[1] | 1 | <!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997)
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| 2 | by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds
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| 3 | * revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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| 4 | * with significant contributions from:
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| 5 | Jens Lippman, Marek Rouchal, Martin Wilck and others -->
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| 6 | <HTML>
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| 7 | <HEAD>
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| 8 | <TITLE>The Monomial Order Package</TITLE>
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| 9 | <META NAME="description" CONTENT="The Monomial Order Package">
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| 10 | <META NAME="keywords" CONTENT="manual">
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| 11 | <META NAME="resource-type" CONTENT="document">
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| 12 | <META NAME="distribution" CONTENT="global">
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| 19 | </HEAD>
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| 20 | <BODY bgcolor="#ffffff">
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| 21 | <!--Navigation Panel-->
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| 22 | <A NAME="tex2html1015"
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| 23 | HREF="node10.html">
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| 24 | <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A>
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| 25 | <A NAME="tex2html1012"
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| 26 | HREF="manual.html">
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| 27 | <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A>
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| 28 | <A NAME="tex2html1006"
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| 29 | HREF="node8.html">
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| 30 | <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A>
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| 31 | <A NAME="tex2html1014"
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| 32 | HREF="node1.html">
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| 33 | <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents_motif.gif"></A>
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| 34 | <BR>
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| 35 | <B> Next:</B> <A NAME="tex2html1016"
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| 36 | HREF="node10.html">The Polynomial Package</A>
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| 37 | <B> Up:</B> <A NAME="tex2html1013"
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| 38 | HREF="manual.html">CGBLisp User Guide and</A>
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| 39 | <B> Previous:</B> <A NAME="tex2html1007"
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| 40 | HREF="node8.html">The Geometric Theorem Prover</A>
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| 41 | <BR>
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| 42 | <BR>
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| 43 | <!--End of Navigation Panel-->
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| 44 | <!--Table of Child-Links-->
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| 45 | <A NAME="CHILD_LINKS"><strong>Subsections</strong></A>
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| 46 | <UL>
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| 47 | <LI><A NAME="tex2html1017"
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| 48 | HREF="node9.html#SECTION00090010000000000000">
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| 49 | <I>lex<MATH CLASS="INLINE">
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| 50 | >
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| 51 | </MATH></I></A>
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| 52 | <LI><A NAME="tex2html1018"
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| 53 | HREF="node9.html#SECTION00090020000000000000">
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| 54 | <I>total<MATH CLASS="INLINE">
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| 55 | -
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| 56 | </MATH>degree</I></A>
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| 57 | <LI><A NAME="tex2html1019"
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| 58 | HREF="node9.html#SECTION00090030000000000000">
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| 59 | <I>grlex<MATH CLASS="INLINE">
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| 60 | >
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| 61 | </MATH></I></A>
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| 62 | <LI><A NAME="tex2html1020"
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| 63 | HREF="node9.html#SECTION00090040000000000000">
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| 64 | <I>grevlex<MATH CLASS="INLINE">
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| 65 | >
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| 66 | </MATH></I></A>
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| 67 | <LI><A NAME="tex2html1021"
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| 68 | HREF="node9.html#SECTION00090050000000000000">
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| 69 | <I>revlex<MATH CLASS="INLINE">
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| 70 | >
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| 71 | </MATH></I></A>
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| 72 | <LI><A NAME="tex2html1022"
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| 73 | HREF="node9.html#SECTION00090060000000000000">
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| 74 | <I>invlex<MATH CLASS="INLINE">
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| 75 | >
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| 76 | </MATH></I></A>
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| 77 | <LI><A NAME="tex2html1023"
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| 78 | HREF="node9.html#SECTION00090070000000000000">
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| 79 | <I>elimination<MATH CLASS="INLINE">
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| 80 | -
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| 81 | </MATH>order</I></A>
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| 82 | <LI><A NAME="tex2html1024"
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| 83 | HREF="node9.html#SECTION00090080000000000000">
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| 84 | <I>elimination<MATH CLASS="INLINE">
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| 85 | -
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| 86 | </MATH>order<MATH CLASS="INLINE">
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| 87 | -
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| 88 | </MATH>1</I></A>
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| 89 | </UL>
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| 90 | <!--End of Table of Child-Links-->
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| 91 | <HR>
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| 92 | <H1><A NAME="SECTION00090000000000000000">
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| 93 | The Monomial Order Package</A>
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| 94 | </H1>
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| 95 | <H4><A NAME="SECTION00090010000000000000">
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| 96 | <I>lex<MATH CLASS="INLINE">
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| 97 | >
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| 98 | </MATH></I></A>
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| 99 | </H4>
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| 100 | <P><IMG WIDTH="580" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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| 101 | SRC="img149.gif"
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| 102 | ALT="$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$"> [<EM>FUNCTION</EM>]
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| 103 | <BLOCKQUOTE>
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| 104 | Return T if P<MATH CLASS="INLINE">
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| 105 | >
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| 106 | </MATH>Q with respect to lexicographic order, otherwise NIL.
