" 1823899 1823919 1824269 1824418) (-1144 "ULSCCAT.spad" 1821636 1821656 1823745 1823894) (-1143 "ULSCCAT.spad" 1819481 1819503 1821592 1821597) (-1142 "ULSCAT.spad" 1817721 1817737 1819327 1819476) (-1141 "ULS2.spad" 1817235 1817288 1817711 1817716) (-1140 "ULS.spad" 1809268 1809296 1810213 1810636) (-1139 "UINT8.spad" 1809145 1809154 1809258 1809263) (-1138 "UINT64.spad" 1809021 1809030 1809135 1809140) (-1137 "UINT32.spad" 1808897 1808906 1809011 1809016) (-1136 "UINT16.spad" 1808773 1808782 1808887 1808892) (-1135 "UFD.spad" 1807838 1807847 1808699 1808768) (-1134 "UFD.spad" 1806965 1806976 1807828 1807833) (-1133 "UDVO.spad" 1805846 1805855 1806955 1806960) (-1132 "UDPO.spad" 1803427 1803438 1805802 1805807) (-1131 "TYPEAST.spad" 1803346 1803355 1803417 1803422) (-1130 "TYPE.spad" 1803278 1803287 1803336 1803341) (-1129 "TWOFACT.spad" 1801930 1801945 1803268 1803273) (-1128 "TUPLE.spad" 1801437 1801448 1801842 1801847) (-1127 "TUBETOOL.spad" 1798304 1798313 1801427 1801432) (-1126 "TUBE.spad" 1796951 1796968 1798294 1798299) (-1125 "TSETCAT.spad" 1785022 1785039 1796919 1796946) (-1124 "TSETCAT.spad" 1773079 1773098 1784978 1784983) (-1123 "TS.spad" 1771707 1771723 1772673 1772770) (-1122 "TRMANIP.spad" 1766071 1766088 1771395 1771400) (-1121 "TRIMAT.spad" 1765034 1765059 1766061 1766066) (-1120 "TRIGMNIP.spad" 1763561 1763578 1765024 1765029) (-1119 "TRIGCAT.spad" 1763073 1763082 1763551 1763556) (-1118 "TRIGCAT.spad" 1762583 1762594 1763063 1763068) (-1117 "TREE.spad" 1761223 1761234 1762255 1762282) (-1116 "TRANFUN.spad" 1761062 1761071 1761213 1761218) (-1115 "TRANFUN.spad" 1760899 1760910 1761052 1761057) (-1114 "TOPSP.spad" 1760573 1760582 1760889 1760894) (-1113 "TOOLSIGN.spad" 1760236 1760247 1760563 1760568) (-1112 "TEXTFILE.spad" 1758797 1758806 1760226 1760231) (-1111 "TEX1.spad" 1758353 1758364 1758787 1758792) (-1110 "TEX.spad" 1755547 1755556 1758343 1758348) (-1109 "TBCMPPK.spad" 1753648 1753671 1755537 1755542) (-1108 "TBAGG.spad" 1752891 1752914 1753616 1753643) (-1107 "TBAGG.spad" 1752154 1752179 1752881 1752886) (-1106 "TANEXP.spad" 1751562 1751573 1752144 1752149) (-1105 "TALGOP.spad" 1751286 1751297 1751552 1751557) (-1104 "TABLEAU.spad" 1750767 1750778 1751276 1751281) (-1103 "TABLE.spad" 1748516 1748539 1748786 1748813) (-1102 "TABLBUMP.spad" 1745295 1745306 1748506 1748511) (-1101 "SYSTEM.spad" 1744523 1744532 1745285 1745290) (-1100 "SYSSOLP.spad" 1742006 1742017 1744513 1744518) (-1099 "SYSPTR.spad" 1741905 1741914 1741996 1742001) (-1098 "SYSNNI.spad" 1741128 1741139 1741895 1741900) (-1097 "SYSINT.spad" 1740532 1740543 1741118 1741123) (-1096 "SYNTAX.spad" 1736866 1736875 1740522 1740527) (-1095 "SYMTAB.spad" 1734934 1734943 1736856 1736861) (-1094 "SYMS.spad" 1730963 1730972 1734924 1734929) (-1093 "SYMPOLY.spad" 1730096 1730107 1730178 1730305) (-1092 "SYMFUNC.spad" 1729597 1729608 1730086 1730091) (-1091 "SYMBOL.spad" 1727092 1727101 1729587 1729592) (-1090 "SUTS.spad" 1724205 1724233 1725624 1725721) (-1089 "SUPXS.spad" 1721547 1721575 1722396 1722545) (-1088 "SUPFRACF.spad" 1720652 1720670 1721537 1721542) (-1087 "SUP2.spad" 1720044 1720057 1720642 1720647) (-1086 "SUP.spad" 1717128 1717139 1717901 1718054) (-1085 "SUMRF.spad" 1716102 1716113 1717118 1717123) (-1084 "SUMFS.spad" 1715731 1715748 1716092 1716097) (-1083 "SULS.spad" 1707751 1707779 1708709 1709132) (-1082 "syntax.spad" 1707520 1707529 1707741 1707746) (-1081 "SUCH.spad" 1707210 1707225 1707510 1707515) (-1080 "SUBSPACE.spad" 1699341 1699356 1707200 1707205) (-1079 "SUBRESP.spad" 1698511 1698525 1699297 1699302) (-1078 "STTFNC.spad" 1694979 1694995 1698501 1698506) (-1077 "STTF.spad" 1691078 1691094 1694969 1694974) (-1076 "STTAYLOR.spad" 1683755 1683766 1690985 1690990) (-1075 "STRTBL.spad" 1681667 1681684 1681816 1681843) (-1074 "STRING.spad" 1680412 1680421 1680797 1680824) (-1073 "STREAM3.spad" 1679985 1680000 1680402 1680407) (-1072 "STREAM2.spad" 1679113 1679126 1679975 1679980) (-1071 "STREAM1.spad" 1678819 1678830 1679103 1679108) (-1070 "STREAM.spad" 1675714 1675725 1678321 1678336) (-1069 "STINPROD.spad" 1674650 1674666 1675704 1675709) (-1068 "STEPAST.spad" 1673884 1673893 1674640 1674645) (-1067 "STEP.spad" 1673201 1673210 1673874 1673879) (-1066 "STBL.spad" 1671053 1671081 1671220 1671247) (-1065 "STAGG.spad" 1669752 1669763 1671043 1671048) (-1064 "STAGG.spad" 1668449 1668462 1669742 1669747) (-1063 "STACK.spad" 1667871 1667882 1668121 1668148) (-1062 "SRING.spad" 1667631 1667640 1667861 1667866) (-1061 "SREGSET.spad" 1665202 1665219 1667104 1667131) (-1060 "SRDCMPK.spad" 1663779 1663799 1665192 1665197) (-1059 "SRAGG.spad" 1658962 1658971 1663747 1663774) (-1058 "SRAGG.spad" 1654165 1654176 1658952 1658957) (-1057 "SQMATRIX.spad" 1651842 1651860 1652758 1652845) (-1056 "SPLTREE.spad" 1646584 1646597 1651380 1651407) (-1055 "SPLNODE.spad" 1643204 1643217 1646574 1646579) (-1054 "SPFCAT.spad" 1642013 1642022 1643194 1643199) (-1053 "SPECOUT.spad" 1640565 1640574 1642003 1642008) (-1052 "SPADXPT.spad" 1632656 1632665 1640555 1640560) (-1051 "spad-parser.spad" 1632121 1632130 1632646 1632651) (-1050 "SPADAST.spad" 1631822 1631831 1632111 1632116) (-1049 "SPACEC.spad" 1616037 1616048 1631812 1631817) (-1048 "SPACE3.spad" 1615813 1615824 1616027 1616032) (-1047 "SORTPAK.spad" 1615362 1615375 1615769 1615774) (-1046 "SOLVETRA.spad" 1613125 1613136 1615352 1615357) (-1045 "SOLVESER.spad" 1611581 1611592 1613115 1613120) (-1044 "SOLVERAD.spad" 1607607 1607618 1611571 1611576) (-1043 "SOLVEFOR.spad" 1606069 1606087 1607597 1607602) (-1042 "SNTSCAT.spad" 1605669 1605686 1606037 1606064) (-1041 "SMTS.spad" 1603986 1604012 1605263 1605360) (-1040 "SMP.spad" 1601794 1601814 1602184 1602311) (-1039 "SMITH.spad" 1600639 1600664 1601784 1601789) (-1038 "SMATCAT.spad" 1598757 1598787 1600583 1600634) (-1037 "SMATCAT.spad" 1596807 1596839 1598635 1598640) (-1036 "aggcat.spad" 1596483 1596494 1596787 1596802) (-1035 "SKAGG.spad" 1595452 1595463 1596451 1596478) (-1034 "SINT.spad" 1594751 1594760 1595318 1595447) (-1033 "SIMPAN.spad" 1594479 1594488 1594741 1594746) (-1032 "SIGNRF.spad" 1593604 1593615 1594469 1594474) (-1031 "SIGNEF.spad" 1592890 1592907 1593594 1593599) (-1030 "syntax.spad" 1592307 1592316 1592880 1592885) (-1029 "SIG.spad" 1591669 1591678 1592297 1592302) (-1028 "SHP.spad" 1589613 1589628 1591625 1591630) (-1027 "SHDP.spad" 1579005 1579032 1579522 1579619) (-1026 "SGROUP.spad" 1578613 1578622 1578995 1579000) (-1025 "SGROUP.spad" 1578219 1578230 1578603 1578608) (-1024 "catdef.spad" 1577929 1577941 1578040 1578214) (-1023 "catdef.spad" 1577485 1577497 1577750 1577924) (-1022 "SGCF.spad" 1570624 1570633 1577475 1577480) (-1021 "SFRTCAT.spad" 1569570 1569587 1570592 1570619) (-1020 "SFRGCD.spad" 1568633 1568653 1569560 1569565) (-1019 "SFQCMPK.spad" 1563446 1563466 1568623 1568628) (-1018 "SEXOF.spad" 1563289 1563329 1563436 1563441) (-1017 "SEXCAT.spad" 1561117 1561157 1563279 1563284) (-1016 "SEX.spad" 1561009 1561018 1561107 1561112) (-1015 "SETMN.spad" 1559469 1559486 1560999 1561004) (-1014 "SETCAT.spad" 1558954 1558963 1559459 1559464) (-1013 "SETCAT.spad" 1558437 1558448 1558944 1558949) (-1012 "SETAGG.spad" 1554986 1554997 1558417 1558432) (-1011 "SETAGG.spad" 1551543 1551556 1554976 1554981) (-1010 "SET.spad" 1549689 1549700 1550788 1550827) (-1009 "syntax.spad" 1549392 1549401 1549679 1549684) (-1008 "SEGXCAT.spad" 1548548 1548561 1549382 1549387) (-1007 "SEGCAT.spad" 1547473 1547484 1548538 1548543) (-1006 "SEGBIND2.spad" 1547171 1547184 1547463 1547468) (-1005 "SEGBIND.spad" 1546929 1546940 1547118 1547123) (-1004 "SEGAST.spad" 1546659 1546668 1546919 1546924) (-1003 "SEG2.spad" 1546094 1546107 1546615 1546620) (-1002 "SEG.spad" 1545907 1545918 1546013 1546018) (-1001 "SDVAR.spad" 1545183 1545194 1545897 1545902) (-1000 "SDPOL.spad" 1542875 1542886 1543166 1543293) (-999 "SCPKG.spad" 1540965 1540975 1542865 1542870) (-998 "SCOPE.spad" 1540143 1540151 1540955 1540960) (-997 "SCACHE.spad" 1538840 1538850 1540133 1540138) (-996 "SASTCAT.spad" 1538750 1538758 1538830 1538835) (-995 "SAOS.spad" 1538623 1538631 1538740 1538745) (-994 "SAERFFC.spad" 1538337 1538356 1538613 1538618) (-993 "SAEFACT.spad" 1538039 1538058 1538327 1538332) (-992 "SAE.spad" 1535690 1535705 1536300 1536435) (-991 "RURPK.spad" 1533350 1533365 1535680 1535685) (-990 "RULESET.spad" 1532804 1532827 1533340 1533345) (-989 "RULECOLD.spad" 1532657 1532669 1532794 1532799) (-988 "RULE.spad" 1530906 1530929 1532647 1532652) (-987 "RTVALUE.spad" 1530642 1530650 1530896 1530901) (-986 "syntax.spad" 1530360 1530368 1530632 1530637) (-985 "RSETGCD.spad" 1526803 1526822 1530350 1530355) (-984 "RSETCAT.spad" 1516772 1516788 1526771 1526798) (-983 "RSETCAT.spad" 1506761 1506779 1516762 1516767) (-982 "RSDCMPK.spad" 1505262 1505281 1506751 1506756) (-981 "RRCC.spad" 1503647 1503676 1505252 1505257) (-980 "RRCC.spad" 1502030 1502061 1503637 1503642) (-979 "RPTAST.spad" 1501733 1501741 1502020 1502025) (-978 "RPOLCAT.spad" 1481238 1481252 1501601 1501728) (-977 "RPOLCAT.spad" 1460536 1460552 1480901 1480906) (-976 "ROMAN.spad" 1459865 1459873 1460402 1460531) (-975 "ROIRC.spad" 1458946 1458977 1459855 1459860) (-974 "RNS.spad" 1457923 1457931 1458848 1458941) (-973 "RNS.spad" 1456986 1456996 1457913 1457918) (-972 "RNGBIND.spad" 1456147 1456160 1456941 1456946) (-971 "RNG.spad" 1455756 1455764 1456137 1456142) (-970 "RNG.spad" 1455363 1455373 1455746 1455751) (-969 "RMODULE.spad" 1455145 1455155 1455353 1455358) (-968 "RMCAT2.spad" 1454566 1454622 1455135 1455140) (-967 "RMATRIX.spad" 1453376 1453394 1453718 1453757) (-966 "RMATCAT.spad" 1449014 1449044 1453332 1453371) (-965 "RMATCAT.spad" 1444542 1444574 1448862 1448867) (-964 "RLINSET.spad" 1444247 1444257 1444532 1444537) (-963 "RINTERP.spad" 1444136 1444155 1444237 1444242) (-962 "RING.spad" 1443607 1443615 1444116 1444131) (-961 "RING.spad" 1443086 1443096 1443597 1443602) (-960 "RIDIST.spad" 1442479 1442487 1443076 1443081) (-959 "RGCHAIN.spad" 1440724 1440739 1441617 1441644) (-958 "RGBCSPC.spad" 1440514 1440525 1440714 1440719) (-957 "RGBCMDL.spad" 1440077 1440088 1440504 1440509) (-956 "RFFACTOR.spad" 1439540 1439550 1440067 1440072) (-955 "RFFACT.spad" 1439276 1439287 1439530 1439535) (-954 "RFDIST.spad" 1438273 1438281 1439266 1439271) (-953 "RF.spad" 1435948 1435958 1438263 1438268) (-952 "RETSOL.spad" 1435368 1435380 1435938 1435943) (-951 "RETRACT.spad" 1434797 1434807 1435358 1435363) (-950 "RETRACT.spad" 1434224 1434236 1434787 1434792) (-949 "RETAST.spad" 1434037 1434045 1434214 1434219) (-948 "RESRING.spad" 1433385 1433431 1433975 1434032) (-947 "RESLATC.spad" 1432710 1432720 1433375 1433380) (-946 "REPSQ.spad" 1432442 1432452 1432700 1432705) (-945 "REPDB.spad" 1432150 1432160 1432432 1432437) (-944 "REP2.spad" 1421865 1421875 1431992 1431997) (-943 "REP1.spad" 1416086 1416096 1421815 1421820) (-942 "REP.spad" 1413641 1413649 1416076 1416081) (-941 "REGSET.spad" 1411306 1411322 1413114 1413141) (-940 "REF.spad" 1410825 1410835 1411296 1411301) (-939 "REDORDER.spad" 1410032 1410048 1410815 1410820) (-938 "RECLOS.spad" 1408929 1408948 1409632 1409725) (-937 "REALSOLV.spad" 1408070 1408078 1408919 1408924) (-936 "REAL0Q.spad" 1405369 1405383 1408060 1408065) (-935 "REAL0.spad" 1402214 1402228 1405359 1405364) (-934 "REAL.spad" 1402087 1402095 1402204 1402209) (-933 "RDUCEAST.spad" 1401809 1401817 1402077 1402082) (-932 "RDIV.spad" 1401465 1401489 1401799 1401804) (-931 "RDIST.spad" 1401033 1401043 1401455 1401460) (-930 "RDETRS.spad" 1399898 1399915 1401023 1401028) (-929 "RDETR.spad" 1398038 1398055 1399888 1399893) (-928 "RDEEFS.spad" 1397138 1397154 1398028 1398033) (-927 "RDEEF.spad" 1396149 1396165 1397128 1397133) (-926 "RCFIELD.spad" 1393368 1393376 1396051 1396144) (-925 "RCFIELD.spad" 1390673 1390683 1393358 1393363) (-924 "RCAGG.spad" 1388610 1388620 1390663 1390668) (-923 "RCAGG.spad" 1386476 1386488 1388531 1388536) (-922 "RATRET.spad" 1385837 1385847 1386466 1386471) (-921 "RATFACT.spad" 1385530 1385541 1385827 1385832) (-920 "RANDSRC.spad" 1384850 1384858 1385520 1385525) (-919 "RADUTIL.spad" 1384607 1384615 1384840 1384845) (-918 "RADIX.spad" 1381652 1381665 1383197 1383290) (-917 "RADFF.spad" 1379569 1379605 1379687 1379843) (-916 "RADCAT.spad" 1379165 1379173 1379559 1379564) (-915 "RADCAT.spad" 1378759 1378769 1379155 1379160) (-914 "QUEUE.spad" 1378173 1378183 1378431 1378458) (-913 "QUATCT2.spad" 1377794 1377812 1378163 1378168) (-912 "QUATCAT.spad" 1375965 1375975 1377724 1377789) (-911 "QUATCAT.spad" 1373901 1373913 1375662 1375667) (-910 "QUAT.spad" 1372508 1372518 1372850 1372915) (-909 "QUAGG.spad" 1371342 1371352 1372476 1372503) (-908 "QQUTAST.spad" 1371111 1371119 1371332 1371337) (-907 "QFORM.spad" 1370730 1370744 1371101 1371106) (-906 "QFCAT2.spad" 1370423 1370439 1370720 1370725) (-905 "QFCAT.spad" 1369126 1369136 1370325 1370418) (-904 "QFCAT.spad" 1367462 1367474 1368663 1368668) (-903 "QEQUAT.spad" 1367021 1367029 1367452 1367457) (-902 "QCMPACK.spad" 1361936 1361955 1367011 1367016) (-901 "QALGSET2.spad" 1359932 1359950 1361926 1361931) (-900 "QALGSET.spad" 1356037 1356069 1359846 1359851) (-899 "PWFFINTB.spad" 1353453 1353474 1356027 1356032) (-898 "PUSHVAR.spad" 1352792 1352811 1353443 1353448) (-897 "PTRANFN.spad" 1348928 1348938 1352782 1352787) (-896 "PTPACK.spad" 1346016 1346026 1348918 1348923) (-895 "PTFUNC2.spad" 1345839 1345853 1346006 1346011) (-894 "PTCAT.spad" 1345094 1345104 1345807 1345834) (-893 "PSQFR.spad" 1344409 1344433 1345084 1345089) (-892 "PSEUDLIN.spad" 1343295 1343305 1344399 1344404) (-891 "PSETPK.spad" 1330000 1330016 1343173 1343178) (-890 "PSETCAT.spad" 1324400 1324423 1329980 1329995) (-889 "PSETCAT.spad" 1318774 1318799 1324356 1324361) (-888 "PSCURVE.spad" 1317773 1317781 1318764 1318769) (-887 "PSCAT.spad" 1316556 1316585 1317671 1317768) (-886 "PSCAT.spad" 1315429 1315460 1316546 1316551) (-885 "PRTITION.spad" 1314127 1314135 1315419 1315424) (-884 "PRTDAST.spad" 1313846 1313854 1314117 1314122) (-883 "PRS.spad" 1303464 1303481 1313802 1313807) (-882 "PRQAGG.spad" 1302899 1302909 1303432 1303459) (-881 "PROPLOG.spad" 1302503 1302511 1302889 1302894) (-880 "PROPFUN2.spad" 1302126 1302139 1302493 1302498) (-879 "PROPFUN1.spad" 1301532 1301543 1302116 1302121) (-878 "PROPFRML.spad" 1300100 1300111 1301522 1301527) (-877 "PROPERTY.spad" 1299596 1299604 1300090 1300095) (-876 "PRODUCT.spad" 1297293 1297305 1297577 1297632) (-875 "PRINT.spad" 1297045 1297053 1297283 1297288) (-874 "PRIMES.spad" 1295306 1295316 1297035 1297040) (-873 "PRIMELT.spad" 1293427 1293441 1295296 