* interp/nruncomp.boot (buildFunctor): Remove $MissingFunctionInfo.

* interp/functor.boot (SetFunctionSlots): Simplify. (SigSlotsMatch): Likewise. (CheckVector): Remove. (makeMissingFunctionEntry): Refer to $SetFunctions.
author: dos-reis <gdr@axiomatics.org> 2009-10-27 17:12:15 +0000
committer: dos-reis <gdr@axiomatics.org> 2009-10-27 17:12:15 +0000
commit: e5585b7d274f667c8439e98d6b5030303d13e319 (patch)
tree: bb09cb82ede9d88efc45eeb6129f13ada8c8f26a /src/share/algebra/browse.daase
parent: 8b5e8f350ff08fee34e36f51db5f73e859e2aa7e (diff)
download: open-axiom-e5585b7d274f667c8439e98d6b5030303d13e319.tar.gz
1 files changed, 32 insertions, 32 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 8908645d..7ceab490 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,5 +1,5 @@
 
-(2262520 . 3465590093)       
+(2262520 . 3465643290)       
 (-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 
@@ -88,7 +88,7 @@ NIL
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -3944 UP UPUP -1615) 
+(-40 -3944 UP UPUP -4234) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
 ((-4409 |has| (-410 |#2|) (-365)) (-4414 |has| (-410 |#2|) (-365)) (-4408 |has| (-410 |#2|) (-365)) ((-4418 "*") . T) (-4410 . T) (-4411 . T) (-4413 . T)) 
 ((|HasCategory| (-410 |#2|) (QUOTE (-145))) (|HasCategory| (-410 |#2|) (QUOTE (-147))) (|HasCategory| (-410 |#2|) (QUOTE (-351))) (-2871 (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-370))) (-2871 (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (-2871 (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -901) (QUOTE (-1176)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -901) (QUOTE (-1176)))) (|HasCategory| (-410 |#2|) (QUOTE (-351))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -640) (QUOTE (-567)))) (-2871 (|HasCategory| (-410 |#2|) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -901) (QUOTE (-1176)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365))))) 
@@ -111,7 +111,7 @@ NIL
 (-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."))) 
 ((-4416 . T) (-4417 . T)) 
-((-2871 (-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4217) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4217) (|devaluate| |#2|))))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4217) (|devaluate| |#2|))))))) 
+((-2871 (-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#2|))))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4215) (|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 
@@ -1088,7 +1088,7 @@ NIL
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
 NIL 
-(-290 S R |Mod| -3793 -4048 |exactQuo|) 
+(-290 S R |Mod| -3097 -3765 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4409 . T) ((-4418 "*") . T) (-4410 . T) (-4411 . T) (-4413 . T)) 
 NIL 
@@ -1115,7 +1115,7 @@ NIL
 (-296 |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."))) 
 ((-4416 . T) (-4417 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4217) (|devaluate| |#2|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) 
+((-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#2|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) 
 (-297) 
 ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) 
 NIL 
@@ -1211,7 +1211,7 @@ NIL
 (-320 FE |var| |cen|) 
 ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) 
 (((-4418 "*") |has| |#1| (-172)) (-4409 |has| |#1| (-559)) (-4414 |has| |#1| (-365)) (-4408 |has| |#1| (-365)) (-4410 . T) (-4411 . T) (-4413 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1176)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1112))) (|HasCategory| |#1| (QUOTE (-365))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2871 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4130) (LIST (|devaluate| |#1|) (QUOTE (-1176)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2871 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1201))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -3337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1176))))) (|HasSignature| |#1| (LIST (QUOTE -2921) (LIST (LIST (QUOTE -645) (QUOTE (-1176))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1176)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1112))) (|HasCategory| |#1| (QUOTE (-365))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2871 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4130) (LIST (|devaluate| |#1|) (QUOTE (-1176)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2871 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1201))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -2186) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1176))))) (|HasSignature| |#1| (LIST (QUOTE -2921) (LIST (LIST (QUOTE -645) (QUOTE (-1176))) (|devaluate| |#1|))))))) 
 (-321 M) 
 ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) 
 NIL 
@@ -1839,11 +1839,11 @@ NIL
 (-477 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
 (((-4418 "*") |has| |#1| (-172)) (-4409 |has| |#1| (-559)) (-4414 |has| |#1| (-365)) (-4408 |has| |#1| (-365)) (-4410 . T) (-4411 . T) (-4413 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1176)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1112))) (|HasCategory| |#1| (QUOTE (-365))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2871 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4130) (LIST (|devaluate| |#1|) (QUOTE (-1176)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2871 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1201))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -3337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1176))))) (|HasSignature| |#1| (LIST (QUOTE -2921) (LIST (LIST (QUOTE -645) (QUOTE (-1176))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1176)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1112))) (|HasCategory| |#1| (QUOTE (-365))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2871 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4130) (LIST (|devaluate| |#1|) (QUOTE (-1176)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2871 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1201))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -2186) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1176))))) (|HasSignature| |#1| (LIST (QUOTE -2921) (LIST (LIST (QUOTE -645) (QUOTE (-1176))) (|devaluate| |#1|))))))) 
 (-478 |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."))) 
