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="&lt;algebra>, &lt;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="&lt;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="&lt;algebra>, &lt;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="&lt;algebra>, &lt;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="&lt;algebra>, &lt;list>, &lt;list2>"/>
102##
103##  <Description>
104##  Given a free algebra <M>A</M>, an ordered (possibly partial)
105##  ordered <C>&lt;list></C> of generators for the algebra <M>A</M>,
106##  and a <C>&lt;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