1295301) (-872 "PRIMCAT.spad" 1293070 1293078 1293417 1293422) (-871 "PRIMARR2.spad" 1291837 1291849 1293060 1293065) (-870 "PRIMARR.spad" 1290731 1290741 1290901 1290928) (-869 "PREASSOC.spad" 1290113 1290125 1290721 1290726) (-868 "PR.spad" 1288631 1288643 1289330 1289457) (-867 "PPCURVE.spad" 1287768 1287776 1288621 1288626) (-866 "PORTNUM.spad" 1287559 1287567 1287758 1287763) (-865 "POLYROOT.spad" 1286408 1286430 1287515 1287520) (-864 "POLYLIFT.spad" 1285673 1285696 1286398 1286403) (-863 "POLYCATQ.spad" 1283799 1283821 1285663 1285668) (-862 "POLYCAT.spad" 1277301 1277322 1283667 1283794) (-861 "POLYCAT.spad" 1270323 1270346 1276691 1276696) (-860 "POLY2UP.spad" 1269775 1269789 1270313 1270318) (-859 "POLY2.spad" 1269372 1269384 1269765 1269770) (-858 "POLY.spad" 1267040 1267050 1267555 1267682) (-857 "POLUTIL.spad" 1266005 1266034 1266996 1267001) (-856 "POLTOPOL.spad" 1264753 1264768 1265995 1266000) (-855 "POINT.spad" 1263475 1263485 1263562 1263589) (-854 "PNTHEORY.spad" 1260177 1260185 1263465 1263470) (-853 "PMTOOLS.spad" 1258952 1258966 1260167 1260172) (-852 "PMSYM.spad" 1258501 1258511 1258942 1258947) (-851 "PMQFCAT.spad" 1258092 1258106 1258491 1258496) (-850 "PMPREDFS.spad" 1257554 1257576 1258082 1258087) (-849 "PMPRED.spad" 1257041 1257055 1257544 1257549) (-848 "PMPLCAT.spad" 1256118 1256136 1256970 1256975) (-847 "PMLSAGG.spad" 1255703 1255717 1256108 1256113) (-846 "PMKERNEL.spad" 1255282 1255294 1255693 1255698) (-845 "PMINS.spad" 1254862 1254872 1255272 1255277) (-844 "PMFS.spad" 1254439 1254457 1254852 1254857) (-843 "PMDOWN.spad" 1253729 1253743 1254429 1254434) (-842 "PMASSFS.spad" 1252704 1252720 1253719 1253724) (-841 "PMASS.spad" 1251722 1251730 1252694 1252699) (-840 "PLOTTOOL.spad" 1251502 1251510 1251712 1251717) (-839 "PLOT3D.spad" 1247966 1247974 1251492 1251497) (-838 "PLOT1.spad" 1247139 1247149 1247956 1247961) (-837 "PLOT.spad" 1242062 1242070 1247129 1247134) (-836 "PLEQN.spad" 1229464 1229491 1242052 1242057) (-835 "PINTERPA.spad" 1229248 1229264 1229454 1229459) (-834 "PINTERP.spad" 1228870 1228889 1229238 1229243) (-833 "PID.spad" 1227844 1227852 1228796 1228865) (-832 "PICOERCE.spad" 1227501 1227511 1227834 1227839) (-831 "PI.spad" 1227118 1227126 1227475 1227496) (-830 "PGROEB.spad" 1225727 1225741 1227108 1227113) (-829 "PGE.spad" 1217400 1217408 1225717 1225722) (-828 "PGCD.spad" 1216354 1216371 1217390 1217395) (-827 "PFRPAC.spad" 1215503 1215513 1216344 1216349) (-826 "PFR.spad" 1212206 1212216 1215405 1215498) (-825 "PFOTOOLS.spad" 1211464 1211480 1212196 1212201) (-824 "PFOQ.spad" 1210834 1210852 1211454 1211459) (-823 "PFO.spad" 1210253 1210280 1210824 1210829) (-822 "PFECAT.spad" 1207963 1207971 1210179 1210248) (-821 "PFECAT.spad" 1205701 1205711 1207919 1207924) (-820 "PFBRU.spad" 1203589 1203601 1205691 1205696) (-819 "PFBR.spad" 1201149 1201172 1203579 1203584) (-818 "PF.spad" 1200723 1200735 1200954 1201047) (-817 "PERMGRP.spad" 1195493 1195503 1200713 1200718) (-816 "PERMCAT.spad" 1194154 1194164 1195473 1195488) (-815 "PERMAN.spad" 1192710 1192724 1194144 1194149) (-814 "PERM.spad" 1188520 1188530 1192543 1192558) (-813 "PENDTREE.spad" 1187934 1187944 1188214 1188219) (-812 "PDSPC.spad" 1186747 1186757 1187924 1187929) (-811 "PDSPC.spad" 1185558 1185570 1186737 1186742) (-810 "PDRING.spad" 1185400 1185410 1185538 1185553) (-809 "PDMOD.spad" 1185216 1185228 1185368 1185395) (-808 "PDECOMP.spad" 1184686 1184703 1185206 1185211) (-807 "PDDOM.spad" 1184124 1184137 1184676 1184681) (-806 "PDDOM.spad" 1183560 1183575 1184114 1184119) (-805 "PCOMP.spad" 1183413 1183426 1183550 1183555) (-804 "PBWLB.spad" 1182011 1182028 1183403 1183408) (-803 "PATTERN2.spad" 1181749 1181761 1182001 1182006) (-802 "PATTERN1.spad" 1180093 1180109 1181739 1181744) (-801 "PATTERN.spad" 1174668 1174678 1180083 1180088) (-800 "PATRES2.spad" 1174340 1174354 1174658 1174663) (-799 "PATRES.spad" 1171923 1171935 1174330 1174335) (-798 "PATMATCH.spad" 1170164 1170195 1171675 1171680) (-797 "PATMAB.spad" 1169593 1169603 1170154 1170159) (-796 "PATLRES.spad" 1168679 1168693 1169583 1169588) (-795 "PATAB.spad" 1168443 1168453 1168669 1168674) (-794 "PARTPERM.spad" 1166499 1166507 1168433 1168438) (-793 "PARSURF.spad" 1165933 1165961 1166489 1166494) (-792 "PARSU2.spad" 1165730 1165746 1165923 1165928) (-791 "script-parser.spad" 1165250 1165258 1165720 1165725) (-790 "PARSCURV.spad" 1164684 1164712 1165240 1165245) (-789 "PARSC2.spad" 1164475 1164491 1164674 1164679) (-788 "PARPCURV.spad" 1163937 1163965 1164465 1164470) (-787 "PARPC2.spad" 1163728 1163744 1163927 1163932) (-786 "PARAMAST.spad" 1162856 1162864 1163718 1163723) (-785 "PAN2EXPR.spad" 1162268 1162276 1162846 1162851) (-784 "PALETTE.spad" 1161382 1161390 1162258 1162263) (-783 "PAIR.spad" 1160456 1160469 1161025 1161030) (-782 "PADICRC.spad" 1157861 1157879 1159024 1159117) (-781 "PADICRAT.spad" 1155921 1155933 1156134 1156227) (-780 "PADICCT.spad" 1154470 1154482 1155847 1155916) (-779 "PADIC.spad" 1154173 1154185 1154396 1154465) (-778 "PADEPAC.spad" 1152862 1152881 1154163 1154168) (-777 "PADE.spad" 1151614 1151630 1152852 1152857) (-776 "OWP.spad" 1150862 1150892 1151472 1151539) (-775 "OVERSET.spad" 1150435 1150443 1150852 1150857) (-774 "OVAR.spad" 1150216 1150239 1150425 1150430) (-773 "OUTFORM.spad" 1139624 1139632 1150206 1150211) (-772 "OUTBFILE.spad" 1139058 1139066 1139614 1139619) (-771 "OUTBCON.spad" 1138128 1138136 1139048 1139053) (-770 "OUTBCON.spad" 1137196 1137206 1138118 1138123) (-769 "OUT.spad" 1136314 1136322 1137186 1137191) (-768 "OSI.spad" 1135789 1135797 1136304 1136309) (-767 "OSGROUP.spad" 1135707 1135715 1135779 1135784) (-766 "ORTHPOL.spad" 1134218 1134228 1135650 1135655) (-765 "OREUP.spad" 1133712 1133740 1133939 1133978) (-764 "ORESUP.spad" 1133054 1133078 1133433 1133472) (-763 "OREPCTO.spad" 1130943 1130955 1132974 1132979) (-762 "OREPCAT.spad" 1125130 1125140 1130899 1130938) (-761 "OREPCAT.spad" 1119207 1119219 1124978 1124983) (-760 "ORDTYPE.spad" 1118444 1118452 1119197 1119202) (-759 "ORDTYPE.spad" 1117679 1117689 1118434 1118439) (-758 "ORDSTRCT.spad" 1117465 1117480 1117628 1117633) (-757 "ORDSET.spad" 1117165 1117173 1117455 1117460) (-756 "ORDRING.spad" 1116982 1116990 1117145 1117160) (-755 "ORDMON.spad" 1116837 1116845 1116972 1116977) (-754 "ORDFUNS.spad" 1115969 1115985 1116827 1116832) (-753 "ORDFIN.spad" 1115789 1115797 1115959 1115964) (-752 "ORDCOMP2.spad" 1115082 1115094 1115779 1115784) (-751 "ORDCOMP.spad" 1113608 1113618 1114690 1114719) (-750 "OPSIG.spad" 1113270 1113278 1113598 1113603) (-749 "OPQUERY.spad" 1112851 1112859 1113260 1113265) (-748 "OPERCAT.spad" 1112317 1112327 1112841 1112846) (-747 "OPERCAT.spad" 1111781 1111793 1112307 1112312) (-746 "OP.spad" 1111523 1111533 1111603 1111670) (-745 "ONECOMP2.spad" 1110947 1110959 1111513 1111518) (-744 "ONECOMP.spad" 1109753 1109763 1110555 1110584) (-743 "OMSAGG.spad" 1109541 1109551 1109709 1109748) (-742 "OMLO.spad" 1108974 1108986 1109427 1109466) (-741 "OINTDOM.spad" 1108737 1108745 1108900 1108969) (-740 "OFMONOID.spad" 1106876 1106886 1108693 1108698) (-739 "ODVAR.spad" 1106137 1106147 1106866 1106871) (-738 "ODR.spad" 1105781 1105807 1105949 1106098) (-737 "ODPOL.spad" 1103429 1103439 1103769 1103896) (-736 "ODP.spad" 1092965 1092985 1093338 1093435) (-735 "ODETOOLS.spad" 1091614 1091633 1092955 1092960) (-734 "ODESYS.spad" 1089308 1089325 1091604 1091609) (-733 "ODERTRIC.spad" 1085341 1085358 1089265 1089270) (-732 "ODERED.spad" 1084740 1084764 1085331 1085336) (-731 "ODERAT.spad" 1082373 1082390 1084730 1084735) (-730 "ODEPRRIC.spad" 1079466 1079488 1082363 1082368) (-729 "ODEPRIM.spad" 1076864 1076886 1079456 1079461) (-728 "ODEPAL.spad" 1076250 1076274 1076854 1076859) (-727 "ODEINT.spad" 1075685 1075701 1076240 1076245) (-726 "ODEEF.spad" 1071180 1071196 1075675 1075680) (-725 "ODECONST.spad" 1070725 1070743 1071170 1071175) (-724 "OCTCT2.spad" 1070366 1070384 1070715 1070720) (-723 "OCT.spad" 1068681 1068691 1069395 1069434) (-722 "OCAMON.spad" 1068529 1068537 1068671 1068676) (-721 "OC.spad" 1066325 1066335 1068485 1068524) (-720 "OC.spad" 1063860 1063872 1066022 1066027) (-719 "OASGP.spad" 1063675 1063683 1063850 1063855) (-718 "OAMONS.spad" 1063197 1063205 1063665 1063670) (-717 "OAMON.spad" 1062955 1062963 1063187 1063192) (-716 "OAMON.spad" 1062711 1062721 1062945 1062950) (-715 "OAGROUP.spad" 1062249 1062257 1062701 1062706) (-714 "OAGROUP.spad" 1061785 1061795 1062239 1062244) (-713 "NUMTUBE.spad" 1061376 1061392 1061775 1061780) (-712 "NUMQUAD.spad" 1049352 1049360 1061366 1061371) (-711 "NUMODE.spad" 1040704 1040712 1049342 1049347) (-710 "NUMFMT.spad" 1039544 1039552 1040694 1040699) (-709 "NUMERIC.spad" 1031659 1031669 1039350 1039355) (-708 "NTSCAT.spad" 1030167 1030183 1031627 1031654) (-707 "NTPOLFN.spad" 1029744 1029754 1030110 1030115) (-706 "NSUP2.spad" 1029136 1029148 1029734 1029739) (-705 "NSUP.spad" 1022573 1022583 1026993 1027146) (-704 "NSMP.spad" 1019485 1019504 1019777 1019904) (-703 "NREP.spad" 1017887 1017901 1019475 1019480) (-702 "NPCOEF.spad" 1017133 1017153 1017877 1017882) (-701 "NORMRETR.spad" 1016731 1016770 1017123 1017128) (-700 "NORMPK.spad" 1014673 1014692 1016721 1016726) (-699 "NORMMA.spad" 1014361 1014387 1014663 1014668) (-698 "NONE1.spad" 1014037 1014047 1014351 1014356) (-697 "NONE.spad" 1013778 1013786 1014027 1014032) (-696 "NODE1.spad" 1013265 1013281 1013768 1013773) (-695 "NNI.spad" 1012160 1012168 1013239 1013260) (-694 "NLINSOL.spad" 1010786 1010796 1012150 1012155) (-693 "NFINTBAS.spad" 1008346 1008363 1010776 1010781) (-692 "NETCLT.spad" 1008320 1008331 1008336 1008341) (-691 "NCODIV.spad" 1006544 1006560 1008310 1008315) (-690 "NCNTFRAC.spad" 1006186 1006200 1006534 1006539) (-689 "NCEP.spad" 1004352 1004366 1006176 1006181) (-688 "NASRING.spad" 1003956 1003964 1004342 1004347) (-687 "NASRING.spad" 1003558 1003568 1003946 1003951) (-686 "NARNG.spad" 1002958 1002966 1003548 1003553) (-685 "NARNG.spad" 1002356 1002366 1002948 1002953) (-684 "NAALG.spad" 1001921 1001931 1002324 1002351) (-683 "NAALG.spad" 1001506 1001518 1001911 1001916) (-682 "MULTSQFR.spad" 998464 998481 1001496 1001501) (-681 "MULTFACT.spad" 997847 997864 998454 998459) (-680 "MTSCAT.spad" 995941 995962 997745 997842) (-679 "MTHING.spad" 995600 995610 995931 995936) (-678 "MSYSCMD.spad" 995034 995042 995590 995595) (-677 "MSETAGG.spad" 994879 994889 995002 995029) (-676 "MSET.spad" 992665 992675 994412 994451) (-675 "MRING.spad" 989642 989654 992373 992440) (-674 "MRF2.spad" 989204 989218 989632 989637) (-673 "MRATFAC.spad" 988750 988767 989194 989199) (-672 "MPRFF.spad" 986790 986809 988740 988745) (-671 "MPOLY.spad" 984594 984609 984953 985080) (-670 "MPCPF.spad" 983858 983877 984584 984589) (-669 "MPC3.spad" 983675 983715 983848 983853) (-668 "MPC2.spad" 983329 983362 983665 983670) (-667 "MONOTOOL.spad" 981680 981697 983319 983324) (-666 "catdef.spad" 981113 981124 981334 981675) (-665 "catdef.spad" 980511 980522 980767 981108) (-664 "MONOID.spad" 979832 979840 980501 980506) (-663 "MONOID.spad" 979151 979161 979822 979827) (-662 "MONOGEN.spad" 977899 977912 979011 979146) (-661 "MONOGEN.spad" 976669 976684 977783 977788) (-660 "MONADWU.spad" 974749 974757 976659 976664) (-659 "MONADWU.spad" 972827 972837 974739 974744) (-658 "MONAD.spad" 971987 971995 972817 972822) (-657 "MONAD.spad" 971145 971155 971977 971982) (-656 "MOEBIUS.spad" 969881 969895 971125 971140) (-655 "MODULE.spad" 969751 969761 969849 969876) (-654 "MODULE.spad" 969641 969653 969741 969746) (-653 "MODRING.spad" 968976 969015 969621 969636) (-652 "MODOP.spad" 967633 967645 968798 968865) (-651 "MODMONOM.spad" 967364 967382 967623 967628) (-650 "MODMON.spad" 964434 964446 965149 965302) (-649 "MODFIELD.spad" 963796 963835 964336 964429) (-648 "MMLFORM.spad" 962656 962664 963786 963791) (-647 "MMAP.spad" 962398 962432 962646 962651) (-646 "MLO.spad" 960857 960867 962354 962393) (-645 "MLIFT.spad" 959469 959486 960847 960852) (-644 "MKUCFUNC.spad" 959004 959022 959459 959464) (-643 "MKRECORD.spad" 958592 958605 958994 958999) (-642 "MKFUNC.spad" 957999 958009 958582 958587) (-641 "MKFLCFN.spad" 956967 956977 957989 957994) (-640 "MKBCFUNC.spad" 956462 956480 956957 956962) (-639 "MHROWRED.spad" 954973 954983 956452 956457) (-638 "MFINFACT.spad" 954373 954395 954963 954968) (-637 "MESH.spad" 952168 952176 954363 954368) (-636 "MDDFACT.spad" 950387 950397 952158 952163) (-635 "MDAGG.spad" 949678 949688 950367 950382) (-634 "MCDEN.spad" 948888 948900 949668 949673) (-633 "MAYBE.spad" 948188 948199 948878 948883) (-632 "MATSTOR.spad" 945504 945514 948178 948183) (-631 "MATRIX.spad" 944283 944293 944767 944794) (-630 "MATLIN.spad" 941651 941675 944167 944172) (-629 "MATCAT2.spad" 940933 940981 941641 941646) (-628 "MATCAT.spad" 932629 932651 940901 940928) (-627 "MATCAT.spad" 924197 924221 932471 932476) (-626 "MAPPKG3.spad" 923112 923126 924187 924192) (-625 "MAPPKG2.spad" 922450 922462 923102 923107) (-624 "MAPPKG1.spad" 921278 921288 922440 922445) (-623 "MAPPAST.spad" 920617 920625 921268 921273) (-622 "MAPHACK3.spad" 920429 920443 920607 920612) (-621 "MAPHACK2.spad" 920198 920210 920419 920424) (-620 "MAPHACK1.spad" 919842 919852 920188 920193) (-619 "MAGMA.spad" 917648 917665 919832 919837) (-618 "MACROAST.spad" 917243 917251 917638 917643) (-617 "LZSTAGG.spad" 914497 914507 917233 917238) (-616 "LZSTAGG.spad" 911749 911761 914487 914492) (-615 "LWORD.spad" 908494 908511 911739 911744) (-614 "LSTAST.spad" 908278 908286 908484 908489) (-613 "LSQM.spad" 906556 906570 906950 907001) (-612 "LSPP.spad" 906091 906108 906546 906551) (-611 "LSMP1.spad" 903934 903948 906081 906086) (-610 "LSMP.spad" 902791 902819 903924 903929) (-609 "LSAGG.spad" 902460 902470 902759 902786) (-608 "LSAGG.spad" 902149 902161 902450 902455) (-607 "LPOLY.spad" 901111 901130 902005 902074) (-606 "LPEFRAC.spad" 900382 900392 901101 901106) (-605 "LOGIC.spad" 899984 899992 900372 900377) (-604 "LOGIC.spad" 899584 899594 899974 899979) (-603 "LODOOPS.spad" 898514 898526 899574 899579) (-602 "LODOF.spad" 897560 897577 898471 898476) (-601 "LODOCAT.spad" 896226 896236 897516 897555) (-600 "LODOCAT.spad" 894890 894902 896182 896187) (-599 "LODO2.spad" 894204 894216 894611 894650) (-598 "LODO1.spad" 893645 893655 893925 893964) (-597 "LODO.spad" 893070 893086 893366 893405) (-596 "LODEEF.spad" 891872 891890 893060 893065) (-595 "LO.spad" 891273 891287 891806 891833) (-594 "LNAGG.spad" 887460 887470 891263 891268) (-593 "LNAGG.spad" 883611 883623 887416 887421) (-592 "LMOPS.spad" 880379 880396 883601 883606) (-591 "LMODULE.spad" 