 ((-4417 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4217) (|devaluate| |#2|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100)))) 
+((-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#2|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100)))) 
 (-479 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)}"))) 
 ((-4417 . T) (-4416 . T)) 
@@ -1859,7 +1859,7 @@ NIL
 (-482 |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."))) 
 ((-4416 . T) (-4417 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4217) (|devaluate| |#2|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) 
+((-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#2|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) 
 (-483) 
 ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) 
 NIL 
@@ -2143,7 +2143,7 @@ NIL
 (-553 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
 ((-4416 . T) (-4417 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4217) (|devaluate| |#2|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) 
+((-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#2|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) 
 (-554 R -3944) 
 ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) 
 NIL 
@@ -2367,7 +2367,7 @@ NIL
 (-609 |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."))) 
 ((-4416 . T) (-4417 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (QUOTE (-1158))) (LIST (QUOTE |:|) (QUOTE -4217) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-1100))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1100))) (|HasCategory| (-1158) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (QUOTE (-1100))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (LIST (QUOTE -614) (QUOTE (-863))))) 
+((-12 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (QUOTE (-1158))) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-1100))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1100))) (|HasCategory| (-1158) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (QUOTE (-1100))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (LIST (QUOTE -614) (QUOTE (-863))))) 
 (-610 S |Key| |Entry|) 
 ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) 
 NIL 
@@ -2463,7 +2463,7 @@ NIL
 (-633) 
 ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) 
 ((-4417 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 (-52))) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (QUOTE (-1158))) (LIST (QUOTE |:|) (QUOTE -4217) (QUOTE (-52))))))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 (-52))) (QUOTE (-1100))) (|HasCategory| (-52) (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 (-52))) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1100))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1100))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1158) (QUOTE (-851))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (QUOTE (-1100))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 (-52))) (QUOTE (-1100)))) 
+((-12 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 (-52))) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (QUOTE (-1158))) (LIST (QUOTE |:|) (QUOTE -4215) (QUOTE (-52))))))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 (-52))) (QUOTE (-1100))) (|HasCategory| (-52) (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 (-52))) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1100))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1100))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1158) (QUOTE (-851))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (QUOTE (-1100))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 (-52))) (QUOTE (-1100)))) 
 (-634 S R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
@@ -2487,7 +2487,7 @@ NIL
 (-639 S R) 
 ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) 
 NIL 
-((-1683 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) 
+((-1681 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) 
 (-640 R) 
 ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) 
 ((-4413 . T)) 
@@ -2564,7 +2564,7 @@ NIL
 ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a, zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
-(-659 A -2842) 
+(-659 A -2122) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) 
 ((-4410 . T) (-4411 . T) (-4413 . T)) 
 ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-365)))) 
@@ -2776,7 +2776,7 @@ NIL
 ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) 
 NIL 
 NIL 
-(-712 R |Mod| -3793 -4048 |exactQuo|) 
+(-712 R |Mod| -3097 -3765 |exactQuo|) 
 ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4408 . T) (-4414 . T) (-4409 . T) ((-4418 "*") . T) (-4410 . T) (-4411 . T) (-4413 . T)) 
 NIL 
@@ -2792,7 +2792,7 @@ NIL
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
 ((-4411 |has| |#1| (-172)) (-4410 |has| |#1| (-172)) (-4413 . T)) 
 ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) 
-(-716 R |Mod| -3793 -4048 |exactQuo|) 
+(-716 R |Mod| -3097 -3765 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4413 . T)) 
 NIL 
@@ -3055,7 +3055,7 @@ NIL
 (-781 R |VarSet|) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) 
