[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 Comprehensive Gröbner basis package</TITLE>
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| 21 | <!--Navigation Panel-->
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| 23 | HREF="node5.html">
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| 34 | <BR>
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| 35 | <B> Next:</B> <A NAME="tex2html856"
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| 36 | HREF="node5.html">The Coefficient Ring package</A>
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| 39 | <B> Previous:</B> <A NAME="tex2html847"
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| 40 | HREF="node3.html">The String Interface to</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="tex2html857"
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| 48 | HREF="node4.html#SECTION00040010000000000000">
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| 49 | <I>*colored<MATH CLASS="INLINE">
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| 50 | -
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| 51 | </MATH>poly<MATH CLASS="INLINE">
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| 52 | -
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| 53 | </MATH>debug*</I></A>
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| 54 | <LI><A NAME="tex2html858"
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| 55 | HREF="node4.html#SECTION00040020000000000000">
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| 56 | <I>debug<MATH CLASS="INLINE">
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| 57 | -
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| 58 | </MATH>cgb</I></A>
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| 59 | <LI><A NAME="tex2html859"
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| 60 | HREF="node4.html#SECTION00040030000000000000">
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| 61 | <I>make<MATH CLASS="INLINE">
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| 62 | -
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| 63 | </MATH>colored<MATH CLASS="INLINE">
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| 64 | -
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| 65 | </MATH>poly</I></A>
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| 66 | <LI><A NAME="tex2html860"
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| 67 | HREF="node4.html#SECTION00040040000000000000">
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| 68 | <I>make<MATH CLASS="INLINE">
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| 69 | -
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| 70 | </MATH>colored<MATH CLASS="INLINE">
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| 71 | -
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| 72 | </MATH>poly<MATH CLASS="INLINE">
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| 73 | -
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| 74 | </MATH>list</I></A>
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| 75 | <LI><A NAME="tex2html861"
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| 76 | HREF="node4.html#SECTION00040050000000000000">
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| 77 | <I>color<MATH CLASS="INLINE">
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| 78 | -
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| 79 | </MATH>poly<MATH CLASS="INLINE">
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| 80 | -
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| 81 | </MATH>list</I></A>
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| 82 | <LI><A NAME="tex2html862"
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| 83 | HREF="node4.html#SECTION00040060000000000000">
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| 84 | <I>color<MATH CLASS="INLINE">
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| 85 | -
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| 86 | </MATH>poly</I></A>
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| 87 | <LI><A NAME="tex2html863"
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| 88 | HREF="node4.html#SECTION00040070000000000000">
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| 89 | <I>colored<MATH CLASS="INLINE">
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| 90 | -
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| 91 | </MATH>poly<MATH CLASS="INLINE">
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| 92 | -
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| 93 | </MATH>to<MATH CLASS="INLINE">
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| 94 | -
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| 95 | </MATH>poly</I></A>
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| 96 | <LI><A NAME="tex2html864"
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| 97 | HREF="node4.html#SECTION00040080000000000000">
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| 98 | <I>colored<MATH CLASS="INLINE">
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| 99 | -
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| 100 | </MATH>poly<MATH CLASS="INLINE">
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| 101 | -
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| 102 | </MATH>print</I></A>
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| 103 | <LI><A NAME="tex2html865"
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| 104 | HREF="node4.html#SECTION00040090000000000000">
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| 105 | <I>colored<MATH CLASS="INLINE">
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| 106 | -
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| 107 | </MATH>poly<MATH CLASS="INLINE">
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| 108 | -
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| 109 | </MATH>print<MATH CLASS="INLINE">
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| 110 | -
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| 111 | </MATH>list</I></A>
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| 112 | <LI><A NAME="tex2html866"
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| 113 | HREF="node4.html#SECTION000400100000000000000">
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| 114 | <I>determine</I></A>
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| 115 | <LI><A NAME="tex2html867"
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| 116 | HREF="node4.html#SECTION000400110000000000000">
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| 117 | <I>determine<MATH CLASS="INLINE">
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| 118 | -
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| 119 | </MATH>1</I></A>
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| 120 | <LI><A NAME="tex2html868"
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| 121 | HREF="node4.html#SECTION000400120000000000000">
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| 122 | <I>determine<MATH CLASS="INLINE">
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| 123 | -
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| 124 | </MATH>white<MATH CLASS="INLINE">
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| 125 | -
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| 126 | </MATH>term</I></A>
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| 127 | <LI><A NAME="tex2html869"
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| 128 | HREF="node4.html#SECTION000400130000000000000">
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| 129 | <I>cond<MATH CLASS="INLINE">
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| 130 | -
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| 131 | </MATH>system<MATH CLASS="INLINE">
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| 132 | -
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| 133 | </MATH>print</I></A>
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| 134 | <LI><A NAME="tex2html870"
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| 135 | HREF="node4.html#SECTION000400140000000000000">
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| 136 | <I>cond<MATH CLASS="INLINE">
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| 137 | -
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| 138 | </MATH>print</I></A>
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| 139 | <LI><A NAME="tex2html871"
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| 140 | HREF="node4.html#SECTION000400150000000000000">
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| 141 | <I>add<MATH CLASS="INLINE">
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| 142 | -
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| 143 | </MATH>pairs</I></A>
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| 144 | <LI><A NAME="tex2html872"
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| 145 | HREF="node4.html#SECTION000400160000000000000">
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| 146 | <I>cond<MATH CLASS="INLINE">
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| 147 | -
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| 148 | </MATH>part</I></A>
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| 149 | <LI><A NAME="tex2html873"
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| 150 | HREF="node4.html#SECTION000400170000000000000">
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| 151 | <I>cond<MATH CLASS="INLINE">
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| 152 | -
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| 153 | </MATH>hm</I></A>
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| 154 | <LI><A NAME="tex2html874"
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| 155 | HREF="node4.html#SECTION000400180000000000000">
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| 156 | <I>delete<MATH CLASS="INLINE">
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| 157 | -
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| 158 | </MATH>green<MATH CLASS="INLINE">
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| 159 | -
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| 160 | </MATH>polys</I></A>
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| 161 | <LI><A NAME="tex2html875"
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| 162 | HREF="node4.html#SECTION000400190000000000000">
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| 163 | <I>grobner<MATH CLASS="INLINE">
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| 164 | -
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| 165 | </MATH>system</I></A>
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| 166 | <LI><A NAME="tex2html876"
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| 167 | HREF="node4.html#SECTION000400200000000000000">
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| 168 | <I>reorder<MATH CLASS="INLINE">
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| 169 | -
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| 170 | </MATH>pairs</I></A>
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| 171 | <LI><A NAME="tex2html877"
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| 172 | HREF="node4.html#SECTION000400210000000000000">
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| 173 | <I>colored<MATH CLASS="INLINE">
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| 174 | -
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| 175 | </MATH>criterion<MATH CLASS="INLINE">
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| 176 | -
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| 177 | </MATH>1</I></A>
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| 178 | <LI><A NAME="tex2html878"
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| 179 | HREF="node4.html#SECTION000400220000000000000">
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| 180 | <I>colored<MATH CLASS="INLINE">
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| 181 | -
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| 182 | </MATH>criterion<MATH CLASS="INLINE">
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| 183 | -
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| 184 | </MATH>2</I></A>
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| 185 | <LI><A NAME="tex2html879"
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| 186 | HREF="node4.html#SECTION000400230000000000000">
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| 187 | <I>cond<MATH CLASS="INLINE">
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| 188 | -
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| 189 | </MATH>normal<MATH CLASS="INLINE">
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| 190 | -
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| 191 | </MATH>form</I></A>
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| 192 | <LI><A NAME="tex2html880"
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| 193 | HREF="node4.html#SECTION000400240000000000000">
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| 194 | <I>cond<MATH CLASS="INLINE">
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| 195 | -
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| 196 | </MATH>spoly</I></A>
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| 197 | <LI><A NAME="tex2html881"
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| 198 | HREF="node4.html#SECTION000400250000000000000">
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| 199 | <I>cond<MATH CLASS="INLINE">
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| 200 | -
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| 201 | </MATH>lm</I></A>
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| 202 | <LI><A NAME="tex2html882"
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| 203 | HREF="node4.html#SECTION000400260000000000000">
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| 204 | <I>cond<MATH CLASS="INLINE">
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| 205 | -
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| 206 | </MATH>lc</I></A>
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| 207 | <LI><A NAME="tex2html883"
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| 208 | HREF="node4.html#SECTION000400270000000000000">
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| 209 | <I>colored<MATH CLASS="INLINE">
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| 210 | -
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| 211 | </MATH>term<MATH CLASS="INLINE">
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| 212 | -
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| 213 | </MATH>times<MATH CLASS="INLINE">
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| 214 | -
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| 215 | </MATH>poly</I></A>
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| 216 | <LI><A NAME="tex2html884"
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| 217 | HREF="node4.html#SECTION000400280000000000000">
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| 218 | <I>colored<MATH CLASS="INLINE">
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| 219 | -
