diff options
Diffstat (limited to 'src/algebra/xpoly.spad.pamphlet')
| -rw-r--r-- | src/algebra/xpoly.spad.pamphlet | 21 |
1 files changed, 8 insertions, 13 deletions
diff --git a/src/algebra/xpoly.spad.pamphlet b/src/algebra/xpoly.spad.pamphlet index 249a5e0e..b2021bf8 100644 --- a/src/algebra/xpoly.spad.pamphlet +++ b/src/algebra/xpoly.spad.pamphlet @@ -142,7 +142,7 @@ import RetractableTo )abbrev category FMCAT FreeModuleCat ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 -++ Date Last Updated: 7 Juillet 92 +++ Date Last Updated: May 19, 2013. ++ Fix History: compilation v 2.1 le 13 dec 98 ++ Basic Functions: ++ Related Constructors: @@ -168,15 +168,12 @@ FreeModuleCat(R, Basis):Category == Exports where Basis: SetCategory TERM ==> Record(k: Basis, c: R) - Exports == Join(BiModule(R,R), RetractableTo Basis) with + Exports == Join(Functorial R,BiModule(R,R),RetractableTo Basis) with * : (R, Basis) -> % ++ \spad{r*b} returns the product of \spad{r} by \spad{b}. coefficient : (%, Basis) -> R ++ \spad{coefficient(x,b)} returns the coefficient ++ of \spad{b} in \spad{x}. - map : (R -> R, %) -> % - ++ \spad{map(fn,u)} maps function \spad{fn} onto the coefficients - ++ of the non-zero monomials of \spad{u}. monom : (Basis, R) -> % ++ \spad{monom(b,r)} returns the element with the single monomial ++ \spad{b} and coefficient \spad{r}. @@ -362,7 +359,7 @@ import RetractableTo )abbrev category XFALG XFreeAlgebra ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 -++ Date Last Updated: 7 Juillet 92 +++ Date Last Updated: May 19, 2013. ++ Fix History: compilation v 2.1 le 13 dec 98 ++ Basic Functions: ++ Related Constructors: @@ -381,7 +378,7 @@ XFreeAlgebra(vl:OrderedSet,R:Ring):Category == Catdef where I ==> Integer TERM ==> Record(k: WORD, c: R) - Catdef == Join(Ring, XAlgebra(R), RetractableTo WORD) + Catdef == Join(Ring, XAlgebra(R), Functorial R,RetractableTo WORD) with *: (vl,%) -> % ++ \spad{v * x} returns the product of a variable \spad{x} by \spad{x}. @@ -432,8 +429,6 @@ XFreeAlgebra(vl:OrderedSet,R:Ring):Category == Catdef where ++ This multiplication is associative and commutative. sh :(%,NNI) -> % ++ \spad{sh(x,n)} returns the shuffle power of \spad{x} to the \spad{n}. - map : (R -> R, %) -> % - ++ \spad{map(fn,x)} returns \spad{Sum(fn(r_i) w_i)} if \spad{x} writes \spad{Sum(r_i w_i)}. varList: % -> List vl ++ \spad{varList(x)} returns the list of variables which appear in \spad{x}. @@ -488,7 +483,7 @@ import FreeMonoidCat )abbrev domain XPR XPolynomialRing ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 -++ Date Last Updated: 7 Juillet 92 +++ Date Last Updated: May 13, 2013. ++ Fix History: compilation v 2.1 le 13 dec 98 ++ Basic Functions: ++ Related Constructors: @@ -509,7 +504,7 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where EX ==> OutputForm NNI ==> NonNegativeInteger - T == Join(Ring, XAlgebra(R), FreeModuleCat(R,E),CoercibleFrom E) with + T == Join(Ring,XAlgebra(R),FreeModuleCat(R,E),CoercibleFrom E,Functorial R) with --operations *: (%,R) -> % ++ \spad{p*r} returns the product of \spad{p} by \spad{r}. @@ -536,8 +531,6 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where ++ \spad{quasiRegular?(x)} return true if \spad{constant(p)} is zero. quasiRegular : % -> % ++ \spad{quasiRegular(x)} return \spad{x} minus its constant term. - map : (R -> R, %) -> % - ++ \spad{map(fn,x)} returns \spad{Sum(fn(r_i) w_i)} if \spad{x} writes \spad{Sum(r_i w_i)}. if R has Field then / : (%,R) -> % ++ \spad{p/r} returns \spad{p*(1/r)}. @@ -1097,6 +1090,8 @@ XPolynomial(R:Ring) == XRecursivePolynomial(Symbol, R) <<license>>= --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. --All rights reserved. +--Copyright (C) 2007-2013, Gabriel Dos Reis. +--All rights reserved. -- --Redistribution and use in source and binary forms, with or without --modification, are permitted provided that the following conditions are |