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1<!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997)
2 by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds
3* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
4* with significant contributions from:
5 Jens Lippman, Marek Rouchal, Martin Wilck and others -->
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8<TITLE>The Monomial Order Package</TITLE>
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45<A NAME="CHILD_LINKS"><strong>Subsections</strong></A>
46<UL>
47<LI><A NAME="tex2html1017"
48 HREF="node9.html#SECTION00090010000000000000">
49<I>lex<MATH CLASS="INLINE">
50&gt;
51</MATH></I></A>
52<LI><A NAME="tex2html1018"
53 HREF="node9.html#SECTION00090020000000000000">
54<I>total<MATH CLASS="INLINE">
55-
56</MATH>degree</I></A>
57<LI><A NAME="tex2html1019"
58 HREF="node9.html#SECTION00090030000000000000">
59<I>grlex<MATH CLASS="INLINE">
60&gt;
61</MATH></I></A>
62<LI><A NAME="tex2html1020"
63 HREF="node9.html#SECTION00090040000000000000">
64<I>grevlex<MATH CLASS="INLINE">
65&gt;
66</MATH></I></A>
67<LI><A NAME="tex2html1021"
68 HREF="node9.html#SECTION00090050000000000000">
69<I>revlex<MATH CLASS="INLINE">
70&gt;
71</MATH></I></A>
72<LI><A NAME="tex2html1022"
73 HREF="node9.html#SECTION00090060000000000000">
74<I>invlex<MATH CLASS="INLINE">
75&gt;
76</MATH></I></A>
77<LI><A NAME="tex2html1023"
78 HREF="node9.html#SECTION00090070000000000000">
79<I>elimination<MATH CLASS="INLINE">
80-
81</MATH>order</I></A>
82<LI><A NAME="tex2html1024"
83 HREF="node9.html#SECTION00090080000000000000">
84<I>elimination<MATH CLASS="INLINE">
85-
86</MATH>order<MATH CLASS="INLINE">
87-
88</MATH>1</I></A>
89</UL>
90<!--End of Table of Child-Links-->
91<HR>
92<H1><A NAME="SECTION00090000000000000000">
93The Monomial Order Package</A>
94</H1>
95<H4><A NAME="SECTION00090010000000000000">
96<I>lex<MATH CLASS="INLINE">
97&gt;
98</MATH></I></A>
99</H4>
100<P><IMG WIDTH="580" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
101 SRC="img149.gif"
102 ALT="$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$"> [<EM>FUNCTION</EM>]
103<BLOCKQUOTE>
104Return T if P<MATH CLASS="INLINE">
105&gt;
106</MATH>Q with respect to lexicographic order, otherwise NIL.
107The second returned value is T if P=Q, otherwise it is NIL.</BLOCKQUOTE><H4><A NAME="SECTION00090020000000000000">
108<I>total<MATH CLASS="INLINE">
109-
110</MATH>degree</I></A>
111</H4>
112<P><IMG WIDTH="522" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
113 SRC="img150.gif"
114 ALT="$\textstyle\parbox{\pboxargslen}{\em m {\sf \&optional} (start 0) (end (length m)) \/}$"> [<EM>FUNCTION</EM>]
115<BLOCKQUOTE>
116Return the todal degree of a monomoal M.</BLOCKQUOTE><H4><A NAME="SECTION00090030000000000000">
117<I>grlex<MATH CLASS="INLINE">
118&gt;
119</MATH></I></A>
120</H4>
121<P><IMG WIDTH="580" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
122 SRC="img149.gif"
123 ALT="$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$"> [<EM>FUNCTION</EM>]
124<BLOCKQUOTE>
125Return T if P<MATH CLASS="INLINE">
126&gt;
127</MATH>Q with respect to graded lexicographic order,
128otherwise NIL. The second returned value is T if P=Q, otherwise it is
129NIL. </BLOCKQUOTE><H4><A NAME="SECTION00090040000000000000">
130<I>grevlex<MATH CLASS="INLINE">
131&gt;
132</MATH></I></A>
133</H4>
134<P><IMG WIDTH="580" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
135 SRC="img149.gif"
136 ALT="$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$"> [<EM>FUNCTION</EM>]
137<BLOCKQUOTE>
138Return T if P<MATH CLASS="INLINE">
139&gt;
140</MATH>Q with respect to graded reverse lexicographic order,
141NIL otherwise. The second returned value is T if P=Q, otherwise it is
142NIL. </BLOCKQUOTE><H4><A NAME="SECTION00090050000000000000">
143<I>revlex<MATH CLASS="INLINE">
144&gt;
145</MATH></I></A>
146</H4>
147<P><IMG WIDTH="580" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
148 SRC="img149.gif"
149 ALT="$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$"> [<EM>FUNCTION</EM>]
150<BLOCKQUOTE>
151Return T if P<MATH CLASS="INLINE">
152&gt;
153</MATH>Q with respect to reverse lexicographic order, NIL
154otherwise. The second returned value is T if P=Q, otherwise it is
155NIL. This is not and admissible monomial order because some sets do
156not have a minimal element. This order is useful in constructing
157other orders.</BLOCKQUOTE><H4><A NAME="SECTION00090060000000000000">
158<I>invlex<MATH CLASS="INLINE">
159&gt;
160</MATH></I></A>
161</H4>
162<P><IMG WIDTH="580" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
163 SRC="img149.gif"
164 ALT="$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$"> [<EM>FUNCTION</EM>]
165<BLOCKQUOTE>
166Return T if P<MATH CLASS="INLINE">
167&gt;
168</MATH>Q with respect to inverse lexicographic order, NIL
169otherwise The second returned value is T if P=Q, otherwise it is NIL.</BLOCKQUOTE><H4><A NAME="SECTION00090070000000000000">
170<I>elimination<MATH CLASS="INLINE">
171-
172</MATH>order</I></A>
173</H4>
174<P><IMG WIDTH="488" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
175 SRC="img151.gif"
176 ALT="$\textstyle\parbox{\pboxargslen}{\em k {\sf \&key} (primary$-$order
177 \char93 'lex$\gt$) (secondary$-$order
178 \char93 'lex$\gt$) \/}$"> [<EM>FUNCTION</EM>]
179<BLOCKQUOTE>
180Return a predicate which compares monomials according to the
181K<MATH CLASS="INLINE">
182-
183</MATH>th elimination order. Two optional arguments are PRIMARY<MATH CLASS="INLINE">
184-
185</MATH>ORDER
186and SECONDARY<MATH CLASS="INLINE">
187-
188</MATH>ORDER and they should be term orders which are used
189on the first K and the remaining variables.</BLOCKQUOTE><H4><A NAME="SECTION00090080000000000000">
190<I>elimination<MATH CLASS="INLINE">
191-
192</MATH>order<MATH CLASS="INLINE">
193-
194</MATH>1</I></A>
195</H4>
196<P><IMG WIDTH="466" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
197 SRC="img152.gif"
198 ALT="$\textstyle\parbox{\pboxargslen}{\em order \/}$"> [<EM>FUNCTION</EM>]
199<BLOCKQUOTE>
200A special case of the ELIMINATION<MATH CLASS="INLINE">
201-
202</MATH>ORDER when there is only
203one primary variable.</BLOCKQUOTE><HR>
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225<ADDRESS>
226<I>Marek Rychlik</I>
227<BR><I>3/21/1998</I>
228</ADDRESS>
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