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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26 | HREF="manual.html">
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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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206 | HREF="node10.html">
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208 | <A NAME="tex2html1012"
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209 | HREF="manual.html">
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212 | HREF="node8.html">
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213 | <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A>
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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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