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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:
5 Jens Lippman, Marek Rouchal, Martin Wilck and others -->
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8<TITLE>The Parser Package</TITLE>
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34<BR>
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38 HREF="manual.html">CGBLisp User Guide and</A>
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40 HREF="node10.html">The Polynomial Package</A>
41<BR>
42<BR>
43<!--End of Navigation Panel-->
44<!--Table of Child-Links-->
45<A NAME="CHILD_LINKS"><strong>Subsections</strong></A>
46<UL>
47<LI><A NAME="tex2html1065"
48 HREF="node11.html#SECTION000110010000000000000">
49<I>parse</I></A>
50<LI><A NAME="tex2html1066"
51 HREF="node11.html#SECTION000110020000000000000">
52<I>alist<MATH CLASS="INLINE">
53-
54</MATH>form</I></A>
55<LI><A NAME="tex2html1067"
56 HREF="node11.html#SECTION000110030000000000000">
57<I>alist<MATH CLASS="INLINE">
58-
59</MATH>form<MATH CLASS="INLINE">
60-
61</MATH>1</I></A>
62<LI><A NAME="tex2html1068"
63 HREF="node11.html#SECTION000110040000000000000">
64<I>powers</I></A>
65<LI><A NAME="tex2html1069"
66 HREF="node11.html#SECTION000110050000000000000">
67<I>parse<MATH CLASS="INLINE">
68-
69</MATH>to<MATH CLASS="INLINE">
70-
71</MATH>alist</I></A>
72<LI><A NAME="tex2html1070"
73 HREF="node11.html#SECTION000110060000000000000">
74<I>parse<MATH CLASS="INLINE">
75-
76</MATH>string<MATH CLASS="INLINE">
77-
78</MATH>to<MATH CLASS="INLINE">
79-
80</MATH>alist</I></A>
81<LI><A NAME="tex2html1071"
82 HREF="node11.html#SECTION000110070000000000000">
83<I>parse<MATH CLASS="INLINE">
84-
85</MATH>to<MATH CLASS="INLINE">
86-
87</MATH>sorted<MATH CLASS="INLINE">
88-
89</MATH>alist</I></A>
90<LI><A NAME="tex2html1072"
91 HREF="node11.html#SECTION000110080000000000000">
92<I>parse<MATH CLASS="INLINE">
93-
94</MATH>string<MATH CLASS="INLINE">
95-
96</MATH>to<MATH CLASS="INLINE">
97-
98</MATH>sorted<MATH CLASS="INLINE">
99-
100</MATH>alist</I></A>
101<LI><A NAME="tex2html1073"
102 HREF="node11.html#SECTION000110090000000000000">
103<I>sort<MATH CLASS="INLINE">
104-
105</MATH>poly<MATH CLASS="INLINE">
106-
107</MATH>1</I></A>
108<LI><A NAME="tex2html1074"
109 HREF="node11.html#SECTION0001100100000000000000">
110<I>sort<MATH CLASS="INLINE">
111-
112</MATH>poly</I></A>
113<LI><A NAME="tex2html1075"
114 HREF="node11.html#SECTION0001100110000000000000">
115<I>poly<MATH CLASS="INLINE">
116-
117</MATH>eval<MATH CLASS="INLINE">
118-
119</MATH>1</I></A>
120<LI><A NAME="tex2html1076"
121 HREF="node11.html#SECTION0001100120000000000000">
122<I>poly<MATH CLASS="INLINE">
123-
124</MATH>eval</I></A>
125<LI><A NAME="tex2html1077"
126 HREF="node11.html#SECTION0001100130000000000000">
127<I>monom<MATH CLASS="INLINE">
128-
129</MATH>basis</I></A>
130<LI><A NAME="tex2html1078"
131 HREF="node11.html#SECTION0001100140000000000000">
132<I>convert<MATH CLASS="INLINE">
133-
