source: CGBLisp/latex-doc/manual/node12.html@ 1

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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 -->
6<HTML>
7<HEAD>
8<TITLE>Other packages</TITLE>
9<META NAME="description" CONTENT="Other packages">
10<META NAME="keywords" CONTENT="manual">
11<META NAME="resource-type" CONTENT="document">
12<META NAME="distribution" CONTENT="global">
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14<LINK REL="STYLESHEET" HREF="manual.css">
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17<LINK REL="up" HREF="manual.html">
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23 HREF="node13.html">
24<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A>
25<A NAME="tex2html1091"
26 HREF="manual.html">
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28<A NAME="tex2html1085"
29 HREF="node11.html">
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31<A NAME="tex2html1093"
32 HREF="node1.html">
33<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents_motif.gif"></A>
34<BR>
35<B> Next:</B> <A NAME="tex2html1095"
36 HREF="node13.html">All examples produced by</A>
37<B> Up:</B> <A NAME="tex2html1092"
38 HREF="manual.html">CGBLisp User Guide and</A>
39<B> Previous:</B> <A NAME="tex2html1086"
40 HREF="node11.html">The Parser 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="tex2html1096"
48 HREF="node12.html#SECTION000120010000000000000">
49<I>makelist<MATH CLASS="INLINE">
50-
51</MATH>1</I></A>
52<LI><A NAME="tex2html1097"
53 HREF="node12.html#SECTION000120020000000000000">
54<I>makelist</I></A>
55<LI><A NAME="tex2html1098"
56 HREF="node12.html#SECTION000120030000000000000">
57<I>sum</I></A>
58<LI><A NAME="tex2html1099"
59 HREF="node12.html#SECTION000120040000000000000">
60<I>list<MATH CLASS="INLINE">
61-
62</MATH>of</I></A>
63<LI><A NAME="tex2html1100"
64 HREF="node12.html#SECTION000120050000000000000">
65<I>list<MATH CLASS="INLINE">
66-
67</MATH>of<MATH CLASS="INLINE">
68-
69</MATH>1</I></A>
70<LI><A NAME="tex2html1101"
71 HREF="node12.html#SECTION000120060000000000000">
72<I>union<MATH CLASS="INLINE">
73-
74</MATH>of</I></A>
75<LI><A NAME="tex2html1102"
76 HREF="node12.html#SECTION000120070000000000000">
77<I>union<MATH CLASS="INLINE">
78-
79</MATH>of<MATH CLASS="INLINE">
80-
81</MATH>1</I></A>
82<LI><A NAME="tex2html1103"
83 HREF="node12.html#SECTION000120080000000000000">
84<I>set<MATH CLASS="INLINE">
85-
86</MATH>of</I></A>
87<LI><A NAME="tex2html1104"
88 HREF="node12.html#SECTION000120090000000000000">
89<I>set<MATH CLASS="INLINE">
90-
91</MATH>of<MATH CLASS="INLINE">
92-
93</MATH>1</I></A>
94<LI><A NAME="tex2html1105"
95 HREF="node12.html#SECTION0001200100000000000000">
96<I>select</I></A>
97<LI><A NAME="tex2html1106"
98 HREF="node12.html#SECTION0001200110000000000000">
99<I>monom/</I></A>
100<LI><A NAME="tex2html1107"
101 HREF="node12.html#SECTION0001200120000000000000">
102<I>monom*</I></A>
103<LI><A NAME="tex2html1108"
104 HREF="node12.html#SECTION0001200130000000000000">
105<I>nmonom*</I></A>
106<LI><A NAME="tex2html1109"
107 HREF="node12.html#SECTION0001200140000000000000">
108<I>monom<MATH CLASS="INLINE">
109-
110</MATH>divides<MATH CLASS="INLINE">
111-
112</MATH>p</I></A>
113<LI><A NAME="tex2html1110"
114 HREF="node12.html#SECTION0001200150000000000000">
115<I>monom<MATH CLASS="INLINE">
116-
117</MATH>divisible<MATH CLASS="INLINE">
118-
119</MATH>by<MATH CLASS="INLINE">
120-
121</MATH>p</I></A>
122<LI><A NAME="tex2html1111"
123 HREF="node12.html#SECTION0001200160000000000000">
124<I>monom<MATH CLASS="INLINE">
125-
126</MATH>rel<MATH CLASS="INLINE">
127-
128</MATH>prime</I></A>
129<LI><A NAME="tex2html1112"
130 HREF="node12.html#SECTION0001200170000000000000">
131<I>monom<MATH CLASS="INLINE">
132-
133</MATH>equal</I></A>
134<LI><A NAME="tex2html1113"
135 HREF="node12.html#SECTION0001200180000000000000">
136<I>monom<MATH CLASS="INLINE">
137-
138</MATH>lcm</I></A>
139<LI><A NAME="tex2html1114"
140 HREF="node12.html#SECTION0001200190000000000000">
141<I>monom<MATH CLASS="INLINE">
142-
143</MATH>gcd</I></A>
144<LI><A NAME="tex2html1115"
145 HREF="node12.html#SECTION0001200200000000000000">
146<I>poly<MATH CLASS="INLINE">
147-
148</MATH>gcd</I></A>
149<LI><A NAME="tex2html1116"
150 HREF="node12.html#SECTION0001200210000000000000">
151<I>poly<MATH CLASS="INLINE">
152-
153</MATH>pseudo<MATH CLASS="INLINE">
154-
155</MATH>divide</I></A>
156<LI><A NAME="tex2html1117"
157 HREF="node12.html#SECTION0001200220000000000000">
158<I>poly<MATH CLASS="INLINE">
159-
160</MATH>pseudo<MATH CLASS="INLINE">
161-
162</MATH>remainder</I></A>
163<LI><A NAME="tex2html1118"
164 HREF="node12.html#SECTION0001200230000000000000">
165<I>mdeg</I></A>
166<LI><A NAME="tex2html1119"
167 HREF="node12.html#SECTION0001200240000000000000">
168<I>lcoeff</I></A>
169<LI><A NAME="tex2html1120"
170 HREF="node12.html#SECTION0001200250000000000000">
171<I>lrest</I></A>
172<LI><A NAME="tex2html1121"
173 HREF="node12.html#SECTION0001200260000000000000">
174<I>lpart</I></A>
175<LI><A NAME="tex2html1122"
176 HREF="node12.html#SECTION0001200270000000000000">
177<I>poly<MATH CLASS="INLINE">
178-
179</MATH>primitive<MATH CLASS="INLINE">
180-
181</MATH>part</I></A>
182<LI><A NAME="tex2html1123"
183 HREF="node12.html#SECTION0001200280000000000000">
184<I>poly<MATH CLASS="INLINE">
185-
186</MATH>content</I></A>
187<LI><A NAME="tex2html1124"
188 HREF="node12.html#SECTION0001200290000000000000">
189<I>poly<MATH CLASS="INLINE">
190-
191</MATH>with<MATH CLASS="INLINE">
192-
193</MATH>sugar<MATH CLASS="INLINE">
194-
195</MATH>poly</I></A>
196<LI><A NAME="tex2html1125"
197 HREF="node12.html#SECTION0001200300000000000000">
198<I>poly<MATH CLASS="INLINE">
199-
200</MATH>with<MATH CLASS="INLINE">