880163 880173 880369 880374) (-590 "LMDICT.spad" 879383 879393 879631 879658) (-589 "LLINSET.spad" 879090 879100 879373 879378) (-588 "LITERAL.spad" 878996 879007 879080 879085) (-587 "LIST3.spad" 878307 878321 878986 878991) (-586 "LIST2MAP.spad" 875234 875246 878297 878302) (-585 "LIST2.spad" 873936 873948 875224 875229) (-584 "LIST.spad" 871657 871667 873000 873027) (-583 "LINSET.spad" 871436 871446 871647 871652) (-582 "LINFORM.spad" 870899 870911 871404 871431) (-581 "LINEXP.spad" 869642 869652 870889 870894) (-580 "LINELT.spad" 869013 869025 869525 869552) (-579 "LINDEP.spad" 867862 867874 868925 868930) (-578 "LINBASIS.spad" 867498 867513 867852 867857) (-577 "LIMITRF.spad" 865445 865455 867488 867493) (-576 "LIMITPS.spad" 864355 864368 865435 865440) (-575 "LIECAT.spad" 863839 863849 864281 864350) (-574 "LIECAT.spad" 863351 863363 863795 863800) (-573 "LIE.spad" 861355 861367 862629 862771) (-572 "LIB.spad" 859196 859204 859642 859669) (-571 "LGROBP.spad" 856549 856568 859186 859191) (-570 "LFCAT.spad" 855608 855616 856539 856544) (-569 "LF.spad" 854563 854579 855598 855603) (-568 "LEXTRIPK.spad" 850186 850201 854553 854558) (-567 "LEXP.spad" 848205 848232 850166 850181) (-566 "LETAST.spad" 847904 847912 848195 848200) (-565 "LEADCDET.spad" 846310 846327 847894 847899) (-564 "LAZM3PK.spad" 845054 845076 846300 846305) (-563 "LAUPOL.spad" 843721 843734 844621 844690) (-562 "LAPLACE.spad" 843304 843320 843711 843716) (-561 "LALG.spad" 843080 843090 843284 843299) (-560 "LALG.spad" 842864 842876 843070 843075) (-559 "LA.spad" 842304 842318 842786 842825) (-558 "KVTFROM.spad" 842047 842057 842294 842299) (-557 "KTVLOGIC.spad" 841591 841599 842037 842042) (-556 "KRCFROM.spad" 841337 841347 841581 841586) (-555 "KOVACIC.spad" 840068 840085 841327 841332) (-554 "KONVERT.spad" 839790 839800 840058 840063) (-553 "KOERCE.spad" 839527 839537 839780 839785) (-552 "KERNEL2.spad" 839230 839242 839517 839522) (-551 "KERNEL.spad" 837950 837960 839079 839084) (-550 "KDAGG.spad" 837059 837081 837930 837945) (-549 "KDAGG.spad" 836176 836200 837049 837054) (-548 "KAFILE.spad" 834591 834607 834826 834853) (-547 "JVMOP.spad" 834504 834512 834581 834586) (-546 "JVMMDACC.spad" 833558 833566 834494 834499) (-545 "JVMFDACC.spad" 832874 832882 833548 833553) (-544 "JVMCSTTG.spad" 831603 831611 832864 832869) (-543 "JVMCFACC.spad" 831049 831057 831593 831598) (-542 "JVMBCODE.spad" 830960 830968 831039 831044) (-541 "JORDAN.spad" 828777 828789 830238 830380) (-540 "JOINAST.spad" 828479 828487 828767 828772) (-539 "IXAGG.spad" 826612 826636 828469 828474) (-538 "IXAGG.spad" 824575 824601 826434 826439) (-537 "ITUPLE.spad" 823751 823761 824565 824570) (-536 "ITRIGMNP.spad" 822598 822617 823741 823746) (-535 "ITFUN3.spad" 822104 822118 822588 822593) (-534 "ITFUN2.spad" 821848 821860 822094 822099) (-533 "ITFORM.spad" 821203 821211 821838 821843) (-532 "ITAYLOR.spad" 819197 819212 821067 821164) (-531 "ISUPS.spad" 811646 811661 818183 818280) (-530 "ISUMP.spad" 811147 811163 811636 811641) (-529 "ISAST.spad" 810866 810874 811137 811142) (-528 "IRURPK.spad" 809583 809602 810856 810861) (-527 "IRSN.spad" 807587 807595 809573 809578) (-526 "IRRF2F.spad" 806080 806090 807543 807548) (-525 "IRREDFFX.spad" 805681 805692 806070 806075) (-524 "IROOT.spad" 804020 804030 805671 805676) (-523 "IRFORM.spad" 803344 803352 804010 804015) (-522 "IR2F.spad" 802558 802574 803334 803339) (-521 "IR2.spad" 801586 801602 802548 802553) (-520 "IR.spad" 799422 799436 801468 801495) (-519 "IPRNTPK.spad" 799182 799190 799412 799417) (-518 "IPF.spad" 798747 798759 798987 799080) (-517 "IPADIC.spad" 798516 798542 798673 798742) (-516 "IP4ADDR.spad" 798073 798081 798506 798511) (-515 "IOMODE.spad" 797595 797603 798063 798068) (-514 "IOBFILE.spad" 796980 796988 797585 797590) (-513 "IOBCON.spad" 796845 796853 796970 796975) (-512 "INVLAPLA.spad" 796494 796510 796835 796840) (-511 "INTTR.spad" 789888 789905 796484 796489) (-510 "INTTOOLS.spad" 787696 787712 789515 789520) (-509 "INTSLPE.spad" 787024 787032 787686 787691) (-508 "INTRVL.spad" 786590 786600 786938 787019) (-507 "INTRF.spad" 785022 785036 786580 786585) (-506 "INTRET.spad" 784454 784464 785012 785017) (-505 "INTRAT.spad" 783189 783206 784444 784449) (-504 "INTPM.spad" 781652 781668 782910 782915) (-503 "INTPAF.spad" 779528 779546 781581 781586) (-502 "INTHERTR.spad" 778802 778819 779518 779523) (-501 "INTHERAL.spad" 778472 778496 778792 778797) (-500 "INTHEORY.spad" 774911 774919 778462 778467) (-499 "INTG0.spad" 768675 768693 774840 774845) (-498 "INTFACT.spad" 767742 767752 768665 768670) (-497 "INTEF.spad" 766153 766169 767732 767737) (-496 "INTDOM.spad" 764776 764784 766079 766148) (-495 "INTDOM.spad" 763461 763471 764766 764771) (-494 "INTCAT.spad" 761728 761738 763375 763456) (-493 "INTBIT.spad" 761235 761243 761718 761723) (-492 "INTALG.spad" 760423 760450 761225 761230) (-491 "INTAF.spad" 759923 759939 760413 760418) (-490 "INTABL.spad" 757779 757810 757942 757969) (-489 "INT8.spad" 757659 757667 757769 757774) (-488 "INT64.spad" 757538 757546 757649 757654) (-487 "INT32.spad" 757417 757425 757528 757533) (-486 "INT16.spad" 757296 757304 757407 757412) (-485 "INT.spad" 756822 756830 757162 757291) (-484 "INS.spad" 754325 754333 756724 756817) (-483 "INS.spad" 751914 751924 754315 754320) (-482 "INPSIGN.spad" 751384 751397 751904 751909) (-481 "INPRODPF.spad" 750480 750499 751374 751379) (-480 "INPRODFF.spad" 749568 749592 750470 750475) (-479 "INNMFACT.spad" 748543 748560 749558 749563) (-478 "INMODGCD.spad" 748047 748077 748533 748538) (-477 "INFSP.spad" 746344 746366 748037 748042) (-476 "INFPROD0.spad" 745424 745443 746334 746339) (-475 "INFORM1.spad" 745049 745059 745414 745419) (-474 "INFORM.spad" 742260 742268 745039 745044) (-473 "INFINITY.spad" 741812 741820 742250 742255) (-472 "INETCLTS.spad" 741789 741797 741802 741807) (-471 "INEP.spad" 740335 740357 741779 741784) (-470 "INDE.spad" 739984 740001 740245 740250) (-469 "INCRMAPS.spad" 739421 739431 739974 739979) (-468 "INBFILE.spad" 738517 738525 739411 739416) (-467 "INBFF.spad" 734367 734378 738507 738512) (-466 "INBCON.spad" 732633 732641 734357 734362) (-465 "INBCON.spad" 730897 730907 732623 732628) (-464 "INAST.spad" 730558 730566 730887 730892) (-463 "IMPTAST.spad" 730266 730274 730548 730553) (-462 "IMATQF.spad" 729360 729404 730222 730227) (-461 "IMATLIN.spad" 727981 728005 729316 729321) (-460 "IFF.spad" 727394 727410 727665 727758) (-459 "IFAST.spad" 727008 727016 727384 727389) (-458 "IFARRAY.spad" 724374 724389 726072 726099) (-457 "IFAMON.spad" 724236 724253 724330 724335) (-456 "IEVALAB.spad" 723649 723661 724226 724231) (-455 "IEVALAB.spad" 723060 723074 723639 723644) (-454 "indexedp.spad" 722616 722628 723050 723055) (-453 "IDPOAMS.spad" 722294 722306 722528 722533) (-452 "IDPOAM.spad" 721936 721948 722206 722211) (-451 "IDPO.spad" 721350 721362 721848 721853) (-450 "IDPC.spad" 720065 720077 721340 721345) (-449 "IDPAM.spad" 719732 719744 719977 719982) (-448 "IDPAG.spad" 719401 719413 719644 719649) (-447 "IDENT.spad" 719053 719061 719391 719396) (-446 "catdef.spad" 718824 718835 718936 719048) (-445 "IDECOMP.spad" 716063 716081 718814 718819) (-444 "IDEAL.spad" 711025 711064 716011 716016) (-443 "ICDEN.spad" 710238 710254 711015 711020) (-442 "ICARD.spad" 709631 709639 710228 710233) (-441 "IBPTOOLS.spad" 708238 708255 709621 709626) (-440 "boolean.spad" 707631 707644 707764 707791) (-439 "IBATOOL.spad" 704616 704635 707621 707626) (-438 "IBACHIN.spad" 703123 703138 704606 704611) (-437 "array2.spad" 702608 702630 702795 702822) (-436 "IARRAY1.spad" 701526 701541 701672 701699) (-435 "IAN.spad" 699908 699916 701357 701450) (-434 "IALGFACT.spad" 699519 699552 699898 699903) (-433 "HYPCAT.spad" 698943 698951 699509 699514) (-432 "HYPCAT.spad" 698365 698375 698933 698938) (-431 "HOSTNAME.spad" 698181 698189 698355 698360) (-430 "HOMOTOP.spad" 697924 697934 698171 698176) (-429 "HOAGG.spad" 695531 695541 697914 697919) (-428 "HOAGG.spad" 692888 692900 695273 695278) (-427 "HEXADEC.spad" 691113 691121 691478 691571) (-426 "HEUGCD.spad" 690204 690215 691103 691108) (-425 "HELLFDIV.spad" 689810 689834 690194 690199) (-424 "HEAP.spad" 689267 689277 689482 689509) (-423 "HEADAST.spad" 688808 688816 689257 689262) (-422 "HDP.spad" 678340 678356 678717 678814) (-421 "HDMP.spad" 675887 675902 676503 676630) (-420 "HB.spad" 674162 674170 675877 675882) (-419 "HASHTBL.spad" 671970 672001 672181 672208) (-418 "HASAST.spad" 671686 671694 671960 671965) (-417 "HACKPI.spad" 671177 671185 671588 671681) (-416 "GTSET.spad" 669943 669959 670650 670677) (-415 "GSTBL.spad" 667788 667823 667962 667989) (-414 "GSERIES.spad" 665160 665187 665979 666128) (-413 "GROUP.spad" 664433 664441 665140 665155) (-412 "GROUP.spad" 663714 663724 664423 664428) (-411 "GROEBSOL.spad" 662208 662229 663704 663709) (-410 "GRMOD.spad" 660789 660801 662198 662203) (-409 "GRMOD.spad" 659368 659382 660779 660784) (-408 "GRIMAGE.spad" 652281 652289 659358 659363) (-407 "GRDEF.spad" 650660 650668 652271 652276) (-406 "GRAY.spad" 649131 649139 650650 650655) (-405 "GRALG.spad" 648226 648238 649121 649126) (-404 "GRALG.spad" 647319 647333 648216 648221) (-403 "GPOLSET.spad" 646616 646639 646828 646855) (-402 "GOSPER.spad" 645893 645911 646606 646611) (-401 "GMODPOL.spad" 645041 645068 645861 645888) (-400 "GHENSEL.spad" 644124 644138 645031 645036) (-399 "GENUPS.spad" 640417 640430 644114 644119) (-398 "GENUFACT.spad" 639994 640004 640407 640412) (-397 "GENPGCD.spad" 639596 639613 639984 639989) (-396 "GENMFACT.spad" 639048 639067 639586 639591) (-395 "GENEEZ.spad" 637007 637020 639038 639043) (-394 "GDMP.spad" 634396 634413 635170 635297) (-393 "GCNAALG.spad" 628319 628346 634190 634257) (-392 "GCDDOM.spad" 627511 627519 628245 628314) (-391 "GCDDOM.spad" 626765 626775 627501 627506) (-390 "GBINTERN.spad" 622785 622823 626755 626760) (-389 "GBF.spad" 618568 618606 622775 622780) (-388 "GBEUCLID.spad" 616450 616488 618558 618563) (-387 "GB.spad" 613976 614014 616406 616411) (-386 "GAUSSFAC.spad" 613289 613297 613966 613971) (-385 "GALUTIL.spad" 611615 611625 613245 613250) (-384 "GALPOLYU.spad" 610069 610082 611605 611610) (-383 "GALFACTU.spad" 608282 608301 610059 610064) (-382 "GALFACT.spad" 598495 598506 608272 608277) (-381 "FUNDESC.spad" 598173 598181 598485 598490) (-380 "FUNCTION.spad" 598022 598034 598163 598168) (-379 "FT.spad" 596322 596330 598012 598017) (-378 "FSUPFACT.spad" 595236 595255 596272 596277) (-377 "FST.spad" 593322 593330 595226 595231) (-376 "FSRED.spad" 592802 592818 593312 593317) (-375 "FSPRMELT.spad" 591668 591684 592759 592764) (-374 "FSPECF.spad" 589759 589775 591658 591663) (-373 "FSINT.spad" 589419 589435 589749 589754) (-372 "FSERIES.spad" 588610 588622 589239 589338) (-371 "FSCINT.spad" 587927 587943 588600 588605) (-370 "FSAGG2.spad" 586662 586678 587917 587922) (-369 "FSAGG.spad" 585779 585789 586618 586657) (-368 "FSAGG.spad" 584858 584870 585699 585704) (-367 "FS2UPS.spad" 579373 579407 584848 584853) (-366 "FS2EXPXP.spad" 578514 578537 579363 579368) (-365 "FS2.spad" 578169 578185 578504 578509) (-364 "FS.spad" 572441 572451 577948 578164) (-363 "FS.spad" 566515 566527 572024 572029) (-362 "FRUTIL.spad" 565469 565479 566505 566510) (-361 "FRNAALG.spad" 560746 560756 565411 565464) (-360 "FRNAALG.spad" 556035 556047 560702 560707) (-359 "FRNAAF2.spad" 555483 555501 556025 556030) (-358 "FRMOD.spad" 554891 554921 555412 555417) (-357 "FRIDEAL2.spad" 554495 554527 554881 554886) (-356 "FRIDEAL.spad" 553720 553741 554475 554490) (-355 "FRETRCT.spad" 553239 553249 553710 553715) (-354 "FRETRCT.spad" 552665 552677 553138 553143) (-353 "FRAMALG.spad" 551045 551058 552621 552660) (-352 "FRAMALG.spad" 549457 549472 551035 551040) (-351 "FRAC2.spad" 549062 549074 549447 549452) (-350 "FRAC.spad" 547049 547059 547436 547609) (-349 "FR2.spad" 546385 546397 547039 547044) (-348 "FR.spad" 540173 540183 545446 545515) (-347 "FPS.spad" 537012 537020 540063 540168) (-346 "FPS.spad" 533879 533889 536932 536937) (-345 "FPC.spad" 532925 532933 533781 533874) (-344 "FPC.spad" 532057 532067 532915 532920) (-343 "FPATMAB.spad" 531819 531829 532047 532052) (-342 "FPARFRAC.spad" 530661 530678 531809 531814) (-341 "FORDER.spad" 530352 530376 530651 530656) (-340 "FNLA.spad" 529776 529798 530320 530347) (-339 "FNCAT.spad" 528371 528379 529766 529771) (-338 "FNAME.spad" 528263 528271 528361 528366) (-337 "FMONOID.spad" 527944 527954 528219 528224) (-336 "FMONCAT.spad" 525113 525123 527934 527939) (-335 "FMCAT.spad" 522789 522807 525081 525108) (-334 "FM1.spad" 522154 522166 522723 522750) (-333 "FM.spad" 521769 521781 522008 522035) (-332 "FLOATRP.spad" 519512 519526 521759 521764) (-331 "FLOATCP.spad" 516951 516965 519502 519507) (-330 "FLOAT.spad" 514042 514050 516817 516946) (-329 "FLINEXP.spad" 513764 513774 514032 514037) (-328 "FLINEXP.spad" 513443 513455 513713 513718) (-327 "FLASORT.spad" 512769 512781 513433 513438) (-326 "FLALG.spad" 510439 510458 512695 512764) (-325 "FLAGG2.spad" 509156 509172 510429 510434) (-324 "FLAGG.spad" 506222 506232 509136 509151) (-323 "FLAGG.spad" 503191 503203 506107 506112) (-322 "FINRALG.spad" 501276 501289 503147 503186) (-321 "FINRALG.spad" 499287 499302 501160 501165) (-320 "FINITE.spad" 498439 498447 499277 499282) (-319 "FINITE.spad" 497589 497599 498429 498434) (-318 "aggcat.spad" 494509 494519 497569 497584) (-317 "FINAGG.spad" 491404 491416 494466 494471) (-316 "FINAALG.spad" 480589 480599 491346 491399) (-315 "FINAALG.spad" 469786 469798 480545 480550) (-314 "FILECAT.spad" 468320 468337 469776 469781) (-313 "FILE.spad" 467903 467913 468310 468315) (-312 "FIELD.spad" 467309 467317 467805 467898) (-311 "FIELD.spad" 466801 466811 467299 467304) (-310 "FGROUP.spad" 465464 465474 466781 466796) (-309 "FGLMICPK.spad" 464259 464274 465454 465459) (-308 "FFX.spad" 463645 463660 463978 464071) (-307 "FFSLPE.spad" 463156 463177 463635 463640) (-306 "FFPOLY2.spad" 462216 462233 463146 463151) (-305 "FFPOLY.spad" 453558 453569 462206 462211) (-304 "FFP.spad" 452966 452986 453277 453370) (-303 "FFNBX.spad" 451489 451509 452685 452778) (-302 "FFNBP.spad" 450013 450030 451208 451301) (-301 "FFNB.spad" 448481 448502 449697 449790) (-300 "FFINTBAS.spad" 445995 446014 448471 448476) (-299 "FFIELDC.spad" 443580 443588 445897 445990) (-298 "FFIELDC.spad" 441251 441261 443570 443575) (-297 "FFHOM.spad" 440023 440040 441241 441246) (-296 "FFF.spad" 437466 437477 440013 440018) (-295 "FFCGX.spad" 436324 436344 437185 437278) (-294 "FFCGP.spad" 435224 435244 436043 436136) (-293 "FFCG.spad" 434019 