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| 220 | </MATH>scalar<MATH CLASS="INLINE">
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| 221 | -
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| 222 | </MATH>times<MATH CLASS="INLINE">
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| 223 | -
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| 224 | </MATH>poly</I></A>
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| 225 | <LI><A NAME="tex2html885"
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| 226 | HREF="node4.html#SECTION000400290000000000000">
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| 227 | <I>colored<MATH CLASS="INLINE">
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| 228 | -
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| 229 | </MATH>term*</I></A>
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| 230 | <LI><A NAME="tex2html886"
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| 231 | HREF="node4.html#SECTION000400300000000000000">
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| 232 | <I>color*</I></A>
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| 233 | <LI><A NAME="tex2html887"
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| 234 | HREF="node4.html#SECTION000400310000000000000">
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| 235 | <I>color+</I></A>
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| 236 | <LI><A NAME="tex2html888"
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| 237 | HREF="node4.html#SECTION000400320000000000000">
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| 238 | <I>color<MATH CLASS="INLINE">
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| 239 | -
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| 240 | </MATH></I></A>
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| 241 | <LI><A NAME="tex2html889"
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| 242 | HREF="node4.html#SECTION000400330000000000000">
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| 243 | <I>colored<MATH CLASS="INLINE">
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| 244 | -
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| 245 | </MATH>poly+</I></A>
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| 246 | <LI><A NAME="tex2html890"
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| 247 | HREF="node4.html#SECTION000400340000000000000">
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| 248 | <I>colored<MATH CLASS="INLINE">
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| 249 | -
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| 250 | </MATH>poly<MATH CLASS="INLINE">
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| 251 | -
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| 252 | </MATH></I></A>
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| 253 | <LI><A NAME="tex2html891"
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| 254 | HREF="node4.html#SECTION000400350000000000000">
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| 255 | <I>colored<MATH CLASS="INLINE">
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| 256 | -
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| 257 | </MATH>term<MATH CLASS="INLINE">
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| 258 | -
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| 259 | </MATH>uminus</I></A>
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| 260 | <LI><A NAME="tex2html892"
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| 261 | HREF="node4.html#SECTION000400360000000000000">
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| 262 | <I>colored<MATH CLASS="INLINE">
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| 263 | -
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| 264 | </MATH>minus<MATH CLASS="INLINE">
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| 265 | -
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| 266 | </MATH>poly</I></A>
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| 267 | <LI><A NAME="tex2html893"
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| 268 | HREF="node4.html#SECTION000400370000000000000">
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| 269 | <I>string<MATH CLASS="INLINE">
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| 270 | -
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| 271 | </MATH>grobner<MATH CLASS="INLINE">
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| 272 | -
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| 273 | </MATH>system</I></A>
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| 274 | <LI><A NAME="tex2html894"
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| 275 | HREF="node4.html#SECTION000400380000000000000">
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| 276 | <I>string<MATH CLASS="INLINE">
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| 277 | -
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| 278 | </MATH>cond</I></A>
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| 279 | <LI><A NAME="tex2html895"
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| 280 | HREF="node4.html#SECTION000400390000000000000">
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| 281 | <I>string<MATH CLASS="INLINE">
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| 282 | -
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| 283 | </MATH>cover</I></A>
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| 284 | <LI><A NAME="tex2html896"
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| 285 | HREF="node4.html#SECTION000400400000000000000">
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| 286 | <I>saturate<MATH CLASS="INLINE">
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| 287 | -
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| 288 | </MATH>cover</I></A>
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| 289 | <LI><A NAME="tex2html897"
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| 290 | HREF="node4.html#SECTION000400410000000000000">
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| 291 | <I>saturate<MATH CLASS="INLINE">
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| 292 | -
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| 293 | </MATH>cond</I></A>
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| 294 | <LI><A NAME="tex2html898"
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| 295 | HREF="node4.html#SECTION000400420000000000000">
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| 296 | <I>string<MATH CLASS="INLINE">
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| 297 | -
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| 298 | </MATH>determine</I></A>
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| 299 | <LI><A NAME="tex2html899"
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| 300 | HREF="node4.html#SECTION000400430000000000000">
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| 301 | <I>tidy<MATH CLASS="INLINE">
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| 302 | -
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| 303 | </MATH>grobner<MATH CLASS="INLINE">
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| 304 | -
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| 305 | </MATH>system</I></A>
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| 306 | <LI><A NAME="tex2html900"
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| 307 | HREF="node4.html#SECTION000400440000000000000">
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| 308 | <I>tidy<MATH CLASS="INLINE">
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| 309 | -
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| 310 | </MATH>pair</I></A>
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| 311 | <LI><A NAME="tex2html901"
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| 312 | HREF="node4.html#SECTION000400450000000000000">
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| 313 | <I>tidy<MATH CLASS="INLINE">
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| 314 | -
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| 315 | </MATH>cond</I></A>
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| 316 | <LI><A NAME="tex2html902"
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| 317 | HREF="node4.html#SECTION000400460000000000000">
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| 318 | <I>colored<MATH CLASS="INLINE">
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| 319 | -
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| 320 | </MATH>reduction</I></A>
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| 321 | <LI><A NAME="tex2html903"
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| 322 | HREF="node4.html#SECTION000400470000000000000">
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| 323 | <I>green<MATH CLASS="INLINE">
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| 324 | -
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| 325 | </MATH>reduce<MATH CLASS="INLINE">
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| 326 | -
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| 327 | </MATH>colored<MATH CLASS="INLINE">
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| 328 | -
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| 329 | </MATH>poly</I></A>
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| 330 | <LI><A NAME="tex2html904"
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| 331 | HREF="node4.html#SECTION000400480000000000000">
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| 332 | <I>green<MATH CLASS="INLINE">
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| 333 | -
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| 334 | </MATH>reduce<MATH CLASS="INLINE">
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| 335 | -
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| 336 | </MATH>colored<MATH CLASS="INLINE">
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| 337 | -
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| 338 | </MATH>list</I></A>
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| 339 | <LI><A NAME="tex2html905"
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| 340 | HREF="node4.html#SECTION000400490000000000000">
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| 341 | <I>cond<MATH CLASS="INLINE">
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| 342 | -
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| 343 | </MATH>system<MATH CLASS="INLINE">
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| 344 | -
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| 345 | </MATH>green<MATH CLASS="INLINE">
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| 346 | -
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| 347 | </MATH>reduce</I></A>
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| 348 | <LI><A NAME="tex2html906"
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| 349 | HREF="node4.html#SECTION000400500000000000000">
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| 350 | <I>parse<MATH CLASS="INLINE">
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| 351 | -
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| 352 | </MATH>to<MATH CLASS="INLINE">
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| 353 | -
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| 354 | </MATH>colored<MATH CLASS="INLINE">
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| 355 | -
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| 356 | </MATH>poly<MATH CLASS="INLINE">
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| 357 | -
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| 358 | </MATH>list</I></A>
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| 359 | <LI><A NAME="tex2html907"
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| 360 | HREF="node4.html#SECTION000400510000000000000">
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| 361 | <I>red<MATH CLASS="INLINE">
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| 362 | -
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| 363 | </MATH>reduction</I></A>
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| 364 | </UL>
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| 365 | <!--End of Table of Child-Links-->
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| 366 | <HR>
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| 367 | <H1><A NAME="SECTION00040000000000000000">
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| 368 | The Comprehensive Gröbner basis package</A>
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| 369 | </H1>
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| 370 | <H4><A NAME="SECTION00040010000000000000">
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| 371 | <I>*colored<MATH CLASS="INLINE">
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| 372 | -
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| 373 | </MATH>poly<MATH CLASS="INLINE">
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| 374 | -
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| 375 | </MATH>debug*</I></A>
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| 376 | </H4>
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| 377 | <P><IMG WIDTH="495" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
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| 378 | SRC="img1.gif"
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| 379 | ALT="$\textstyle\parbox{\pboxargslen}{\em nil \/}$"> [<EM>VARIABLE</EM>]
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| 380 | <BLOCKQUOTE>
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| 381 | If true debugging output is on.</BLOCKQUOTE><H4><A NAME="SECTION00040020000000000000">
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| 382 | <I>debug<MATH CLASS="INLINE">
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| 383 | -
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| 384 | </MATH>cgb</I></A>
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| 385 | </H4>
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| 386 | <P><IMG WIDTH="576" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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| 387 | SRC="img7.gif"
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| 388 | ALT="$\textstyle\parbox{\pboxargslen}{\em {\sf \&rest} args \/}$"> [<EM>MACRO</EM>]
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| 389 | <BLOCKQUOTE>
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| 390 | </BLOCKQUOTE><H4><A NAME="SECTION00040030000000000000">
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| 391 | <I>make<MATH CLASS="INLINE">
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| 392 | -
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| 393 | </MATH>colored<MATH CLASS="INLINE">
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| 394 | -
|
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| 395 | </MATH>poly</I></A>
|
---|
| 396 | </H4>
|
---|
| 397 | <P><IMG WIDTH="471" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
|
---|
| 398 | SRC="img67.gif"
|
---|
| 399 | ALT="$\textstyle\parbox{\pboxargslen}{\em poly k {\sf \&key} (key
|
---|
| 400 | \char93 'identity)...