201-
202</MATH>sugar<MATH CLASS="INLINE">
203-
204</MATH>sugar</I></A>
205<LI><A NAME="tex2html1126"
206 HREF="node12.html#SECTION0001200310000000000000">
207<I>poly<MATH CLASS="INLINE">
208-
209</MATH>with<MATH CLASS="INLINE">
210-
211</MATH>sugar<MATH CLASS="INLINE">
212-
213</MATH>tail</I></A>
214<LI><A NAME="tex2html1127"
215 HREF="node12.html#SECTION0001200320000000000000">
216<I>(setf poly<MATH CLASS="INLINE">
217-
218</MATH>with<MATH CLASS="INLINE">
219-
220</MATH>sugar<MATH CLASS="INLINE">
221-
222</MATH>poly)</I></A>
223<LI><A NAME="tex2html1128"
224 HREF="node12.html#SECTION0001200330000000000000">
225<I>(setf poly<MATH CLASS="INLINE">
226-
227</MATH>with<MATH CLASS="INLINE">
228-
229</MATH>sugar<MATH CLASS="INLINE">
230-
231</MATH>sugar)</I></A>
232<LI><A NAME="tex2html1129"
233 HREF="node12.html#SECTION0001200340000000000000">
234<I>(setf poly<MATH CLASS="INLINE">
235-
236</MATH>with<MATH CLASS="INLINE">
237-
238</MATH>sugar<MATH CLASS="INLINE">
239-
240</MATH>tail)</I></A>
241<LI><A NAME="tex2html1130"
242 HREF="node12.html#SECTION0001200350000000000000">
243<I>monom<MATH CLASS="INLINE">
244-
245</MATH>sugar</I></A>
246<LI><A NAME="tex2html1131"
247 HREF="node12.html#SECTION0001200360000000000000">
248<I>coefficient<MATH CLASS="INLINE">
249-
250</MATH>sugar</I></A>
251<LI><A NAME="tex2html1132"
252 HREF="node12.html#SECTION0001200370000000000000">
253<I>term<MATH CLASS="INLINE">
254-
255</MATH>sugar</I></A>
256<LI><A NAME="tex2html1133"
257 HREF="node12.html#SECTION0001200380000000000000">
258<I>poly<MATH CLASS="INLINE">
259-
260</MATH>add<MATH CLASS="INLINE">
261-
262</MATH>sugar</I></A>
263<LI><A NAME="tex2html1134"
264 HREF="node12.html#SECTION0001200390000000000000">
265<I>scalar<MATH CLASS="INLINE">
266-
267</MATH>times<MATH CLASS="INLINE">
268-
269</MATH>poly<MATH CLASS="INLINE">
270-
271</MATH>with<MATH CLASS="INLINE">
272-
273</MATH>sugar</I></A>
274<LI><A NAME="tex2html1135"
275 HREF="node12.html#SECTION0001200400000000000000">
276<I>term<MATH CLASS="INLINE">
277-
278</MATH>times<MATH CLASS="INLINE">
279-
280</MATH>poly<MATH CLASS="INLINE">
281-
282</MATH>with<MATH CLASS="INLINE">
283-
284</MATH>sugar</I></A>
285<LI><A NAME="tex2html1136"
286 HREF="node12.html#SECTION0001200410000000000000">
287<I>monom<MATH CLASS="INLINE">
288-
289</MATH>times<MATH CLASS="INLINE">
290-
291</MATH>poly<MATH CLASS="INLINE">
292-
293</MATH>with<MATH CLASS="INLINE">
294-
295</MATH>sugar</I></A>
296<LI><A NAME="tex2html1137"
297 HREF="node12.html#SECTION0001200420000000000000">
298<I>minus<MATH CLASS="INLINE">
299-
300</MATH>poly<MATH CLASS="INLINE">
301-
302</MATH>with<MATH CLASS="INLINE">
303-
304</MATH>sugar</I></A>
305<LI><A NAME="tex2html1138"
306 HREF="node12.html#SECTION0001200430000000000000">
307<I>poly<MATH CLASS="INLINE">
308-
309</MATH>with<MATH CLASS="INLINE">
310-
311</MATH>sugar+</I></A>
312<LI><A NAME="tex2html1139"
313 HREF="node12.html#SECTION0001200440000000000000">
314<I>poly<MATH CLASS="INLINE">
315-
316</MATH>with<MATH CLASS="INLINE">
317-
318</MATH>sugar<MATH CLASS="INLINE">
319-
320</MATH></I></A>
321<LI><A NAME="tex2html1140"
322 HREF="node12.html#SECTION0001200450000000000000">
323<I>poly<MATH CLASS="INLINE">
324-
325</MATH>with<MATH CLASS="INLINE">
326-
327</MATH>sugar<MATH CLASS="INLINE">
328-
329</MATH>op</I></A>
330<LI><A NAME="tex2html1141"
331 HREF="node12.html#SECTION0001200460000000000000">
332<I>poly<MATH CLASS="INLINE">
333-
334</MATH>with<MATH CLASS="INLINE">
335-
336</MATH>sugar<MATH CLASS="INLINE">
337-
338</MATH>nreverse</I></A>
339<LI><A NAME="tex2html1142"
340 HREF="node12.html#SECTION0001200470000000000000">
341<I>poly<MATH CLASS="INLINE">
342-
343</MATH>with<MATH CLASS="INLINE">
344-
345</MATH>sugar<MATH CLASS="INLINE">
346-
347</MATH>append</I></A>
348<LI><A NAME="tex2html1143"
349 HREF="node12.html#SECTION0001200480000000000000">
350<I>poly<MATH CLASS="INLINE">
351-
352</MATH>with<MATH CLASS="INLINE">
353-
354</MATH>sugar<MATH CLASS="INLINE">
355-
356</MATH>zerop</I></A>
357<LI><A NAME="tex2html1144"
358 HREF="node12.html#SECTION0001200490000000000000">
359<I>poly<MATH CLASS="INLINE">
360-
361</MATH>with<MATH CLASS="INLINE">
362-
363</MATH>sugar<MATH CLASS="INLINE">
364-
365</MATH>lm</I></A>
366<LI><A NAME="tex2html1145"
367 HREF="node12.html#SECTION0001200500000000000000">
368<I>poly<MATH CLASS="INLINE">
369-
370</MATH>with<MATH CLASS="INLINE">
371-
372</MATH>sugar<MATH CLASS="INLINE">
373-
374</MATH>lc</I></A>
375<LI><A NAME="tex2html1146"
376 HREF="node12.html#SECTION0001200510000000000000">
377<I>poly<MATH CLASS="INLINE">
378-
379</MATH>with<MATH CLASS="INLINE">
380-
381</MATH>sugar<MATH CLASS="INLINE">
382-
383</MATH>lt</I></A>
384<LI><A NAME="tex2html1147"
385 HREF="node12.html#SECTION0001200520000000000000">
386<I>poly<MATH CLASS="INLINE">
387-
388</MATH>print</I></A>
389<LI><A NAME="tex2html1148"
390 HREF="node12.html#SECTION0001200530000000000000">
391<I>poly<MATH CLASS="INLINE">
392-
393</MATH>print<MATH CLASS="INLINE">
394-
395</MATH>1</I></A>
396<LI><A NAME="tex2html1149"
397 HREF="node12.html#SECTION0001200540000000000000">
398<I>poly<MATH CLASS="INLINE">
399-
400</MATH>print<MATH CLASS="INLINE">
401-
402</MATH>2</I></A>
403<LI><A NAME="tex2html1150"
404 HREF="node12.html#SECTION0001200550000000000000">
405<I>print<MATH CLASS="INLINE">
406-
407</MATH>term</I></A>
408<LI><A NAME="tex2html1151"
409 HREF="node12.html#SECTION0001200560000000000000">
410<I>print<MATH CLASS="INLINE">
411-
412</MATH>monom</I></A>
413<LI><A NAME="tex2html1152"
414 HREF="node12.html#SECTION0001200570000000000000">
415<I>num</I></A>
416<LI><A NAME="tex2html1153"
417 HREF="node12.html#SECTION0001200580000000000000">
418<I>denom</I></A>
419<LI><A NAME="tex2html1154"