434040 434908 435001) (-292 "FFCAT2.spad" 433766 433806 434009 434014) (-291 "FFCAT.spad" 426931 426953 433605 433761) (-290 "FFCAT.spad" 420175 420199 426851 426856) (-289 "FF.spad" 419626 419642 419859 419952) (-288 "FEVALAB.spad" 419334 419344 419616 419621) (-287 "FEVALAB.spad" 418818 418830 419102 419107) (-286 "FDIVCAT.spad" 416914 416938 418808 418813) (-285 "FDIVCAT.spad" 415008 415034 416904 416909) (-284 "FDIV2.spad" 414664 414704 414998 415003) (-283 "FDIV.spad" 414122 414146 414654 414659) (-282 "FCTRDATA.spad" 413130 413138 414112 414117) (-281 "FCOMP.spad" 412509 412519 413120 413125) (-280 "FAXF.spad" 405544 405558 412411 412504) (-279 "FAXF.spad" 398631 398647 405500 405505) (-278 "FARRAY.spad" 396662 396672 397695 397722) (-277 "FAMR.spad" 394806 394818 396560 396657) (-276 "FAMR.spad" 392934 392948 394690 394695) (-275 "FAMONOID.spad" 392618 392628 392888 392893) (-274 "FAMONC.spad" 390938 390950 392608 392613) (-273 "FAGROUP.spad" 390578 390588 390834 390861) (-272 "FACUTIL.spad" 388790 388807 390568 390573) (-271 "FACTFUNC.spad" 387992 388002 388780 388785) (-270 "EXPUPXS.spad" 384884 384907 386183 386332) (-269 "EXPRTUBE.spad" 382172 382180 384874 384879) (-268 "EXPRODE.spad" 379340 379356 382162 382167) (-267 "EXPR2UPS.spad" 375462 375475 379330 379335) (-266 "EXPR2.spad" 375167 375179 375452 375457) (-265 "EXPR.spad" 370812 370822 371526 371813) (-264 "EXPEXPAN.spad" 367757 367782 368389 368482) (-263 "EXITAST.spad" 367493 367501 367747 367752) (-262 "EXIT.spad" 367164 367172 367483 367488) (-261 "EVALCYC.spad" 366624 366638 367154 367159) (-260 "EVALAB.spad" 366204 366214 366614 366619) (-259 "EVALAB.spad" 365782 365794 366194 366199) (-258 "EUCDOM.spad" 363372 363380 365708 365777) (-257 "EUCDOM.spad" 361024 361034 363362 363367) (-256 "ES2.spad" 360537 360553 361014 361019) (-255 "ES1.spad" 360107 360123 360527 360532) (-254 "ES.spad" 352978 352986 360097 360102) (-253 "ES.spad" 345770 345780 352891 352896) (-252 "ERROR.spad" 343097 343105 345760 345765) (-251 "EQTBL.spad" 340907 340929 341116 341143) (-250 "EQ2.spad" 340625 340637 340897 340902) (-249 "EQ.spad" 335531 335541 338326 338432) (-248 "EP.spad" 331857 331867 335521 335526) (-247 "ENV.spad" 330535 330543 331847 331852) (-246 "ENTIRER.spad" 330203 330211 330479 330530) (-245 "ENTIRER.spad" 329915 329925 330193 330198) (-244 "EMR.spad" 329203 329244 329841 329910) (-243 "ELTAGG.spad" 327457 327476 329193 329198) (-242 "ELTAGG.spad" 325675 325696 327413 327418) (-241 "ELTAB.spad" 325150 325163 325665 325670) (-240 "ELFUTS.spad" 324585 324604 325140 325145) (-239 "ELEMFUN.spad" 324274 324282 324575 324580) (-238 "ELEMFUN.spad" 323961 323971 324264 324269) (-237 "ELAGG.spad" 321932 321942 323941 323956) (-236 "ELAGG.spad" 319842 319854 321853 321858) (-235 "ELABOR.spad" 319188 319196 319832 319837) (-234 "ELABEXPR.spad" 318120 318128 319178 319183) (-233 "EFUPXS.spad" 314896 314926 318076 318081) (-232 "EFULS.spad" 311732 311755 314852 314857) (-231 "EFSTRUC.spad" 309747 309763 311722 311727) (-230 "EF.spad" 304523 304539 309737 309742) (-229 "EAB.spad" 302823 302831 304513 304518) (-228 "DVARCAT.spad" 299829 299839 302813 302818) (-227 "DVARCAT.spad" 296833 296845 299819 299824) (-226 "DSMP.spad" 294566 294580 294871 294998) (-225 "DSEXT.spad" 293868 293878 294556 294561) (-224 "DSEXT.spad" 293090 293102 293780 293785) (-223 "DROPT1.spad" 292755 292765 293080 293085) (-222 "DROPT0.spad" 287620 287628 292745 292750) (-221 "DROPT.spad" 281579 281587 287610 287615) (-220 "DRAWPT.spad" 279752 279760 281569 281574) (-219 "DRAWHACK.spad" 279060 279070 279742 279747) (-218 "DRAWCX.spad" 276538 276546 279050 279055) (-217 "DRAWCURV.spad" 276085 276100 276528 276533) (-216 "DRAWCFUN.spad" 265617 265625 276075 276080) (-215 "DRAW.spad" 258493 258506 265607 265612) (-214 "DQAGG.spad" 256671 256681 258461 258488) (-213 "DPOLCAT.spad" 252028 252044 256539 256666) (-212 "DPOLCAT.spad" 247471 247489 251984 251989) (-211 "DPMO.spad" 240073 240089 240211 240417) (-210 "DPMM.spad" 232688 232706 232813 233019) (-209 "DOMTMPLT.spad" 232459 232467 232678 232683) (-208 "DOMCTOR.spad" 232214 232222 232449 232454) (-207 "DOMAIN.spad" 231325 231333 232204 232209) (-206 "DMP.spad" 228918 228933 229488 229615) (-205 "DMEXT.spad" 228785 228795 228886 228913) (-204 "DLP.spad" 228145 228155 228775 228780) (-203 "DLIST.spad" 226605 226615 227209 227236) (-202 "DLAGG.spad" 225022 225032 226595 226600) (-201 "DIVRING.spad" 224564 224572 224966 225017) (-200 "DIVRING.spad" 224150 224160 224554 224559) (-199 "DISPLAY.spad" 222340 222348 224140 224145) (-198 "DIRPROD2.spad" 221158 221176 222330 222335) (-197 "DIRPROD.spad" 210427 210443 211067 211164) (-196 "DIRPCAT.spad" 209710 209726 210325 210422) (-195 "DIRPCAT.spad" 208619 208637 209236 209241) (-194 "DIOSP.spad" 207444 207452 208609 208614) (-193 "DIOPS.spad" 206440 206450 207424 207439) (-192 "DIOPS.spad" 205383 205395 206369 206374) (-191 "catdef.spad" 205241 205249 205373 205378) (-190 "DIFRING.spad" 205079 205087 205221 205236) (-189 "DIFFSPC.spad" 204658 204666 205069 205074) (-188 "DIFFSPC.spad" 204235 204245 204648 204653) (-187 "DIFFMOD.spad" 203724 203734 204203 204230) (-186 "DIFFDOM.spad" 202889 202900 203714 203719) (-185 "DIFFDOM.spad" 202052 202065 202879 202884) (-184 "DIFEXT.spad" 201871 201881 202032 202047) (-183 "DIAGG.spad" 201501 201511 201851 201866) (-182 "DIAGG.spad" 201139 201151 201491 201496) (-181 "DHMATRIX.spad" 199516 199526 200661 200688) (-180 "DFSFUN.spad" 193156 193164 199506 199511) (-179 "DFLOAT.spad" 189763 189771 193046 193151) (-178 "DFINTTLS.spad" 187994 188010 189753 189758) (-177 "DERHAM.spad" 185908 185940 187974 187989) (-176 "DEQUEUE.spad" 185297 185307 185580 185607) (-175 "DEGRED.spad" 184914 184928 185287 185292) (-174 "DEFINTRF.spad" 182496 182506 184904 184909) (-173 "DEFINTEF.spad" 181034 181050 182486 182491) (-172 "DEFAST.spad" 180418 180426 181024 181029) (-171 "DECIMAL.spad" 178647 178655 179008 179101) (-170 "DDFACT.spad" 176468 176485 178637 178642) (-169 "DBLRESP.spad" 176068 176092 176458 176463) (-168 "DBASIS.spad" 175694 175709 176058 176063) (-167 "DBASE.spad" 174358 174368 175684 175689) (-166 "DATAARY.spad" 173844 173857 174348 174353) (-165 "CYCLOTOM.spad" 173350 173358 173834 173839) (-164 "CYCLES.spad" 170142 170150 173340 173345) (-163 "CVMP.spad" 169559 169569 170132 170137) (-162 "CTRIGMNP.spad" 168059 168075 169549 169554) (-161 "CTORKIND.spad" 167662 167670 168049 168054) (-160 "CTORCAT.spad" 166903 166911 167652 167657) (-159 "CTORCAT.spad" 166142 166152 166893 166898) (-158 "CTORCALL.spad" 165731 165741 166132 166137) (-157 "CTOR.spad" 165422 165430 165721 165726) (-156 "CSTTOOLS.spad" 164667 164680 165412 165417) (-155 "CRFP.spad" 158439 158452 164657 164662) (-154 "CRCEAST.spad" 158159 158167 158429 158434) (-153 "CRAPACK.spad" 157226 157236 158149 158154) (-152 "CPMATCH.spad" 156727 156742 157148 157153) (-151 "CPIMA.spad" 156432 156451 156717 156722) (-150 "COORDSYS.spad" 151441 151451 156422 156427) (-149 "CONTOUR.spad" 150868 150876 151431 151436) (-148 "CONTFRAC.spad" 146618 146628 150770 150863) (-147 "CONDUIT.spad" 146376 146384 146608 146613) (-146 "COMRING.spad" 146050 146058 146314 146371) (-145 "COMPPROP.spad" 145568 145576 146040 146045) (-144 "COMPLPAT.spad" 145335 145350 145558 145563) (-143 "COMPLEX2.spad" 145050 145062 145325 145330) (-142 "COMPLEX.spad" 140756 140766 141000 141258) (-141 "COMPILER.spad" 140305 140313 140746 140751) (-140 "COMPFACT.spad" 139907 139921 140295 140300) (-139 "COMPCAT.spad" 137982 137992 139644 139902) (-138 "COMPCAT.spad" 135798 135810 137462 137467) (-137 "COMMUPC.spad" 135546 135564 135788 135793) (-136 "COMMONOP.spad" 135079 135087 135536 135541) (-135 "COMMAAST.spad" 134842 134850 135069 135074) (-134 "COMM.spad" 134653 134661 134832 134837) (-133 "COMBOPC.spad" 133576 133584 134643 134648) (-132 "COMBINAT.spad" 132343 132353 133566 133571) (-131 "COMBF.spad" 129765 129781 132333 132338) (-130 "COLOR.spad" 128602 128610 129755 129760) (-129 "COLONAST.spad" 128268 128276 128592 128597) (-128 "CMPLXRT.spad" 127979 127996 128258 128263) (-127 "CLLCTAST.spad" 127641 127649 127969 127974) (-126 "CLIP.spad" 123749 123757 127631 127636) (-125 "CLIF.spad" 122404 122420 123705 123744) (-124 "CLAGG.spad" 120396 120406 122394 122399) (-123 "CLAGG.spad" 118247 118259 120247 120252) (-122 "CINTSLPE.spad" 117602 117615 118237 118242) (-121 "CHVAR.spad" 115740 115762 117592 117597) (-120 "CHARZ.spad" 115655 115663 115720 115735) (-119 "CHARPOL.spad" 115181 115191 115645 115650) (-118 "CHARNZ.spad" 114943 114951 115161 115176) (-117 "CHAR.spad" 112311 112319 114933 114938) (-116 "CFCAT.spad" 111639 111647 112301 112306) (-115 "CDEN.spad" 110859 110873 111629 111634) (-114 "CCLASS.spad" 108916 108924 110178 110217) (-113 "CATEGORY.spad" 107990 107998 108906 108911) (-112 "CATCTOR.spad" 107881 107889 107980 107985) (-111 "CATAST.spad" 107507 107515 107871 107876) (-110 "CASEAST.spad" 107221 107229 107497 107502) (-109 "CARTEN2.spad" 106611 106638 107211 107216) (-108 "CARTEN.spad" 102363 102387 106601 106606) (-107 "CARD.spad" 99658 99666 102337 102358) (-106 "CAPSLAST.spad" 99440 99448 99648 99653) (-105 "CACHSET.spad" 99064 99072 99430 99435) (-104 "CABMON.spad" 98619 98627 99054 99059) (-103 "BYTEORD.spad" 98294 98302 98609 98614) (-102 "BYTEBUF.spad" 96218 96226 97424 97451) (-101 "BYTE.spad" 95693 95701 96208 96213) (-100 "BTREE.spad" 94831 94841 95365 95392) (-99 "BTOURN.spad" 93902 93911 94503 94530) (-98 "BTCAT.spad" 93460 93469 93870 93897) (-97 "BTCAT.spad" 93038 93049 93450 93455) (-96 "BTAGG.spad" 92505 92512 93006 93033) (-95 "BTAGG.spad" 91992 92001 92495 92500) (-94 "BSTREE.spad" 90799 90808 91664 91691) (-93 "BRILL.spad" 89005 89015 90789 90794) (-92 "BRAGG.spad" 87962 87971 88995 89000) (-91 "BRAGG.spad" 86883 86894 87918 87923) (-90 "BPADICRT.spad" 84943 84954 85189 85282) (-89 "BPADIC.spad" 84616 84627 84869 84938) (-88 "BOUNDZRO.spad" 84273 84289 84606 84611) (-87 "BOP1.spad" 81732 81741 84263 84268) (-86 "BOP.spad" 76875 76882 81722 81727) (-85 "BOOLEAN.spad" 76424 76431 76865 76870) (-84 "BOOLE.spad" 76075 76082 76414 76419) (-83 "BOOLE.spad" 75724 75733 76065 76070) (-82 "BMODULE.spad" 75437 75448 75692 75719) (-81 "BITS.spad" 74749 74756 74963 74990) (-80 "catdef.spad" 74632 74642 74739 74744) (-79 "catdef.spad" 74383 74393 74622 74627) (-78 "BINDING.spad" 73805 73812 74373 74378) (-77 "BINARY.spad" 72040 72047 72395 72488) (-76 "BGAGG.spad" 71360 71369 72020 72035) (-75 "BGAGG.spad" 70688 70699 71350 71355) (-74 "BEZOUT.spad" 69829 69855 70638 70643) (-73 "BBTREE.spad" 66772 66781 69501 69528) (-72 "BASTYPE.spad" 66272 66279 66762 66767) (-71 "BASTYPE.spad" 65770 65779 66262 66267) (-70 "BALFACT.spad" 65230 65242 65760 65765) (-69 "AUTOMOR.spad" 64681 64690 65210 65225) (-68 "ATTREG.spad" 61813 61820 64457 64676) (-67 "ATTRAST.spad" 61530 61537 61803 61808) (-66 "ATRIG.spad" 61000 61007 61520 61525) (-65 "ATRIG.spad" 60468 60477 60990 60995) (-64 "ASTCAT.spad" 60372 60379 60458 60463) (-63 "ASTCAT.spad" 60274 60283 60362 60367) (-62 "ASTACK.spad" 59678 59687 59946 59973) (-61 "ASSOCEQ.spad" 58512 58523 59634 59639) (-60 "ARRAY2.spad" 58035 58044 58184 58211) (-59 "ARRAY12.spad" 56748 56759 58025 58030) (-58 "ARRAY1.spad" 55466 55475 55812 55839) (-57 "ARR2CAT.spad" 51506 51527 55434 55461) (-56 "ARR2CAT.spad" 47566 47589 51496 51501) (-55 "ARITY.spad" 46938 46945 47556 47561) (-54 "APPRULE.spad" 46222 46244 46928 46933) (-53 "APPLYORE.spad" 45841 45854 46212 46217) (-52 "ANY1.spad" 44912 44921 45831 45836) (-51 "ANY.spad" 43763 43770 44902 44907) (-50 "ANTISYM.spad" 42208 42224 43743 43758) (-49 "ANON.spad" 41917 41924 42198 42203) (-48 "AN.spad" 40385 40392 41748 41841) (-47 "AMR.spad" 38570 38581 40283 40380) (-46 "AMR.spad" 36618 36631 38333 38338) (-45 "ALIST.spad" 33330 33351 33680 33707) (-44 "ALGSC.spad" 32465 32491 33202 33255) (-43 "ALGPKG.spad" 28248 28259 32421 32426) (-42 "ALGMFACT.spad" 27441 27455 28238 28243) (-41 "ALGMANIP.spad" 24942 24957 27285 27290) (-40 "ALGFF.spad" 22760 22787 22977 23133) (-39 "ALGFACT.spad" 21879 21889 22750 22755) (-38 "ALGEBRA.spad" 21712 21721 21835 21874) (-37 "ALGEBRA.spad" 21577 21588 21702 21707) (-36 "ALAGG.spad" 21093 21114 21545 21572) (-35 "AHYP.spad" 20474 20481 21083 21088) (-34 "AGG.spad" 19288 19295 20464 20469) (-33 "AGG.spad" 18066 18075 19244 19249) (-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 1969242 1969247 1969252 1969257) (-2 NIL 1969222 1969227 1969232 1969237) (-1 NIL 1969202 1969207 1969212 1969217) (0 NIL 1969182 1969187 1969192 1969197) (-1210 "ZMOD.spad" 1968991 1969004 1969120 1969177) (-1209 "ZLINDEP.spad" 1968089 1968100 1968981 1968986) (-1208 "ZDSOLVE.spad" 1958050 1958072 1968079 1968084) (-1207 "YSTREAM.spad" 1957545 1957556 1958040 1958045) (-1206 "YDIAGRAM.spad" 1957179 1957188 1957535 1957540) (-1205 "XRPOLY.spad" 1956399 1956419 1957035 1957104) (-1204 "XPR.spad" 1954194 1954207 1956117 1956216) (-1203 "XPOLYC.spad" 1953513 1953529 1954120 1954189) (-1202 "XPOLY.spad" 1953068 1953079 1953369 1953438) (-1201 "XPBWPOLY.spad" 1951539 1951559 1952874 1952943) (-1200 "XFALG.spad" 1948587 1948603 1951465 1951534) (-1199 "XF.spad" 1947050 1947065 1948489 1948582) (-1198 "XF.spad" 1945493 1945510 1946934 1946939) (-1197 "XEXPPKG.spad" 1944752 1944778 1945483 1945488) (-1196 "XDPOLY.spad" 1944366 1944382 1944608 1944677) (-1195 "XALG.spad" 1944034 1944045 1944322 1944361) (-1194 "WUTSET.spad" 1939888 1939905 1943519 1943534) (-1193 "WP.spad" 1939095 1939139 1939746 1939813) (-1192 "WHILEAST.spad" 1938893 1938902 1939085 1939090) (-1191 "WHEREAST.spad" 1938564 1938573 1938883 1938888) (-1190 "WFFINTBS.spad" 1936227 1936249 1938554 1938559) (-1189 "WEIER.spad" 1934449 1934460 1936217 1936222) (-1188 "VSPACE.spad" 1934122 1934133 1934417 1934444) (-1187 "VSPACE.spad" 1933815 1933828 1934112 1934117) (-1186 "VOID.spad" 1933492 1933501 1933805 1933810) (-1185 "VIEWDEF.spad" 1928693 1928702 1933482 1933487) (-1184 "VIEW3D.spad" 1912654 1912663 1928683 1928688) (-1183 "VIEW2D.spad" 1900553 1900562 1912644 1912649) (-1182 "VIEW.spad" 1898273 1898282 1900543 1900548) (-1181 "VECTOR2.spad" 1896912 1896925 1898263 1898268) (-1180 "VECTOR.spad" 1895482 1895493 1895733 1895748) (-1179 "VECTCAT.spad" 1893406 1893417 1895462 1895477) (-1178 "VECTCAT.spad" 1891127 1891140 1893185 1893190) (-1177 "VARIABLE.spad" 1890907 1890922 1891117 1891122) (-1176 "UTYPE.spad" 1890551 1890560 1890897 1890902) (-1175 "UTSODETL.spad" 1889846 1889870 1890507 1890512) (-1174 "UTSODE.spad" 1888062 