134</MATH>number</I></A>
135<LI><A NAME="tex2html1079"
136 HREF="node11.html#SECTION0001100150000000000000">
137<I>$poly+</I></A>
138<LI><A NAME="tex2html1080"
139 HREF="node11.html#SECTION0001100160000000000000">
140<I>$poly<MATH CLASS="INLINE">
141-
142</MATH></I></A>
143<LI><A NAME="tex2html1081"
144 HREF="node11.html#SECTION0001100170000000000000">
145<I>$minus<MATH CLASS="INLINE">
146-
147</MATH>poly</I></A>
148<LI><A NAME="tex2html1082"
149 HREF="node11.html#SECTION0001100180000000000000">
150<I>$poly*</I></A>
151<LI><A NAME="tex2html1083"
152 HREF="node11.html#SECTION0001100190000000000000">
153<I>$poly/</I></A>
154<LI><A NAME="tex2html1084"
155 HREF="node11.html#SECTION0001100200000000000000">
156<I>$poly<MATH CLASS="INLINE">
157-
158</MATH>expt</I></A>
159</UL>
160<!--End of Table of Child-Links-->
161<HR>
162<H1><A NAME="SECTION000110000000000000000">
163The Parser Package</A>
164</H1>
165<H4><A NAME="SECTION000110010000000000000">
166<I>parse</I></A>
167</H4>
168<P><IMG WIDTH="576" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
169 SRC="img162.gif"
170 ALT="$\textstyle\parbox{\pboxargslen}{\em {\sf \&optional} stream \/}$"> [<EM>FUNCTION</EM>]
171<BLOCKQUOTE>
172Parser of infis expressions with integer/rational coefficients
173The parser will recognize two kinds of polynomial expressions:
174<MATH CLASS="INLINE">
175-
176</MATH> polynomials in fully expanded forms with coefficients
177 written in front of symbolic expressions; constants can be
178optionally enclosed in (); for example, the infix form
179X&#94;2<MATH CLASS="INLINE">
180-
181</MATH>Y&#94;2+(<MATH CLASS="INLINE">
182-
183</MATH>4/3)*U&#94;2*W&#94;3<MATH CLASS="INLINE">
184-
185</MATH>5 parses to
186 (+ (<MATH CLASS="INLINE">
187-
188</MATH> (EXPT X 2) (EXPT Y 2)) (* (<MATH CLASS="INLINE">
189-
190</MATH> (/ 4 3)) (EXPT U 2) (EXPT W
1913)) (<MATH CLASS="INLINE">
192-
193</MATH> 5))
194<MATH CLASS="INLINE">
195-
196</MATH> lists of polynomials; for example
197 [X<MATH CLASS="INLINE">
198-
199</MATH>Y, X&#94;2+3*Z]
200 parses to
201 (:[ (<MATH CLASS="INLINE">
202-
203</MATH> X Y) (+ (EXPT X 2) (* 3 Z)))
204 where the first symbol [ marks a list of polynomials.
205<MATH CLASS="INLINE">
206-
207</MATH>other infix expressions, for example
208 [(X<MATH CLASS="INLINE">
209-
210</MATH>Y)*(X+Y)/Z,(X+1)&#94;2]
211parses to:
212 (:[ (/ (* (<MATH CLASS="INLINE">
213-
214</MATH> X Y) (+ X Y)) Z) (EXPT (+ X 1) 2))
215Currently this function is implemented using M. Kantrowitz's INFIX
216package. </BLOCKQUOTE><H4><A NAME="SECTION000110020000000000000">
217<I>alist<MATH CLASS="INLINE">
218-
219</MATH>form</I></A>
220</H4>
221<P><IMG WIDTH="539" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
222 SRC="img163.gif"
223 ALT="$\textstyle\parbox{\pboxargslen}{\em plist vars \/}$"> [<EM>FUNCTION</EM>]
224<BLOCKQUOTE>
225Translates an expression PLIST, which should be a list of polynomials
226in variables VARS, to an alist representation of a polynomial.