420 HREF="node12.html#SECTION0001200590000000000000">
421<I>rat<MATH CLASS="INLINE">
422-
423</MATH>simplify<MATH CLASS="INLINE">
424-
425</MATH>2</I></A>
426<LI><A NAME="tex2html1155"
427 HREF="node12.html#SECTION0001200600000000000000">
428<I>rat<MATH CLASS="INLINE">
429-
430</MATH>simplify</I></A>
431<LI><A NAME="tex2html1156"
432 HREF="node12.html#SECTION0001200610000000000000">
433<I>rat+</I></A>
434<LI><A NAME="tex2html1157"
435 HREF="node12.html#SECTION0001200620000000000000">
436<I>rat<MATH CLASS="INLINE">
437-
438</MATH></I></A>
439<LI><A NAME="tex2html1158"
440 HREF="node12.html#SECTION0001200630000000000000">
441<I>rat*</I></A>
442<LI><A NAME="tex2html1159"
443 HREF="node12.html#SECTION0001200640000000000000">
444<I>rat/</I></A>
445<LI><A NAME="tex2html1160"
446 HREF="node12.html#SECTION0001200650000000000000">
447<I>scalar<MATH CLASS="INLINE">
448-
449</MATH>times<MATH CLASS="INLINE">
450-
451</MATH>rat</I></A>
452<LI><A NAME="tex2html1161"
453 HREF="node12.html#SECTION0001200660000000000000">
454<I>scalar<MATH CLASS="INLINE">
455-
456</MATH>div<MATH CLASS="INLINE">
457-
458</MATH>rat</I></A>
459<LI><A NAME="tex2html1162"
460 HREF="node12.html#SECTION0001200670000000000000">
461<I>rat<MATH CLASS="INLINE">
462-
463</MATH>zerop</I></A>
464<LI><A NAME="tex2html1163"
465 HREF="node12.html#SECTION0001200680000000000000">
466<I>rat<MATH CLASS="INLINE">
467-
468</MATH>uminus</I></A>
469<LI><A NAME="tex2html1164"
470 HREF="node12.html#SECTION0001200690000000000000">
471<I>rat<MATH CLASS="INLINE">
472-
473</MATH>expt</I></A>
474<LI><A NAME="tex2html1165"
475 HREF="node12.html#SECTION0001200700000000000000">
476<I>rat<MATH CLASS="INLINE">
477-
478</MATH>constant</I></A>
479<LI><A NAME="tex2html1166"
480 HREF="node12.html#SECTION0001200710000000000000">
481<I>rat<MATH CLASS="INLINE">
482-
483</MATH>to<MATH CLASS="INLINE">
484-
485</MATH>poly</I></A>
486<LI><A NAME="tex2html1167"
487 HREF="node12.html#SECTION0001200720000000000000">
488<I>ratpoly+</I></A>
489<LI><A NAME="tex2html1168"
490 HREF="node12.html#SECTION0001200730000000000000">
491<I>ratpoly<MATH CLASS="INLINE">
492-
493</MATH></I></A>
494<LI><A NAME="tex2html1169"
495 HREF="node12.html#SECTION0001200740000000000000">
496<I>ratpoly<MATH CLASS="INLINE">
497-
498</MATH>uminus</I></A>
499<LI><A NAME="tex2html1170"
500 HREF="node12.html#SECTION0001200750000000000000">
501<I>ratpoly*</I></A>
502<LI><A NAME="tex2html1171"
503 HREF="node12.html#SECTION0001200760000000000000">
504<I>scalar<MATH CLASS="INLINE">
505-
506</MATH>times<MATH CLASS="INLINE">
507-
508</MATH>ratpoly</I></A>
509<LI><A NAME="tex2html1172"
510 HREF="node12.html#SECTION0001200770000000000000">
511<I>rat<MATH CLASS="INLINE">
512-
513</MATH>times<MATH CLASS="INLINE">
514-
515</MATH>ratpoly</I></A>
516<LI><A NAME="tex2html1173"
517 HREF="node12.html#SECTION0001200780000000000000">
518<I>ratpoly<MATH CLASS="INLINE">
519-
520</MATH>divide</I></A>
521<LI><A NAME="tex2html1174"
522 HREF="node12.html#SECTION0001200790000000000000">
523<I>ratpoly<MATH CLASS="INLINE">
524-
525</MATH>remainder</I></A>
526<LI><A NAME="tex2html1175"
527 HREF="node12.html#SECTION0001200800000000000000">
528<I>ratpoly<MATH CLASS="INLINE">
529-
530</MATH>gcd</I></A>
531<LI><A NAME="tex2html1176"
532 HREF="node12.html#SECTION0001200810000000000000">
533<I>ratpoly<MATH CLASS="INLINE">
534-
535</MATH>diff</I></A>
536<LI><A NAME="tex2html1177"
537 HREF="node12.html#SECTION0001200820000000000000">
538<I>ratpoly<MATH CLASS="INLINE">
539-
540</MATH>square<MATH CLASS="INLINE">
541-
542</MATH>free</I></A>
543<LI><A NAME="tex2html1178"
544 HREF="node12.html#SECTION0001200830000000000000">
545<I>ratpoly<MATH CLASS="INLINE">
546-
547</MATH>normalize</I></A>
548<LI><A NAME="tex2html1179"
549 HREF="node12.html#SECTION0001200840000000000000">
550<I>ratpoly<MATH CLASS="INLINE">
551-
552</MATH>resultant</I></A>
553<LI><A NAME="tex2html1180"
554 HREF="node12.html#SECTION0001200850000000000000">
555<I>deg</I></A>
556<LI><A NAME="tex2html1181"
557 HREF="node12.html#SECTION0001200860000000000000">
558<I>lead</I></A>
559<LI><A NAME="tex2html1182"
560 HREF="node12.html#SECTION0001200870000000000000">
561<I>ratpoly<MATH CLASS="INLINE">
562-
563</MATH>discriminant</I></A>
564<LI><A NAME="tex2html1183"
565 HREF="node12.html#SECTION0001200880000000000000">
566<I>ratpoly<MATH CLASS="INLINE">
567-
568</MATH>print</I></A>
569<LI><A NAME="tex2html1184"
570 HREF="node12.html#SECTION0001200890000000000000">
571<I>poly<MATH CLASS="INLINE">
572-
573</MATH>to<MATH CLASS="INLINE">
574-
575</MATH>ratpoly</I></A>
576<LI><A NAME="tex2html1185"
577 HREF="node12.html#SECTION0001200900000000000000">
578<I>poly<MATH CLASS="INLINE">
579-
580</MATH>to<MATH CLASS="INLINE">
581-
582</MATH>poly1</I></A>
583<LI><A NAME="tex2html1186"
584 HREF="node12.html#SECTION0001200910000000000000">
585<I>poly1<MATH CLASS="INLINE">
586-
587</MATH>to<MATH CLASS="INLINE">
588-
589</MATH>ratpoly</I></A>
590<LI><A NAME="tex2html1187"
591 HREF="node12.html#SECTION0001200920000000000000">
592<I>ratpoly<MATH CLASS="INLINE">
593-
594</MATH>to<MATH CLASS="INLINE">
595-
596</MATH>poly1</I></A>
597<LI><A NAME="tex2html1188"
598 HREF="node12.html#SECTION0001200930000000000000">
599<I>poly1<MATH CLASS="INLINE">
600-
601</MATH>to<MATH CLASS="INLINE">
602-
603</MATH>poly</I></A>
604<LI><A NAME="tex2html1189"
605 HREF="node12.html#SECTION0001200940000000000000">
606<I>ratpoly<MATH CLASS="INLINE">
607-
608</MATH>to<MATH CLASS="INLINE">
609-
610</MATH>poly</I></A>
611<LI><A NAME="tex2html1190"
612 HREF="node12.html#SECTION0001200950000000000000">
613<I>poly<MATH CLASS="INLINE">
614-
615</MATH>resultant</I></A>
616<LI><A NAME="tex2html1191"
617 HREF="node12.html#SECTION0001200960000000000000">
618<I>term*</I></A>