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| 107 | The second returned value is T if P=Q, otherwise it is NIL.</BLOCKQUOTE><H4><A NAME="SECTION00090020000000000000">
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| 108 | <I>total<MATH CLASS="INLINE">
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| 109 | -
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| 110 | </MATH>degree</I></A>
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| 111 | </H4>
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| 112 | <P><IMG WIDTH="522" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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| 113 | SRC="img150.gif"
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| 114 | ALT="$\textstyle\parbox{\pboxargslen}{\em m {\sf \&optional} (start 0) (end (length m)) \/}$"> [<EM>FUNCTION</EM>]
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| 115 | <BLOCKQUOTE>
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| 116 | Return the todal degree of a monomoal M.</BLOCKQUOTE><H4><A NAME="SECTION00090030000000000000">
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| 117 | <I>grlex<MATH CLASS="INLINE">
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| 118 | >
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| 119 | </MATH></I></A>
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| 120 | </H4>
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| 121 | <P><IMG WIDTH="580" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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| 122 | SRC="img149.gif"
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| 123 | ALT="$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$"> [<EM>FUNCTION</EM>]
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| 124 | <BLOCKQUOTE>
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| 125 | Return T if P<MATH CLASS="INLINE">
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| 126 | >
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| 127 | </MATH>Q with respect to graded lexicographic order,
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| 128 | otherwise NIL. The second returned value is T if P=Q, otherwise it is
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| 129 | NIL. </BLOCKQUOTE><H4><A NAME="SECTION00090040000000000000">
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| 130 | <I>grevlex<MATH CLASS="INLINE">
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| 131 | >
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| 132 | </MATH></I></A>
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| 133 | </H4>
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| 134 | <P><IMG WIDTH="580" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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| 135 | SRC="img149.gif"
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| 136 | ALT="$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$"> [<EM>FUNCTION</EM>]
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| 137 | <BLOCKQUOTE>
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| 138 | Return T if P<MATH CLASS="INLINE">
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| 139 | >
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| 140 | </MATH>Q with respect to graded reverse lexicographic order,
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| 141 | NIL otherwise. The second returned value is T if P=Q, otherwise it is
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| 142 | NIL. </BLOCKQUOTE><H4><A NAME="SECTION00090050000000000000">
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| 143 | <I>revlex<MATH CLASS="INLINE">
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| 144 | >
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| 145 | </MATH></I></A>
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| 146 | </H4>
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| 147 | <P><IMG WIDTH="580" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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| 148 | SRC="img149.gif"
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| 149 | ALT="$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$"> [<EM>FUNCTION</EM>]
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| 150 | <BLOCKQUOTE>
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| 151 | Return T if P<MATH CLASS="INLINE">
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| 152 | >
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| 153 | </MATH>Q with respect to reverse lexicographic order, NIL
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| 154 | otherwise. The second returned value is T if P=Q, otherwise it is
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| 155 | NIL. This is not and admissible monomial order because some sets do
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| 156 | not have a minimal element. This order is useful in constructing
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| 157 | other orders.</BLOCKQUOTE><H4><A NAME="SECTION00090060000000000000">
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| 158 | <I>invlex<MATH CLASS="INLINE">
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| 159 | >
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| 160 | </MATH></I></A>
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| 161 | </H4>
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| 162 | <P><IMG WIDTH="580" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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| 163 | SRC="img149.gif"