|
---|
| 401 | ...er
|
---|
| 402 | \char93 'lex$\gt$) (parameter$-$order
|
---|
| 403 | \char93 'lex$\gt$) {\sf \&aux} l \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 404 | <BLOCKQUOTE>
|
---|
| 405 | Colored poly is represented as a list
|
---|
| 406 | (TERM1 TERM2 ... TERMS)
|
---|
| 407 | where each term is a triple
|
---|
| 408 | (MONOM . (POLY . COLOR))
|
---|
| 409 | where monoms and polys have common number of variables while color is
|
---|
| 410 | one of the three: :RED, :GREEN or :WHITE. This function translates
|
---|
| 411 | an ordinary polynomial into a colored one by dividing variables into
|
---|
| 412 | K and N<MATH CLASS="INLINE">
|
---|
| 413 | -
|
---|
| 414 | </MATH>K, where N is the total number of variables in the
|
---|
| 415 | polynomial poly; the function KEY can be called to select variables
|
---|
| 416 | in arbitrary order.</BLOCKQUOTE><H4><A NAME="SECTION00040040000000000000">
|
---|
| 417 | <I>make<MATH CLASS="INLINE">
|
---|
| 418 | -
|
---|
| 419 | </MATH>colored<MATH CLASS="INLINE">
|
---|
| 420 | -
|
---|
| 421 | </MATH>poly<MATH CLASS="INLINE">
|
---|
| 422 | -
|
---|
| 423 | </MATH>list</I></A>
|
---|
| 424 | </H4>
|
---|
| 425 | <P><IMG WIDTH="438" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 426 | SRC="img68.gif"
|
---|
| 427 | ALT="$\textstyle\parbox{\pboxargslen}{\em plist {\sf \&rest} rest \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 428 | <BLOCKQUOTE>
|
---|
| 429 | Translate a list of polynomials PLIST into a list of colored
|
---|
| 430 | polynomials by calling MAKE<MATH CLASS="INLINE">
|
---|
| 431 | -
|
---|
| 432 | </MATH>COLORED<MATH CLASS="INLINE">
|
---|
| 433 | -
|
---|
| 434 | </MATH>POLY. Returns the resulting
|
---|
| 435 | list. </BLOCKQUOTE><H4><A NAME="SECTION00040050000000000000">
|
---|
| 436 | <I>color<MATH CLASS="INLINE">
|
---|
| 437 | -
|
---|
| 438 | </MATH>poly<MATH CLASS="INLINE">
|
---|
| 439 | -
|
---|
| 440 | </MATH>list</I></A>
|
---|
| 441 | </H4>
|
---|
| 442 | <P><IMG WIDTH="503" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
---|
| 443 | SRC="img69.gif"
|
---|
| 444 | ALT="$\textstyle\parbox{\pboxargslen}{\em flist {\sf \&optional} (cond (list nil nil)) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 445 | <BLOCKQUOTE>
|
---|
| 446 | Add colors to an ordinary list of polynomials FLIST, according to a
|
---|
| 447 | condition COND. A condition is a pair of polynomial lists. Each
|
---|
| 448 | polynomial in COND is a polynomial in parameters only. The list
|
---|
| 449 | (FIRST COND) is called the ``green list'' and it consists of
|
---|
| 450 | polynomials which vanish for the parameters associated with the
|
---|
| 451 | condition. The list (SECOND COND) is called the ``red list</BLOCKQUOTE><H4><A NAME="SECTION00040060000000000000">
|
---|
| 452 | <I>color<MATH CLASS="INLINE">
|
---|
| 453 | -
|
---|
| 454 | </MATH>poly</I></A>
|
---|
| 455 | </H4>
|
---|
| 456 | <P><IMG WIDTH="536" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
---|
| 457 | SRC="img70.gif"
|
---|
| 458 | ALT="$\textstyle\parbox{\pboxargslen}{\em f {\sf \&optional} (cond (list nil nil)) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 459 | <BLOCKQUOTE>
|
---|
| 460 | Add color to a single polynomial F, according to condition COND.
|
---|
| 461 | See the documentation of COLOR<MATH CLASS="INLINE">
|
---|
| 462 | -
|
---|
| 463 | </MATH>POLY<MATH CLASS="INLINE">
|
---|
| 464 | -
|
---|
| 465 | </MATH>LIST.</BLOCKQUOTE><H4><A NAME="SECTION00040070000000000000">
|
---|
| 466 | <I>colored<MATH CLASS="INLINE">
|
---|
| 467 | -
|
---|
| 468 | </MATH>poly<MATH CLASS="INLINE">
|
---|
| 469 | -
|
---|
| 470 | </MATH>to<MATH CLASS="INLINE">
|
---|
| 471 | -
|
---|
| 472 | </MATH>poly</I></A>
|
---|
| 473 | </H4>
|
---|
| 474 | <P><IMG WIDTH="451" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 475 | SRC="img71.gif"
|
---|
| 476 | ALT="$\textstyle\parbox{\pboxargslen}{\em cpoly \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 477 | <BLOCKQUOTE>
|
---|
| 478 | For a given colored polynomial CPOLY, removes the colors and
|
---|
| 479 | it returns the polynomial as an ordinary polynomial with
|
---|
| 480 | coefficients which are polynomials in parameters.</BLOCKQUOTE><H4><A NAME="SECTION00040080000000000000">
|
---|
| 481 | <I>colored<MATH CLASS="INLINE">
|
---|
| 482 | -
|
---|
| 483 | </MATH>poly<MATH CLASS="INLINE">
|
---|
| 484 | -
|
---|
| 485 | </MATH>print</I></A>
|
---|
| 486 | </H4>
|
---|
| 487 | <P><IMG WIDTH="475" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
|
---|
| 488 | SRC="img72.gif"
|
---|
| 489 | ALT="$\textstyle\parbox{\pboxargslen}{\em poly vars {\sf \&key} (stream
|
---|
| 490 | t) (beg
|
---|
| 491 | t) (print$-$green$-$part
|
---|
| 492 | nil) (mark$-$coefficients
|
---|
| 493 | nil) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 494 | <BLOCKQUOTE>
|
---|
| 495 | Print a colored polynomial POLY. Use variables VARS to represent
|
---|
| 496 | the variables. Some of the variables are going to be used as
|
---|
| 497 | parameters, according to the length of the monomials in the main
|
---|
| 498 | monomial and coefficient part of each term in POLY. The key variable
|
---|
| 499 | STREAM may be used to redirect the output. If parameter
|
---|
| 500 | PRINT<MATH CLASS="INLINE">
|
---|
| 501 | -
|
---|
| 502 | </MATH>GREEN<MATH CLASS="INLINE">
|
---|
| 503 | -
|
---|
| 504 | </MATH>PART is set then the coefficients which have color
|
---|
| 505 | :GREEN will be printed, otherwise they are discarded silently. If
|
---|
| 506 | MARK<MATH CLASS="INLINE">
|
---|
| 507 | -
|
---|
| 508 | </MATH>COEFFICIENTS is not NIL then every coefficient will be marked
|
---|
| 509 | according to its color, for instance G(U<MATH CLASS="INLINE">
|
---|
| 510 | -
|
---|
| 511 | </MATH>1) would mean that U<MATH CLASS="INLINE">
|
---|
| 512 | -
|
---|
| 513 | </MATH>1
|
---|
| 514 | is in the green list. Returns P.</BLOCKQUOTE><H4><A NAME="SECTION00040090000000000000">
|
---|
| 515 | <I>colored<MATH CLASS="INLINE">
|
---|
| 516 | -
|
---|
| 517 | </MATH>poly<MATH CLASS="INLINE">
|
---|
| 518 | -
|
---|
| 519 | </MATH>print<MATH CLASS="INLINE">
|
---|
| 520 | -
|
---|
| 521 | </MATH>list</I></A>
|
---|
| 522 | </H4>
|
---|
| 523 | <P><IMG WIDTH="442" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
|
---|
| 524 | SRC="img73.gif"
|
---|
| 525 | ALT="$\textstyle\parbox{\pboxargslen}{\em poly$-$list vars {\sf \&key} (stream
|
---|
| 526 | t) (beg
|
---|
| 527 | t) (print$-$green$-$part
|
---|
| 528 | nil) (mark$-$coefficients
|
---|
| 529 | nil) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 530 | <BLOCKQUOTE>
|
---|
| 531 | Pring a list of colored polynomials via a call to
|
---|
| 532 | COLORED<MATH CLASS="INLINE">
|
---|
| 533 | -
|
---|
| 534 | </MATH>POLY<MATH CLASS="INLINE">
|
---|
| 535 | -
|
---|
| 536 | </MATH>PRINT.</BLOCKQUOTE><H4><A NAME="SECTION000400100000000000000">
|
---|
| 537 | <I>determine</I></A>
|
---|
| 538 | </H4>
|
---|
| 539 | <P><IMG WIDTH="543" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
---|
| 540 | SRC="img74.gif"
|
---|
| 541 | ALT="$\textstyle\parbox{\pboxargslen}{\em f {\sf \&optional} (cond (list nil nil)) (order
|
---|
| 542 | \char93 'lex$\gt$) (ring
|
---|
| 543 | *coefficient$-$ring*) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 544 | <BLOCKQUOTE>
|
---|
| 545 | This function takes a list of colored polynomials F and a condition
|
---|
| 546 | COND, and it returns a list of pairs (COND' F') such that COND' cover
|
---|
| 547 | COND and F' is a ``determined'' version of the colored polynomial
|
---|
| 548 | list F, i.e. every polynomial has its leading coefficient determined.