619<LI><A NAME="tex2html1192"
620 HREF="node12.html#SECTION0001200970000000000000">
621<I>term/</I></A>
622<LI><A NAME="tex2html1193"
623 HREF="node12.html#SECTION0001200980000000000000">
624<I>monom<MATH CLASS="INLINE">
625-
626</MATH>times<MATH CLASS="INLINE">
627-
628</MATH>term</I></A>
629<LI><A NAME="tex2html1194"
630 HREF="node12.html#SECTION0001200990000000000000">
631<I>term<MATH CLASS="INLINE">
632-
633</MATH>divides<MATH CLASS="INLINE">
634-
635</MATH>p</I></A>
636<LI><A NAME="tex2html1195"
637 HREF="node12.html#SECTION00012001000000000000000">
638<I>term<MATH CLASS="INLINE">
639-
640</MATH>monom</I></A>
641<LI><A NAME="tex2html1196"
642 HREF="node12.html#SECTION00012001010000000000000">
643<I>term<MATH CLASS="INLINE">
644-
645</MATH>coefficient</I></A>
646<LI><A NAME="tex2html1197"
647 HREF="node12.html#SECTION00012001020000000000000">
648<I>(setf term<MATH CLASS="INLINE">
649-
650</MATH>monom)</I></A>
651<LI><A NAME="tex2html1198"
652 HREF="node12.html#SECTION00012001030000000000000">
653<I>(setf term<MATH CLASS="INLINE">
654-
655</MATH>coefficient)</I></A>
656<LI><A NAME="tex2html1199"
657 HREF="node12.html#SECTION00012001040000000000000">
658<I>xgcd</I></A>
659</UL>
660<!--End of Table of Child-Links-->
661<HR>
662<H1><A NAME="SECTION000120000000000000000">
663Other packages</A>
664</H1>
665<H4><A NAME="SECTION000120010000000000000">
666<I>makelist<MATH CLASS="INLINE">
667-
668</MATH>1</I></A>
669</H4>
670<P><IMG WIDTH="577" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
671 SRC="img180.gif"
672 ALT="$\textstyle\parbox{\pboxargslen}{\em expr var lo hi {\sf \&optional} (step 1) \/}$"> [<EM>MACRO</EM>]
673<BLOCKQUOTE>
674 </BLOCKQUOTE><H4><A NAME="SECTION000120020000000000000">
675<I>makelist</I></A>
676</H4>
677<P><IMG WIDTH="598" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
678 SRC="img181.gif"
679 ALT="$\textstyle\parbox{\pboxargslen}{\em expr (var lo hi {\sf \&optional} (step 1)) {\sf \&rest} more \/}$"> [<EM>MACRO</EM>]
680<BLOCKQUOTE>
681 </BLOCKQUOTE><H4><A NAME="SECTION000120030000000000000">
682<I>sum</I></A>
683</H4>
684<P><IMG WIDTH="627" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
685 SRC="img182.gif"
686 ALT="$\textstyle\parbox{\pboxargslen}{\em {\sf \&body} body \/}$"> [<EM>MACRO</EM>]
687<BLOCKQUOTE>
688 </BLOCKQUOTE><H4><A NAME="SECTION000120040000000000000">
689<I>list<MATH CLASS="INLINE">
690-
691</MATH>of</I></A>
692</H4>
693<P><IMG WIDTH="608" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
694 SRC="img183.gif"
695 ALT="$\textstyle\parbox{\pboxargslen}{\em expr (var lst) {\sf \&rest} more \/}$"> [<EM>MACRO</EM>]
696<BLOCKQUOTE>
697 </BLOCKQUOTE><H4><A NAME="SECTION000120050000000000000">
698<I>list<MATH CLASS="INLINE">
699-
700</MATH>of<MATH CLASS="INLINE">
701-
702</MATH>1</I></A>
703</H4>
704<P><IMG WIDTH="587" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
705 SRC="img184.gif"
706 ALT="$\textstyle\parbox{\pboxargslen}{\em expr var lst \/}$"> [<EM>MACRO</EM>]
707<BLOCKQUOTE>
708 </BLOCKQUOTE><H4><A NAME="SECTION000120060000000000000">
709<I>union<MATH CLASS="INLINE">
710-
711</MATH>of</I></A>
712</H4>
713<P><IMG WIDTH="608" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
714 SRC="img183.gif"
715 ALT="$\textstyle\parbox{\pboxargslen}{\em expr (var lst) {\sf \&rest} more \/}$"> [<EM>MACRO</EM>]
716<BLOCKQUOTE>
717 </BLOCKQUOTE><H4><A NAME="SECTION000120070000000000000">
718<I>union<MATH CLASS="INLINE">
719-
720</MATH>of<MATH CLASS="INLINE">
721-
722</MATH>1</I></A>
723</H4>
724<P><IMG WIDTH="587" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
725 SRC="img184.gif"
726 ALT="$\textstyle\parbox{\pboxargslen}{\em expr var lst \/}$"> [<EM>MACRO</EM>]
727<BLOCKQUOTE>
728 </BLOCKQUOTE><H4><A NAME="SECTION000120080000000000000">
729<I>set<MATH CLASS="INLINE">
730-
731</MATH>of</I></A>
732</H4>
733<P><IMG WIDTH="608" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
734 SRC="img183.gif"
735 ALT="$\textstyle\parbox{\pboxargslen}{\em expr (var lst) {\sf \&rest} more \/}$"> [<EM>MACRO</EM>]
736<BLOCKQUOTE>
737 </BLOCKQUOTE><H4><A NAME="SECTION000120090000000000000">
738<I>set<MATH CLASS="INLINE">
739-
740</MATH>of<MATH CLASS="INLINE">
741-
742</MATH>1</I></A>
743</H4>
744<P><IMG WIDTH="587" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
745 SRC="img184.gif"
746 ALT="$\textstyle\parbox{\pboxargslen}{\em expr var lst \/}$"> [<EM>MACRO</EM>]
747<BLOCKQUOTE>
748 </BLOCKQUOTE><H4><A NAME="SECTION0001200100000000000000">
749<I>select</I></A>
750</H4>
751<P><IMG WIDTH="573" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
752 SRC="img185.gif"
753 ALT="$\textstyle\parbox{\pboxargslen}{\em ind lst \/}$"> [<EM>FUNCTION</EM>]
754<BLOCKQUOTE>
755 </BLOCKQUOTE><H4><A NAME="SECTION0001200110000000000000">
756<I>monom/</I></A>
757</H4>
758<P><IMG WIDTH="552" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
759 SRC="img186.gif"
760 ALT="$\textstyle\parbox{\pboxargslen}{\em m1 m2 \/}$"> [<EM>FUNCTION</EM>]
761<BLOCKQUOTE>
762Divide monomial M1 by monomial M2.</BLOCKQUOTE><H4><A NAME="SECTION0001200120000000000000">
763<I>monom*</I></A>
764</H4>
765<P><IMG WIDTH="552" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
766 SRC="img186.gif"
767 ALT="$\textstyle\parbox{\pboxargslen}{\em m1 m2 \/}$"> [<EM>FUNCTION</EM>]
768<BLOCKQUOTE>
769Multiply monomial M1 by monomial M2.</BLOCKQUOTE><H4><A NAME="SECTION0001200130000000000000">
770<I>nmonom*</I></A>
771</H4>
772<P><IMG WIDTH="552" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
773 SRC="img186.gif"
774 ALT="$\textstyle\parbox{\pboxargslen}{\em m1 m2 \/}$"> [<EM>FUNCTION</EM>]
775<BLOCKQUOTE>
776Multiply monomials M1 and M2 <MATH CLASS="INLINE">
777-
778</MATH> destructive version.