227It returns the alist. See also PARSE<MATH CLASS="INLINE">
228-
229</MATH>TO<MATH CLASS="INLINE">
230-
231</MATH>ALIST.</BLOCKQUOTE><H4><A NAME="SECTION000110030000000000000">
232<I>alist<MATH CLASS="INLINE">
233-
234</MATH>form<MATH CLASS="INLINE">
235-
236</MATH>1</I></A>
237</H4>
238<P><IMG WIDTH="517" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
239 SRC="img164.gif"
240 ALT="$\textstyle\parbox{\pboxargslen}{\em p vars {\sf \&aux} (ht
241 (make$-$hash$-$table
242 :test
243 \char93 'equal
244 :size
245 16)) stack \/}$"> [<EM>FUNCTION</EM>]
246<BLOCKQUOTE>
247 </BLOCKQUOTE><H4><A NAME="SECTION000110040000000000000">
248<I>powers</I></A>
249</H4>
250<P><IMG WIDTH="564" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
251 SRC="img165.gif"
252 ALT="$\textstyle\parbox{\pboxargslen}{\em monom vars {\sf \&aux} (tab
253 (pairlis vars
254 (make$-$list (length vars)
255 :initial$-$element 0))) \/}$"> [<EM>FUNCTION</EM>]
256<BLOCKQUOTE>
257 </BLOCKQUOTE><H4><A NAME="SECTION000110050000000000000">
258<I>parse<MATH CLASS="INLINE">
259-
260</MATH>to<MATH CLASS="INLINE">
261-
262</MATH>alist</I></A>
263</H4>
264<P><IMG WIDTH="508" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
265 SRC="img166.gif"
266 ALT="$\textstyle\parbox{\pboxargslen}{\em vars {\sf \&optional} stream \/}$"> [<EM>FUNCTION</EM>]
267<BLOCKQUOTE>
268Parse an expression already in prefix form to an association list
269form according to the internal CGBlisp polynomial syntax: a
270polynomial is an alist of pairs (MONOM . COEFFICIENT). For example:
271 (WITH<MATH CLASS="INLINE">
272-
273</MATH>INPUT<MATH CLASS="INLINE">
274-
275</MATH>FROM<MATH CLASS="INLINE">
276-
277</MATH>STRING (S
278&quot;X&#94;2<MATH CLASS="INLINE">
279-
280</MATH>Y&#94;2+(<MATH CLASS="INLINE">
281-
282</MATH>4/3)*U&#94;2*W&#94;3<MATH CLASS="INLINE">
283-
284</MATH>5&quot;) (PARSE<MATH CLASS="INLINE">
285-
286</MATH>TO<MATH CLASS="INLINE">
287-
288</MATH>ALIST '(X Y U W) S))
289evaluates to
290(((0 0 2 3) . <MATH CLASS="INLINE">
291-
292</MATH>4/3) ((0 2 0 0) . <MATH CLASS="INLINE">
293-
294</MATH>1) ((2 0 0 0) . 1) ((0 0 0 0) .
295<MATH CLASS="INLINE">
296-
297</MATH>5)) </BLOCKQUOTE><H4><A NAME="SECTION000110060000000000000">
298<I>parse<MATH CLASS="INLINE">
299-
300</MATH>string<MATH CLASS="INLINE">
301-
302</MATH>to<MATH CLASS="INLINE">
303-
304</MATH>alist</I></A>
305</H4>
306<P><IMG WIDTH="456" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
307 SRC="img167.gif"
308 ALT="$\textstyle\parbox{\pboxargslen}{\em str vars \/}$"> [<EM>FUNCTION</EM>]
309<BLOCKQUOTE>
310Parse string STR and return a polynomial as a sorted association
311list of pairs (MONOM . COEFFICIENT). For example:
312(parse<MATH CLASS="INLINE">
313-