|
---|
| 549 | This means that some of the initial coefficients in each polynomial
|
---|
| 550 | in F' are in the green list of COND, and the first non<MATH CLASS="INLINE">
|
---|
| 551 | -
|
---|
| 552 | </MATH>green
|
---|
| 553 | coefficient is in the red list of COND. We note that F' differs from
|
---|
| 554 | F only by different colors: some of the terms marked :WHITE are now
|
---|
| 555 | marked either :GREEN or :RED. Coloring is done either by explicitly
|
---|
| 556 | checking membership in red or green list of COND, or implicitly by
|
---|
| 557 | performing Grobner basis calculations in the polynomial ring over the
|
---|
| 558 | parameters. The admissible monomial order ORDER is used only in the
|
---|
| 559 | parameter space. Also, the ring structure RING is used only for
|
---|
| 560 | calculations on polynomials of the parameters only.</BLOCKQUOTE><H4><A NAME="SECTION000400110000000000000">
|
---|
| 561 | <I>determine<MATH CLASS="INLINE">
|
---|
| 562 | -
|
---|
| 563 | </MATH>1</I></A>
|
---|
| 564 | </H4>
|
---|
| 565 | <P><IMG WIDTH="522" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 566 | SRC="img75.gif"
|
---|
| 567 | ALT="$\textstyle\parbox{\pboxargslen}{\em cond p end gp order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 568 | <BLOCKQUOTE>
|
---|
| 569 | Determine a single colored polynomial P according to condition COND.
|
---|
| 570 | Prepend green part GP to P. Cons the result with END, which should be
|
---|
| 571 | a list of colored polynomials, and return the resulting list of
|
---|
| 572 | polynomials. This is an auxillary function of DETERMINE.</BLOCKQUOTE><H4><A NAME="SECTION000400120000000000000">
|
---|
| 573 | <I>determine<MATH CLASS="INLINE">
|
---|
| 574 | -
|
---|
| 575 | </MATH>white<MATH CLASS="INLINE">
|
---|
| 576 | -
|
---|
| 577 | </MATH>term</I></A>
|
---|
| 578 | </H4>
|
---|
| 579 | <P><IMG WIDTH="448" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 580 | SRC="img76.gif"
|
---|
| 581 | ALT="$\textstyle\parbox{\pboxargslen}{\em cond term restp end gp order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 582 | <BLOCKQUOTE>
|
---|
| 583 | This is an auxillary function of DETERMINE. In this function the
|
---|
| 584 | parameter COND is a condition. The parameters TERM, RESTP and GP are
|
---|
| 585 | three parts of a polynomial being processed, where TERM is colored
|
---|
| 586 | :WHITE. We test the membership in the red and green list of COND we
|
---|
| 587 | try to determine whether the term is :RED or :GREEN. This is done by
|
---|
| 588 | performing ideal membership tests in the polynomial ring. Let C be
|
---|
| 589 | the coefficient of TERM. Thus, C is a polynomial in parameters. We
|
---|
| 590 | find whether C is in the green list by performing a plain ideal
|
---|
| 591 | membership test. However, to test properly whether C is in the red
|
---|
| 592 | list, one needs a different strategy. In fact, we test whether
|
---|
| 593 | adding C to the red list would produce a non<MATH CLASS="INLINE">
|
---|
| 594 | -
|
---|
| 595 | </MATH>empty set of
|
---|
| 596 | parameters in some algebraic extension. The test is whether 1 belongs
|
---|
| 597 | to the saturation ideal of (FIRST COND) in (CONS C (SECOND COND)).
|
---|
| 598 | Thus, we use POLY<MATH CLASS="INLINE">
|
---|
| 599 | -
|
---|
| 600 | </MATH>SATURATION. If we are successful in determining
|
---|
| 601 | the color of TERM, we simply change the color of the term and return
|
---|
| 602 | the list ((COND P)) where P is obtained by appending GP, (LIST TERM)
|
---|
| 603 | and RESTP. If we cannot determine whether TERM is :RED or :GREEN, we
|
---|
| 604 | return the list ((COND' P') (COND'' P</BLOCKQUOTE><H4><A NAME="SECTION000400130000000000000">
|
---|
| 605 | <I>cond<MATH CLASS="INLINE">
|
---|
| 606 | -
|
---|
| 607 | </MATH>system<MATH CLASS="INLINE">
|
---|
| 608 | -
|
---|
| 609 | </MATH>print</I></A>
|
---|
| 610 | </H4>
|
---|
| 611 | <P><IMG WIDTH="474" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
|
---|
| 612 | SRC="img77.gif"
|
---|
| 613 | ALT="$\textstyle\parbox{\pboxargslen}{\em system vars params {\sf \&key} (suppress$-$...
|
---|
| 614 | ...rint$-$green$-$part
|
---|
| 615 | nil) (mark$-$coefficients
|
---|
| 616 | nil) {\sf \&aux} (label
|
---|
| 617 | 0) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 618 | <BLOCKQUOTE>
|
---|
| 619 | A conditional system SYSTEM is a list of pairs (COND PLIST), where
|
---|
| 620 | COND is a condition (a pair (GREEN<MATH CLASS="INLINE">
|
---|
| 621 | -
|
---|
| 622 | </MATH>LIST RED<MATH CLASS="INLINE">
|
---|
| 623 | -
|
---|
| 624 | </MATH>LIST)) and PLIST is a
|
---|
| 625 | list of colored polynomials. This function pretty<MATH CLASS="INLINE">
|
---|
| 626 | -
|
---|
| 627 | </MATH>prints this list
|
---|
| 628 | of pairs. A conditional system is the data structure returned by
|
---|
| 629 | GROBNER<MATH CLASS="INLINE">
|
---|
| 630 | -
|
---|
| 631 | </MATH>SYSTEM. This function returns SYSTEM, if SUPPRESS<MATH CLASS="INLINE">
|
---|
| 632 | -
|
---|
| 633 | </MATH>VALUE
|
---|
| 634 | is non<MATH CLASS="INLINE">
|
---|
| 635 | -
|
---|
| 636 | </MATH>NIL and no value otherwise. If MARK<MATH CLASS="INLINE">
|
---|
| 637 | -
|
---|
| 638 | </MATH>COEFFICIENTS is
|
---|
| 639 | non<MATH CLASS="INLINE">
|
---|
| 640 | -
|
---|
| 641 | </MATH>NIL coefficients will be marked as in G(u<MATH CLASS="INLINE">
|
---|
| 642 | -
|
---|
| 643 | </MATH>1)*x+R(2)*y, which
|
---|
| 644 | means that u<MATH CLASS="INLINE">
|
---|
| 645 | -
|
---|
| 646 | </MATH>1 is :GREEN and 2 is :RED. </BLOCKQUOTE><H4><A NAME="SECTION000400140000000000000">
|
---|
| 647 | <I>cond<MATH CLASS="INLINE">
|
---|
| 648 | -
|
---|
| 649 | </MATH>print</I></A>
|
---|
| 650 | </H4>
|
---|
| 651 | <P><IMG WIDTH="533" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 652 | SRC="img78.gif"
|
---|
| 653 | ALT="$\textstyle\parbox{\pboxargslen}{\em cond params \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 654 | <BLOCKQUOTE>
|
---|
| 655 | Pretty<MATH CLASS="INLINE">
|
---|
| 656 | -
|
---|
| 657 | </MATH>print a condition COND, using symbol list PARAMS as
|
---|
| 658 | parameter names. </BLOCKQUOTE><H4><A NAME="SECTION000400150000000000000">
|
---|
| 659 | <I>add<MATH CLASS="INLINE">
|
---|
| 660 | -
|
---|
| 661 | </MATH>pairs</I></A>
|
---|
| 662 | </H4>
|
---|
| 663 | <P><IMG WIDTH="541" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 664 | SRC="img79.gif"
|
---|
| 665 | ALT="$\textstyle\parbox{\pboxargslen}{\em gs pred \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 666 | <BLOCKQUOTE>
|
---|
| 667 | The parameter GS shoud be a Grobner system, i.e. a set of pairs
|
---|
| 668 | (CONDITION POLY<MATH CLASS="INLINE">
|
---|
| 669 | -
|
---|
| 670 | </MATH>LIST) This functions adds the third component: the
|
---|
| 671 | list of initial critical pairs (I J), as in the ordinary Grobner
|
---|
| 672 | basis algorithm. In addition, it adds the length of of the
|
---|
| 673 | POLY<MATH CLASS="INLINE">
|
---|
| 674 | -
|
---|
| 675 | </MATH>LIST, less 1, as the fourth component. The resulting list of
|
---|
| 676 | quadruples is returned.</BLOCKQUOTE><H4><A NAME="SECTION000400160000000000000">
|
---|
| 677 | <I>cond<MATH CLASS="INLINE">
|
---|
| 678 | -
|
---|
| 679 | </MATH>part</I></A>
|
---|
| 680 | </H4>
|
---|
| 681 | <P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
|
---|
| 682 | SRC="img80.gif"
|
---|
| 683 | ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 684 | <BLOCKQUOTE>
|
---|
| 685 | Find the part of a colored polynomial P starting with the first
|
---|
| 686 | non<MATH CLASS="INLINE">
|
---|
| 687 | -
|
---|
| 688 | </MATH>green term.</BLOCKQUOTE><H4><A NAME="SECTION000400170000000000000">
|
---|
| 689 | <I>cond<MATH CLASS="INLINE">
|
---|
| 690 | -
|
---|
| 691 | </MATH>hm</I></A>
|
---|
| 692 | </H4>
|
---|
| 693 | <P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
|
---|
| 694 | SRC="img80.gif"
|
---|
| 695 | ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 696 | <BLOCKQUOTE>
|
---|
| 697 | Return the conditional head monomial of a colored polynomial P.</BLOCKQUOTE><H4><A NAME="SECTION000400180000000000000">
|
---|
| 698 | <I>delete<MATH CLASS="INLINE">
|
---|
| 699 | -
|
---|
| 700 | </MATH>green<MATH CLASS="INLINE">
|
---|
| 701 | -
|
---|
| 702 | </MATH>polys</I></A>
|
---|
| 703 | </H4>
|
---|
| 704 | <P><IMG WIDTH="472" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
|
---|
| 705 | SRC="img81.gif"
|
---|
| 706 | ALT="$\textstyle\parbox{\pboxargslen}{\em gamma \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 707 | <BLOCKQUOTE>
|
---|
| 708 | Delete totally green polynomials from in a grobner system GAMMA.</BLOCKQUOTE><H4><A NAME="SECTION000400190000000000000">
|
---|
| 709 | <I>grobner<MATH CLASS="INLINE">
|
---|
| 710 | -
|
---|
| 711 | </MATH>system</I></A>
|
---|
| 712 | </H4>
|
---|
| 713 | <P><IMG WIDTH="499" HEIGHT="130" ALIGN="MIDDLE" BORDER="0"
|
---|
| 714 | SRC="img82.gif"
|
---|
| 715 | ALT="$\textstyle\parbox{\pboxargslen}{\em f {\sf \&key} (cover (list '(nil nil))) (ma...