1888082 1889836 1889841) (-1173 "UTSCAT.spad" 1885541 1885557 1887960 1888057) (-1172 "UTSCAT.spad" 1882688 1882706 1885109 1885114) (-1171 "UTS2.spad" 1882283 1882318 1882678 1882683) (-1170 "UTS.spad" 1877295 1877323 1880815 1880912) (-1169 "URAGG.spad" 1872016 1872027 1877285 1877290) (-1168 "URAGG.spad" 1866701 1866714 1871972 1871977) (-1167 "UPXSSING.spad" 1864469 1864495 1865905 1866038) (-1166 "UPXSCONS.spad" 1862287 1862307 1862660 1862809) (-1165 "UPXSCCA.spad" 1860858 1860878 1862133 1862282) (-1164 "UPXSCCA.spad" 1859571 1859593 1860848 1860853) (-1163 "UPXSCAT.spad" 1858160 1858176 1859417 1859566) (-1162 "UPXS2.spad" 1857703 1857756 1858150 1858155) (-1161 "UPXS.spad" 1855058 1855086 1855894 1856043) (-1160 "UPSQFREE.spad" 1853473 1853487 1855048 1855053) (-1159 "UPSCAT.spad" 1851268 1851292 1853371 1853468) (-1158 "UPSCAT.spad" 1848764 1848790 1850869 1850874) (-1157 "UPOLYC2.spad" 1848235 1848254 1848754 1848759) (-1156 "UPOLYC.spad" 1843315 1843326 1848077 1848230) (-1155 "UPOLYC.spad" 1838313 1838326 1843077 1843082) (-1154 "UPMP.spad" 1837245 1837258 1838303 1838308) (-1153 "UPDIVP.spad" 1836810 1836824 1837235 1837240) (-1152 "UPDECOMP.spad" 1835071 1835085 1836800 1836805) (-1151 "UPCDEN.spad" 1834288 1834304 1835061 1835066) (-1150 "UP2.spad" 1833652 1833673 1834278 1834283) (-1149 "UP.spad" 1831122 1831137 1831509 1831662) (-1148 "UNISEG2.spad" 1830619 1830632 1831078 1831083) (-1147 "UNISEG.spad" 1829972 1829983 1830538 1830543) (-1146 "UNIFACT.spad" 1829075 1829087 1829962 1829967) (-1145 "ULSCONS.spad" 1822921 1822941 1823291 1823440) (-1144 "ULSCCAT.spad" 1820658 1820678 1822767 1822916) (-1143 "ULSCCAT.spad" 1818503 1818525 1820614 1820619) (-1142 "ULSCAT.spad" 1816743 1816759 1818349 1818498) (-1141 "ULS2.spad" 1816257 1816310 1816733 1816738) (-1140 "ULS.spad" 1808290 1808318 1809235 1809658) (-1139 "UINT8.spad" 1808167 1808176 1808280 1808285) (-1138 "UINT64.spad" 1808043 1808052 1808157 1808162) (-1137 "UINT32.spad" 1807919 1807928 1808033 1808038) (-1136 "UINT16.spad" 1807795 1807804 1807909 1807914) (-1135 "UFD.spad" 1806860 1806869 1807721 1807790) (-1134 "UFD.spad" 1805987 1805998 1806850 1806855) (-1133 "UDVO.spad" 1804868 1804877 1805977 1805982) (-1132 "UDPO.spad" 1802449 1802460 1804824 1804829) (-1131 "TYPEAST.spad" 1802368 1802377 1802439 1802444) (-1130 "TYPE.spad" 1802300 1802309 1802358 1802363) (-1129 "TWOFACT.spad" 1800952 1800967 1802290 1802295) (-1128 "TUPLE.spad" 1800459 1800470 1800864 1800869) (-1127 "TUBETOOL.spad" 1797326 1797335 1800449 1800454) (-1126 "TUBE.spad" 1795973 1795990 1797316 1797321) (-1125 "TSETCAT.spad" 1784056 1784073 1795953 1795968) (-1124 "TSETCAT.spad" 1772113 1772132 1784012 1784017) (-1123 "TS.spad" 1770741 1770757 1771707 1771804) (-1122 "TRMANIP.spad" 1765105 1765122 1770429 1770434) (-1121 "TRIMAT.spad" 1764068 1764093 1765095 1765100) (-1120 "TRIGMNIP.spad" 1762595 1762612 1764058 1764063) (-1119 "TRIGCAT.spad" 1762107 1762116 1762585 1762590) (-1118 "TRIGCAT.spad" 1761617 1761628 1762097 1762102) (-1117 "TREE.spad" 1760269 1760280 1761301 1761316) (-1116 "TRANFUN.spad" 1760108 1760117 1760259 1760264) (-1115 "TRANFUN.spad" 1759945 1759956 1760098 1760103) (-1114 "TOPSP.spad" 1759619 1759628 1759935 1759940) (-1113 "TOOLSIGN.spad" 1759282 1759293 1759609 1759614) (-1112 "TEXTFILE.spad" 1757843 1757852 1759272 1759277) (-1111 "TEX1.spad" 1757399 1757410 1757833 1757838) (-1110 "TEX.spad" 1754593 1754602 1757389 1757394) (-1109 "TBCMPPK.spad" 1752694 1752717 1754583 1754588) (-1108 "TBAGG.spad" 1751949 1751972 1752674 1752689) (-1107 "TBAGG.spad" 1751212 1751237 1751939 1751944) (-1106 "TANEXP.spad" 1750620 1750631 1751202 1751207) (-1105 "TALGOP.spad" 1750344 1750355 1750610 1750615) (-1104 "TABLEAU.spad" 1749825 1749836 1750334 1750339) (-1103 "TABLE.spad" 1747586 1747609 1747856 1747871) (-1102 "TABLBUMP.spad" 1744365 1744376 1747576 1747581) (-1101 "SYSTEM.spad" 1743593 1743602 1744355 1744360) (-1100 "SYSSOLP.spad" 1741076 1741087 1743583 1743588) (-1099 "SYSPTR.spad" 1740975 1740984 1741066 1741071) (-1098 "SYSNNI.spad" 1740198 1740209 1740965 1740970) (-1097 "SYSINT.spad" 1739602 1739613 1740188 1740193) (-1096 "SYNTAX.spad" 1735936 1735945 1739592 1739597) (-1095 "SYMTAB.spad" 1734004 1734013 1735926 1735931) (-1094 "SYMS.spad" 1730033 1730042 1733994 1733999) (-1093 "SYMPOLY.spad" 1729166 1729177 1729248 1729375) (-1092 "SYMFUNC.spad" 1728667 1728678 1729156 1729161) (-1091 "SYMBOL.spad" 1726162 1726171 1728657 1728662) (-1090 "SUTS.spad" 1723275 1723303 1724694 1724791) (-1089 "SUPXS.spad" 1720617 1720645 1721466 1721615) (-1088 "SUPFRACF.spad" 1719722 1719740 1720607 1720612) (-1087 "SUP2.spad" 1719114 1719127 1719712 1719717) (-1086 "SUP.spad" 1716198 1716209 1716971 1717124) (-1085 "SUMRF.spad" 1715172 1715183 1716188 1716193) (-1084 "SUMFS.spad" 1714801 1714818 1715162 1715167) (-1083 "SULS.spad" 1706821 1706849 1707779 1708202) (-1082 "syntax.spad" 1706590 1706599 1706811 1706816) (-1081 "SUCH.spad" 1706280 1706295 1706580 1706585) (-1080 "SUBSPACE.spad" 1698411 1698426 1706270 1706275) (-1079 "SUBRESP.spad" 1697581 1697595 1698367 1698372) (-1078 "STTFNC.spad" 1694049 1694065 1697571 1697576) (-1077 "STTF.spad" 1690148 1690164 1694039 1694044) (-1076 "STTAYLOR.spad" 1682825 1682836 1690055 1690060) (-1075 "STRTBL.spad" 1680749 1680766 1680898 1680913) (-1074 "STRING.spad" 1679506 1679515 1679891 1679906) (-1073 "STREAM3.spad" 1679079 1679094 1679496 1679501) (-1072 "STREAM2.spad" 1678207 1678220 1679069 1679074) (-1071 "STREAM1.spad" 1677913 1677924 1678197 1678202) (-1070 "STREAM.spad" 1674808 1674819 1677415 1677430) (-1069 "STINPROD.spad" 1673744 1673760 1674798 1674803) (-1068 "STEPAST.spad" 1672978 1672987 1673734 1673739) (-1067 "STEP.spad" 1672295 1672304 1672968 1672973) (-1066 "STBL.spad" 1670159 1670187 1670326 1670341) (-1065 "STAGG.spad" 1668858 1668869 1670149 1670154) (-1064 "STAGG.spad" 1667555 1667568 1668848 1668853) (-1063 "STACK.spad" 1666989 1667000 1667239 1667254) (-1062 "SRING.spad" 1666749 1666758 1666979 1666984) (-1061 "SREGSET.spad" 1664332 1664349 1666234 1666249) (-1060 "SRDCMPK.spad" 1662909 1662929 1664322 1664327) (-1059 "SRAGG.spad" 1658104 1658113 1662889 1662904) (-1058 "SRAGG.spad" 1653307 1653318 1658094 1658099) (-1057 "SQMATRIX.spad" 1650996 1651014 1651912 1651987) (-1056 "SPLTREE.spad" 1645750 1645763 1650546 1650561) (-1055 "SPLNODE.spad" 1642370 1642383 1645740 1645745) (-1054 "SPFCAT.spad" 1641179 1641188 1642360 1642365) (-1053 "SPECOUT.spad" 1639731 1639740 1641169 1641174) (-1052 "SPADXPT.spad" 1631822 1631831 1639721 1639726) (-1051 "spad-parser.spad" 1631287 1631296 1631812 1631817) (-1050 "SPADAST.spad" 1630988 1630997 1631277 1631282) (-1049 "SPACEC.spad" 1615203 1615214 1630978 1630983) (-1048 "SPACE3.spad" 1614979 1614990 1615193 1615198) (-1047 "SORTPAK.spad" 1614528 1614541 1614935 1614940) (-1046 "SOLVETRA.spad" 1612291 1612302 1614518 1614523) (-1045 "SOLVESER.spad" 1610747 1610758 1612281 1612286) (-1044 "SOLVERAD.spad" 1606773 1606784 1610737 1610742) (-1043 "SOLVEFOR.spad" 1605235 1605253 1606763 1606768) (-1042 "SNTSCAT.spad" 1604847 1604864 1605215 1605230) (-1041 "SMTS.spad" 1603164 1603190 1604441 1604538) (-1040 "SMP.spad" 1600972 1600992 1601362 1601489) (-1039 "SMITH.spad" 1599817 1599842 1600962 1600967) (-1038 "SMATCAT.spad" 1597947 1597977 1599773 1599812) (-1037 "SMATCAT.spad" 1595997 1596029 1597825 1597830) (-1036 "aggcat.spad" 1595673 1595684 1595977 1595992) (-1035 "SKAGG.spad" 1594654 1594665 1595653 1595668) (-1034 "SINT.spad" 1593953 1593962 1594520 1594649) (-1033 "SIMPAN.spad" 1593681 1593690 1593943 1593948) (-1032 "SIGNRF.spad" 1592806 1592817 1593671 1593676) (-1031 "SIGNEF.spad" 1592092 1592109 1592796 1592801) (-1030 "syntax.spad" 1591509 1591518 1592082 1592087) (-1029 "SIG.spad" 1590871 1590880 1591499 1591504) (-1028 "SHP.spad" 1588815 1588830 1590827 1590832) (-1027 "SHDP.spad" 1578219 1578246 1578736 1578821) (-1026 "SGROUP.spad" 1577827 1577836 1578209 1578214) (-1025 "SGROUP.spad" 1577433 1577444 1577817 1577822) (-1024 "catdef.spad" 1577143 1577155 1577254 1577428) (-1023 "catdef.spad" 1576699 1576711 1576964 1577138) (-1022 "SGCF.spad" 1569838 1569847 1576689 1576694) (-1021 "SFRTCAT.spad" 1568796 1568813 1569818 1569833) (-1020 "SFRGCD.spad" 1567859 1567879 1568786 1568791) (-1019 "SFQCMPK.spad" 1562672 1562692 1567849 1567854) (-1018 "SEXOF.spad" 1562515 1562555 1562662 1562667) (-1017 "SEXCAT.spad" 1560343 1560383 1562505 1562510) (-1016 "SEX.spad" 1560235 1560244 1560333 1560338) (-1015 "SETMN.spad" 1558695 1558712 1560225 1560230) (-1014 "SETCAT.spad" 1558180 1558189 1558685 1558690) (-1013 "SETCAT.spad" 1557663 1557674 1558170 1558175) (-1012 "SETAGG.spad" 1554212 1554223 1557643 1557658) (-1011 "SETAGG.spad" 1550769 1550782 1554202 1554207) (-1010 "SET.spad" 1548927 1548938 1550026 1550053) (-1009 "syntax.spad" 1548630 1548639 1548917 1548922) (-1008 "SEGXCAT.spad" 1547786 1547799 1548620 1548625) (-1007 "SEGCAT.spad" 1546711 1546722 1547776 1547781) (-1006 "SEGBIND2.spad" 1546409 1546422 1546701 1546706) (-1005 "SEGBIND.spad" 1546167 1546178 1546356 1546361) (-1004 "SEGAST.spad" 1545897 1545906 1546157 1546162) (-1003 "SEG2.spad" 1545332 1545345 1545853 1545858) (-1002 "SEG.spad" 1545145 1545156 1545251 1545256) (-1001 "SDVAR.spad" 1544421 1544432 1545135 1545140) (-1000 "SDPOL.spad" 1542113 1542124 1542404 1542531) (-999 "SCPKG.spad" 1540203 1540213 1542103 1542108) (-998 "SCOPE.spad" 1539381 1539389 1540193 1540198) (-997 "SCACHE.spad" 1538078 1538088 1539371 1539376) (-996 "SASTCAT.spad" 1537988 1537996 1538068 1538073) (-995 "SAOS.spad" 1537861 1537869 1537978 1537983) (-994 "SAERFFC.spad" 1537575 1537594 1537851 1537856) (-993 "SAEFACT.spad" 1537277 1537296 1537565 1537570) (-992 "SAE.spad" 1534928 1534943 1535538 1535673) (-991 "RURPK.spad" 1532588 1532603 1534918 1534923) (-990 "RULESET.spad" 1532042 1532065 1532578 1532583) (-989 "RULECOLD.spad" 1531895 1531907 1532032 1532037) (-988 "RULE.spad" 1530144 1530167 1531885 1531890) (-987 "RTVALUE.spad" 1529880 1529888 1530134 1530139) (-986 "syntax.spad" 1529598 1529606 1529870 1529875) (-985 "RSETGCD.spad" 1526041 1526060 1529588 1529593) (-984 "RSETCAT.spad" 1516022 1516038 1526021 1526036) (-983 "RSETCAT.spad" 1506011 1506029 1516012 1516017) (-982 "RSDCMPK.spad" 1504512 1504531 1506001 1506006) (-981 "RRCC.spad" 1502897 1502926 1504502 1504507) (-980 "RRCC.spad" 1501280 1501311 1502887 1502892) (-979 "RPTAST.spad" 1500983 1500991 1501270 1501275) (-978 "RPOLCAT.spad" 1480488 1480502 1500851 1500978) (-977 "RPOLCAT.spad" 1459786 1459802 1480151 1480156) (-976 "ROMAN.spad" 1459115 1459123 1459652 1459781) (-975 "ROIRC.spad" 1458196 1458227 1459105 1459110) (-974 "RNS.spad" 1457173 1457181 1458098 1458191) (-973 "RNS.spad" 1456236 1456246 1457163 1457168) (-972 "RNGBIND.spad" 1455397 1455410 1456191 1456196) (-971 "RNG.spad" 1455006 1455014 1455387 1455392) (-970 "RNG.spad" 1454613 1454623 1454996 1455001) (-969 "RMODULE.spad" 1454395 1454405 1454603 1454608) (-968 "RMCAT2.spad" 1453816 1453872 1454385 1454390) (-967 "RMATRIX.spad" 1452638 1452656 1452980 1453007) (-966 "RMATCAT.spad" 1448288 1448318 1452606 1452633) (-965 "RMATCAT.spad" 1443816 1443848 1448136 1448141) (-964 "RLINSET.spad" 1443521 1443531 1443806 1443811) (-963 "RINTERP.spad" 1443410 1443429 1443511 1443516) (-962 "RING.spad" 1442881 1442889 1443390 1443405) (-961 "RING.spad" 1442360 1442370 1442871 1442876) (-960 "RIDIST.spad" 1441753 1441761 1442350 1442355) (-959 "RGCHAIN.spad" 1440010 1440025 1440903 1440918) (-958 "RGBCSPC.spad" 1439800 1439811 1440000 1440005) (-957 "RGBCMDL.spad" 1439363 1439374 1439790 1439795) (-956 "RFFACTOR.spad" 1438826 1438836 1439353 1439358) (-955 "RFFACT.spad" 1438562 1438573 1438816 1438821) (-954 "RFDIST.spad" 1437559 1437567 1438552 1438557) (-953 "RF.spad" 1435234 1435244 1437549 1437554) (-952 "RETSOL.spad" 1434654 1434666 1435224 1435229) (-951 "RETRACT.spad" 1434083 1434093 1434644 1434649) (-950 "RETRACT.spad" 1433510 1433522 1434073 1434078) (-949 "RETAST.spad" 1433323 1433331 1433500 1433505) (-948 "RESRING.spad" 1432671 1432717 1433261 1433318) (-947 "RESLATC.spad" 1431996 1432006 1432661 1432666) (-946 "REPSQ.spad" 1431728 1431738 1431986 1431991) (-945 "REPDB.spad" 1431436 1431446 1431718 1431723) (-944 "REP2.spad" 1421151 1421161 1431278 1431283) (-943 "REP1.spad" 1415372 1415382 1421101 1421106) (-942 "REP.spad" 1412927 1412935 1415362 1415367) (-941 "REGSET.spad" 1410604 1410620 1412412 1412427) (-940 "REF.spad" 1410123 1410133 1410594 1410599) (-939 "REDORDER.spad" 1409330 1409346 1410113 1410118) (-938 "RECLOS.spad" 1408227 1408246 1408930 1409023) (-937 "REALSOLV.spad" 1407368 1407376 1408217 1408222) (-936 "REAL0Q.spad" 1404667 1404681 1407358 1407363) (-935 "REAL0.spad" 1401512 1401526 1404657 1404662) (-934 "REAL.spad" 1401385 1401393 1401502 1401507) (-933 "RDUCEAST.spad" 1401107 1401115 1401375 1401380) (-932 "RDIV.spad" 1400763 1400787 1401097 1401102) (-931 "RDIST.spad" 1400331 1400341 1400753 1400758) (-930 "RDETRS.spad" 1399196 1399213 1400321 1400326) (-929 "RDETR.spad" 1397336 1397353 1399186 1399191) (-928 "RDEEFS.spad" 1396436 1396452 1397326 1397331) (-927 "RDEEF.spad" 1395447 1395463 1396426 1396431) (-926 "RCFIELD.spad" 1392666 1392674 1395349 1395442) (-925 "RCFIELD.spad" 1389971 1389981 1392656 1392661) (-924 "RCAGG.spad" 1387908 1387918 1389961 1389966) (-923 "RCAGG.spad" 1385774 1385786 1387829 1387834) (-922 "RATRET.spad" 1385135 1385145 1385764 1385769) (-921 "RATFACT.spad" 1384828 1384839 1385125 1385130) (-920 "RANDSRC.spad" 1384148 1384156 1384818 1384823) (-919 "RADUTIL.spad" 1383905 1383913 1384138 1384143) (-918 "RADIX.spad" 1380950 1380963 1382495 1382588) (-917 "RADFF.spad" 1378867 1378903 1378985 1379141) (-916 "RADCAT.spad" 1378463 1378471 1378857 1378862) (-915 "RADCAT.spad" 1378057 1378067 1378453 1378458) (-914 "QUEUE.spad" 1377483 1377493 1377741 1377756) (-913 "QUATCT2.spad" 1377104 1377122 1377473 1377478) (-912 "QUATCAT.spad" 1375275 1375285 1377034 1377099) (-911 "QUATCAT.spad" 1373211 1373223 1374972 1374977) (-910 "QUAT.spad" 1371818 1371828 1372160 1372225) (-909 "QUAGG.spad" 1370664 1370674 1371798 1371813) (-908 "QQUTAST.spad" 1370433 1370441 1370654 1370659) (-907 "QFORM.spad" 1370052 1370066 1370423 1370428) (-906 "QFCAT2.spad" 1369745 1369761 1370042 1370047) (-905 "QFCAT.spad" 1368448 1368458 1369647 1369740) (-904 "QFCAT.spad" 1366784 1366796 1367985 1367990) (-903 "QEQUAT.spad" 1366343 1366351 1366774 1366779) (-902 "QCMPACK.spad" 1361258 1361277 1366333 1366338) (-901 "QALGSET2.spad" 1359254 1359272 1361248 1361253) (-900 "QALGSET.spad" 1355359 1355391 1359168 1359173) (-899 "PWFFINTB.spad" 1352775 1352796 1355349 1355354) (-898 "PUSHVAR.spad" 1352114 1352133 1352765 1352770) (-897 "PTRANFN.spad" 1348250 1348260 1352104 1352109) (-896 "PTPACK.spad" 1345338 1345348 1348240 1348245) (-895 "PTFUNC2.spad" 1345161 1345175 1345328 1345333) (-894 "PTCAT.spad" 1344428 1344438 1345141 1345156) (-893 "PSQFR.spad" 1343743 1343767 1344418 1344423) (-892 "PSEUDLIN.spad" 1342629 1342639 1343733 1343738) (-891 "PSETPK.spad" 1329334 1329350 1342507 1342512) (-890 "PSETCAT.spad" 1323744 1323767 1329324 1329329) (-889 "PSETCAT.spad" 1318118 1318143 1323700 1323705) (-888 "PSCURVE.spad" 1317117 1317125 1318108 1318113) (-887 "PSCAT.spad" 1315900 1315929 1317015 1317112) (-886 "PSCAT.spad" 1314773 1314804 1315890 1315895) (-885 "PRTITION.spad" 1313471 1313479 1314763 1314768) (-884 "PRTDAST.spad" 1313190 1313198 1313461 1313466) (-883 "PRS.spad" 1302808 1302825 1313146 1313151) (-882 "PRQAGG.spad" 1302255 1302265 1302788 1302803) (-881 "PROPLOG.spad" 1301859 1301867 1302245 1302250) (-880 "PROPFUN2.spad" 1301482 1301495 1301849 1301854) (-879 "PROPFUN1.spad" 1300888 1300899 1301472 1301477) (-878 "PROPFRML.spad" 1299456 1299467 1300878 1300883) (-877 "PROPERTY.spad" 1298952 1298960 1299446 1299451) (-876 "PRODUCT.spad" 1296649 1296661 1296933 1296988) (-875 "PRINT.spad" 1296401 1296409 1296639 1296644) (-874 "PRIMES.spad" 1294662 1294672 1296391 1296396) (-873 "PRIMELT.spad" 1292783 1292797 1294652 1294657) (-872 "PRIMCAT.spad" 1292426 1292434 1292773 1292778) (-871 "PRIMARR2.spad" 1291193 1291205 1292416 1292421) (-870 "PRIMARR.spad" 1290099 1290109 1290269 1290284) (-869 "PREASSOC.spad" 1289481 1289493 1290089 1290094) (-868 "PR.spad" 1287999 1288011 1288698 1288825) (-867 "PPCURVE.spad" 1287136 1287144 1287989 1287994) (-866 "PORTNUM.spad" 1286927 1286935 1287126 1287131) (-865 "POLYROOT.spad" 1285776 1285798 1286883 1286888) (-864 "POLYLIFT.spad" 1285041 1285064 1285766 1285771) (-863 "POLYCATQ.spad" 1283167 1283189 1285031 1285036) (-862 "POLYCAT.spad" 1276669 1276690 1283035 1283162) (-861 "POLYCAT.spad" 1269691 1269714 1276059 1276064) (-860 "POLY2UP.spad" 1269143 1269157 1269681 1269686) (-859 "POLY2.spad" 1268740 1268752 1269133 1269138) (-858 "POLY.spad" 1266408 1266418 1266923 1267050) (-857 "POLUTIL.spad" 1265373 1265402 1266364 1266369) (-856 "POLTOPOL.spad" 1264121 1264136 1265363 1265368) (-855 "POINT.spad" 1262855 1262865 1262942 1262957) (-854 "PNTHEORY.spad" 1259557 1259565 1262845 1262850) (-853 "PMTOOLS.spad" 1258332 1258346 1259547 1259552) (-852 "PMSYM.spad" 1257881 1257891 1258322 1258327) (-851 "PMQFCAT.spad" 1257472 1257486 1257871 1257876) (-850 "PMPREDFS.spad" 1256934 1256956 1257462 1257467) (-849 "PMPRED.spad" 1256421 1256435 1256924 1256929) (-848 "PMPLCAT.spad" 1255498 1255516 1256350 1256355) (-847 "PMLSAGG.spad" 1255083 1255097 1255488 1255493) (-846 "PMKERNEL.spad" 1254662 1254674 1255073 1255078) (-845 "PMINS.spad" 1254242 1254252 1254652 1254657) (-844 "PMFS.spad" 1253819 1253837 1254232 1254237) (-843 "PMDOWN.spad" 1253109 1253123 1253809 1253814) (-842 "PMASSFS.spad" 1252084 1252100 1253099 1253104) (-841 "PMASS.spad" 1251102 1251110 1252074 1252079) (-840 "PLOTTOOL.spad" 1250882 1250890 1251092 1251097) (-839 "PLOT3D.spad" 1247346 1247354 1250872 1250877) (-838 "PLOT1.spad" 1246519 1246529 1247336 1247341) (-837 "PLOT.spad" 1241442 1241450 1246509 1246514) (-836 "PLEQN.spad" 1228844 1228871 1241432 1241437) (-835 "PINTERPA.spad" 1228628 1228644 1228834 1228839) (-834 "PINTERP.spad" 1228250 1228269 1228618 1228623) (-833 "PID.spad" 1227224 1227232 1228176 1228245) (-832 "PICOERCE.spad" 1226881 1226891 1227214 1227219) (-831 "PI.spad" 1226498 1226506 1226855 1226876) (-830 "PGROEB.spad" 1225107 1225121 1226488 1226493) (-829 "PGE.spad" 1216780 1216788 1225097 1225102) (-828 "PGCD.spad" 1215734 1215751 1216770 1216775) (-827 "PFRPAC.spad" 1214883 1214893 1215724 1215729) (-826 "PFR.spad" 1211586 1211596 1214785 1214878) (-825 "PFOTOOLS.spad" 1210844 1210860 1211576 1211581) (-824 "PFOQ.spad" 1210214 1210232 1210834 1210839) (-823 "PFO.spad" 1209633 1209660 1210204 1210209) (-822 "PFECAT.spad" 1207343 1207351 1209559 1209628) (-821 "PFECAT.spad" 1205081 1205091 1207299 1207304) (-820 "PFBRU.spad" 1202969 1202981 1205071 1205076) (-819 "PFBR.spad" 1200529 1200552 1202959 1202964) (-818 "PF.spad" 1200103 1200115 1200334 1200427) (-817 "PERMGRP.spad" 1194873 1194883 1200093 1200098) (-816 "PERMCAT.spad" 1193534 1193544 1194853 1194868) (-815 "PERMAN.spad" 1192090 1192104 1193524 1193529) (-814 "PERM.spad" 1187900 1187910 1191923 1191938) (-813 "PENDTREE.spad" 1187314 1187324 1187594 1187599) (-812 "PDSPC.spad" 1186127 1186137 1187304 1187309) (-811 "PDSPC.spad" 1184938 1184950 1186117 1186122) (-810 "PDRING.spad" 1184780 1184790 1184918 1184933) (-809 "PDMOD.spad" 1184596 1184608 1184748 1184775) (-808 "PDECOMP.spad" 1184066 1184083 1184586 1184591) (-807 "PDDOM.spad" 1183504 1183517 1184056 1184061) (-806 "PDDOM.spad" 1182940 1182955 1183494 1183499) (-805 "PCOMP.spad" 1182793 1182806 1182930 1182935) (-804 "PBWLB.spad" 1181391 1181408 1182783 1182788) (-803 "PATTERN2.spad" 1181129 1181141 1181381 1181386) (-802 "PATTERN1.spad" 1179473 1179489 1181119 1181124) (-801 "PATTERN.spad" 1174048 1174058 1179463 1179468) (-800 "PATRES2.spad" 1173720 1173734 1174038 1174043) (-799 "PATRES.spad" 1171303 1171315 1173710 1173715) (-798 "PATMATCH.spad" 1169544 1169575 1171055 1171060) (-797 "PATMAB.spad" 1168973 1168983 1169534 1169539) (-796 "PATLRES.spad" 1168059 1168073 1168963 1168968) (-795 "PATAB.spad" 1167823 1167833 1168049 1168054) (-794 "PARTPERM.spad" 1165879 1165887 1167813 1167818) (-793 "PARSURF.spad" 1165313 1165341 1165869 1165874) (-792 "PARSU2.spad" 1165110 1165126 1165303 1165308) (-791 "script-parser.spad" 1164630 1164638 1165100 1165105) (-790 "PARSCURV.spad" 1164064 1164092 1164620 1164625) (-789 "PARSC2.spad" 1163855 1163871 1164054 1164059) (-788 "PARPCURV.spad" 1163317 1163345 1163845 1163850) (-787 "PARPC2.spad" 1163108 1163124 1163307 1163312) (-786 "PARAMAST.spad" 1162236 1162244 1163098 1163103) (-785 "PAN2EXPR.spad" 1161648 1161656 1162226 1162231) (-784 "PALETTE.spad" 1160762 1160770 1161638 1161643) (-783 "PAIR.spad" 1159836 1159849 1160405 1160410) (-782 "PADICRC.spad" 1157241 1157259 1158404 1158497) (-781 "PADICRAT.spad" 1155301 1155313 1155514 1155607) (-780 "PADICCT.spad" 1153850 1153862 1155227 1155296) (-779 "PADIC.spad" 1153553 1153565 1153776 1153845) (-778 "PADEPAC.spad" 1152242 1152261 1153543 1153548) (-777 "PADE.spad" 1150994 1151010 1152232 1152237) (-776 "OWP.spad" 1150242 1150272 1150852 1150919) (-775 "OVERSET.spad" 1149815 1149823 1150232 1150237) (-774 "OVAR.spad" 1149596 1149619 1149805 1149810) (-773 "OUTFORM.spad" 1139004 1139012 1149586 1149591) (-772 "OUTBFILE.spad" 1138438 1138446 1138994 1138999) (-771 "OUTBCON.spad" 1137508 1137516 1138428 1138433) (-770 "OUTBCON.spad" 1136576 1136586 1137498 1137503) (-769 "OUT.spad" 1135694 1135702 1136566 1136571) (-768 "OSI.spad" 1135169 1135177 1135684 1135689) (-767 "OSGROUP.spad" 1135087 1135095 1135159 1135164) (-766 "ORTHPOL.spad" 1133598 1133608 1135030 1135035) (-765 "OREUP.spad" 1133092 1133120 1133319 1133358) (-764 "ORESUP.spad" 1132434 1132458 1132813 1132852) (-763 "OREPCTO.spad" 1130323 1130335 1132354 1132359) (-762 "OREPCAT.spad" 1124510 1124520 1130279 1130318) (-761 "OREPCAT.spad" 1118587 1118599 1124358 1124363) (-760 "ORDTYPE.spad" 1117824 1117832 1118577 1118582) (-759 "ORDTYPE.spad" 1117059 1117069 1117814 1117819) (-758 "ORDSTRCT.spad" 1116845 1116860 1117008 1117013) (-757 "ORDSET.spad" 1116545 1116553 1116835 1116840) (-756 "ORDRING.spad" 1116362 1116370 1116525 1116540) (-755 "ORDMON.spad" 1116217 1116225 1116352 1116357) (-754 "ORDFUNS.spad" 1115349 1115365 1116207 1116212) (-753 "ORDFIN.spad" 1115169 1115177 1115339 1115344) (-752 "ORDCOMP2.spad" 1114462 1114474 1115159 1115164) (-751 "ORDCOMP.spad" 1112988 1112998 1114070 1114099) (-750 "OPSIG.spad" 1112650 1112658 1112978 1112983) (-749 "OPQUERY.spad" 1112231 1112239 1112640 1112645) (-748 "OPERCAT.spad" 1111697 1111707 1112221 1112226) (-747 "OPERCAT.spad" 1111161 1111173 1111687 1111692) (-746 "OP.spad" 1110903 1110913 1110983 1111050) (-745 "ONECOMP2.spad" 1110327 1110339 1110893 1110898) (-744 "ONECOMP.spad" 1109133 1109143 1109935 1109964) (-743 "OMSAGG.spad" 1108933 1108943 1109101 1109128) (-742 "OMLO.spad" 1108366 1108378 1108819 1108858) (-741 "OINTDOM.spad" 1108129 1108137 1108292 1108361) (-740 "OFMONOID.spad" 1106268 1106278 1108085 1108090) (-739 "ODVAR.spad" 1105529 1105539 1106258 1106263) (-738 "ODR.spad" 1105173 1105199 1105341 1105490) (-737 "ODPOL.spad" 1102821 1102831 1103161 1103288) (-736 "ODP.spad" 1092369 1092389 1092742 1092827) (-735 "ODETOOLS.spad" 1091018 1091037 1092359 1092364) (-734 "ODESYS.spad" 1088712 1088729 1091008 1091013) (-733 "ODERTRIC.spad" 1084745 1084762 1088669 1088674) (-732 "ODERED.spad" 1084144 1084168 1084735 1084740) (-731 "ODERAT.spad" 1081777 1081794 1084134 1084139) (-730 "ODEPRRIC.spad" 1078870 1078892 1081767 1081772) (-729 "ODEPRIM.spad" 1076268 1076290 1078860 1078865) (-728 "ODEPAL.spad" 1075654 1075678 1076258 1076263) (-727 "ODEINT.spad" 1075089 1075105 1075644 1075649) (-726 "ODEEF.spad" 1070584 1070600 1075079 1075084) (-725 "ODECONST.spad" 1070129 1070147 1070574 1070579) (-724 "OCTCT2.spad" 1069770 1069788 1070119 1070124) (-723 "OCT.spad" 1068085 1068095 1068799 1068838) (-722 "OCAMON.spad" 1067933 1067941 1068075 1068080) (-721 "OC.spad" 1065729 1065739 1067889 1067928) (-720 "OC.spad" 1063264 1063276 1065426 1065431) (-719 "OASGP.spad" 1063079 1063087 1063254 1063259) (-718 "OAMONS.spad" 1062601 1062609 1063069 1063074) (-717 "OAMON.spad" 1062359 1062367 1062591 1062596) (-716 "OAMON.spad" 1062115 1062125 1062349 1062354) (-715 "OAGROUP.spad" 1061653 1061661 1062105 1062110) (-714 "OAGROUP.spad" 1061189 1061199 1061643 1061648) (-713 "NUMTUBE.spad" 1060780 1060796 1061179 1061184) (-712 "NUMQUAD.spad" 1048756 1048764 1060770 1060775) (-711 "NUMODE.spad" 1040108 1040116 1048746 1048751) (-710 "NUMFMT.spad" 1038948 1038956 1040098 1040103) (-709 "NUMERIC.spad" 1031063 1031073 1038754 1038759) (-708 "NTSCAT.spad" 1029583 1029599 1031043 1031058) (-707 "NTPOLFN.spad" 1029160 1029170 1029526 1029531) (-706 "NSUP2.spad" 1028552 1028564 1029150 1029155) (-705 "NSUP.spad" 1021989 1021999 1026409 1026562) (-704 "NSMP.spad" 1018901 1018920 1019193 1019320) (-703 "NREP.spad" 1017303 1017317 1018891 1018896) (-702 "NPCOEF.spad" 1016549 1016569 1017293 1017298) (-701 "NORMRETR.spad" 1016147 1016186 1016539 1016544) (-700 "NORMPK.spad" 1014089 1014108 1016137 1016142) (-699 "NORMMA.spad" 1013777 1013803 1014079 1014084) (-698 "NONE1.spad" 1013453 1013463 1013767 1013772) (-697 "NONE.spad" 1013194 1013202 1013443 1013448) (-696 "NODE1.spad" 1012681 1012697 1013184 1013189) (-695 "NNI.spad" 1011576 1011584 1012655 1012676) (-694 "NLINSOL.spad" 1010202 1010212 1011566 1011571) (-693 "NFINTBAS.spad" 1007762 1007779 1010192 1010197) (-692 "NETCLT.spad" 1007736 1007747 1007752 1007757) (-691 "NCODIV.spad" 1005960 1005976 1007726 1007731) (-690 "NCNTFRAC.spad" 1005602 1005616 1005950 1005955) (-689 "NCEP.spad" 1003768 1003782 1005592 1005597) (-688 "NASRING.spad" 1003372 1003380 1003758 1003763) (-687 "NASRING.spad" 1002974 1002984 1003362 1003367) (-686 "NARNG.spad" 1002374 1002382 1002964 1002969) (-685 "NARNG.spad" 1001772 1001782 1002364 1002369) (-684 "NAALG.spad" 1001337 1001347 1001740 1001767) (-683 "NAALG.spad" 1000922 1000934 1001327 1001332) (-682 "MULTSQFR.spad" 997880 997897 1000912 1000917) (-681 "MULTFACT.spad" 997263 997280 997870 997875) (-680 "MTSCAT.spad" 995357 995378 997161 997258) (-679 "MTHING.spad" 995016 995026 995347 995352) (-678 "MSYSCMD.spad" 994450 994458 995006 995011) (-677 "MSETAGG.spad" 994295 994305 994418 994445) (-676 "MSET.spad" 992093 992103 993840 993867) (-675 "MRING.spad" 989070 989082 991801 991868) (-674 "MRF2.spad" 988632 988646 989060 989065) (-673 "MRATFAC.spad" 988178 988195 988622 988627) (-672 "MPRFF.spad" 986218 986237 988168 988173) (-671 "MPOLY.spad" 984022 984037 984381 984508) (-670 "MPCPF.spad" 983286 983305 984012 984017) (-669 "MPC3.spad" 983103 983143 983276 983281) (-668 "MPC2.spad" 982757 982790 983093 983098) (-667 "MONOTOOL.spad" 981108 981125 982747 982752) (-666 "catdef.spad" 980541 980552 980762 981103) (-665 "catdef.spad" 979939 979950 980195 980536) (-664 "MONOID.spad" 979260 979268 979929 979934) (-663 "MONOID.spad" 978579 978589 979250 979255) (-662 "MONOGEN.spad" 977327 977340 978439 978574) (-661 "MONOGEN.spad" 976097 976112 977211 977216) (-660 "MONADWU.spad" 974177 974185 976087 976092) (-659 "MONADWU.spad" 972255 972265 974167 974172) (-658 "MONAD.spad" 971415 971423 972245 972250) (-657 "MONAD.spad" 970573 970583 971405 971410) (-656 "MOEBIUS.spad" 969309 969323 970553 970568) (-655 "MODULE.spad" 969179 969189 969277 969304) (-654 "MODULE.spad" 969069 969081 969169 969174) (-653 "MODRING.spad" 968404 968443 969049 969064) (-652 "MODOP.spad" 967061 967073 968226 968293) (-651 "MODMONOM.spad" 966792 966810 967051 967056) (-650 "MODMON.spad" 963862 963874 964577 964730) (-649 "MODFIELD.spad" 963224 963263 963764 963857) (-648 "MMLFORM.spad" 962084 962092 963214 963219) (-647 "MMAP.spad" 961826 961860 962074 962079) (-646 "MLO.spad" 960285 960295 961782 961821) (-645 "MLIFT.spad" 958897 958914 960275 960280) (-644 "MKUCFUNC.spad" 958432 958450 958887 958892) (-643 "MKRECORD.spad" 958020 958033 958422 958427) (-642 "MKFUNC.spad" 957427 957437 958010 958015) (-641 "MKFLCFN.spad" 956395 956405 957417 957422) (-640 "MKBCFUNC.spad" 955890 955908 956385 956390) (-639 "MHROWRED.spad" 954401 954411 955880 955885) (-638 "MFINFACT.spad" 953801 953823 954391 954396) (-637 "MESH.spad" 951596 951604 953791 953796) (-636 "MDDFACT.spad" 949815 949825 951586 951591) (-635 "MDAGG.spad" 949106 949116 949795 949810) (-634 "MCDEN.spad" 948316 948328 949096 949101) (-633 "MAYBE.spad" 947616 947627 948306 948311) (-632 "MATSTOR.spad" 944932 944942 947606 947611) (-631 "MATRIX.spad" 943723 943733 944207 944222) (-630 "MATLIN.spad" 941091 941115 943607 943612) (-629 "MATCAT2.spad" 940373 940421 941081 941086) (-628 "MATCAT.spad" 932081 932103 940353 940368) (-627 "MATCAT.spad" 923649 923673 931923 931928) (-626 "MAPPKG3.spad" 922564 922578 923639 923644) (-625 "MAPPKG2.spad" 921902 921914 922554 922559) (-624 "MAPPKG1.spad" 920730 920740 921892 921897) (-623 "MAPPAST.spad" 920069 