779 M1 is destructively modified, M2 is not modified.</BLOCKQUOTE><H4><A NAME="SECTION0001200140000000000000">
780<I>monom<MATH CLASS="INLINE">
781-
782</MATH>divides<MATH CLASS="INLINE">
783-
784</MATH>p</I></A>
785</H4>
786<P><IMG WIDTH="552" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
787 SRC="img186.gif"
788 ALT="$\textstyle\parbox{\pboxargslen}{\em m1 m2 \/}$"> [<EM>FUNCTION</EM>]
789<BLOCKQUOTE>
790Returns T if monomial M1 divides monomial M2, NIL otherwise.</BLOCKQUOTE><H4><A NAME="SECTION0001200150000000000000">
791<I>monom<MATH CLASS="INLINE">
792-
793</MATH>divisible<MATH CLASS="INLINE">
794-
795</MATH>by<MATH CLASS="INLINE">
796-
797</MATH>p</I></A>
798</H4>
799<P><IMG WIDTH="552" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
800 SRC="img186.gif"
801 ALT="$\textstyle\parbox{\pboxargslen}{\em m1 m2 \/}$"> [<EM>FUNCTION</EM>]
802<BLOCKQUOTE>
803Returns T if monomial M1 is divisible by monomial M2, NIL otherwise.</BLOCKQUOTE><H4><A NAME="SECTION0001200160000000000000">
804<I>monom<MATH CLASS="INLINE">
805-
806</MATH>rel<MATH CLASS="INLINE">
807-
808</MATH>prime</I></A>
809</H4>
810<P><IMG WIDTH="552" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
811 SRC="img186.gif"
812 ALT="$\textstyle\parbox{\pboxargslen}{\em m1 m2 \/}$"> [<EM>FUNCTION</EM>]
813<BLOCKQUOTE>
814Returns T if two monomials M1 and M2 are relatively prime (disjoint).</BLOCKQUOTE><H4><A NAME="SECTION0001200170000000000000">
815<I>monom<MATH CLASS="INLINE">
816-
817</MATH>equal</I></A>
818</H4>
819<P><IMG WIDTH="552" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
820 SRC="img186.gif"
821 ALT="$\textstyle\parbox{\pboxargslen}{\em m1 m2 \/}$"> [<EM>FUNCTION</EM>]
822<BLOCKQUOTE>
823Returns T if two monomials M1 and M2 are equal.</BLOCKQUOTE><H4><A NAME="SECTION0001200180000000000000">
824<I>monom<MATH CLASS="INLINE">
825-
826</MATH>lcm</I></A>
827</H4>
828<P><IMG WIDTH="552" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
829 SRC="img186.gif"
830 ALT="$\textstyle\parbox{\pboxargslen}{\em m1 m2 \/}$"> [<EM>FUNCTION</EM>]
831<BLOCKQUOTE>
832Returns least common multiple of monomials M1 and M2.</BLOCKQUOTE><H4><A NAME="SECTION0001200190000000000000">
833<I>monom<MATH CLASS="INLINE">
834-
835</MATH>gcd</I></A>
836</H4>
837<P><IMG WIDTH="552" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
838 SRC="img186.gif"
839 ALT="$\textstyle\parbox{\pboxargslen}{\em m1 m2 \/}$"> [<EM>FUNCTION</EM>]
840<BLOCKQUOTE>
841Returns greatest common divisor of monomials M1 and M2.</BLOCKQUOTE><H4><A NAME="SECTION0001200200000000000000">
842<I>poly<MATH CLASS="INLINE">
843-
844</MATH>gcd</I></A>
845</H4>
846<P><IMG WIDTH="504" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
847 SRC="img140.gif"
848 ALT="$\textstyle\parbox{\pboxargslen}{\em a b \/}$"> [<EM>FUNCTION</EM>]
849<BLOCKQUOTE>
850 </BLOCKQUOTE><H4><A NAME="SECTION0001200210000000000000">
851<I>poly<MATH CLASS="INLINE">
852-
853</MATH>pseudo<MATH CLASS="INLINE">
854-
855</MATH>divide</I></A>
856</H4>
857<P><IMG WIDTH="469" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
858 SRC="img187.gif"
859 ALT="$\textstyle\parbox{\pboxargslen}{\em f g \/}$"> [<EM>FUNCTION</EM>]
860<BLOCKQUOTE>
861 </BLOCKQUOTE><H4><A NAME="SECTION0001200220000000000000">
862<I>poly<MATH CLASS="INLINE">
863-
864</MATH>pseudo<MATH CLASS="INLINE">
865-
866</MATH>remainder</I></A>
867</H4>
868<P><IMG WIDTH="469" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
869 SRC="img187.gif"
870 ALT="$\textstyle\parbox{\pboxargslen}{\em f g \/}$"> [<EM>FUNCTION</EM>]
871<BLOCKQUOTE>
872 </BLOCKQUOTE><H4><A NAME="SECTION0001200230000000000000">
873<I>mdeg</I></A>
874</H4>
875<P><IMG WIDTH="574" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
876 SRC="img188.gif"
877 ALT="$\textstyle\parbox{\pboxargslen}{\em b \/}$"> [<EM>FUNCTION</EM>]
878<BLOCKQUOTE>
879 </BLOCKQUOTE><H4><A NAME="SECTION0001200240000000000000">
880<I>lcoeff</I></A>
881</H4>
882<P><IMG WIDTH="574" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
883 SRC="img188.gif"
884 ALT="$\textstyle\parbox{\pboxargslen}{\em b \/}$"> [<EM>FUNCTION</EM>]
885<BLOCKQUOTE>
886 </BLOCKQUOTE><H4><A NAME="SECTION0001200250000000000000">
887<I>lrest</I></A>
888</H4>
889<P><IMG WIDTH="574" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
890 SRC="img188.gif"
891 ALT="$\textstyle\parbox{\pboxargslen}{\em b \/}$"> [<EM>FUNCTION</EM>]
892<BLOCKQUOTE>
893 </BLOCKQUOTE><H4><A NAME="SECTION0001200260000000000000">
894<I>lpart</I></A>
895</H4>
896<P><IMG WIDTH="574" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
897 SRC="img188.gif"
898 ALT="$\textstyle\parbox{\pboxargslen}{\em b \/}$"> [<EM>FUNCTION</EM>]
899<BLOCKQUOTE>
900 </BLOCKQUOTE><H4><A NAME="SECTION0001200270000000000000">
901<I>poly<MATH CLASS="INLINE">
902-
903</MATH>primitive<MATH CLASS="INLINE">
904-
905</MATH>part</I></A>
906</H4>
907<P><IMG WIDTH="549" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
908 SRC="img88.gif"
909 ALT="$\textstyle\parbox{\pboxargslen}{\em f \/}$"> [<EM>FUNCTION</EM>]
910<BLOCKQUOTE>
911 </BLOCKQUOTE><H4><A NAME="SECTION0001200280000000000000">
912<I>poly<MATH CLASS="INLINE">
913-
914</MATH>content</I></A>
915</H4>
916<P><IMG WIDTH="549" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
917 SRC="img88.gif"
918 ALT="$\textstyle\parbox{\pboxargslen}{\em f \/}$"> [<EM>FUNCTION</EM>]
919<BLOCKQUOTE>
920 </BLOCKQUOTE><H4><A NAME="SECTION0001200290000000000000">
921<I>poly<MATH CLASS="INLINE">
922-
923</MATH>with<MATH CLASS="INLINE">
924-
925</MATH>sugar<MATH CLASS="INLINE">
926-
927</MATH>poly</I></A>
928</H4>
929<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
930 SRC="img80.gif"
931 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
932<BLOCKQUOTE>
933 </BLOCKQUOTE><H4><A NAME="SECTION0001200300000000000000">
934<I>poly<MATH CLASS="INLINE">
935-
936</MATH>with<MATH CLASS="INLINE">
937-
938</MATH>sugar<MATH CLASS="INLINE">
939-
940</MATH>sugar</I></A>
941</H4>
942<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
943 SRC="img80.gif"
944 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
945<BLOCKQUOTE>
946 </BLOCKQUOTE><H4><A NAME="SECTION0001200310000000000000">
947<I>poly<MATH CLASS="INLINE">
948-
949</MATH>with<MATH CLASS="INLINE">
950-
951</MATH>sugar<MATH CLASS="INLINE">
952-
953</MATH>tail</I></A>
954</H4>
955<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
956 SRC="img80.gif"
957 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
958<BLOCKQUOTE>
959 </BLOCKQUOTE><H4><A NAME="SECTION0001200320000000000000">
960<I>(setf poly<MATH CLASS="INLINE">
961-
962</MATH>with<MATH CLASS="INLINE">
963-
964</MATH>sugar<MATH CLASS="INLINE">
965-
966</MATH>poly)</I></A>
967</H4>
968<P><IMG WIDTH="348" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
969 SRC="img189.gif"
970 ALT="$\textstyle\parbox{\pboxargslen}{\em poly \/}$"> [<EM>SETF MAPPING</EM>]
971<BLOCKQUOTE>
972 </BLOCKQUOTE><H4><A NAME="SECTION0001200330000000000000">
973<I>(setf poly<MATH CLASS="INLINE">
974-
975</MATH>with<MATH CLASS="INLINE">
976-
977</MATH>sugar<MATH CLASS="INLINE">
978-
979</MATH>sugar)</I></A>
980</H4>
981<P><IMG WIDTH="340" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
982 SRC="img190.gif"
983 ALT="$\textstyle\parbox{\pboxargslen}{\em sugar \/}$"> [<EM>SETF MAPPING</EM>]
984<BLOCKQUOTE>
985 </BLOCKQUOTE><H4><A NAME="SECTION0001200340000000000000">
986<I>(setf poly<MATH CLASS="INLINE">
987-
988</MATH>with<MATH CLASS="INLINE">
989-
990</MATH>sugar<MATH CLASS="INLINE">
991-
992</MATH>tail)</I></A>
993</H4>
