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author | Gabriel Dos Reis <gdr@axiomatics.org> | 2016-01-17 17:04:36 -0800 |
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committer | Gabriel Dos Reis <gdr@axiomatics.org> | 2016-01-17 17:04:36 -0800 |
commit | 68ee78c1a740a9fc60f04a20b685d46a44570360 (patch) | |
tree | 619a65766f1bb0920109b64feab99a5636b63c6b /src/algebra/xlpoly.spad.pamphlet | |
parent | b759bc632b404afd4b3f62ea4ac8a429d1a5d8d7 (diff) | |
download | open-axiom-68ee78c1a740a9fc60f04a20b685d46a44570360.tar.gz |
Rename Magma to FreeMagma
A breeze, given previous compiler work.
Renaming matches FriCAS's.
Diffstat (limited to 'src/algebra/xlpoly.spad.pamphlet')
-rw-r--r-- | src/algebra/xlpoly.spad.pamphlet | 36 |
1 files changed, 18 insertions, 18 deletions
diff --git a/src/algebra/xlpoly.spad.pamphlet b/src/algebra/xlpoly.spad.pamphlet index 0ce1f1b0..8a153e51 100644 --- a/src/algebra/xlpoly.spad.pamphlet +++ b/src/algebra/xlpoly.spad.pamphlet @@ -10,12 +10,12 @@ \tableofcontents \eject -\section{domain MAGMA Magma} +\section{domain FMAGMA FreeMagma} -<<domain MAGMA Magma>>= +<<domain FMAGMA FreeMagma>>= import OrderedSet import RetractableTo -)abbrev domain MAGMA Magma +)abbrev domain FMAGMA FreeMagma ++ Author: Michel Petitot (petitot@lifl.fr). ++ Date Created: 91 ++ Date Last Updated: 7 Juillet 92 @@ -31,7 +31,7 @@ import RetractableTo ++ parenthesized words (binary trees over arbitrary symbols) ++ useful in \spadtype{LiePolynomial}. \newline Author: Michel Petitot (petitot@lifl.fr). -Magma(VarSet:OrderedSet):Public == Private where +FreeMagma(VarSet:OrderedSet):Public == Private where WORD ==> OrderedFreeMonoid(VarSet) EX ==> OutputForm @@ -42,7 +42,7 @@ Magma(VarSet:OrderedSet):Public == Private where ++ \axiom{first(x)} returns the first entry of the tree \axiom{x}. left : $ -> $ ++ \axiom{left(x)} returns left subtree of \axiom{x} or - ++ error if \axiomOpFrom{retractable?}{Magma}(\axiom{x}) is true. + ++ error if \axiomOpFrom{retractable?}{FreeMagma}(\axiom{x}) is true. length : $ -> PositiveInteger ++ \axiom{length(x)} returns the number of entries in \axiom{x}. lexico : ($,$) -> Boolean @@ -52,16 +52,16 @@ Magma(VarSet:OrderedSet):Public == Private where ++ its arguments. Thus this is not a total ordering. mirror : $ -> $ ++ \axiom{mirror(x)} returns the reversed word of \axiom{x}. - ++ That is \axiom{x} itself if \axiomOpFrom{retractable?}{Magma}(\axiom{x}) is true and + ++ That is \axiom{x} itself if \axiomOpFrom{retractable?}{FreeMagma}(\axiom{x}) is true and ++ \axiom{mirror(z) * mirror(y)} if \axiom{x} is \axiom{y*z}. rest : $ -> $ ++ \axiom{rest(x)} return \axiom{x} without the first entry or - ++ error if \axiomOpFrom{retractable?}{Magma}(\axiom{x}) is true. + ++ error if \axiomOpFrom{retractable?}{FreeMagma}(\axiom{x}) is true. retractable? : $ -> Boolean ++ \axiom{retractable?(x)} tests if \axiom{x} is a tree with only one entry. right : $ -> $ ++ \axiom{right(x)} returns right subtree of \axiom{x} or - ++ error if \axiomOpFrom{retractable?}{Magma}(\axiom{x}) is true. + ++ error if \axiomOpFrom{retractable?