920077 920720 920725) (-622 "MAPHACK3.spad" 919881 919895 920059 920064) (-621 "MAPHACK2.spad" 919650 919662 919871 919876) (-620 "MAPHACK1.spad" 919294 919304 919640 919645) (-619 "MAGMA.spad" 917100 917117 919284 919289) (-618 "MACROAST.spad" 916695 916703 917090 917095) (-617 "LZSTAGG.spad" 913949 913959 916685 916690) (-616 "LZSTAGG.spad" 911201 911213 913939 913944) (-615 "LWORD.spad" 907946 907963 911191 911196) (-614 "LSTAST.spad" 907730 907738 907936 907941) (-613 "LSQM.spad" 906020 906034 906414 906453) (-612 "LSPP.spad" 905555 905572 906010 906015) (-611 "LSMP1.spad" 903398 903412 905545 905550) (-610 "LSMP.spad" 902255 902283 903388 903393) (-609 "LSAGG.spad" 901936 901946 902235 902250) (-608 "LSAGG.spad" 901625 901637 901926 901931) (-607 "LPOLY.spad" 900587 900606 901481 901550) (-606 "LPEFRAC.spad" 899858 899868 900577 900582) (-605 "LOGIC.spad" 899460 899468 899848 899853) (-604 "LOGIC.spad" 899060 899070 899450 899455) (-603 "LODOOPS.spad" 897990 898002 899050 899055) (-602 "LODOF.spad" 897036 897053 897947 897952) (-601 "LODOCAT.spad" 895702 895712 896992 897031) (-600 "LODOCAT.spad" 894366 894378 895658 895663) (-599 "LODO2.spad" 893680 893692 894087 894126) (-598 "LODO1.spad" 893121 893131 893401 893440) (-597 "LODO.spad" 892546 892562 892842 892881) (-596 "LODEEF.spad" 891348 891366 892536 892541) (-595 "LO.spad" 890749 890763 891282 891309) (-594 "LNAGG.spad" 886936 886946 890739 890744) (-593 "LNAGG.spad" 883087 883099 886892 886897) (-592 "LMOPS.spad" 879855 879872 883077 883082) (-591 "LMODULE.spad" 879639 879649 879845 879850) (-590 "LMDICT.spad" 878871 878881 879119 879134) (-589 "LLINSET.spad" 878578 878588 878861 878866) (-588 "LITERAL.spad" 878484 878495 878568 878573) (-587 "LIST3.spad" 877795 877809 878474 878479) (-586 "LIST2MAP.spad" 874722 874734 877785 877790) (-585 "LIST2.spad" 873424 873436 874712 874717) (-584 "LIST.spad" 871157 871167 872500 872515) (-583 "LINSET.spad" 870936 870946 871147 871152) (-582 "LINFORM.spad" 870399 870411 870904 870931) (-581 "LINEXP.spad" 869142 869152 870389 870394) (-580 "LINELT.spad" 868513 868525 869025 869052) (-579 "LINDEP.spad" 867362 867374 868425 868430) (-578 "LINBASIS.spad" 866998 867013 867352 867357) (-577 "LIMITRF.spad" 864945 864955 866988 866993) (-576 "LIMITPS.spad" 863855 863868 864935 864940) (-575 "LIECAT.spad" 863339 863349 863781 863850) (-574 "LIECAT.spad" 862851 862863 863295 863300) (-573 "LIE.spad" 860855 860867 862129 862271) (-572 "LIB.spad" 858708 858716 859154 859169) (-571 "LGROBP.spad" 856061 856080 858698 858703) (-570 "LFCAT.spad" 855120 855128 856051 856056) (-569 "LF.spad" 854075 854091 855110 855115) (-568 "LEXTRIPK.spad" 849698 849713 854065 854070) (-567 "LEXP.spad" 847717 847744 849678 849693) (-566 "LETAST.spad" 847416 847424 847707 847712) (-565 "LEADCDET.spad" 845822 845839 847406 847411) (-564 "LAZM3PK.spad" 844566 844588 845812 845817) (-563 "LAUPOL.spad" 843233 843246 844133 844202) (-562 "LAPLACE.spad" 842816 842832 843223 843228) (-561 "LALG.spad" 842592 842602 842796 842811) (-560 "LALG.spad" 842376 842388 842582 842587) (-559 "LA.spad" 841816 841830 842298 842337) (-558 "KVTFROM.spad" 841559 841569 841806 841811) (-557 "KTVLOGIC.spad" 841103 841111 841549 841554) (-556 "KRCFROM.spad" 840849 840859 841093 841098) (-555 "KOVACIC.spad" 839580 839597 840839 840844) (-554 "KONVERT.spad" 839302 839312 839570 839575) (-553 "KOERCE.spad" 839039 839049 839292 839297) (-552 "KERNEL2.spad" 838742 838754 839029 839034) (-551 "KERNEL.spad" 837462 837472 838591 838596) (-550 "KDAGG.spad" 836571 836593 837442 837457) (-549 "KDAGG.spad" 835688 835712 836561 836566) (-548 "KAFILE.spad" 834115 834131 834350 834365) (-547 "JVMOP.spad" 834028 834036 834105 834110) (-546 "JVMMDACC.spad" 833082 833090 834018 834023) (-545 "JVMFDACC.spad" 832398 832406 833072 833077) (-544 "JVMCSTTG.spad" 831127 831135 832388 832393) (-543 "JVMCFACC.spad" 830573 830581 831117 831122) (-542 "JVMBCODE.spad" 830484 830492 830563 830568) (-541 "JORDAN.spad" 828301 828313 829762 829904) (-540 "JOINAST.spad" 828003 828011 828291 828296) (-539 "IXAGG.spad" 826136 826160 827993 827998) (-538 "IXAGG.spad" 824099 824125 825958 825963) (-537 "ITUPLE.spad" 823275 823285 824089 824094) (-536 "ITRIGMNP.spad" 822122 822141 823265 823270) (-535 "ITFUN3.spad" 821628 821642 822112 822117) (-534 "ITFUN2.spad" 821372 821384 821618 821623) (-533 "ITFORM.spad" 820727 820735 821362 821367) (-532 "ITAYLOR.spad" 818721 818736 820591 820688) (-531 "ISUPS.spad" 811170 811185 817707 817804) (-530 "ISUMP.spad" 810671 810687 811160 811165) (-529 "ISAST.spad" 810390 810398 810661 810666) (-528 "IRURPK.spad" 809107 809126 810380 810385) (-527 "IRSN.spad" 807111 807119 809097 809102) (-526 "IRRF2F.spad" 805604 805614 807067 807072) (-525 "IRREDFFX.spad" 805205 805216 805594 805599) (-524 "IROOT.spad" 803544 803554 805195 805200) (-523 "IRFORM.spad" 802868 802876 803534 803539) (-522 "IR2F.spad" 802082 802098 802858 802863) (-521 "IR2.spad" 801110 801126 802072 802077) (-520 "IR.spad" 798946 798960 800992 801019) (-519 "IPRNTPK.spad" 798706 798714 798936 798941) (-518 "IPF.spad" 798271 798283 798511 798604) (-517 "IPADIC.spad" 798040 798066 798197 798266) (-516 "IP4ADDR.spad" 797597 797605 798030 798035) (-515 "IOMODE.spad" 797119 797127 797587 797592) (-514 "IOBFILE.spad" 796504 796512 797109 797114) (-513 "IOBCON.spad" 796369 796377 796494 796499) (-512 "INVLAPLA.spad" 796018 796034 796359 796364) (-511 "INTTR.spad" 789412 789429 796008 796013) (-510 "INTTOOLS.spad" 787220 787236 789039 789044) (-509 "INTSLPE.spad" 786548 786556 787210 787215) (-508 "INTRVL.spad" 786114 786124 786462 786543) (-507 "INTRF.spad" 784546 784560 786104 786109) (-506 "INTRET.spad" 783978 783988 784536 784541) (-505 "INTRAT.spad" 782713 782730 783968 783973) (-504 "INTPM.spad" 781176 781192 782434 782439) (-503 "INTPAF.spad" 779052 779070 781105 781110) (-502 "INTHERTR.spad" 778326 778343 779042 779047) (-501 "INTHERAL.spad" 777996 778020 778316 778321) (-500 "INTHEORY.spad" 774435 774443 777986 777991) (-499 "INTG0.spad" 768199 768217 774364 774369) (-498 "INTFACT.spad" 767266 767276 768189 768194) (-497 "INTEF.spad" 765677 765693 767256 767261) (-496 "INTDOM.spad" 764300 764308 765603 765672) (-495 "INTDOM.spad" 762985 762995 764290 764295) (-494 "INTCAT.spad" 761252 761262 762899 762980) (-493 "INTBIT.spad" 760759 760767 761242 761247) (-492 "INTALG.spad" 759947 759974 760749 760754) (-491 "INTAF.spad" 759447 759463 759937 759942) (-490 "INTABL.spad" 757315 757346 757478 757493) (-489 "INT8.spad" 757195 757203 757305 757310) (-488 "INT64.spad" 757074 757082 757185 757190) (-487 "INT32.spad" 756953 756961 757064 757069) (-486 "INT16.spad" 756832 756840 756943 756948) (-485 "INT.spad" 756358 756366 756698 756827) (-484 "INS.spad" 753861 753869 756260 756353) (-483 "INS.spad" 751450 751460 753851 753856) (-482 "INPSIGN.spad" 750920 750933 751440 751445) (-481 "INPRODPF.spad" 750016 750035 750910 750915) (-480 "INPRODFF.spad" 749104 749128 750006 750011) (-479 "INNMFACT.spad" 748079 748096 749094 749099) (-478 "INMODGCD.spad" 747583 747613 748069 748074) (-477 "INFSP.spad" 745880 745902 747573 747578) (-476 "INFPROD0.spad" 744960 744979 745870 745875) (-475 "INFORM1.spad" 744585 744595 744950 744955) (-474 "INFORM.spad" 741796 741804 744575 744580) (-473 "INFINITY.spad" 741348 741356 741786 741791) (-472 "INETCLTS.spad" 741325 741333 741338 741343) (-471 "INEP.spad" 739871 739893 741315 741320) (-470 "INDE.spad" 739520 739537 739781 739786) (-469 "INCRMAPS.spad" 738957 738967 739510 739515) (-468 "INBFILE.spad" 738053 738061 738947 738952) (-467 "INBFF.spad" 733903 733914 738043 738048) (-466 "INBCON.spad" 732169 732177 733893 733898) (-465 "INBCON.spad" 730433 730443 732159 732164) (-464 "INAST.spad" 730094 730102 730423 730428) (-463 "IMPTAST.spad" 729802 729810 730084 730089) (-462 "IMATQF.spad" 728896 728940 729758 729763) (-461 "IMATLIN.spad" 727517 727541 728852 728857) (-460 "IFF.spad" 726930 726946 727201 727294) (-459 "IFAST.spad" 726544 726552 726920 726925) (-458 "IFARRAY.spad" 723922 723937 725620 725635) (-457 "IFAMON.spad" 723784 723801 723878 723883) (-456 "IEVALAB.spad" 723197 723209 723774 723779) (-455 "IEVALAB.spad" 722608 722622 723187 723192) (-454 "indexedp.spad" 722164 722176 722598 722603) (-453 "IDPOAMS.spad" 721842 721854 722076 722081) (-452 "IDPOAM.spad" 721484 721496 721754 721759) (-451 "IDPO.spad" 720898 720910 721396 721401) (-450 "IDPC.spad" 719613 719625 720888 720893) (-449 "IDPAM.spad" 719280 719292 719525 719530) (-448 "IDPAG.spad" 718949 718961 719192 719197) (-447 "IDENT.spad" 718601 718609 718939 718944) (-446 "catdef.spad" 718372 718383 718484 718596) (-445 "IDECOMP.spad" 715611 715629 718362 718367) (-444 "IDEAL.spad" 710573 710612 715559 715564) (-443 "ICDEN.spad" 709786 709802 710563 710568) (-442 "ICARD.spad" 709179 709187 709776 709781) (-441 "IBPTOOLS.spad" 707786 707803 709169 709174) (-440 "boolean.spad" 707191 707204 707324 707339) (-439 "IBATOOL.spad" 704176 704195 707181 707186) (-438 "IBACHIN.spad" 702683 702698 704166 704171) (-437 "array2.spad" 702180 702202 702367 702382) (-436 "IARRAY1.spad" 701110 701125 701256 701271) (-435 "IAN.spad" 699492 699500 700941 701034) (-434 "IALGFACT.spad" 699103 699136 699482 699487) (-433 "HYPCAT.spad" 698527 698535 699093 699098) (-432 "HYPCAT.spad" 697949 697959 698517 698522) (-431 "HOSTNAME.spad" 697765 697773 697939 697944) (-430 "HOMOTOP.spad" 697508 697518 697755 697760) (-429 "HOAGG.spad" 695115 695125 697498 697503) (-428 "HOAGG.spad" 692472 692484 694857 694862) (-427 "HEXADEC.spad" 690697 690705 691062 691155) (-426 "HEUGCD.spad" 689788 689799 690687 690692) (-425 "HELLFDIV.spad" 689394 689418 689778 689783) (-424 "HEAP.spad" 688863 688873 689078 689093) (-423 "HEADAST.spad" 688404 688412 688853 688858) (-422 "HDP.spad" 677948 677964 678325 678410) (-421 "HDMP.spad" 675495 675510 676111 676238) (-420 "HB.spad" 673770 673778 675485 675490) (-419 "HASHTBL.spad" 671590 671621 671801 671816) (-418 "HASAST.spad" 671306 671314 671580 671585) (-417 "HACKPI.spad" 670797 670805 671208 671301) (-416 "GTSET.spad" 669575 669591 670282 670297) (-415 "GSTBL.spad" 667432 667467 667606 667621) (-414 "GSERIES.spad" 664804 664831 665623 665772) (-413 "GROUP.spad" 664077 664085 664784 664799) (-412 "GROUP.spad" 663358 663368 664067 664072) (-411 "GROEBSOL.spad" 661852 661873 663348 663353) (-410 "GRMOD.spad" 660433 660445 661842 661847) (-409 "GRMOD.spad" 659012 659026 660423 660428) (-408 "GRIMAGE.spad" 651925 651933 659002 659007) (-407 "GRDEF.spad" 650304 650312 651915 651920) (-406 "GRAY.spad" 648775 648783 650294 650299) (-405 "GRALG.spad" 647870 647882 648765 648770) (-404 "GRALG.spad" 646963 646977 647860 647865) (-403 "GPOLSET.spad" 646272 646295 646484 646499) (-402 "GOSPER.spad" 645549 645567 646262 646267) (-401 "GMODPOL.spad" 644697 644724 645517 645544) (-400 "GHENSEL.spad" 643780 643794 644687 644692) (-399 "GENUPS.spad" 640073 640086 643770 643775) (-398 "GENUFACT.spad" 639650 639660 640063 640068) (-397 "GENPGCD.spad" 639252 639269 639640 639645) (-396 "GENMFACT.spad" 638704 638723 639242 639247) (-395 "GENEEZ.spad" 636663 636676 638694 638699) (-394 "GDMP.spad" 634052 634069 634826 634953) (-393 "GCNAALG.spad" 627975 628002 633846 633913) (-392 "GCDDOM.spad" 627167 627175 627901 627970) (-391 "GCDDOM.spad" 626421 626431 627157 627162) (-390 "GBINTERN.spad" 622441 622479 626411 626416) (-389 "GBF.spad" 618224 618262 622431 622436) (-388 "GBEUCLID.spad" 616106 616144 618214 618219) (-387 "GB.spad" 613632 613670 616062 616067) (-386 "GAUSSFAC.spad" 612945 612953 613622 613627) (-385 "GALUTIL.spad" 611271 611281 612901 612906) (-384 "GALPOLYU.spad" 609725 609738 611261 611266) (-383 "GALFACTU.spad" 607938 607957 609715 609720) (-382 "GALFACT.spad" 598151 598162 607928 607933) (-381 "FUNDESC.spad" 597829 597837 598141 598146) (-380 "FUNCTION.spad" 597678 597690 597819 597824) (-379 "FT.spad" 595978 595986 597668 597673) (-378 "FSUPFACT.spad" 594892 594911 595928 595933) (-377 "FST.spad" 592978 592986 594882 594887) (-376 "FSRED.spad" 592458 592474 592968 592973) (-375 "FSPRMELT.spad" 591324 591340 592415 592420) (-374 "FSPECF.spad" 589415 589431 591314 591319) (-373 "FSINT.spad" 589075 589091 589405 589410) (-372 "FSERIES.spad" 588266 588278 588895 588994) (-371 "FSCINT.spad" 587583 587599 588256 588261) (-370 "FSAGG2.spad" 586318 586334 587573 587578) (-369 "FSAGG.spad" 585447 585457 586286 586313) (-368 "FSAGG.spad" 584526 584538 585367 585372) (-367 "FS2UPS.spad" 579041 579075 584516 584521) (-366 "FS2EXPXP.spad" 578182 578205 579031 579036) (-365 "FS2.spad" 577837 577853 578172 578177) (-364 "FS.spad" 572109 572119 577616 577832) (-363 "FS.spad" 566183 566195 571692 571697) (-362 "FRUTIL.spad" 565137 565147 566173 566178) (-361 "FRNAALG.spad" 560414 560424 565079 565132) (-360 "FRNAALG.spad" 555703 555715 560370 560375) (-359 "FRNAAF2.spad" 555151 555169 555693 555698) (-358 "FRMOD.spad" 554559 554589 555080 555085) (-357 "FRIDEAL2.spad" 554163 554195 554549 554554) (-356 "FRIDEAL.spad" 553388 553409 554143 554158) (-355 "FRETRCT.spad" 552907 552917 553378 553383) (-354 "FRETRCT.spad" 552333 552345 552806 552811) (-353 "FRAMALG.spad" 550713 550726 552289 552328) (-352 "FRAMALG.spad" 549125 549140 550703 550708) (-351 "FRAC2.spad" 548730 548742 549115 549120) (-350 "FRAC.spad" 546717 546727 547104 547277) (-349 "FR2.spad" 546053 546065 546707 546712) (-348 "FR.spad" 539841 539851 545114 545183) (-347 "FPS.spad" 536680 536688 539731 539836) (-346 "FPS.spad" 533547 533557 536600 536605) (-345 "FPC.spad" 532593 532601 533449 533542) (-344 "FPC.spad" 531725 531735 532583 532588) (-343 "FPATMAB.spad" 531487 531497 531715 531720) (-342 "FPARFRAC.spad" 530329 530346 531477 531482) (-341 "FORDER.spad" 530020 530044 530319 530324) (-340 "FNLA.spad" 529444 529466 529988 530015) (-339 "FNCAT.spad" 528039 528047 529434 529439) (-338 "FNAME.spad" 527931 527939 528029 528034) (-337 "FMONOID.spad" 527612 527622 527887 527892) (-336 "FMONCAT.spad" 524781 524791 527602 527607) (-335 "FMCAT.spad" 522457 522475 524749 524776) (-334 "FM1.spad" 521822 521834 522391 522418) (-333 "FM.spad" 521437 521449 521676 521703) (-332 "FLOATRP.spad" 519180 519194 521427 521432) (-331 "FLOATCP.spad" 516619 516633 519170 519175) (-330 "FLOAT.spad" 513710 513718 516485 516614) (-329 "FLINEXP.spad" 513432 513442 513700 513705) (-328 "FLINEXP.spad" 513111 513123 513381 513386) (-327 "FLASORT.spad" 512437 512449 513101 513106) (-326 "FLALG.spad" 510107 510126 512363 512432) (-325 "FLAGG2.spad" 508824 