994<P><IMG WIDTH="355" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
995 SRC="img191.gif"
996 ALT="$\textstyle\parbox{\pboxargslen}{\em tail \/}$"> [<EM>SETF MAPPING</EM>]
997<BLOCKQUOTE>
998 </BLOCKQUOTE><H4><A NAME="SECTION0001200350000000000000">
999<I>monom<MATH CLASS="INLINE">
1000-
1001</MATH>sugar</I></A>
1002</H4>
1003<P><IMG WIDTH="511" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
1004 SRC="img192.gif"
1005 ALT="$\textstyle\parbox{\pboxargslen}{\em m \/}$"> [<EM>FUNCTION</EM>]
1006<BLOCKQUOTE>
1007 </BLOCKQUOTE><H4><A NAME="SECTION0001200360000000000000">
1008<I>coefficient<MATH CLASS="INLINE">
1009-
1010</MATH>sugar</I></A>
1011</H4>
1012<P><IMG WIDTH="492" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
1013 SRC="img193.gif"
1014 ALT="$\textstyle\parbox{\pboxargslen}{\em c ring \/}$"> [<EM>FUNCTION</EM>]
1015<BLOCKQUOTE>
1016 </BLOCKQUOTE><H4><A NAME="SECTION0001200370000000000000">
1017<I>term<MATH CLASS="INLINE">
1018-
1019</MATH>sugar</I></A>
1020</H4>
1021<P><IMG WIDTH="455" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
1022 SRC="img94.gif"
1023 ALT="$\textstyle\parbox{\pboxargslen}{\em term ring \/}$"> [<EM>FUNCTION</EM>]
1024<BLOCKQUOTE>
1025 </BLOCKQUOTE><H4><A NAME="SECTION0001200380000000000000">
1026<I>poly<MATH CLASS="INLINE">
1027-
1028</MATH>add<MATH CLASS="INLINE">
1029-
1030</MATH>sugar</I></A>
1031</H4>
1032<P><IMG WIDTH="495" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1033 SRC="img194.gif"
1034 ALT="$\textstyle\parbox{\pboxargslen}{\em poly ring \/}$"> [<EM>FUNCTION</EM>]
1035<BLOCKQUOTE>
1036 </BLOCKQUOTE><H4><A NAME="SECTION0001200390000000000000">
1037<I>scalar<MATH CLASS="INLINE">
1038-
1039</MATH>times<MATH CLASS="INLINE">
1040-
1041</MATH>poly<MATH CLASS="INLINE">
1042-
1043</MATH>with<MATH CLASS="INLINE">
1044-
1045</MATH>sugar</I></A>
1046</H4>
1047<P><IMG WIDTH="389" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
1048 SRC="img195.gif"
1049 ALT="$\textstyle\parbox{\pboxargslen}{\em c p ring \/}$"> [<EM>FUNCTION</EM>]
1050<BLOCKQUOTE>
1051 </BLOCKQUOTE><H4><A NAME="SECTION0001200400000000000000">
1052<I>term<MATH CLASS="INLINE">
1053-
1054</MATH>times<MATH CLASS="INLINE">
1055-
1056</MATH>poly<MATH CLASS="INLINE">
1057-
1058</MATH>with<MATH CLASS="INLINE">
1059-
1060</MATH>sugar</I></A>
1061</H4>
1062<P><IMG WIDTH="396" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1063 SRC="img196.gif"
1064 ALT="$\textstyle\parbox{\pboxargslen}{\em term f ring \/}$"> [<EM>FUNCTION</EM>]
1065<BLOCKQUOTE>
1066 </BLOCKQUOTE><H4><A NAME="SECTION0001200410000000000000">
1067<I>monom<MATH CLASS="INLINE">
1068-
1069</MATH>times<MATH CLASS="INLINE">
1070-
1071</MATH>poly<MATH CLASS="INLINE">
1072-
1073</MATH>with<MATH CLASS="INLINE">
1074-
1075</MATH>sugar</I></A>
1076</H4>
1077<P><IMG WIDTH="453" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1078 SRC="img129.gif"
1079 ALT="$\textstyle\parbox{\pboxargslen}{\em m f \/}$"> [<EM>FUNCTION</EM>]
1080<BLOCKQUOTE>
1081 </BLOCKQUOTE><H4><A NAME="SECTION0001200420000000000000">
1082<I>minus<MATH CLASS="INLINE">
1083-
1084</MATH>poly<MATH CLASS="INLINE">
1085-
1086</MATH>with<MATH CLASS="INLINE">
1087-
1088</MATH>sugar</I></A>
1089</H4>
1090<P><IMG WIDTH="437" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1091 SRC="img197.gif"
1092 ALT="$\textstyle\parbox{\pboxargslen}{\em f ring \/}$"> [<EM>FUNCTION</EM>]
1093<BLOCKQUOTE>
1094 </BLOCKQUOTE><H4><A NAME="SECTION0001200430000000000000">
1095<I>poly<MATH CLASS="INLINE">
1096-
1097</MATH>with<MATH CLASS="INLINE">
1098-
1099</MATH>sugar+</I></A>
1100</H4>
1101<P><IMG WIDTH="478" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1102 SRC="img198.gif"
1103 ALT="$\textstyle\parbox{\pboxargslen}{\em p q pred ring \/}$"> [<EM>FUNCTION</EM>]
1104<BLOCKQUOTE>
1105 </BLOCKQUOTE><H4><A NAME="SECTION0001200440000000000000">
1106<I>poly<MATH CLASS="INLINE">
1107-
1108</MATH>with<MATH CLASS="INLINE">
1109-
1110</MATH>sugar<MATH CLASS="INLINE">
1111-
1112</MATH></I></A>
1113</H4>
1114<P><IMG WIDTH="478" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1115 SRC="img198.gif"
1116 ALT="$\textstyle\parbox{\pboxargslen}{\em p q pred ring \/}$"> [<EM>FUNCTION</EM>]
1117<BLOCKQUOTE>
1118 </BLOCKQUOTE><H4><A NAME="SECTION0001200450000000000000">
1119<I>poly<MATH CLASS="INLINE">
1120-
1121</MATH>with<MATH CLASS="INLINE">
1122-
1123</MATH>sugar<MATH CLASS="INLINE">
1124-
1125</MATH>op</I></A>
1126</H4>
1127<P><IMG WIDTH="461" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1128 SRC="img199.gif"
1129 ALT="$\textstyle\parbox{\pboxargslen}{\em f term g pred ring \/}$"> [<EM>FUNCTION</EM>]
1130<BLOCKQUOTE>
1131 </BLOCKQUOTE><H4><A NAME="SECTION0001200460000000000000">
1132<I>poly<MATH CLASS="INLINE">
1133-
1134</MATH>with<MATH CLASS="INLINE">
1135-
1136</MATH>sugar<MATH CLASS="INLINE">
1137-
1138</MATH>nreverse</I></A>
1139</H4>
1140<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1141 SRC="img80.gif"
1142 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1143<BLOCKQUOTE>
1144 </BLOCKQUOTE><H4><A NAME="SECTION0001200470000000000000">
1145<I>poly<MATH CLASS="INLINE">
1146-
1147</MATH>with<MATH CLASS="INLINE">
1148-
1149</MATH>sugar<MATH CLASS="INLINE">
1150-
1151</MATH>append</I></A>
1152</H4>
1153<P><IMG WIDTH="427" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1154 SRC="img200.gif"
1155 ALT="$\textstyle\parbox{\pboxargslen}{\em p q \/}$"> [<EM>FUNCTION</EM>]
1156<BLOCKQUOTE>
1157 </BLOCKQUOTE><H4><A NAME="SECTION0001200480000000000000">
1158<I>poly<MATH CLASS="INLINE">
1159-
1160</MATH>with<MATH CLASS="INLINE">
1161-
1162</MATH>sugar<MATH CLASS="INLINE">
1163-
1164</MATH>zerop</I></A>
1165</H4>
1166<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1167 SRC="img80.gif"
1168 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1169<BLOCKQUOTE>
1170 </BLOCKQUOTE><H4><A NAME="SECTION0001200490000000000000">
1171<I>poly<MATH CLASS="INLINE">
1172-
1173</MATH>with<MATH CLASS="INLINE">
1174-
1175</MATH>sugar<MATH CLASS="INLINE">
1176-
1177</MATH>lm</I></A>
1178</H4>
1179<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1180 SRC="img80.gif"
1181 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1182<BLOCKQUOTE>
1183 </BLOCKQUOTE><H4><A NAME="SECTION0001200500000000000000">
1184<I>poly<MATH CLASS="INLINE">
1185-
1186</MATH>with<MATH CLASS="INLINE">
1187-
1188</MATH>sugar<MATH CLASS="INLINE">
1189-
1190</MATH>lc</I></A>
1191</H4>
1192<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1193 SRC="img80.gif"
1194 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1195<BLOCKQUOTE>
1196 </BLOCKQUOTE><H4><A NAME="SECTION0001200510000000000000">
1197<I>poly<MATH CLASS="INLINE">
1198-
1199</MATH>with<MATH CLASS="INLINE">
1200-
1201</MATH>sugar<MATH CLASS="INLINE">
1202-
1203</MATH>lt</I></A>
1204</H4>
1205<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1206 SRC="img80.gif"
1207 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1208<BLOCKQUOTE>
1209 </BLOCKQUOTE><H4><A NAME="SECTION0001200520000000000000">
1210<I>poly<MATH CLASS="INLINE">
1211-
1212</MATH>print</I></A>
1213</H4>
1214<P><IMG WIDTH="537" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
1215 SRC="img201.gif"
1216 ALT="$\textstyle\parbox{\pboxargslen}{\em plist vars {\sf \&optional} (stream t) \/}$"> [<EM>FUNCTION</EM>]
1217<BLOCKQUOTE>
1218Prints a polynomial or a list of polynomials PLIST using infix
1219syntax compatible with most software systems. The following data
1220representations are assumed: 1) Polynomial list is ([ poly1 poly2
1221...) 2) Polynomial is a list (term1 term2 ...)
