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Diffstat (limited to 'src/algebra/xlpoly.spad.pamphlet')
| -rw-r--r-- | src/algebra/xlpoly.spad.pamphlet | 50 |
1 files changed, 49 insertions, 1 deletions
diff --git a/src/algebra/xlpoly.spad.pamphlet b/src/algebra/xlpoly.spad.pamphlet index 6d79566d..26870df1 100644 --- a/src/algebra/xlpoly.spad.pamphlet +++ b/src/algebra/xlpoly.spad.pamphlet @@ -4,13 +4,17 @@ \title{\$SPAD/src/algebra xlpoly.spad} \author{Michel Petitot} \maketitle + \begin{abstract} \end{abstract} -\eject \tableofcontents \eject + \section{domain MAGMA Magma} + <<domain MAGMA Magma>>= +import OrderedSet +import RetractableTo )abbrev domain MAGMA Magma ++ Author: Michel Petitot (petitot@lifl.fr). ++ Date Created: 91 @@ -152,13 +156,20 @@ Magma(VarSet:OrderedSet):Public == Private where lx < ly @ + \section{domain LWORD LyndonWord} + A function $f \epsilon \lbrace 0,1 \rbrace$ is called acyclic if $C(F)$ consists of $n$ different objects. The canonical representative of the orbit of an acyclic function is usually called a Lyndon Word \cite{1}. If $f$ is acyclic, then all elements in the orbit $C(f)$ are acyclic as well, and we call $C(f)$ an acyclic orbit. + <<domain LWORD LyndonWord>>= +import OrderedSet +import RetractableTo +import Boolean +import Magma )abbrev domain LWORD LyndonWord ++ Author: Michel Petitot (petitot@lifl.fr). ++ Date Created: 91 @@ -319,8 +330,12 @@ LyndonWord(VarSet:OrderedSet):Public == Private where "append"/ [v.i for i in 1..n] @ + \section{category LIECAT LieAlgebra} + <<category LIECAT LieAlgebra>>= +import CommutativeRing +import Field )abbrev category LIECAT LieAlgebra ++ Author: Michel Petitot (petitot@lifl.fr). ++ Date Created: 91 @@ -355,8 +370,13 @@ LieAlgebra(R: CommutativeRing): Category == Module(R) with if R has Field then x / r == inv(r)$R * x @ + \section{category FLALG FreeLieAlgebra} + <<category FLALG FreeLieAlgebra>>= +import OrderedSet +import CommutativeRing +import LieAlgebra )abbrev category FLALG FreeLieAlgebra ++ Author: Michel Petitot (petitot@lifl.fr) ++ Date Created: 91 @@ -415,8 +435,13 @@ FreeLieAlgebra(VarSet:OrderedSet, R:CommutativeRing) :Category == CatDef where ++ in \axiom{p}. @ + \section{package XEXPPKG XExponentialPackage} + <<package XEXPPKG XExponentialPackage>>= +import OrderedSet +import XPolynomialsCat +import NonNegativeInteger )abbrev package XEXPPKG XExponentialPackage ++ Author: Michel Petitot (petitot@lifl.fr). ++ Date Created: 91 @@ -487,8 +512,15 @@ XExponentialPackage(R, VarSet, XPOLY): Public == Private where log(p1*q1, n) @ + \section{domain LPOLY LiePolynomial} + <<domain LPOLY LiePolynomial>>= +import OrderedSet +import CommutativeRing +import FreeLieAlgebra +import FreeModuleCat +import LyndonWord )abbrev domain LPOLY LiePolynomial ++ Author: Michel Petitot (petitot@lifl.fr). ++ Date Created: 91 @@ -682,8 +714,13 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where -- mkNary("+" :: EX,le) @ + \section{domain PBWLB PoincareBirkhoffWittLyndonBasis} + <<domain PBWLB PoincareBirkhoffWittLyndonBasis>>= +import OrderedSet +import RetractableTo +import LyndonWord )abbrev domain PBWLB PoincareBirkhoffWittLyndonBasis ++ Author: Michel Petitot (petitot@lifl.fr). ++ Date Created: 91 @@ -793,8 +830,12 @@ PoincareBirkhoffWittLyndonBasis(VarSet: OrderedSet): Public == Private where lx < ly @ + \section{domain XPBWPOLY XPBWPolynomial} + <<domain XPBWPOLY XPBWPolynomial>>= +import OrderedSet +import CommutativeRing )abbrev domain XPBWPOLY XPBWPolynomial ++ Author: Michel Petitot (petitot@lifl.fr). ++ Date Created: 91 @@ -1026,8 +1067,13 @@ XPBWPolynomial(VarSet:OrderedSet,R:CommutativeRing): XDPcat == XDPdef where +/ [t.c * mirror1(t.k) for t in p] @ + \section{domain LEXP LieExponentials} + <<domain LEXP LieExponentials>>= +import OrderedSet +import CommutativeRing +import Module )abbrev domain LEXP LieExponentials ++ Author: Michel Petitot (petitot@lifl.fr). ++ Date Created: 91 @@ -1162,7 +1208,9 @@ LieExponentials(VarSet, R, Order): XDPcat == XDPdef where lt pretend $ @ + \section{License} + <<license>>= --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. --All rights reserved. |