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| 164 | ALT="$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$"> [<EM>FUNCTION</EM>]
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| 165 | <BLOCKQUOTE>
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| 166 | Return T if P<MATH CLASS="INLINE">
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| 167 | >
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| 168 | </MATH>Q with respect to inverse lexicographic order, NIL
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| 169 | otherwise The second returned value is T if P=Q, otherwise it is NIL.</BLOCKQUOTE><H4><A NAME="SECTION00090070000000000000">
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| 170 | <I>elimination<MATH CLASS="INLINE">
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| 171 | -
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| 172 | </MATH>order</I></A>
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| 173 | </H4>
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| 174 | <P><IMG WIDTH="488" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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| 175 | SRC="img151.gif"
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| 176 | ALT="$\textstyle\parbox{\pboxargslen}{\em k {\sf \&key} (primary$-$order
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| 177 | \char93 'lex$\gt$) (secondary$-$order
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| 178 | \char93 'lex$\gt$) \/}$"> [<EM>FUNCTION</EM>]
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| 179 | <BLOCKQUOTE>
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| 180 | Return a predicate which compares monomials according to the
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| 181 | K<MATH CLASS="INLINE">
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| 182 | -
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| 183 | </MATH>th elimination order. Two optional arguments are PRIMARY<MATH CLASS="INLINE">
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| 184 | -
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| 185 | </MATH>ORDER
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| 186 | and SECONDARY<MATH CLASS="INLINE">
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| 187 | -
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| 188 | </MATH>ORDER and they should be term orders which are used
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| 189 | on the first K and the remaining variables.</BLOCKQUOTE><H4><A NAME="SECTION00090080000000000000">
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| 190 | <I>elimination<MATH CLASS="INLINE">
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| 191 | -
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| 192 | </MATH>order<MATH CLASS="INLINE">
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| 193 | -
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| 194 | </MATH>1</I></A>
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| 195 | </H4>
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| 196 | <P><IMG WIDTH="466" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
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| 197 | SRC="img152.gif"
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| 198 | ALT="$\textstyle\parbox{\pboxargslen}{\em order \/}$"> [<EM>FUNCTION</EM>]
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| 199 | <BLOCKQUOTE>
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| 200 | A special case of the ELIMINATION<MATH CLASS="INLINE">
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| 201 | -
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| 202 | </MATH>ORDER when there is only
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| 203 | one primary variable.</BLOCKQUOTE><HR>
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| 204 | <!--Navigation Panel-->
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| 205 | <A NAME="tex2html1015"
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| 215 | HREF="node1.html">
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| 216 | <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents_motif.gif"></A>
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| 217 | <BR>
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| 218 | <B> Next:</B> <A NAME="tex2html1016"
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| 219 | HREF="node10.html">The Polynomial Package</A>
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| 220 | <B> Up:</B> <A NAME="tex2html1013"
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| 221 | HREF="manual.html">CGBLisp User Guide and</A>
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| 222 | <B> Previous:</B> <A NAME="tex2html1007"
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| 223 | HREF="node8.html">The Geometric Theorem Prover</A>
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| 224 | <!--End of Navigation Panel-->
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| 225 | <ADDRESS>
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| 226 | <I>Marek Rychlik</I>
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| 227 | <BR><I>3/21/1998</I>
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| 228 | </ADDRESS>
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| 229 | </BODY>
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| 230 | </HTML>
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