12223) Term is (monom . number)
12234) Monom is (number1 number2 ...) and is a list of powers at
1224corresponding variables
1225Variable names must be provided to the printer explicitly.</BLOCKQUOTE><H4><A NAME="SECTION0001200530000000000000">
1226<I>poly<MATH CLASS="INLINE">
1227-
1228</MATH>print<MATH CLASS="INLINE">
1229-
1230</MATH>1</I></A>
1231</H4>
1232<P><IMG WIDTH="516" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
1233 SRC="img202.gif"
1234 ALT="$\textstyle\parbox{\pboxargslen}{\em p vars {\sf \&optional} (stream t) \/}$"> [<EM>FUNCTION</EM>]
1235<BLOCKQUOTE>
1236An auxillary function of POLY<MATH CLASS="INLINE">
1237-
1238</MATH>PRINT. It prints a single polynomial
1239P. </BLOCKQUOTE><H4><A NAME="SECTION0001200540000000000000">
1240<I>poly<MATH CLASS="INLINE">
1241-
1242</MATH>print<MATH CLASS="INLINE">
1243-
1244</MATH>2</I></A>
1245</H4>
1246<P><IMG WIDTH="516" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
1247 SRC="img203.gif"
1248 ALT="$\textstyle\parbox{\pboxargslen}{\em plist vars stream {\sf \&optional} (beg t) \/}$"> [<EM>FUNCTION</EM>]
1249<BLOCKQUOTE>
1250An auxillary function of POLY<MATH CLASS="INLINE">
1251-
1252</MATH>PRINT. It prints a comma<MATH CLASS="INLINE">
1253-
1254</MATH>separated
1255list of polynomials PLIST. </BLOCKQUOTE><H4><A NAME="SECTION0001200550000000000000">
1256<I>print<MATH CLASS="INLINE">
1257-
1258</MATH>term</I></A>
1259</H4>
1260<P><IMG WIDTH="534" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
1261 SRC="img204.gif"
1262 ALT="$\textstyle\parbox{\pboxargslen}{\em l vars {\sf \&optional} (stream t) beg \/}$"> [<EM>FUNCTION</EM>]
1263<BLOCKQUOTE>
1264An auxillary function of POLY<MATH CLASS="INLINE">
1265-
1266</MATH>PRINT. It prints a single term L.</BLOCKQUOTE><H4><A NAME="SECTION0001200560000000000000">
1267<I>print<MATH CLASS="INLINE">
1268-
1269</MATH>monom</I></A>
1270</H4>
1271<P><IMG WIDTH="534" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
1272 SRC="img204.gif"
1273 ALT="$\textstyle\parbox{\pboxargslen}{\em l vars {\sf \&optional} (stream t) beg \/}$"> [<EM>FUNCTION</EM>]
1274<BLOCKQUOTE>
1275An auxillary function of POLY<MATH CLASS="INLINE">
1276-
1277</MATH>PRINT. It prints a single monomial L.</BLOCKQUOTE><H4><A NAME="SECTION0001200570000000000000">
1278<I>num</I></A>
1279</H4>
1280<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1281 SRC="img80.gif"
1282 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1283<BLOCKQUOTE>
1284 </BLOCKQUOTE><H4><A NAME="SECTION0001200580000000000000">
1285<I>denom</I></A>
1286</H4>
1287<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1288 SRC="img80.gif"
1289 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1290<BLOCKQUOTE>
1291 </BLOCKQUOTE><H4><A NAME="SECTION0001200590000000000000">
1292<I>rat<MATH CLASS="INLINE">
1293-
1294</MATH>simplify<MATH CLASS="INLINE">
1295-
1296</MATH>2</I></A>
1297</H4>
1298<P><IMG WIDTH="505" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1299 SRC="img205.gif"
1300 ALT="$\textstyle\parbox{\pboxargslen}{\em num denom \/}$"> [<EM>FUNCTION</EM>]
1301<BLOCKQUOTE>
1302 </BLOCKQUOTE><H4><A NAME="SECTION0001200600000000000000">
1303<I>rat<MATH CLASS="INLINE">
1304-
1305</MATH>simplify</I></A>
1306</H4>
1307<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1308 SRC="img80.gif"
1309 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1310<BLOCKQUOTE>
1311 </BLOCKQUOTE><H4><A NAME="SECTION0001200610000000000000">
1312<I>rat+</I></A>
1313</H4>
1314<P><IMG WIDTH="427" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1315 SRC="img200.gif"
1316 ALT="$\textstyle\parbox{\pboxargslen}{\em p q \/}$"> [<EM>FUNCTION</EM>]
1317<BLOCKQUOTE>
1318 </BLOCKQUOTE><H4><A NAME="SECTION0001200620000000000000">
1319<I>rat<MATH CLASS="INLINE">
1320-
1321</MATH></I></A>
1322</H4>
1323<P><IMG WIDTH="427" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1324 SRC="img200.gif"
1325 ALT="$\textstyle\parbox{\pboxargslen}{\em p q \/}$"> [<EM>FUNCTION</EM>]
1326<BLOCKQUOTE>
1327 </BLOCKQUOTE><H4><A NAME="SECTION0001200630000000000000">
1328<I>rat*</I></A>
1329</H4>
1330<P><IMG WIDTH="427" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1331 SRC="img200.gif"
1332 ALT="$\textstyle\parbox{\pboxargslen}{\em p q \/}$"> [<EM>FUNCTION</EM>]
1333<BLOCKQUOTE>
1334 </BLOCKQUOTE><H4><A NAME="SECTION0001200640000000000000">
1335<I>rat/</I></A>
1336</H4>
1337<P><IMG WIDTH="427" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1338 SRC="img200.gif"
1339 ALT="$\textstyle\parbox{\pboxargslen}{\em p q \/}$"> [<EM>FUNCTION</EM>]
1340<BLOCKQUOTE>
1341 </BLOCKQUOTE><H4><A NAME="SECTION0001200650000000000000">
1342<I>scalar<MATH CLASS="INLINE">
1343-
1344</MATH>times<MATH CLASS="INLINE">
1345-
1346</MATH>rat</I></A>
1347</H4>
1348<P><IMG WIDTH="490" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1349 SRC="img206.gif"
1350 ALT="$\textstyle\parbox{\pboxargslen}{\em scalar p \/}$"> [<EM>FUNCTION</EM>]
1351<BLOCKQUOTE>
1352 </BLOCKQUOTE><H4><A NAME="SECTION0001200660000000000000">
1353<I>scalar<MATH CLASS="INLINE">
1354-
1355</MATH>div<MATH CLASS="INLINE">
1356-
1357</MATH>rat</I></A>
1358</H4>
1359<P><IMG WIDTH="490" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1360 SRC="img206.gif"
1361 ALT="$\textstyle\parbox{\pboxargslen}{\em scalar p \/}$"> [<EM>FUNCTION</EM>]
1362<BLOCKQUOTE>
1363 </BLOCKQUOTE><H4><A NAME="SECTION0001200670000000000000">
1364<I>rat<MATH CLASS="INLINE">
1365-
1366</MATH>zerop</I></A>
1367</H4>
1368<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1369 SRC="img80.gif"
1370 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1371<BLOCKQUOTE>
1372 </BLOCKQUOTE><H4><A NAME="SECTION0001200680000000000000">
1373<I>rat<MATH CLASS="INLINE">