|
---|
| 716 | ...char93 '(lambda (cond) (determine f cond parameter$-$order ring))
|
---|
| 717 | cover))) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 718 | <BLOCKQUOTE>
|
---|
| 719 | This function returns a grobner system, given a list of colored
|
---|
| 720 | polynomials F, Other parameters are:
|
---|
| 721 | A cover COVER, i.e. a list of conditions, i.e. pairs of the form
|
---|
| 722 | (GREEN<MATH CLASS="INLINE">
|
---|
| 723 | -
|
---|
| 724 | </MATH>LIST RED<MATH CLASS="INLINE">
|
---|
| 725 | -
|
---|
| 726 | </MATH>LIST), where GREEN<MATH CLASS="INLINE">
|
---|
| 727 | -
|
---|
| 728 | </MATH>LIST and RED<MATH CLASS="INLINE">
|
---|
| 729 | -
|
---|
| 730 | </MATH>LIST are to
|
---|
| 731 | lists of ordinary polynomials in parameters. A monomial order
|
---|
| 732 | MAIN<MATH CLASS="INLINE">
|
---|
| 733 | -
|
---|
| 734 | </MATH>ORDER used on main variables (not parameters). A monomial
|
---|
| 735 | order PARAMETER<MATH CLASS="INLINE">
|
---|
| 736 | -
|
---|
| 737 | </MATH>ORDER used in calculations with parameters only.
|
---|
| 738 | REDUCE, a flag deciding whether COLORED<MATH CLASS="INLINE">
|
---|
| 739 | -
|
---|
| 740 | </MATH>REDUCTION will be performed
|
---|
| 741 | on the resulting grobner system. GREEN<MATH CLASS="INLINE">
|
---|
| 742 | -
|
---|
| 743 | </MATH>REDUCE, a flag deciding
|
---|
| 744 | whether the green list of each condition will be reduced in a form of
|
---|
| 745 | a reduced Grobner basis. TOP<MATH CLASS="INLINE">
|
---|
| 746 | -
|
---|
| 747 | </MATH>REDUCTION<MATH CLASS="INLINE">
|
---|
| 748 | -
|
---|
| 749 | </MATH>ONLY, a flag deciding
|
---|
| 750 | whether in the internal calculations in the space of parameters top
|
---|
| 751 | reduction only will be used. RING, a structure as in the package
|
---|
| 752 | COEFFICIENT<MATH CLASS="INLINE">
|
---|
| 753 | -
|
---|
| 754 | </MATH>RING, used in operations on the coefficients of the
|
---|
| 755 | polynomials in parameters. </BLOCKQUOTE><H4><A NAME="SECTION000400200000000000000">
|
---|
| 756 | <I>reorder<MATH CLASS="INLINE">
|
---|
| 757 | -
|
---|
| 758 | </MATH>pairs</I></A>
|
---|
| 759 | </H4>
|
---|
| 760 | <P><IMG WIDTH="518" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
---|
| 761 | SRC="img83.gif"
|
---|
| 762 | ALT="$\textstyle\parbox{\pboxargslen}{\em b bnew g pred {\sf \&optional} (sort$-$first nil) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 763 | <BLOCKQUOTE>
|
---|
| 764 | Reorder pairs according to some heuristic. The heuristic at this time
|
---|
| 765 | is ad hoc, in the future it should be replaced with sugar strategy
|
---|
| 766 | and a mechanism for implementing new heuristic strategies, as in the
|
---|
| 767 | GROBNER package. </BLOCKQUOTE><H4><A NAME="SECTION000400210000000000000">
|
---|
| 768 | <I>colored<MATH CLASS="INLINE">
|
---|
| 769 | -
|
---|
| 770 | </MATH>criterion<MATH CLASS="INLINE">
|
---|
| 771 | -
|
---|
| 772 | </MATH>1</I></A>
|
---|
| 773 | </H4>
|
---|
| 774 | <P><IMG WIDTH="471" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 775 | SRC="img84.gif"
|
---|
| 776 | ALT="$\textstyle\parbox{\pboxargslen}{\em i j f \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 777 | <BLOCKQUOTE>
|
---|
| 778 | Buchberger criterion 1 for colored polynomials.</BLOCKQUOTE><H4><A NAME="SECTION000400220000000000000">
|
---|
| 779 | <I>colored<MATH CLASS="INLINE">
|
---|
| 780 | -
|
---|
| 781 | </MATH>criterion<MATH CLASS="INLINE">
|
---|
| 782 | -
|
---|
| 783 | </MATH>2</I></A>
|
---|
| 784 | </H4>
|
---|
| 785 | <P><IMG WIDTH="471" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 786 | SRC="img85.gif"
|
---|
| 787 | ALT="$\textstyle\parbox{\pboxargslen}{\em i j f b s \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 788 | <BLOCKQUOTE>
|
---|
| 789 | Buchberger criterion 2 for colored polynomials.</BLOCKQUOTE><H4><A NAME="SECTION000400230000000000000">
|
---|
| 790 | <I>cond<MATH CLASS="INLINE">
|
---|
| 791 | -
|
---|
| 792 | </MATH>normal<MATH CLASS="INLINE">
|
---|
| 793 | -
|
---|
| 794 | </MATH>form</I></A>
|
---|
| 795 | </H4>
|
---|
| 796 | <P><IMG WIDTH="474" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 797 | SRC="img86.gif"
|
---|
| 798 | ALT="$\textstyle\parbox{\pboxargslen}{\em f fl main$-$order parameter$-$order top$-$reduction$-$only ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 799 | <BLOCKQUOTE>
|
---|
| 800 | Returns the conditional normal form of a colored polynomial F with
|
---|
| 801 | respect to the list of colored polynomials FL. The list FL is assumed
|
---|
| 802 | to consist of determined polynomials, i.e. such that the first term
|
---|
| 803 | which is not marked :GREEN is :RED.</BLOCKQUOTE><H4><A NAME="SECTION000400240000000000000">
|
---|
| 804 | <I>cond<MATH CLASS="INLINE">
|
---|
| 805 | -
|
---|
| 806 | </MATH>spoly</I></A>
|
---|
| 807 | </H4>
|
---|
| 808 | <P><IMG WIDTH="530" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 809 | SRC="img87.gif"
|
---|
| 810 | ALT="$\textstyle\parbox{\pboxargslen}{\em f g main$-$order parameter$-$order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 811 | <BLOCKQUOTE>
|
---|
| 812 | Returns the conditional S<MATH CLASS="INLINE">
|
---|
| 813 | -
|
---|
| 814 | </MATH>polynomial of two colored polynomials F
|
---|
| 815 | and G. Both polynomials are assumed to be determined.</BLOCKQUOTE><H4><A NAME="SECTION000400250000000000000">
|
---|
| 816 | <I>cond<MATH CLASS="INLINE">
|
---|
| 817 | -
|
---|
| 818 | </MATH>lm</I></A>
|
---|
| 819 | </H4>
|
---|
| 820 | <P><IMG WIDTH="549" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 821 | SRC="img88.gif"
|
---|
| 822 | ALT="$\textstyle\parbox{\pboxargslen}{\em f \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 823 | <BLOCKQUOTE>
|
---|
| 824 | Returns the conditional leading monomial of a colored polynomial F,
|
---|
| 825 | which is assumed to be determined.</BLOCKQUOTE><H4><A NAME="SECTION000400260000000000000">
|
---|
| 826 | <I>cond<MATH CLASS="INLINE">
|
---|
| 827 | -
|
---|
| 828 | </MATH>lc</I></A>
|
---|
| 829 | </H4>
|
---|
| 830 | <P><IMG WIDTH="549" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 831 | SRC="img88.gif"
|
---|
| 832 | ALT="$\textstyle\parbox{\pboxargslen}{\em f \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 833 | <BLOCKQUOTE>
