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1<!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997)
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45<A NAME="CHILD_LINKS"><strong>Subsections</strong></A>
46<UL>
47<LI><A NAME="tex2html919"
48 HREF="node5.html#SECTION00050010000000000000">
49<I>ring</I></A>
50<LI><A NAME="tex2html920"
51 HREF="node5.html#SECTION00050020000000000000">
52<I>*ring<MATH CLASS="INLINE">
53-
54</MATH>of<MATH CLASS="INLINE">
55-
56</MATH>integers*</I></A>
57<LI><A NAME="tex2html921"
58 HREF="node5.html#SECTION00050030000000000000">
59<I>*field<MATH CLASS="INLINE">
60-
61</MATH>of<MATH CLASS="INLINE">
62-
63</MATH>rationals*</I></A>
64<LI><A NAME="tex2html922"
65 HREF="node5.html#SECTION00050040000000000000">
66<I>field<MATH CLASS="INLINE">
67-
68</MATH>modulo<MATH CLASS="INLINE">
69-
70</MATH>prime</I></A>
71<LI><A NAME="tex2html923"
72 HREF="node5.html#SECTION00050050000000000000">
73<I>*coefficient<MATH CLASS="INLINE">
74-
75</MATH>ring*</I></A>
76</UL>
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78<HR>
79<H1><A NAME="SECTION00050000000000000000">
80The Coefficient Ring package</A>
81</H1>
82<H4><A NAME="SECTION00050010000000000000">
83<I>ring</I></A>
84</H4>
85<P><IMG WIDTH="565" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
86 SRC="img109.gif"
87 ALT="$\textstyle\parbox{\pboxargslen}{\em + $-$\space * / gcd lcm zerop unit length signum numerator denominator \/}$"> [<EM>STRUCTURE</EM>]
88<BLOCKQUOTE>
89The structure whose slots are bound to functions
90performing usual ring operations. In addition to usual arithmetical
91operations, bindings for other common operations
92which increase efficiency of Grobner basis calculations are also
93included. They are as follows:
94 GCD <MATH CLASS="INLINE">
95-
96</MATH> greatest common divisor;
97 LCM <MATH CLASS="INLINE">
98-
99</MATH> least common multiple;
100 ZEROP <MATH CLASS="INLINE">
101-
102</MATH> test whether an element is zero;
103 SIGNUM <MATH CLASS="INLINE">
104-
105</MATH> the sign of a ring element (+1, <MATH CLASS="INLINE">
106-
107</MATH>1 or zero);
108 UNIT <MATH CLASS="INLINE">
109-
110</MATH> the unit of the ring;
111 NUMERATOR <MATH CLASS="INLINE">
112-
113</MATH> the numerator, if a ring of fractions
114 DENOMINATOR <MATH CLASS="INLINE">
115-
116</MATH> the denominator, if a ring of fractions
117 LENGTH <MATH CLASS="INLINE">
118-
119</MATH> an integer giving the approximate length
120 of the representation; for example, for integers
121 its default binding is #'integer<MATH CLASS="INLINE">
122-
123</MATH>length;</BLOCKQUOTE><H4><A NAME="SECTION00050020000000000000">
124<I>*ring<MATH CLASS="INLINE">
125-
126</MATH>of<MATH CLASS="INLINE">
127-
128</MATH>integers*</I></A>
129</H4>
130<P><IMG WIDTH="482" HEIGHT="90" ALIGN="MIDDLE" BORDER="0"
131 SRC="img110.gif"
132 ALT="$\textstyle\parbox{\pboxargslen}{\em (make$-$ring :+ \char93 '+ :$-$\space \char...
133 ...$-$length :numerator \char93 'numerator
134 :denominator \char93 'denominator) \/}$"> [<EM>VARIABLE</EM>]
135<BLOCKQUOTE>
136Operations in the ring of integers.</BLOCKQUOTE><H4><A NAME="SECTION00050030000000000000">
137<I>*field<MATH CLASS="INLINE">
138-
139</MATH>of<MATH CLASS="INLINE">
140-
141</MATH>rationals*</I></A>
142</H4>
143<P><IMG WIDTH="475" HEIGHT="110" ALIGN="MIDDLE" BORDER="0"
144 SRC="img111.gif"
145 ALT="$\textstyle\parbox{\pboxargslen}{\em (make$-$ring :+ \char93 '+ :$-$\space \char...
146 ...or x))))
147 :numerator \char93 'numerator :denominator
148 \char93 'denominator) \/}$"> [<EM>VARIABLE</EM>]
149<BLOCKQUOTE>
150Operations on the field of rational numbers.</BLOCKQUOTE><H4><A NAME="SECTION00050040000000000000">
151<I>field<MATH CLASS="INLINE">
152-
153</MATH>modulo<MATH CLASS="INLINE">
154-
155</MATH>prime</I></A>
156</H4>
157<P><IMG WIDTH="467" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
158 SRC="img112.gif"
159 ALT="$\textstyle\parbox{\pboxargslen}{\em modulus \/}$"> [<EM>FUNCTION</EM>]
160<BLOCKQUOTE>
161Return a RING structure with operations bound
162to the arithmetical operations modulo MODULUS, which
163should be a prime.</BLOCKQUOTE><H4><A NAME="SECTION00050050000000000000">
164<I>*coefficient<MATH CLASS="INLINE">
165-
166</MATH>ring*</I></A>
167</H4>
168<P><IMG WIDTH="492" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
169 SRC="img113.gif"
170 ALT="$\textstyle\parbox{\pboxargslen}{\em *ring$-$of$-$integers* \/}$"> [<EM>VARIABLE</EM>]
171<BLOCKQUOTE>
172The default RING structure, used in most operations
173on the coefficients of polynomials. It should be carefully
174set if rings other than the default ring is used.</BLOCKQUOTE><HR>
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196<ADDRESS>
197<I>Marek Rychlik</I>
198<BR><I>3/21/1998</I>
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