314</MATH>string<MATH CLASS="INLINE">
315-
316</MATH>to<MATH CLASS="INLINE">
317-
318</MATH>alist
319&quot;[x&#94;2<MATH CLASS="INLINE">
320-
321</MATH>y&#94;2+(<MATH CLASS="INLINE">
322-
323</MATH>4/3)*u&#94;2*w&#94;3<MATH CLASS="INLINE">
324-
325</MATH>5,y]&quot; '(x y u w)) ([ (((0 0 2 3) . <MATH CLASS="INLINE">
326-
327</MATH>4/3) ((0 2 0 0) . <MATH CLASS="INLINE">
328-
329</MATH>1) ((2 0 0 0) . 1)
330 ((0 0 0 0) . <MATH CLASS="INLINE">
331-
332</MATH>5))
333 (((0 1 0 0) . 1)))
334The functions PARSE<MATH CLASS="INLINE">
335-
336</MATH>TO<MATH CLASS="INLINE">
337-
338</MATH>SORTED<MATH CLASS="INLINE">
339-
340</MATH>ALIST and
341PARSE<MATH CLASS="INLINE">
342-
343</MATH>STRING<MATH CLASS="INLINE">
344-
345</MATH>TO<MATH CLASS="INLINE">
346-
347</MATH>SORTED<MATH CLASS="INLINE">
348-
349</MATH>ALIST sort terms by the predicate
350defined in the ORDER package. </BLOCKQUOTE><H4><A NAME="SECTION000110070000000000000">
351<I>parse<MATH CLASS="INLINE">
352-
353</MATH>to<MATH CLASS="INLINE">
354-
355</MATH>sorted<MATH CLASS="INLINE">
356-
357</MATH>alist</I></A>
358</H4>
359<P><IMG WIDTH="453" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
360 SRC="img168.gif"
361 ALT="$\textstyle\parbox{\pboxargslen}{\em vars {\sf \&optional} (order
362 \char93 'lex$\gt$) (stream t) \/}$"> [<EM>FUNCTION</EM>]
363<BLOCKQUOTE>
364Parses streasm STREAM and returns a polynomial represented as
365a sorted alist. For example:
366(WITH<MATH CLASS="INLINE">
367-
368</MATH>INPUT<MATH CLASS="INLINE">
369-
370</MATH>FROM<MATH CLASS="INLINE">
371-
372</MATH>STRING (S
373&quot;X&#94;2<MATH CLASS="INLINE">
374-
375</MATH>Y&#94;2+(<MATH CLASS="INLINE">
376-
377</MATH>4/3)*U&#94;2*W&#94;3<MATH CLASS="INLINE">
378-
379</MATH>5&quot;) (PARSE<MATH CLASS="INLINE">
380-
381</MATH>TO<MATH CLASS="INLINE">
382-
383</MATH>SORTED<MATH CLASS="INLINE">
384-
385</MATH>ALIST '(X Y U W) S))
386returns
387(((2 0 0 0) . 1) ((0 2 0 0) . <MATH CLASS="INLINE">
388-
389</MATH>1) ((0 0 2 3) . <MATH CLASS="INLINE">
390-
391</MATH>4/3) ((0 0 0 0) .
392<MATH CLASS="INLINE">
393-
394</MATH>5)) and
395(WITH<MATH CLASS="INLINE">
396-
397</MATH>INPUT<MATH CLASS="INLINE">
398-
399</MATH>FROM<MATH CLASS="INLINE">
400-
401</MATH>STRING (S
402&quot;X&#94;2<MATH CLASS="INLINE">
403-
404</MATH>Y&#94;2+(<MATH CLASS="INLINE">
405-
406</MATH>4/3)*U&#94;2*W&#94;3<MATH CLASS="INLINE">
407-
408</MATH>5&quot;) (PARSE<MATH CLASS="INLINE">
409-
410</MATH>TO<MATH CLASS="INLINE">
411-
412</MATH>SORTED<MATH CLASS="INLINE">
413-
414</MATH>ALIST '(X Y U W) T #'GRLEX<MATH CLASS="INLINE">
415&gt;
416</MATH>) S)
417returns
418(((0 0 2 3) . <MATH CLASS="INLINE">
419-
420</MATH>4/3) ((2 0 0 0) . 1) ((0 2 0 0) . <MATH CLASS="INLINE">
421-
422</MATH>1) ((0 0 0 0) .