|
---|
| 834 | Returns the conditional leading coefficient of a colored polynomial
|
---|
| 835 | F, which is assumed to be determined.</BLOCKQUOTE><H4><A NAME="SECTION000400270000000000000">
|
---|
| 836 | <I>colored<MATH CLASS="INLINE">
|
---|
| 837 | -
|
---|
| 838 | </MATH>term<MATH CLASS="INLINE">
|
---|
| 839 | -
|
---|
| 840 | </MATH>times<MATH CLASS="INLINE">
|
---|
| 841 | -
|
---|
| 842 | </MATH>poly</I></A>
|
---|
| 843 | </H4>
|
---|
| 844 | <P><IMG WIDTH="426" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 845 | SRC="img89.gif"
|
---|
| 846 | ALT="$\textstyle\parbox{\pboxargslen}{\em term f order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 847 | <BLOCKQUOTE>
|
---|
| 848 | Returns the product of a colored term TERM and a colored polynomial
|
---|
| 849 | F. </BLOCKQUOTE><H4><A NAME="SECTION000400280000000000000">
|
---|
| 850 | <I>colored<MATH CLASS="INLINE">
|
---|
| 851 | -
|
---|
| 852 | </MATH>scalar<MATH CLASS="INLINE">
|
---|
| 853 | -
|
---|
| 854 | </MATH>times<MATH CLASS="INLINE">
|
---|
| 855 | -
|
---|
| 856 | </MATH>poly</I></A>
|
---|
| 857 | </H4>
|
---|
| 858 | <P><IMG WIDTH="419" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 859 | SRC="img90.gif"
|
---|
| 860 | ALT="$\textstyle\parbox{\pboxargslen}{\em c f ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 861 | <BLOCKQUOTE>
|
---|
| 862 | Returns the product of an element of the coefficient ring C a colored
|
---|
| 863 | polynomial F. </BLOCKQUOTE><H4><A NAME="SECTION000400290000000000000">
|
---|
| 864 | <I>colored<MATH CLASS="INLINE">
|
---|
| 865 | -
|
---|
| 866 | </MATH>term*</I></A>
|
---|
| 867 | </H4>
|
---|
| 868 | <P><IMG WIDTH="509" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 869 | SRC="img91.gif"
|
---|
| 870 | ALT="$\textstyle\parbox{\pboxargslen}{\em term1 term2 order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 871 | <BLOCKQUOTE>
|
---|
| 872 | Returns the product of two colored terms TERM1 and TERM2.</BLOCKQUOTE><H4><A NAME="SECTION000400300000000000000">
|
---|
| 873 | <I>color*</I></A>
|
---|
| 874 | </H4>
|
---|
| 875 | <P><IMG WIDTH="570" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
|
---|
| 876 | SRC="img92.gif"
|
---|
| 877 | ALT="$\textstyle\parbox{\pboxargslen}{\em c1 c2 \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 878 | <BLOCKQUOTE>
|
---|
| 879 | Returns a product of two colores. Rules:
|
---|
| 880 | :red * :red yields :red
|
---|
| 881 | any * :green yields :green
|
---|
| 882 | otherwise the result is :white.</BLOCKQUOTE><H4><A NAME="SECTION000400310000000000000">
|
---|
| 883 | <I>color+</I></A>
|
---|
| 884 | </H4>
|
---|
| 885 | <P><IMG WIDTH="570" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
|
---|
| 886 | SRC="img92.gif"
|
---|
| 887 | ALT="$\textstyle\parbox{\pboxargslen}{\em c1 c2 \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 888 | <BLOCKQUOTE>
|
---|
| 889 | Returns a sum of colors. Rules:
|
---|
| 890 | :green + :green yields :green,
|
---|
| 891 | :red + :green yields :red
|
---|
| 892 | any other result is :white.</BLOCKQUOTE><H4><A NAME="SECTION000400320000000000000">
|
---|
| 893 | <I>color<MATH CLASS="INLINE">
|
---|
| 894 | -
|
---|
| 895 | </MATH></I></A>
|
---|
| 896 | </H4>
|
---|
| 897 | <P><IMG WIDTH="570" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
|
---|
| 898 | SRC="img92.gif"
|
---|
| 899 | ALT="$\textstyle\parbox{\pboxargslen}{\em c1 c2 \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 900 | <BLOCKQUOTE>
|
---|
| 901 | Identical to COLOR+.</BLOCKQUOTE><H4><A NAME="SECTION000400330000000000000">
|
---|
| 902 | <I>colored<MATH CLASS="INLINE">
|
---|
| 903 | -
|
---|
| 904 | </MATH>poly+</I></A>
|
---|
| 905 | </H4>
|
---|
| 906 | <P><IMG WIDTH="508" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 907 | SRC="img93.gif"
|
---|
| 908 | ALT="$\textstyle\parbox{\pboxargslen}{\em p q main$-$order parameter$-$order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 909 | <BLOCKQUOTE>
|
---|
| 910 | Returns the sum of colored polynomials P and Q.</BLOCKQUOTE><H4><A NAME="SECTION000400340000000000000">
|
---|
| 911 | <I>colored<MATH CLASS="INLINE">
|
---|
| 912 | -
|
---|
| 913 | </MATH>poly<MATH CLASS="INLINE">
|
---|
| 914 | -
|
---|
| 915 | </MATH></I></A>
|
---|
| 916 | </H4>
|
---|
| 917 | <P><IMG WIDTH="508" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 918 | SRC="img93.gif"
|
---|
| 919 | ALT="$\textstyle\parbox{\pboxargslen}{\em p q main$-$order parameter$-$order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 920 | <BLOCKQUOTE>
|
---|
| 921 | Returns the difference of colored polynomials P and Q.</BLOCKQUOTE><H4><A NAME="SECTION000400350000000000000">
|
---|
| 922 | <I>colored<MATH CLASS="INLINE">
|
---|
| 923 | -
|
---|
| 924 | </MATH>term<MATH CLASS="INLINE">
|
---|
| 925 | -
|
---|
| 926 | </MATH>uminus</I></A>
|
---|
| 927 | </H4>
|
---|
| 928 | <P><IMG WIDTH="455" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
|
---|
| 929 | SRC="img94.gif"
|
---|
| 930 | ALT="$\textstyle\parbox{\pboxargslen}{\em term ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 931 | <BLOCKQUOTE>
|
---|
| 932 | Returns the negation of a colored term TERM.</BLOCKQUOTE><H4><A NAME="SECTION000400360000000000000">
|
---|
| 933 | <I>colored<MATH CLASS="INLINE">
|
---|
| 934 | -
|
---|
| 935 | </MATH>minus<MATH CLASS="INLINE">
|
---|
| 936 | -
|
---|
| 937 | </MATH>poly</I></A>
|
---|
| 938 | </H4>
|
---|
| 939 | <P><IMG WIDTH="446" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
|
---|
| 940 | SRC="img9.gif"
|
---|
| 941 | ALT="$\textstyle\parbox{\pboxargslen}{\em p ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 942 | <BLOCKQUOTE>
|
---|
| 943 | Returns the negation of a colored polynomial P.</BLOCKQUOTE><H4><A NAME="SECTION000400370000000000000">
|
---|
| 944 | <I>string<MATH CLASS="INLINE">
|
---|
| 945 | -
|
---|
| 946 | </MATH>grobner<MATH CLASS="INLINE">
|
---|
| 947 | -
|
---|
| 948 | </MATH>system</I></A>
|
---|
| 949 | </H4>
|
---|
| 950 | <P><IMG WIDTH="447" HEIGHT="150" ALIGN="MIDDLE" BORDER="0"
|
---|
| 951 | SRC="img95.gif"
|
---|
| 952 | ALT="$\textstyle\parbox{\pboxargslen}{\em f vars params {\sf \&key} (cover
|
---|
| 953 | (list
|
---|
| 954 | (l...