 (((-4418 "*") |has| |#1| (-172)) (-4409 |has| |#1| (-559)) (-4414 |has| |#1| (-6 -4414)) (-4411 . T) (-4410 . T) (-4413 . T)) 
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 (-782 R S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) 
 NIL 
@@ -3483,7 +3483,7 @@ NIL
 (-888 |Base| |Subject| |Pat|) 
 ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) 
 NIL 
-((-12 (-1683 (|HasCategory| |#2| (QUOTE (-1050)))) (-1683 (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1176)))))) (-12 (|HasCategory| |#2| (QUOTE (-1050))) (-1683 (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1176)))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1176))))) 
+((-12 (-1681 (|HasCategory| |#2| (QUOTE (-1050)))) (-1681 (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1176)))))) (-12 (|HasCategory| |#2| (QUOTE (-1050))) (-1681 (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1176)))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1176))))) 
 (-889 R A B) 
 ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) 
 NIL 
@@ -4075,7 +4075,7 @@ NIL
 (-1036) 
 ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) 
 ((-4416 . T) (-4417 . T)) 
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+((-12 (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (QUOTE (-1176))) (LIST (QUOTE |:|) (QUOTE -4215) (QUOTE (-52))))))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (QUOTE (-1100))) (|HasCategory| (-52) (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1100))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1100))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (QUOTE (-1100))) (|HasCategory| (-1176) (QUOTE (-851))) (|HasCategory| (-52) (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (LIST (QUOTE -614) (QUOTE (-863))))) 
 (-1037) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
@@ -4183,7 +4183,7 @@ NIL
 (-1063) 
 ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) 
 ((-4416 . T) (-4417 . T)) 
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+((-12 (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (QUOTE (-1176))) (LIST (QUOTE |:|) (QUOTE -4215) (QUOTE (-52))))))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (QUOTE (-1100))) (|HasCategory| (-52) (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1100))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1100))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (QUOTE (-1100))) (|HasCategory| (-1176) (QUOTE (-851))) (|HasCategory| (-52) (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 (-1176)) (|:| -4215 (-52))) (LIST (QUOTE -614) (QUOTE (-863))))) 
 (-1064 S R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
@@ -4531,7 +4531,7 @@ NIL
 (-1150 |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."))) 
 ((-4417 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4217) (|devaluate| |#2|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4217 |#2|)) (QUOTE (-1100)))) 
+((-12 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#2|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| |#2| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2871 (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1100))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 |#1|) (|:| -4215 |#2|)) (QUOTE (-1100)))) 
 (-1151) 
 ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) 
 NIL 
@@ -4567,7 +4567,7 @@ NIL
 (-1159 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
 ((-4416 . T) (-4417 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (QUOTE (-1158))) (LIST (QUOTE |:|) (QUOTE -4217) (|devaluate| |#1|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (QUOTE (-1100))) (|HasCategory| |#1| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#1| (QUOTE (-1100))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-1100))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (QUOTE (-1100))) (|HasCategory| (-1158) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4217 |#1|)) (LIST (QUOTE -614) (QUOTE (-863))))) 
+((-12 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1812) (QUOTE (-1158))) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#1|)))))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (QUOTE (-1100))) (|HasCategory| |#1| (QUOTE (-1100)))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (QUOTE (-1100))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#1| (QUOTE (-1100))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-1100))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (QUOTE (-1100))) (|HasCategory| (-1158) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1100))) (-2871 (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1812 (-1158)) (|:| -4215 |#1|)) (LIST (QUOTE -614) (QUOTE (-863))))) 
 (-1160 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 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) 
 NIL 
@@ -4599,7 +4599,7 @@ NIL
 (-1167 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
 (((-4418 "*") -2871 (-1692 (|has| |#1| (-365)) (|has| (-1174 |#1| |#2| |#3|) (-821))) (|has| |#1| (-172)) (-1692 (|has| |#1| (-365)) (|has| (-1174 |#1| |#2| |#3|) (-910)))) (-4409 -2871 (-1692 (|has| |#1| (-365)) (|has| (-1174 |#1| |#2| |#3|) (-821))) (|has| |#1| (-559)) (-1692 (|has| |#1| (-365)) (|has| (-1174 |#1| |#2| |#3|) (-910)))) (-4414 |has| |#1| (-365)) (-4408 |has| |#1| (-365)) (-4410 . T) (-4411 . T) (-4413 . T)) 