423<MATH CLASS="INLINE">
424-
425</MATH>5)) </BLOCKQUOTE><H4><A NAME="SECTION000110080000000000000">
426<I>parse<MATH CLASS="INLINE">
427-
428</MATH>string<MATH CLASS="INLINE">
429-
430</MATH>to<MATH CLASS="INLINE">
431-
432</MATH>sorted<MATH CLASS="INLINE">
433-
434</MATH>alist</I></A>
435</H4>
436<P><IMG WIDTH="401" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
437 SRC="img169.gif"
438 ALT="$\textstyle\parbox{\pboxargslen}{\em str vars {\sf \&optional} (order
439 \char93 'lex$\gt$) \/}$"> [<EM>FUNCTION</EM>]
440<BLOCKQUOTE>
441Parse a string to a sorted alist form, the internal representation
442of polynomials used by our system.</BLOCKQUOTE><H4><A NAME="SECTION000110090000000000000">
443<I>sort<MATH CLASS="INLINE">
444-
445</MATH>poly<MATH CLASS="INLINE">
446-
447</MATH>1</I></A>
448</H4>
449<P><IMG WIDTH="523" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
450 SRC="img170.gif"
451 ALT="$\textstyle\parbox{\pboxargslen}{\em p order \/}$"> [<EM>FUNCTION</EM>]
452<BLOCKQUOTE>
453Sort the terms of a single polynomial P using an admissible monomial
454order ORDER. Returns the sorted polynomial. Destructively modifies P.</BLOCKQUOTE><H4><A NAME="SECTION0001100100000000000000">
455<I>sort<MATH CLASS="INLINE">
456-
457</MATH>poly</I></A>
458</H4>
459<P><IMG WIDTH="544" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
460 SRC="img171.gif"
461 ALT="$\textstyle\parbox{\pboxargslen}{\em poly$-$or$-$poly$-$list {\sf \&optional} (order \char93 'lex$\gt$) \/}$"> [<EM>FUNCTION</EM>]
462<BLOCKQUOTE>
463Sort POLY<MATH CLASS="INLINE">
464-
465</MATH>OR<MATH CLASS="INLINE">
466-
467</MATH>POLY<MATH CLASS="INLINE">
468-
469</MATH>LIST, which could be either a single
470polynomial or a list of polynomials in internal alist representation,
471using admissible monomial order ORDER. Each polynomial is sorted
472using SORT<MATH CLASS="INLINE">
473-
474</MATH>POLY<MATH CLASS="INLINE">
475-
476</MATH>1.</BLOCKQUOTE><H4><A NAME="SECTION0001100110000000000000">
477<I>poly<MATH CLASS="INLINE">
478-
479</MATH>eval<MATH CLASS="INLINE">
480-
481</MATH>1</I></A>
482</H4>
483<P><IMG WIDTH="521" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
484 SRC="img172.gif"
485 ALT="$\textstyle\parbox{\pboxargslen}{\em expr vars order ring {\sf \&aux} (n (length vars)) \/}$"> [<EM>FUNCTION</EM>]
486<BLOCKQUOTE>
487Evaluate an expression EXPR as polynomial
488by substituting operators + <MATH CLASS="INLINE">
489-
490</MATH> * expt with
491corresponding polynomial operators
492and variables VARS with monomials (1 0 ... 0), (0 1 ... 0) etc.
493We use special versions of binary
494operators $poly+, $poly<MATH CLASS="INLINE">
495-
496</MATH>, $minus<MATH CLASS="INLINE">
497-
498</MATH>poly, $poly* and
499$poly<MATH CLASS="INLINE">
500-
501</MATH>expt which work like the corresponding functions in the
502POLY package, but accept scalars as arguments as well.</BLOCKQUOTE><H4><A NAME="SECTION0001100120000000000000">
503<I>poly<MATH CLASS="INLINE">
504-
505</MATH>eval</I></A>
506</H4>
507<P><IMG WIDTH="543" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
508 SRC="img173.gif"
509 ALT="$\textstyle\parbox{\pboxargslen}{\em expr vars {\sf \&optional} (order
510 \char93 'lex$\gt$) (ring
511 *coefficient$-$ring*) \/}$"> [<EM>FUNCTION</EM>]
512<BLOCKQUOTE>
513Evaluate an expression EXPR, which should be a polynomial
514expression or a list of polynomial expressions (a list of expressions
515marked by prepending keyword :[ to it) given in lisp prefix notation,
516in variables VARS, which should be a list of symbols. The result of
517the evaluation is a polynomial or a list of polynomials (marked by
518prepending symbol '[) in the internal alist form. This evaluator is
519used by the PARSE package to convert input from strings directly to
520internal form.</BLOCKQUOTE><H4><A NAME="SECTION0001100130000000000000">
521<I>monom<MATH CLASS="INLINE">
522-
523</MATH>basis</I></A>
524</H4>
525<P><IMG WIDTH="514" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
526 SRC="img174.gif"
527 ALT="$\textstyle\parbox{\pboxargslen}{\em n {\sf \&aux} (basis
528 (copy$-$tree
529 (make$-...
530 ...
531 (list 'quote
532 (list
533 (cons
534 (make$-$list n :initial$-$element 0)
535 1)))))) \/}$"> [<EM>FUNCTION</EM>]
536<BLOCKQUOTE>
537Generate a list of monomials ((1 0 ... 0) (0 1 0 ... 0) ... (0 0 ...