|
---|
| 955 | ...meter$-$order)) (cover
|
---|
| 956 | (string$-$cover
|
---|
| 957 | cover
|
---|
| 958 | params
|
---|
| 959 | parameter$-$order)) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 960 | <BLOCKQUOTE>
|
---|
| 961 | An interface to GROBNER<MATH CLASS="INLINE">
|
---|
| 962 | -
|
---|
| 963 | </MATH>SYSTEM in which polynomials can be
|
---|
| 964 | specified in infix notations as strings. Lists of polynomials are
|
---|
| 965 | comma<MATH CLASS="INLINE">
|
---|
| 966 | -
|
---|
| 967 | </MATH>separated list marked by a matchfix operators [] </BLOCKQUOTE><H4><A NAME="SECTION000400380000000000000">
|
---|
| 968 | <I>string<MATH CLASS="INLINE">
|
---|
| 969 | -
|
---|
| 970 | </MATH>cond</I></A>
|
---|
| 971 | </H4>
|
---|
| 972 | <P><IMG WIDTH="527" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
---|
| 973 | SRC="img96.gif"
|
---|
| 974 | ALT="$\textstyle\parbox{\pboxargslen}{\em cond params {\sf \&optional} (order \char93 'lex$\gt$) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 975 | <BLOCKQUOTE>
|
---|
| 976 | Return the internal representation of a condition COND, specified
|
---|
| 977 | as pairs of strings (GREEN<MATH CLASS="INLINE">
|
---|
| 978 | -
|
---|
| 979 | </MATH>LIST RED<MATH CLASS="INLINE">
|
---|
| 980 | -
|
---|
| 981 | </MATH>LIST). GREEN<MATH CLASS="INLINE">
|
---|
| 982 | -
|
---|
| 983 | </MATH>LIST and
|
---|
| 984 | RED<MATH CLASS="INLINE">
|
---|
| 985 | -
|
---|
| 986 | </MATH>LIST in the input are assumed to be strings which parse to two
|
---|
| 987 | lists of polynomials with respect to variables whose names are in the
|
---|
| 988 | list of symbols PARAMS. ORDER is the predicate used to sort the terms
|
---|
| 989 | of the polynomials.</BLOCKQUOTE><H4><A NAME="SECTION000400390000000000000">
|
---|
| 990 | <I>string<MATH CLASS="INLINE">
|
---|
| 991 | -
|
---|
| 992 | </MATH>cover</I></A>
|
---|
| 993 | </H4>
|
---|
| 994 | <P><IMG WIDTH="523" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
---|
| 995 | SRC="img97.gif"
|
---|
| 996 | ALT="$\textstyle\parbox{\pboxargslen}{\em cover params {\sf \&optional} (order \char93 'lex$\gt$) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 997 | <BLOCKQUOTE>
|
---|
| 998 | Returns the internal representation of COVER, given in the form of
|
---|
| 999 | a list of conditions. See STRING<MATH CLASS="INLINE">
|
---|
| 1000 | -
|
---|
| 1001 | </MATH>COND for description of a
|
---|
| 1002 | condition. </BLOCKQUOTE><H4><A NAME="SECTION000400400000000000000">
|
---|
| 1003 | <I>saturate<MATH CLASS="INLINE">
|
---|
| 1004 | -
|
---|
| 1005 | </MATH>cover</I></A>
|
---|
| 1006 | </H4>
|
---|
| 1007 | <P><IMG WIDTH="506" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1008 | SRC="img98.gif"
|
---|
| 1009 | ALT="$\textstyle\parbox{\pboxargslen}{\em cover order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1010 | <BLOCKQUOTE>
|
---|
| 1011 | Brings every condition of a list of conditions COVER to the form (G
|
---|
| 1012 | R) where G is saturated with respect to R and G is a Grobner basis
|
---|
| 1013 | We could reduce R so that the elements of R are relatively prime,
|
---|
| 1014 | but this is not currently done.</BLOCKQUOTE><H4><A NAME="SECTION000400410000000000000">
|
---|
| 1015 | <I>saturate<MATH CLASS="INLINE">
|
---|
| 1016 | -
|
---|
| 1017 | </MATH>cond</I></A>
|
---|
| 1018 | </H4>
|
---|
| 1019 | <P><IMG WIDTH="510" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1020 | SRC="img99.gif"
|
---|
| 1021 | ALT="$\textstyle\parbox{\pboxargslen}{\em cond order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1022 | <BLOCKQUOTE>
|
---|
| 1023 | Saturate a single condition COND. An auxillary function of
|
---|
| 1024 | SATURATE<MATH CLASS="INLINE">
|
---|
| 1025 | -
|
---|
| 1026 | </MATH>COVER. </BLOCKQUOTE><H4><A NAME="SECTION000400420000000000000">
|
---|
| 1027 | <I>string<MATH CLASS="INLINE">
|
---|
| 1028 | -
|
---|
| 1029 | </MATH>determine</I></A>
|
---|
| 1030 | </H4>
|
---|
| 1031 | <P><IMG WIDTH="492" HEIGHT="130" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1032 | SRC="img100.gif"
|
---|
| 1033 | ALT="$\textstyle\parbox{\pboxargslen}{\em f vars params {\sf \&key} (cond
|
---|
| 1034 | '([] [])) ...
|
---|
| 1035 | ...arameter$-$order)) (cond
|
---|
| 1036 | (string$-$cond
|
---|
| 1037 | cond
|
---|
| 1038 | params
|
---|
| 1039 | parameter$-$order)) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1040 | <BLOCKQUOTE>
|
---|
| 1041 | A string interface to DETERMINE. See the documentation of
|
---|
| 1042 | STRING<MATH CLASS="INLINE">
|
---|
| 1043 | -
|
---|
| 1044 | </MATH>GROBNER<MATH CLASS="INLINE">
|
---|
| 1045 | -
|
---|
| 1046 | </MATH>SYSTEM. </BLOCKQUOTE><H4><A NAME="SECTION000400430000000000000">
|
---|
| 1047 | <I>tidy<MATH CLASS="INLINE">
|
---|
| 1048 | -
|
---|
| 1049 | </MATH>grobner<MATH CLASS="INLINE">
|
---|
| 1050 | -
|
---|
| 1051 | </MATH>system</I></A>
|
---|
| 1052 | </H4>
|
---|
| 1053 | <P><IMG WIDTH="460" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1054 | SRC="img101.gif"
|
---|
| 1055 | ALT="$\textstyle\parbox{\pboxargslen}{\em gs main$-$order parameter$-$order reduce green$-$reduce ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1056 | <BLOCKQUOTE>
|
---|
| 1057 | Apply TIDY<MATH CLASS="INLINE">
|
---|
| 1058 | -
|
---|
| 1059 | </MATH>PAIR to every pair of a Grobner system.</BLOCKQUOTE><H4><A NAME="SECTION000400440000000000000">
|
---|
| 1060 | <I>tidy<MATH CLASS="INLINE">
|
---|
| 1061 | -
|
---|
| 1062 | </MATH>pair</I></A>
|
---|
| 1063 | </H4>
|
---|
| 1064 | <P><IMG WIDTH="546" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1065 | SRC="img102.gif"
|
---|
| 1066 | ALT="$\textstyle\parbox{\pboxargslen}{\em pair main$-$order parameter$-$order reduce green$-$reduce ring {\sf \&aux} gs \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1067 | <BLOCKQUOTE>
|
---|
| 1068 | Make the output of Grobner system more readable by performing
|
---|
| 1069 | certain simplifications on an element of a Grobner system.
|
---|
| 1070 | If REDUCE is non<MATH CLASS="INLINE">
|
---|
| 1071 | -
|
---|
| 1072 | </MATH>NIL then COLORED<MATH CLASS="INLINE">
|
---|
| 1073 | -
|
---|
| 1074 | </MATH>reduction will be performed.