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 ((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) 
 NIL 
@@ -4623,11 +4623,11 @@ NIL
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 ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) 
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 (-1174 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
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 (-1175) 
 ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) 
 NIL 
@@ -4687,7 +4687,7 @@ NIL
 (-1189 |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}"))) 
 ((-4416 . T) (-4417 . T)) 
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 (-1190 R) 
 ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) 
 NIL 
@@ -4847,11 +4847,11 @@ NIL
 (-1229 |Coef| UTS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) 
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 (-1231 ZP) 
 ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) 
 NIL 
@@ -4931,11 +4931,11 @@ NIL
 (-1250 |Coef| ULS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) 
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 (-1251 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) 
 (((-4418 "*") |has| |#1| (-172)) (-4409 |has| |#1| (-559)) (-4414 |has| |#1| (-365)) (-4408 |has| |#1| (-365)) (-4410 . T) (-4411 . T) (-4413 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1176)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1112))) (|HasCategory| |#1| (QUOTE (-365))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2871 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4130) (LIST (|devaluate| |#1|) (QUOTE (-1176)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2871 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1201))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -3337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1176))))) (|HasSignature| |#1| (LIST (QUOTE -2921) (LIST (LIST (QUOTE -645) (QUOTE (-1176))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1176)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1112))) (|HasCategory| |#1| (QUOTE (-365))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2871 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4130) (LIST (|devaluate| |#1|) (QUOTE (-1176)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2871 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1201))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -2186) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1176))))) (|HasSignature| |#1| (LIST (QUOTE -2921) (LIST (LIST (QUOTE -645) (QUOTE (-1176))) (|devaluate| |#1|))))))) 
 (-1252 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) 
 (((-4418 "*") |has| (-1251 |#2| |#3| |#4|) (-172)) (-4409 |has| (-1251 |#2| |#3| |#4|) (-559)) (-4410 . T) (-4411 . T) (-4413 . T)) 
@@ -4955,7 +4955,7 @@ NIL
 (-1256 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-1201))) (|HasSignature| |#2| (LIST (QUOTE -2921) (LIST (LIST (QUOTE -645) (QUOTE (-1176))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3337) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1176))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365)))) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-1201))) (|HasSignature| |#2| (LIST (QUOTE -2921) (LIST (LIST (QUOTE -645) (QUOTE (-1176))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2186) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1176))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365)))) 
 (-1257 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
 (((-4418 "*") |has| |#1| (-172)) (-4409 |has| |#1| (-559)) (-4410 . T) (-4411 . T) (-4413 . T)) 
@@ -4963,7 +4963,7 @@ NIL
 (-1258 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
 (((-4418 "*") |has| |#1| (-172)) (-4409 |has| |#1| (-559)) (-4410 . T) (-4411 . T) (-4413 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2871 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1176)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|)))) (|HasCategory| (-772) (QUOTE (-1112))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasSignature| |#1| (LIST (QUOTE -4130) (LIST (|devaluate| |#1|) (QUOTE (-1176)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasCategory| |#1| (QUOTE (-365))) (-2871 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1201))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -3337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1176))))) (|HasSignature| |#1| (LIST (QUOTE -2921) (LIST (LIST (QUOTE -645) (QUOTE (-1176))) (|devaluate| |#1|))))))) 
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 (-1259 |Coef| UTS) 
 ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) 
 NIL
author	dos-reis <gdr@axiomatics.org>	2009-10-27 17:12:15 +0000
committer	dos-reis <gdr@axiomatics.org>	2009-10-27 17:12:15 +0000
commit	e5585b7d274f667c8439e98d6b5030303d13e319 (patch)
tree	bb09cb82ede9d88efc45eeb6129f13ada8c8f26a /src/share/algebra/browse.daase
parent	8b5e8f350ff08fee34e36f51db5f73e859e2aa7e (diff)
download	open-axiom-e5585b7d274f667c8439e98d6b5030303d13e319.tar.gz