5381) which correspond to linear monomials X1, X2, ... XN.</BLOCKQUOTE><H4><A NAME="SECTION0001100140000000000000">
539<I>convert<MATH CLASS="INLINE">
540-
541</MATH>number</I></A>
542</H4>
543<P><IMG WIDTH="495" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
544 SRC="img175.gif"
545 ALT="$\textstyle\parbox{\pboxargslen}{\em number$-$or$-$poly n \/}$"> [<EM>FUNCTION</EM>]
546<BLOCKQUOTE>
547Returns NUMBER<MATH CLASS="INLINE">
548-
549</MATH>OR<MATH CLASS="INLINE">
550-
551</MATH>POLY, if it is a polynomial. If it is a number,
552it converts it to the constant monomial in N variables. If the result
553is a number then convert it to a polynomial in N variables.</BLOCKQUOTE><H4><A NAME="SECTION0001100150000000000000">
554<I>$poly+</I></A>
555</H4>
556<P><IMG WIDTH="561" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
557 SRC="img176.gif"
558 ALT="$\textstyle\parbox{\pboxargslen}{\em p q n order ring \/}$"> [<EM>FUNCTION</EM>]
559<BLOCKQUOTE>
560Add two polynomials P and Q, where each polynomial is either a
561numeric constant or a polynomial in internal representation. If the
562result is a number then convert it to a polynomial in N variables.</BLOCKQUOTE><H4><A NAME="SECTION0001100160000000000000">
563<I>$poly<MATH CLASS="INLINE">
564-
565</MATH></I></A>
566</H4>
567<P><IMG WIDTH="561" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
568 SRC="img176.gif"
569 ALT="$\textstyle\parbox{\pboxargslen}{\em p q n order ring \/}$"> [<EM>FUNCTION</EM>]
570<BLOCKQUOTE>
571Subtract two polynomials P and Q, where each polynomial is either a
572numeric constant or a polynomial in internal representation. If the
573result is a number then convert it to a polynomial in N variables.</BLOCKQUOTE><H4><A NAME="SECTION0001100170000000000000">
574<I>$minus<MATH CLASS="INLINE">
575-
576</MATH>poly</I></A>
577</H4>
578<P><IMG WIDTH="521" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
579 SRC="img177.gif"
580 ALT="$\textstyle\parbox{\pboxargslen}{\em p n ring \/}$"> [<EM>FUNCTION</EM>]
581<BLOCKQUOTE>
582Negation of P is a polynomial is either a numeric constant or a
583polynomial in internal representation. If the result is a number then
584convert it to a polynomial in N variables.</BLOCKQUOTE><H4><A NAME="SECTION0001100180000000000000">
585<I>$poly*</I></A>
586</H4>
587<P><IMG WIDTH="561" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
588 SRC="img176.gif"
589 ALT="$\textstyle\parbox{\pboxargslen}{\em p q n order ring \/}$"> [<EM>FUNCTION</EM>]
590<BLOCKQUOTE>
591Multiply two polynomials P and Q, where each polynomial is either a
592numeric constant or a polynomial in internal representation. If the
593result is a number then convert it to a polynomial in N variables.</BLOCKQUOTE><H4><A NAME="SECTION0001100190000000000000">
594<I>$poly/</I></A>
595</H4>
596<P><IMG WIDTH="566" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
597 SRC="img178.gif"
598 ALT="$\textstyle\parbox{\pboxargslen}{\em p q ring \/}$"> [<EM>FUNCTION</EM>]
599<BLOCKQUOTE>
600Divide a polynomials P which is either a numeric constant or a
601polynomial in internal representation, by a number Q.</BLOCKQUOTE><H4><A NAME="SECTION0001100200000000000000">
602<I>$poly<MATH CLASS="INLINE">
603-
604</MATH>expt</I></A>
605</H4>
606<P><IMG WIDTH="532" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
607 SRC="img179.gif"
608 ALT="$\textstyle\parbox{\pboxargslen}{\em p l n order ring \/}$"> [<EM>FUNCTION</EM>]
609<BLOCKQUOTE>
610Raise polynomial P, which is a polynomial in internal
611representation or a numeric constant, to power L. If P is a number,
612convert the result to a polynomial in N variables.</BLOCKQUOTE><HR>
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634<ADDRESS>
635<I>Marek Rychlik</I>
636<BR><I>3/21/1998</I>
637</ADDRESS>
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