508840 510097 510102) (-324 "FLAGG.spad" 505900 505910 508814 508819) (-323 "FLAGG.spad" 502869 502881 505785 505790) (-322 "FINRALG.spad" 500954 500967 502825 502864) (-321 "FINRALG.spad" 498965 498980 500838 500843) (-320 "FINITE.spad" 498117 498125 498955 498960) (-319 "FINITE.spad" 497267 497277 498107 498112) (-318 "aggcat.spad" 494197 494207 497257 497262) (-317 "FINAGG.spad" 491092 491104 494154 494159) (-316 "FINAALG.spad" 480277 480287 491034 491087) (-315 "FINAALG.spad" 469474 469486 480233 480238) (-314 "FILECAT.spad" 468008 468025 469464 469469) (-313 "FILE.spad" 467591 467601 467998 468003) (-312 "FIELD.spad" 466997 467005 467493 467586) (-311 "FIELD.spad" 466489 466499 466987 466992) (-310 "FGROUP.spad" 465152 465162 466469 466484) (-309 "FGLMICPK.spad" 463947 463962 465142 465147) (-308 "FFX.spad" 463333 463348 463666 463759) (-307 "FFSLPE.spad" 462844 462865 463323 463328) (-306 "FFPOLY2.spad" 461904 461921 462834 462839) (-305 "FFPOLY.spad" 453246 453257 461894 461899) (-304 "FFP.spad" 452654 452674 452965 453058) (-303 "FFNBX.spad" 451177 451197 452373 452466) (-302 "FFNBP.spad" 449701 449718 450896 450989) (-301 "FFNB.spad" 448169 448190 449385 449478) (-300 "FFINTBAS.spad" 445683 445702 448159 448164) (-299 "FFIELDC.spad" 443268 443276 445585 445678) (-298 "FFIELDC.spad" 440939 440949 443258 443263) (-297 "FFHOM.spad" 439711 439728 440929 440934) (-296 "FFF.spad" 437154 437165 439701 439706) (-295 "FFCGX.spad" 436012 436032 436873 436966) (-294 "FFCGP.spad" 434912 434932 435731 435824) (-293 "FFCG.spad" 433707 433728 434596 434689) (-292 "FFCAT2.spad" 433454 433494 433697 433702) (-291 "FFCAT.spad" 426619 426641 433293 433449) (-290 "FFCAT.spad" 419863 419887 426539 426544) (-289 "FF.spad" 419314 419330 419547 419640) (-288 "FEVALAB.spad" 419022 419032 419304 419309) (-287 "FEVALAB.spad" 418506 418518 418790 418795) (-286 "FDIVCAT.spad" 416602 416626 418496 418501) (-285 "FDIVCAT.spad" 414696 414722 416592 416597) (-284 "FDIV2.spad" 414352 414392 414686 414691) (-283 "FDIV.spad" 413810 413834 414342 414347) (-282 "FCTRDATA.spad" 412818 412826 413800 413805) (-281 "FCOMP.spad" 412197 412207 412808 412813) (-280 "FAXF.spad" 405232 405246 412099 412192) (-279 "FAXF.spad" 398319 398335 405188 405193) (-278 "FARRAY.spad" 396362 396372 397395 397410) (-277 "FAMR.spad" 394506 394518 396260 396357) (-276 "FAMR.spad" 392634 392648 394390 394395) (-275 "FAMONOID.spad" 392318 392328 392588 392593) (-274 "FAMONC.spad" 390638 390650 392308 392313) (-273 "FAGROUP.spad" 390278 390288 390534 390561) (-272 "FACUTIL.spad" 388490 388507 390268 390273) (-271 "FACTFUNC.spad" 387692 387702 388480 388485) (-270 "EXPUPXS.spad" 384584 384607 385883 386032) (-269 "EXPRTUBE.spad" 381872 381880 384574 384579) (-268 "EXPRODE.spad" 379040 379056 381862 381867) (-267 "EXPR2UPS.spad" 375162 375175 379030 379035) (-266 "EXPR2.spad" 374867 374879 375152 375157) (-265 "EXPR.spad" 370512 370522 371226 371513) (-264 "EXPEXPAN.spad" 367457 367482 368089 368182) (-263 "EXITAST.spad" 367193 367201 367447 367452) (-262 "EXIT.spad" 366864 366872 367183 367188) (-261 "EVALCYC.spad" 366324 366338 366854 366859) (-260 "EVALAB.spad" 365904 365914 366314 366319) (-259 "EVALAB.spad" 365482 365494 365894 365899) (-258 "EUCDOM.spad" 363072 363080 365408 365477) (-257 "EUCDOM.spad" 360724 360734 363062 363067) (-256 "ES2.spad" 360237 360253 360714 360719) (-255 "ES1.spad" 359807 359823 360227 360232) (-254 "ES.spad" 352678 352686 359797 359802) (-253 "ES.spad" 345470 345480 352591 352596) (-252 "ERROR.spad" 342797 342805 345460 345465) (-251 "EQTBL.spad" 340619 340641 340828 340843) (-250 "EQ2.spad" 340337 340349 340609 340614) (-249 "EQ.spad" 335243 335253 338038 338144) (-248 "EP.spad" 331569 331579 335233 335238) (-247 "ENV.spad" 330247 330255 331559 331564) (-246 "ENTIRER.spad" 329915 329923 330191 330242) (-245 "ENTIRER.spad" 329627 329637 329905 329910) (-244 "EMR.spad" 328915 328956 329553 329622) (-243 "ELTAGG.spad" 327169 327188 328905 328910) (-242 "ELTAGG.spad" 325387 325408 327125 327130) (-241 "ELTAB.spad" 324862 324875 325377 325382) (-240 "ELFUTS.spad" 324297 324316 324852 324857) (-239 "ELEMFUN.spad" 323986 323994 324287 324292) (-238 "ELEMFUN.spad" 323673 323683 323976 323981) (-237 "ELAGG.spad" 321644 321654 323653 323668) (-236 "ELAGG.spad" 319554 319566 321565 321570) (-235 "ELABOR.spad" 318900 318908 319544 319549) (-234 "ELABEXPR.spad" 317832 317840 318890 318895) (-233 "EFUPXS.spad" 314608 314638 317788 317793) (-232 "EFULS.spad" 311444 311467 314564 314569) (-231 "EFSTRUC.spad" 309459 309475 311434 311439) (-230 "EF.spad" 304235 304251 309449 309454) (-229 "EAB.spad" 302535 302543 304225 304230) (-228 "DVARCAT.spad" 299541 299551 302525 302530) (-227 "DVARCAT.spad" 296545 296557 299531 299536) (-226 "DSMP.spad" 294278 294292 294583 294710) (-225 "DSEXT.spad" 293580 293590 294268 294273) (-224 "DSEXT.spad" 292802 292814 293492 293497) (-223 "DROPT1.spad" 292467 292477 292792 292797) (-222 "DROPT0.spad" 287332 287340 292457 292462) (-221 "DROPT.spad" 281291 281299 287322 287327) (-220 "DRAWPT.spad" 279464 279472 281281 281286) (-219 "DRAWHACK.spad" 278772 278782 279454 279459) (-218 "DRAWCX.spad" 276250 276258 278762 278767) (-217 "DRAWCURV.spad" 275797 275812 276240 276245) (-216 "DRAWCFUN.spad" 265329 265337 275787 275792) (-215 "DRAW.spad" 258205 258218 265319 265324) (-214 "DQAGG.spad" 256395 256405 258185 258200) (-213 "DPOLCAT.spad" 251752 251768 256263 256390) (-212 "DPOLCAT.spad" 247195 247213 251708 251713) (-211 "DPMO.spad" 239809 239825 239947 240141) (-210 "DPMM.spad" 232436 232454 232561 232755) (-209 "DOMTMPLT.spad" 232207 232215 232426 232431) (-208 "DOMCTOR.spad" 231962 231970 232197 232202) (-207 "DOMAIN.spad" 231073 231081 231952 231957) (-206 "DMP.spad" 228666 228681 229236 229363) (-205 "DMEXT.spad" 228533 228543 228634 228661) (-204 "DLP.spad" 227893 227903 228523 228528) (-203 "DLIST.spad" 226365 226375 226969 226984) (-202 "DLAGG.spad" 224782 224792 226355 226360) (-201 "DIVRING.spad" 224324 224332 224726 224777) (-200 "DIVRING.spad" 223910 223920 224314 224319) (-199 "DISPLAY.spad" 222100 222108 223900 223905) (-198 "DIRPROD2.spad" 220918 220936 222090 222095) (-197 "DIRPROD.spad" 210199 210215 210839 210924) (-196 "DIRPCAT.spad" 209494 209510 210109 210194) (-195 "DIRPCAT.spad" 208403 208421 209020 209025) (-194 "DIOSP.spad" 207228 207236 208393 208398) (-193 "DIOPS.spad" 206224 206234 207208 207223) (-192 "DIOPS.spad" 205167 205179 206153 206158) (-191 "catdef.spad" 205025 205033 205157 205162) (-190 "DIFRING.spad" 204863 204871 205005 205020) (-189 "DIFFSPC.spad" 204442 204450 204853 204858) (-188 "DIFFSPC.spad" 204019 204029 204432 204437) (-187 "DIFFMOD.spad" 203508 203518 203987 204014) (-186 "DIFFDOM.spad" 202673 202684 203498 203503) (-185 "DIFFDOM.spad" 201836 201849 202663 202668) (-184 "DIFEXT.spad" 201655 201665 201816 201831) (-183 "DIAGG.spad" 201285 201295 201635 201650) (-182 "DIAGG.spad" 200923 200935 201275 201280) (-181 "DHMATRIX.spad" 199312 199322 200457 200472) (-180 "DFSFUN.spad" 192952 192960 199302 199307) (-179 "DFLOAT.spad" 189559 189567 192842 192947) (-178 "DFINTTLS.spad" 187790 187806 189549 189554) (-177 "DERHAM.spad" 185704 185736 187770 187785) (-176 "DEQUEUE.spad" 185105 185115 185388 185403) (-175 "DEGRED.spad" 184722 184736 185095 185100) (-174 "DEFINTRF.spad" 182304 182314 184712 184717) (-173 "DEFINTEF.spad" 180842 180858 182294 182299) (-172 "DEFAST.spad" 180226 180234 180832 180837) (-171 "DECIMAL.spad" 178455 178463 178816 178909) (-170 "DDFACT.spad" 176276 176293 178445 178450) (-169 "DBLRESP.spad" 175876 175900 176266 176271) (-168 "DBASIS.spad" 175502 175517 175866 175871) (-167 "DBASE.spad" 174166 174176 175492 175497) (-166 "DATAARY.spad" 173652 173665 174156 174161) (-165 "CYCLOTOM.spad" 173158 173166 173642 173647) (-164 "CYCLES.spad" 169950 169958 173148 173153) (-163 "CVMP.spad" 169367 169377 169940 169945) (-162 "CTRIGMNP.spad" 167867 167883 169357 169362) (-161 "CTORKIND.spad" 167470 167478 167857 167862) (-160 "CTORCAT.spad" 166711 166719 167460 167465) (-159 "CTORCAT.spad" 165950 165960 166701 166706) (-158 "CTORCALL.spad" 165539 165549 165940 165945) (-157 "CTOR.spad" 165230 165238 165529 165534) (-156 "CSTTOOLS.spad" 164475 164488 165220 165225) (-155 "CRFP.spad" 158247 158260 164465 164470) (-154 "CRCEAST.spad" 157967 157975 158237 158242) (-153 "CRAPACK.spad" 157034 157044 157957 157962) (-152 "CPMATCH.spad" 156535 156550 156956 156961) (-151 "CPIMA.spad" 156240 156259 156525 156530) (-150 "COORDSYS.spad" 151249 151259 156230 156235) (-149 "CONTOUR.spad" 150676 150684 151239 151244) (-148 "CONTFRAC.spad" 146426 146436 150578 150671) (-147 "CONDUIT.spad" 146184 146192 146416 146421) (-146 "COMRING.spad" 145858 145866 146122 146179) (-145 "COMPPROP.spad" 145376 145384 145848 145853) (-144 "COMPLPAT.spad" 145143 145158 145366 145371) (-143 "COMPLEX2.spad" 144858 144870 145133 145138) (-142 "COMPLEX.spad" 140564 140574 140808 141066) (-141 "COMPILER.spad" 140113 140121 140554 140559) (-140 "COMPFACT.spad" 139715 139729 140103 140108) (-139 "COMPCAT.spad" 137790 137800 139452 139710) (-138 "COMPCAT.spad" 135606 135618 137270 137275) (-137 "COMMUPC.spad" 135354 135372 135596 135601) (-136 "COMMONOP.spad" 134887 134895 135344 135349) (-135 "COMMAAST.spad" 134650 134658 134877 134882) (-134 "COMM.spad" 134461 134469 134640 134645) (-133 "COMBOPC.spad" 133384 133392 134451 134456) (-132 "COMBINAT.spad" 132151 132161 133374 133379) (-131 "COMBF.spad" 129573 129589 132141 132146) (-130 "COLOR.spad" 128410 128418 129563 129568) (-129 "COLONAST.spad" 128076 128084 128400 128405) (-128 "CMPLXRT.spad" 127787 127804 128066 128071) (-127 "CLLCTAST.spad" 127449 127457 127777 127782) (-126 "CLIP.spad" 123557 123565 127439 127444) (-125 "CLIF.spad" 122212 122228 123513 123552) (-124 "CLAGG.spad" 120204 120214 122202 122207) (-123 "CLAGG.spad" 118055 118067 120055 120060) (-122 "CINTSLPE.spad" 117410 117423 118045 118050) (-121 "CHVAR.spad" 115548 115570 117400 117405) (-120 "CHARZ.spad" 115463 115471 115528 115543) (-119 "CHARPOL.spad" 114989 114999 115453 115458) (-118 "CHARNZ.spad" 114751 114759 114969 114984) (-117 "CHAR.spad" 112119 112127 114741 114746) (-116 "CFCAT.spad" 111447 111455 112109 112114) (-115 "CDEN.spad" 110667 110681 111437 111442) (-114 "CCLASS.spad" 108736 108744 109998 110025) (-113 "CATEGORY.spad" 107810 107818 108726 108731) (-112 "CATCTOR.spad" 107701 107709 107800 107805) (-111 "CATAST.spad" 107327 107335 107691 107696) (-110 "CASEAST.spad" 107041 107049 107317 107322) (-109 "CARTEN2.spad" 106431 106458 107031 107036) (-108 "CARTEN.spad" 102183 102207 106421 106426) (-107 "CARD.spad" 99478 99486 102157 102178) (-106 "CAPSLAST.spad" 99260 99268 99468 99473) (-105 "CACHSET.spad" 98884 98892 99250 99255) (-104 "CABMON.spad" 98439 98447 98874 98879) (-103 "BYTEORD.spad" 98114 98122 98429 98434) (-102 "BYTEBUF.spad" 96050 96058 97256 97271) (-101 "BYTE.spad" 95525 95533 96040 96045) (-100 "BTREE.spad" 94675 94685 95209 95224) (-99 "BTOURN.spad" 93758 93767 94359 94374) (-98 "BTCAT.spad" 93328 93337 93738 93753) (-97 "BTCAT.spad" 92906 92917 93318 93323) (-96 "BTAGG.spad" 92385 92392 92886 92901) (-95 "BTAGG.spad" 91872 91881 92375 92380) (-94 "BSTREE.spad" 90691 90700 91556 91571) (-93 "BRILL.spad" 88897 88907 90681 90686) (-92 "BRAGG.spad" 87854 87863 88887 88892) (-91 "BRAGG.spad" 86775 86786 87810 87815) (-90 "BPADICRT.spad" 84835 84846 85081 85174) (-89 "BPADIC.spad" 84508 84519 84761 84830) (-88 "BOUNDZRO.spad" 84165 84181 84498 84503) (-87 "BOP1.spad" 81624 81633 84155 84160) (-86 "BOP.spad" 76767 76774 81614 81619) (-85 "BOOLEAN.spad" 76316 76323 76757 76762) (-84 "BOOLE.spad" 75967 75974 76306 76311) (-83 "BOOLE.spad" 75616 75625 75957 75962) (-82 "BMODULE.spad" 75329 75340 75584 75611) (-81 "BITS.spad" 74653 74660 74867 74882) (-80 "catdef.spad" 74536 74546 74643 74648) (-79 "catdef.spad" 74287 74297 74526 74531) (-78 "BINDING.spad" 73709 73716 74277 74282) (-77 "BINARY.spad" 71944 71951 72299 72392) (-76 "BGAGG.spad" 71264 71273 71924 71939) (-75 "BGAGG.spad" 70592 70603 71254 71259) (-74 "BEZOUT.spad" 69733 69759 70542 70547) (-73 "BBTREE.spad" 66688 66697 69417 69432) (-72 "BASTYPE.spad" 66188 66195 66678 66683) (-71 "BASTYPE.spad" 65686 65695 66178 66183) (-70 "BALFACT.spad" 65146 65158 65676 65681) (-69 "AUTOMOR.spad" 64597 64606 65126 65141) (-68 "ATTREG.spad" 61729 61736 64373 64592) (-67 "ATTRAST.spad" 61446 61453 61719 61724) (-66 "ATRIG.spad" 60916 60923 61436 61441) (-65 "ATRIG.spad" 60384 60393 60906 60911) (-64 "ASTCAT.spad" 60288 60295 60374 60379) (-63 "ASTCAT.spad" 60190 60199 60278 60283) (-62 "ASTACK.spad" 59606 59615 59874 59889) (-61 "ASSOCEQ.spad" 58440 58451 59562 59567) (-60 "ARRAY2.spad" 57975 57984 58124 58139) (-59 "ARRAY12.spad" 56688 56699 57965 57970) (-58 "ARRAY1.spad" 55418 55427 55764 55779) (-57 "ARR2CAT.spad" 51470 51491 55398 55413) (-56 "ARR2CAT.spad" 47530 47553 51460 51465) (-55 "ARITY.spad" 46902 46909 47520 47525) (-54 "APPRULE.spad" 46186 46208 46892 46897) (-53 "APPLYORE.spad" 45805 45818 46176 46181) (-52 "ANY1.spad" 44876 44885 45795 45800) (-51 "ANY.spad" 43727 43734 44866 44871) (-50 "ANTISYM.spad" 42172 42188 43707 43722) (-49 "ANON.spad" 41881 41888 42162 42167) (-48 "AN.spad" 40349 40356 41712 41805) (-47 "AMR.spad" 38534 38545 40247 40344) (-46 "AMR.spad" 36582 36595 38297 38302) (-45 "ALIST.spad" 33306 33327 33656 33671) (-44 "ALGSC.spad" 32441 32467 33178 33231) (-43 "ALGPKG.spad" 28224 28235 32397 32402) (-42 "ALGMFACT.spad" 27417 27431 28214 28219) (-41 "ALGMANIP.spad" 24918 24933 27261 27266) (-40 "ALGFF.spad" 22736 22763 22953 23109) (-39 "ALGFACT.spad" 21855 21865 22726 22731) (-38 "ALGEBRA.spad" 21688 21697 21811 21850) (-37 "ALGEBRA.spad" 21553 21564 21678 21683) (-36 "ALAGG.spad" 21081 21102 21533 21548) (-35 "AHYP.spad" 20462 20469 21071 21076) (-34 "AGG.spad" 19276 19283 20452 20457) (-33 "AGG.spad" 18054 18063 19232 19237) (-32 "AF.spad" 16499 16514 18003 18008) (-31 "ADDAST.spad" 16185 16192 16489 16494) (-30 "ACPLOT.spad" 15062 15069 16175 16180) (-29 "ACFS.spad" 12919 12928 14964 15057) (-28 "ACFS.spad" 10862 10873 12909 12914) (-27 "ACF.spad" 7616 7623 10764 10857) (-26 "ACF.spad" 4456 4465 7606 7611) (-25 "ABELSG.spad" 3997 4004 4446 4451) (-24 "ABELSG.spad" 3536 3545 3987 3992) (-23 "ABELMON.spad" 2964 2971 3526 3531) (-22 "ABELMON.spad" 2390 2399 2954 2959) (-21 "ABELGRP.spad" 2055 2062 2380 2385) (-20 "ABELGRP.spad" 1718 1727 2045 2050) (-19 "A1AGG.spad" 870 879 1698 1713) (-18 "A1AGG.spad" 30 41 860 865)) \ No newline at end of file