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1<!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997)
2 by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds
3* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
4* with significant contributions from:
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8<TITLE>The Division Package</TITLE>
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45<A NAME="CHILD_LINKS"><strong>Subsections</strong></A>
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47<LI><A NAME="tex2html935"
48 HREF="node6.html#SECTION00060010000000000000">
49<I>divide</I></A>
50<LI><A NAME="tex2html936"
51 HREF="node6.html#SECTION00060020000000000000">
52<I>poly<MATH CLASS="INLINE">
53-
54</MATH>exact<MATH CLASS="INLINE">
55-
56</MATH>divide</I></A>
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60<H1><A NAME="SECTION00060000000000000000">
61The Division Package</A>
62</H1>
63<H4><A NAME="SECTION00060010000000000000">
64<I>divide</I></A>
65</H4>
66<P><IMG WIDTH="571" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
67 SRC="img114.gif"
68 ALT="$\textstyle\parbox{\pboxargslen}{\em f fl {\sf \&optional} (pred \char93 'lex$\gt$) (ring
69 *coefficient$-$ring*) {\sf \&aux} (s
70 (length
71 fl)) \/}$"> [<EM>FUNCTION</EM>]
72<BLOCKQUOTE>
73Divide polynomial F by a list of polynomials FL; use predicate PRED
74to sort monomials; assumes that the polynomials have initially been
75sorted according to PRED. It returnes multiple values. The first
76value is a list of quotients A. The second value is the remainder R.
77These object satisfy the quation F = SUM A[J]*FL[I] + R.</BLOCKQUOTE><H4><A NAME="SECTION00060020000000000000">
78<I>poly<MATH CLASS="INLINE">
79-
80</MATH>exact<MATH CLASS="INLINE">
81-
82</MATH>divide</I></A>
83</H4>
84<P><IMG WIDTH="480" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
85 SRC="img115.gif"
86 ALT="$\textstyle\parbox{\pboxargslen}{\em f g {\sf \&optional} (order
87 \char93 'lex$\gt$) (ring
88 *coefficient$-$ring*) \/}$"> [<EM>FUNCTION</EM>]
89<BLOCKQUOTE>
90Divide a polynomial F by another polynomial G. Assume that exact
91division with no remainder is possible. Returns the quotient.</BLOCKQUOTE>
92<BR><HR>
93<ADDRESS>
94<I>Marek Rychlik</I>
95<BR><I>3/21/1998</I>
96</ADDRESS>
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