}{FreeMagma}(\axiom{x}) is true. varList : $ -> List VarSet ++ \axiom{varList(x)} returns the list of distinct entries of \axiom{x}. @@ -120,7 +120,7 @@ Magma(VarSet:OrderedSet):Public == Private where first x.left rest x == - x case VarSet => error "rest$Magma: inexistant rest" + x case VarSet => error "rest$FreeMagma: inexistant rest" lx:$ := x.left lx case VarSet => x.right [rest lx , x.right]$VWORD @@ -166,7 +166,7 @@ as well, and we call $C(f)$ an acyclic orbit. import OrderedSet import RetractableTo import Boolean -import Magma +import FreeMagma )abbrev domain LWORD LyndonWord ++ Author: Michel Petitot (petitot@lifl.fr). ++ Date Created: 91 @@ -188,7 +188,7 @@ import Magma ++ Parenthesized Lyndon words can be generated from symbols by using the following ++ rule: \axiom{[[a,b],c]} is a Lyndon word iff \axiom{a*b < c <= b} holds. ++ Lyndon words are internally represented by binary trees using the -++ \spadtype{Magma} domain constructor. +++ \spadtype{FreeMagma} domain constructor. ++ Two ordering are provided: lexicographic and ++ length-lexicographic. \newline ++ Author : Michel Petitot (petitot@lifl.fr). @@ -201,7 +201,7 @@ LyndonWord(VarSet:OrderedSet):Public == Private where OF ==> OutputForm ARRAY1==> OneDimensionalArray - Public == Join(OrderedSet,RetractableTo VarSet,CoercibleTo OFMON,CoercibleTo Magma VarSet) with + Public == Join(OrderedSet,RetractableTo VarSet,CoercibleTo OFMON,CoercibleTo FreeMagma VarSet) with retractable? : $ -> Boolean ++ \axiom{retractable?(x)} tests if \axiom{x} is a tree with only one entry. left : $ -> $ @@ -233,9 +233,9 @@ LyndonWord(VarSet:OrderedSet):Public == Private where ++ \axiom{LyndonWordsList(vl, n)} returns the list of Lyndon ++ words over the alphabet \axiom{vl}, up to order \axiom{n}. - Private == Magma(VarSet) add + Private == FreeMagma(VarSet) add -- Representation - Rep:= Magma(VarSet) + Rep:= FreeMagma(VarSet) -- Fonctions locales LetterList : OFMON -> List VarSet @@ -290,7 +290,7 @@ LyndonWord(VarSet:OrderedSet):Public == Private where lx < ly coerce(x:$):OF == bracket(x::OFMON::OF) - coerce(x:$):Magma VarSet == x::Rep + coerce(x:$):FreeMagma VarSet == x::Rep LyndonWordsList1 (vl,n) == -- a ameliorer !!!!!!!!!!! null vl => error "empty list" @@ -520,7 +520,7 @@ import LyndonWord ++ (Oxford science publications). \newline Author: Michel Petitot (petitot@lifl.fr). LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where - MAGMA ==> Magma(VarSet) + FMAGMA ==> FreeMagma(VarSet) LWORD ==> LyndonWord(VarSet) WORD ==> OrderedFreeMonoid(VarSet) XDPOLY ==> XDistributedPolynomial(VarSet,R) @@ -618,7 +618,7 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where r --definitions locales - makeLyndon(u,v) == (u::MAGMA * v::MAGMA) pretend LWORD + makeLyndon(u,v) == (u::FMAGMA * v::FMAGMA) pretend LWORD crw(u,v) == -- u et v sont des mots de Lyndon u = v => 0 @@ -1217,7 +1217,7 @@ LieExponentials(VarSet, R, Order): XDPcat == XDPdef where <<*>>= <<license>> -<<domain MAGMA Magma>> +<<domain FMAGMA FreeMagma>> <<domain LWORD LyndonWord>> <<category LIECAT LieAlgebra>> <<category FLALG FreeLieAlgebra>> |