1############################################################################# 2## 3#W ncorderings.gd 4#W NMO: Low-level (Less-than) functions for orderings Randall Cone 5## 6## 7## (C) 2010 Mathematics Dept., Virginia Polytechnic Institute, USA 8## 9############################################################################# 10 11############################################################################# 12## 13## <#GAPDoc Label="NCMonomialLeftLengthLexicographicOrdering"> 14## <Func Name="NCMonomialLeftLengthLexicographicOrdering" 15## Arg="<algebra>, <list>"/> 16## 17## <Description> 18## Given a free algebra <M>A</M>, and an optional ordered (possibly partial) 19## ordered list of generators for the algebra <M>A</M>, 20## <C>NCMonomialLeftLengthLexicographicOrdering</C> returns a noncommutative length 21## lexicographic ordering object. If an ordered list of generators 22## is provided, its order is used in creation of the ordering object. 23## If a list is not provided, then the ordering object is created 24## based on the order of the generators when the free algebra <M>A</M> 25## was created. 26## <P/> 27## Note: the synonym <C>NCMonomialLeftLengthLexOrdering</C> may also be used. 28## <P/> 29## </Description> 30## 31## <#/GAPDoc> 32## 33DeclareGlobalFunction("NCMonomialLeftLengthLexicographicOrdering"); 34DeclareSynonym("NCMonomialLeftLengthLexOrdering", 35 NCMonomialLeftLengthLexicographicOrdering); 36 37 38############################################################################# 39## 40## <#GAPDoc Label="NCMonomialLengthOrdering"> 41## <Func Name="NCMonomialLengthOrdering" 42## Arg="<algebra>"/> 43## 44## <Description> 45## Given a free algebra <M>A</M>, 46## <C>NCMonomialLengthOrdering</C> returns a noncommutative length 47## ordering object. Only the lengths of the words of monomials in <M>A</M> 48## are compared using this ordering. 49## <P/> 50## </Description> 51## 52## <#/GAPDoc> 53## 54DeclareGlobalFunction("NCMonomialLengthOrdering"); 55 56 57############################################################################# 58## 59## <#GAPDoc Label="NCMonomialLeftLexicographicOrdering"> 60## <Func Name="NCMonomialLeftLexicographicOrdering" 61## Arg="<algebra>, <list>"/> 62## 63## <Description> 64## Given a free algebra <M>A</M>, and an optional ordered (possibly partial) 65## ordered list of generators for the algebra <M>A</M>, 66## <C>NCMonomialLeftLexicographicOrdering</C> returns a simple noncommutative 67## left-lexicographic ordering object. 68## <P/> 69## </Description> 70## 71## <#/GAPDoc> 72## 73DeclareGlobalFunction("NCMonomialLeftLexicographicOrdering"); 74 75 76############################################################################# 77## 78## <#GAPDoc Label="NCMonomialCommutativeLexicographicOrdering"> 79## <Func Name="NCMonomialCommutativeLexicographicOrdering" 80## Arg="<algebra>, <list>"/> 81## 82## <Description> 83## Given a free algebra <M>A</M>, and an optional ordered (possibly partial) 84## ordered list of generators for the algebra <M>A</M>, 85## <C>NCMonomialCommutativeLexicographicOrdering</C> returns a commutative 86## left-lexicographic ordering object. 87## Under this ordering, monomials from <M>A</M> are compared 88## using their respective commutative analogues. 89## <P/> 90## </Description> 91## 92## <#/GAPDoc> 93## 94DeclareGlobalFunction("NCMonomialCommutativeLexicographicOrdering"); 95 96 97############################################################################# 98## 99## <#GAPDoc Label="NCMonomialWeightOrdering"> 100## <Func Name="NCMonomialWeightOrdering" 101## Arg="<algebra>, <list>, <list2>"/> 102## 103## <Description> 104## Given a free algebra <M>A</M>, an ordered (possibly partial) 105## ordered <C><list></C> of generators for the algebra <M>A</M>, 106## and a <C><list2></C> of respective weights for the generators, 107## <C>NCMonomialWeightOrdering</C> returns a noncommutative 108## weight ordering object. 109## <P/> 110## </Description> 111## 112## <#/GAPDoc> 113## 114DeclareGlobalFunction("NCMonomialWeightOrdering"); 115 116DeclareGlobalFunction("NCMonomialLLLTestOrdering"); 117 118## 119#E 120