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Diffstat (limited to 'src/algebra/xpoly.spad.pamphlet')
| -rw-r--r-- | src/algebra/xpoly.spad.pamphlet | 60 |
1 files changed, 58 insertions, 2 deletions
diff --git a/src/algebra/xpoly.spad.pamphlet b/src/algebra/xpoly.spad.pamphlet index 160ee646..4049f1b6 100644 --- a/src/algebra/xpoly.spad.pamphlet +++ b/src/algebra/xpoly.spad.pamphlet @@ -1,16 +1,21 @@ \documentclass{article} \usepackage{axiom} \begin{document} -\title{\$SPAD/src/algebra xpoly.spad} +\title{src/algebra xpoly.spad} \author{Michel Petitot} \maketitle + \begin{abstract} \end{abstract} -\eject \tableofcontents \eject + \section{domain OFMONOID OrderedFreeMonoid} + <<domain OFMONOID OrderedFreeMonoid>>= +import OrderedSet +import OrderedMonoid +import RetractableTo )abbrev domain OFMONOID OrderedFreeMonoid ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 @@ -162,8 +167,14 @@ OrderedFreeMonoid(S: OrderedSet): OFMcategory == OFMdefinition where mirror x == reverse(x)$Rep @ + \section{category FMCAT FreeModuleCat} + <<category FMCAT FreeModuleCat>>= +import Ring +import SetCategory +import BiModule +import RetractableTo )abbrev category FMCAT FreeModuleCat ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 @@ -235,8 +246,12 @@ FreeModuleCat(R, Basis):Category == Exports where if R has CommutativeRing then Module(R) @ + \section{domain FM1 FreeModule1} + <<domain FM1 FreeModule1>>= +import Ring +import OrderedSet )abbrev domain FM1 FreeModule1 ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 @@ -337,8 +352,14 @@ FreeModule1(R:Ring,S:OrderedSet): FMcat == FMdef where 0$R @ + \section{category XALG XAlgebra} + <<category XALG XAlgebra>>= +import Ring +import BiModule +import CommutativeRing +import Algebra )abbrev category XALG XAlgebra ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 @@ -369,8 +390,14 @@ XAlgebra(R: Ring): Category == -- coerce(x:R):% == x * 1$% @ + \section{category XFALG XFreeAlgebra} + <<category XFALG XFreeAlgebra>>= +import OrderedSet +import Ring +import XAlgebra +import RetractableTo )abbrev category XFALG XFreeAlgebra ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 @@ -453,8 +480,12 @@ XFreeAlgebra(vl:OrderedSet,R:Ring):Category == Catdef where if R has noZeroDivisors then noZeroDivisors @ + \section{category XPOLYC XPolynomialsCat} + <<category XPOLYC XPolynomialsCat>>= +import OrderedSet +import XFreeAlgebra )abbrev category XPOLYC XPolynomialsCat ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 @@ -485,8 +516,14 @@ XPolynomialsCat(vl:OrderedSet,R:Ring):Category == Export where ++ \spad{trunc(p,n)} returns the polynomial \spad{p} truncated at order \spad{n}. @ + \section{domain XPR XPolynomialRing} + <<domain XPR XPolynomialRing>>= +import Ring +import OrderedMonoid +import XAlgebra +import FreeMonoidCat )abbrev domain XPR XPolynomialRing ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 @@ -644,7 +681,9 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where x/r == inv(r)*x @ + \section{domain XDPOLY XDistributedPolynomial} + Polynomial arithmetic with non-commutative variables has been improved by a contribution of Michel Petitot (University of Lille I, France). The domain constructor @@ -652,7 +691,13 @@ The domain constructor representation for these polynomials. It is the non-commutative equivalent for the {\bf DistributedMultivariatePolynomial} constructor. + <<domain XDPOLY XDistributedPolynomial>>= +import OrderedSet +import Ring +import FreeModuleCat +import XPolynomialRing +import XPolynomialsCat )abbrev domain XDPOLY XDistributedPolynomial ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 @@ -759,13 +804,19 @@ XDistributedPolynomial(vl:OrderedSet,R:Ring): XDPcat == XDPdef where return p.first.c * q.first.c + coef(p.rest,q.rest) @ + \section{domain XRPOLY XRecursivePolynomial} Polynomial arithmetic with non-commutative variables has been improved by a contribution of Michel Petitot (University of Lille I, France). The domain constructors {\bf XRecursivePolynomial} provides a recursive for these polynomials. It is the non-commutative equivalents for the {\bf SparseMultivariatePolynomial} constructor. + <<domain XRPOLY XRecursivePolynomial>>= +import OrderedSet +import Ring +import XPolynomialsCat +import XDistributedPolynomial )abbrev domain XRPOLY XRecursivePolynomial ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 @@ -1052,8 +1103,11 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where sort_!(lv) @ + \section{domain XPOLY XPolynomial} + <<domain XPOLY XPolynomial>>= +import XRecursivePolynomial )abbrev domain XPOLY XPolynomial ++ Author: Michel Petitot petitot@lifl.fr ++ Date Created: 91 @@ -1078,7 +1132,9 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where XPolynomial(R:Ring) == XRecursivePolynomial(Symbol, R) @ + \section{License} + <<license>>= --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. --All rights reserved. |