|
---|
| 1075 | In addition TIDY<MATH CLASS="INLINE">
|
---|
| 1076 | -
|
---|
| 1077 | </MATH>COND is called on the condition part of the pair
|
---|
| 1078 | PAIR. </BLOCKQUOTE><H4><A NAME="SECTION000400450000000000000">
|
---|
| 1079 | <I>tidy<MATH CLASS="INLINE">
|
---|
| 1080 | -
|
---|
| 1081 | </MATH>cond</I></A>
|
---|
| 1082 | </H4>
|
---|
| 1083 | <P><IMG WIDTH="510" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1084 | SRC="img99.gif"
|
---|
| 1085 | ALT="$\textstyle\parbox{\pboxargslen}{\em cond order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1086 | <BLOCKQUOTE>
|
---|
| 1087 | Currently saturates condition COND and does RED<MATH CLASS="INLINE">
|
---|
| 1088 | -
|
---|
| 1089 | </MATH>REDUCTION on the
|
---|
| 1090 | red list. </BLOCKQUOTE><H4><A NAME="SECTION000400460000000000000">
|
---|
| 1091 | <I>colored<MATH CLASS="INLINE">
|
---|
| 1092 | -
|
---|
| 1093 | </MATH>reduction</I></A>
|
---|
| 1094 | </H4>
|
---|
| 1095 | <P><IMG WIDTH="485" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1096 | SRC="img103.gif"
|
---|
| 1097 | ALT="$\textstyle\parbox{\pboxargslen}{\em cond p main$-$order parameter$-$order ring {\sf \&aux} (open
|
---|
| 1098 | (list
|
---|
| 1099 | (list
|
---|
| 1100 | cond
|
---|
| 1101 | nil
|
---|
| 1102 | p))) closed \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1103 | <BLOCKQUOTE>
|
---|
| 1104 | Reduce a list of colored polynomials P. The difficulty as compared
|
---|
| 1105 | to the usual Buchberger algorithm is that the polys may have the same
|
---|
| 1106 | leading monomial which may result in cancellations and polynomials
|
---|
| 1107 | which may not be determined. Thus, when we find those, we will have
|
---|
| 1108 | to split the condition by calling determine. Returns a list of pairs
|
---|
| 1109 | (COND' P') where P' is a reduced grobner basis with respect to any
|
---|
| 1110 | parameter choice compatible with condition COND'. Moreover, COND'
|
---|
| 1111 | form a cover of COND.</BLOCKQUOTE><H4><A NAME="SECTION000400470000000000000">
|
---|
| 1112 | <I>green<MATH CLASS="INLINE">
|
---|
| 1113 | -
|
---|
| 1114 | </MATH>reduce<MATH CLASS="INLINE">
|
---|
| 1115 | -
|
---|
| 1116 | </MATH>colored<MATH CLASS="INLINE">
|
---|
| 1117 | -
|
---|
| 1118 | </MATH>poly</I></A>
|
---|
| 1119 | </H4>
|
---|
| 1120 | <P><IMG WIDTH="413" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1121 | SRC="img104.gif"
|
---|
| 1122 | ALT="$\textstyle\parbox{\pboxargslen}{\em cond f parameter$-$order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1123 | <BLOCKQUOTE>
|
---|
| 1124 | It takes a colored polynomial F and it returns a modified
|
---|
| 1125 | polynomial obtained by reducing coefficient of F modulo green list of
|
---|
| 1126 | the condition COND.</BLOCKQUOTE><H4><A NAME="SECTION000400480000000000000">
|
---|
| 1127 | <I>green<MATH CLASS="INLINE">
|
---|
| 1128 | -
|
---|
| 1129 | </MATH>reduce<MATH CLASS="INLINE">
|
---|
| 1130 | -
|
---|
| 1131 | </MATH>colored<MATH CLASS="INLINE">
|
---|
| 1132 | -
|
---|
| 1133 | </MATH>list</I></A>
|
---|
| 1134 | </H4>
|
---|
| 1135 | <P><IMG WIDTH="421" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1136 | SRC="img105.gif"
|
---|
| 1137 | ALT="$\textstyle\parbox{\pboxargslen}{\em cond fl parameter$-$order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1138 | <BLOCKQUOTE>
|
---|
| 1139 | Apply GREEN<MATH CLASS="INLINE">
|
---|
| 1140 | -
|
---|
| 1141 | </MATH>REDUCE<MATH CLASS="INLINE">
|
---|
| 1142 | -
|
---|
| 1143 | </MATH>COLORED<MATH CLASS="INLINE">
|
---|
| 1144 | -
|
---|
| 1145 | </MATH>POLY to a list of polynomials FL.</BLOCKQUOTE><H4><A NAME="SECTION000400490000000000000">
|
---|
| 1146 | <I>cond<MATH CLASS="INLINE">
|
---|
| 1147 | -
|
---|
| 1148 | </MATH>system<MATH CLASS="INLINE">
|
---|
| 1149 | -
|
---|
| 1150 | </MATH>green<MATH CLASS="INLINE">
|
---|
| 1151 | -
|
---|
| 1152 | </MATH>reduce</I></A>
|
---|
| 1153 | </H4>
|
---|
| 1154 | <P><IMG WIDTH="411" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1155 | SRC="img106.gif"
|
---|
| 1156 | ALT="$\textstyle\parbox{\pboxargslen}{\em gs parameter$-$order ring \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1157 | <BLOCKQUOTE>
|
---|
| 1158 | Apply GREEN<MATH CLASS="INLINE">
|
---|
| 1159 | -
|
---|
| 1160 | </MATH>REDUCE<MATH CLASS="INLINE">
|
---|
| 1161 | -
|
---|
| 1162 | </MATH>COLORED<MATH CLASS="INLINE">
|
---|
| 1163 | -
|
---|
| 1164 | </MATH>LIST to every pair of
|
---|
| 1165 | a grobner system GS.</BLOCKQUOTE><H4><A NAME="SECTION000400500000000000000">
|
---|
| 1166 | <I>parse<MATH CLASS="INLINE">
|
---|
| 1167 | -
|
---|
| 1168 | </MATH>to<MATH CLASS="INLINE">
|
---|
| 1169 | -
|
---|
| 1170 | </MATH>colored<MATH CLASS="INLINE">
|
---|
| 1171 | -
|
---|
| 1172 | </MATH>poly<MATH CLASS="INLINE">
|
---|
| 1173 | -
|
---|
| 1174 | </MATH>list</I></A>
|
---|
| 1175 | </H4>
|
---|
| 1176 | <P><IMG WIDTH="412" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1177 | SRC="img107.gif"
|
---|
| 1178 | ALT="$\textstyle\parbox{\pboxargslen}{\em f vars params main$-$order parameter$-$order {\sf \&aux} (k
|
---|
| 1179 | (length
|
---|
| 1180 | vars)) (vars$-$params
|
---|
| 1181 | (append
|
---|
| 1182 | vars
|
---|
| 1183 | params)) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1184 | <BLOCKQUOTE>
|
---|
| 1185 | Parse a list of polynomials F, given as a string, with respect to
|
---|
| 1186 | a list of variables VARS, given as a list of symbols, to the internal
|
---|
| 1187 | representation of a colored polynomial. The polynomials will be
|
---|
| 1188 | properly sorted by MAIN<MATH CLASS="INLINE">
|
---|
| 1189 | -
|
---|
| 1190 | </MATH>ORDER, with the coefficients, which are
|
---|
| 1191 | polynomials in parameters, sorted by PARAMETER<MATH CLASS="INLINE">
|
---|
| 1192 | -
|
---|
| 1193 | </MATH>ORDER. Both orders
|
---|
| 1194 | must be admissible monomial orders. This form is suitable for parsing
|
---|
| 1195 | polynomials with integer coefficients.</BLOCKQUOTE><H4><A NAME="SECTION000400510000000000000">
|
---|
| 1196 | <I>red<MATH CLASS="INLINE">
|
---|
| 1197 | -
|
---|
| 1198 | </MATH>reduction</I></A>
|
---|
| 1199 | </H4>
|
---|
| 1200 | <P><IMG WIDTH="513" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
---|
| 1201 | SRC="img108.gif"
|
---|
| 1202 | ALT="$\textstyle\parbox{\pboxargslen}{\em p pred ring {\sf \&aux} (p
|
---|
| 1203 | (remove$-$if
|
---|
| 1204 | \char93 'poly$-$constant$-$p
|
---|
| 1205 | p)) \/}$"> [<EM>FUNCTION</EM>]
|
---|
| 1206 | <BLOCKQUOTE>
|
---|
| 1207 | Takes a family of polynomials and produce a list whose prime factors
|
---|
| 1208 | are the same but they are relatively prime
|
---|
| 1209 | Repetitively used the following procedure: it finds two elements f, g
|
---|
| 1210 | of P which are not relatively prime; it replaces f and g with
|
---|
| 1211 | f/GCD(f,g), g/ GCD(f,f) and GCD(f,g).</BLOCKQUOTE><HR>
|
---|
| 1212 | <!--Navigation Panel-->
|
---|
| 1213 | <A NAME="tex2html855"
|
---|
| 1214 | HREF="node5.html">
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|
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| 1217 | HREF="manual.html">
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| 1218 | <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A>
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| 1219 | <A NAME="tex2html846"
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| 1220 | HREF="node3.html">
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| 1221 | <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A>
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| 1222 | <A NAME="tex2html854"
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| 1223 | HREF="node1.html">
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| 1224 | <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents_motif.gif"></A>
|
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| 1225 | <BR>
|
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| 1226 | <B> Next:</B> <A NAME="tex2html856"
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| 1227 | HREF="node5.html">The Coefficient Ring package</A>
|
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| 1228 | <B> Up:</B> <A NAME="tex2html853"
|
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| 1229 | HREF="manual.html">CGBLisp User Guide and</A>
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| 1230 | <B> Previous:</B> <A NAME="tex2html847"
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| 1231 | HREF="node3.html">The String Interface to</A>
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| 1232 | <!--End of Navigation Panel-->
|
---|
| 1233 | <ADDRESS>
|
---|
| 1234 | <I>Marek Rychlik</I>
|
---|
| 1235 | <BR><I>3/21/1998</I>
|
---|
| 1236 | </ADDRESS>
|
---|
| 1237 | </BODY>
|
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| 1238 | </HTML>
|
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