1374-
1375</MATH>uminus</I></A>
1376</H4>
1377<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1378 SRC="img80.gif"
1379 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1380<BLOCKQUOTE>
1381 </BLOCKQUOTE><H4><A NAME="SECTION0001200690000000000000">
1382<I>rat<MATH CLASS="INLINE">
1383-
1384</MATH>expt</I></A>
1385</H4>
1386<P><IMG WIDTH="549" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1387 SRC="img207.gif"
1388 ALT="$\textstyle\parbox{\pboxargslen}{\em p n \/}$"> [<EM>FUNCTION</EM>]
1389<BLOCKQUOTE>
1390 </BLOCKQUOTE><H4><A NAME="SECTION0001200700000000000000">
1391<I>rat<MATH CLASS="INLINE">
1392-
1393</MATH>constant</I></A>
1394</H4>
1395<P><IMG WIDTH="520" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
1396 SRC="img208.gif"
1397 ALT="$\textstyle\parbox{\pboxargslen}{\em c n \/}$"> [<EM>FUNCTION</EM>]
1398<BLOCKQUOTE>
1399Make a constant rational function equal to c with n variables</BLOCKQUOTE><H4><A NAME="SECTION0001200710000000000000">
1400<I>rat<MATH CLASS="INLINE">
1401-
1402</MATH>to<MATH CLASS="INLINE">
1403-
1404</MATH>poly</I></A>
1405</H4>
1406<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1407 SRC="img80.gif"
1408 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1409<BLOCKQUOTE>
1410Attempt to convert a rational function to a polynomial by
1411dividing numerator by denominator. Error if not divisible</BLOCKQUOTE><H4><A NAME="SECTION0001200720000000000000">
1412<I>ratpoly+</I></A>
1413</H4>
1414<P><IMG WIDTH="427" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1415 SRC="img200.gif"
1416 ALT="$\textstyle\parbox{\pboxargslen}{\em p q \/}$"> [<EM>FUNCTION</EM>]
1417<BLOCKQUOTE>
1418Add polynomials P and Q.</BLOCKQUOTE><H4><A NAME="SECTION0001200730000000000000">
1419<I>ratpoly<MATH CLASS="INLINE">
1420-
1421</MATH></I></A>
1422</H4>
1423<P><IMG WIDTH="427" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1424 SRC="img200.gif"
1425 ALT="$\textstyle\parbox{\pboxargslen}{\em p q \/}$"> [<EM>FUNCTION</EM>]
1426<BLOCKQUOTE>
1427 </BLOCKQUOTE><H4><A NAME="SECTION0001200740000000000000">
1428<I>ratpoly<MATH CLASS="INLINE">
1429-
1430</MATH>uminus</I></A>
1431</H4>
1432<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1433 SRC="img80.gif"
1434 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1435<BLOCKQUOTE>
1436 </BLOCKQUOTE><H4><A NAME="SECTION0001200750000000000000">
1437<I>ratpoly*</I></A>
1438</H4>
1439<P><IMG WIDTH="427" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1440 SRC="img200.gif"
1441 ALT="$\textstyle\parbox{\pboxargslen}{\em p q \/}$"> [<EM>FUNCTION</EM>]
1442<BLOCKQUOTE>
1443Multiply polynomials P and Q.</BLOCKQUOTE><H4><A NAME="SECTION0001200760000000000000">
1444<I>scalar<MATH CLASS="INLINE">
1445-
1446</MATH>times<MATH CLASS="INLINE">
1447-
1448</MATH>ratpoly</I></A>
1449</H4>
1450<P><IMG WIDTH="490" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1451 SRC="img206.gif"
1452 ALT="$\textstyle\parbox{\pboxargslen}{\em scalar p \/}$"> [<EM>FUNCTION</EM>]
1453<BLOCKQUOTE>
1454Multiply scalar SCALAR by a polynomial P.</BLOCKQUOTE><H4><A NAME="SECTION0001200770000000000000">
1455<I>rat<MATH CLASS="INLINE">
1456-
1457</MATH>times<MATH CLASS="INLINE">
1458-
1459</MATH>ratpoly</I></A>
1460</H4>
1461<P><IMG WIDTH="490" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1462 SRC="img206.gif"
1463 ALT="$\textstyle\parbox{\pboxargslen}{\em scalar p \/}$"> [<EM>FUNCTION</EM>]
1464<BLOCKQUOTE>
1465Multiply rational function SCALAR by a polynomial P.</BLOCKQUOTE><H4><A NAME="SECTION0001200780000000000000">
1466<I>ratpoly<MATH CLASS="INLINE">
1467-
1468</MATH>divide</I></A>
1469</H4>
1470<P><IMG WIDTH="469" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1471 SRC="img187.gif"
1472 ALT="$\textstyle\parbox{\pboxargslen}{\em f g \/}$"> [<EM>FUNCTION</EM>]
1473<BLOCKQUOTE>
1474Divide polynomial F by G. Return quotient and remainder as multiple
1475values. </BLOCKQUOTE><H4><A NAME="SECTION0001200790000000000000">
1476<I>ratpoly<MATH CLASS="INLINE">
1477-
1478</MATH>remainder</I></A>
1479</H4>
1480<P><IMG WIDTH="469" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1481 SRC="img187.gif"
1482 ALT="$\textstyle\parbox{\pboxargslen}{\em f g \/}$"> [<EM>FUNCTION</EM>]
1483<BLOCKQUOTE>
1484The remainder of the division of a polynomial F by G.</BLOCKQUOTE><H4><A NAME="SECTION0001200800000000000000">
1485<I>ratpoly<MATH CLASS="INLINE">
1486-
1487</MATH>gcd</I></A>
1488</H4>
1489<P><IMG WIDTH="469" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1490 SRC="img187.gif"
1491 ALT="$\textstyle\parbox{\pboxargslen}{\em f g \/}$"> [<EM>FUNCTION</EM>]
1492<BLOCKQUOTE>
1493Return GCD of polynomials F and G.</BLOCKQUOTE><H4><A NAME="SECTION0001200810000000000000">
1494<I>ratpoly<MATH CLASS="INLINE">
1495-
1496</MATH>diff</I></A>
1497</H4>
1498<P><IMG WIDTH="549" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1499 SRC="img88.gif"
1500 ALT="$\textstyle\parbox{\pboxargslen}{\em f \/}$"> [<EM>FUNCTION</EM>]
1501<BLOCKQUOTE>
1502Differentiate a polynomial.</BLOCKQUOTE><H4><A NAME="SECTION0001200820000000000000">
1503<I>ratpoly<MATH CLASS="INLINE">
1504-
1505</MATH>square<MATH CLASS="INLINE">
1506-
1507</MATH>free</I></A>
1508</H4>
1509<P><IMG WIDTH="549" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1510 SRC="img88.gif"
1511 ALT="$\textstyle\parbox{\pboxargslen}{\em f \/}$"> [<EM>FUNCTION</EM>]
1512<BLOCKQUOTE>
1513Return the square<MATH CLASS="INLINE">
1514-
1515</MATH>free part of a polynomial F.</BLOCKQUOTE><H4><A NAME="SECTION0001200830000000000000">
1516<I>ratpoly<MATH CLASS="INLINE">
1517-
1518</MATH>normalize</I></A>
1519</H4>
1520<P><IMG WIDTH="549" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1521 SRC="img88.gif"
1522 ALT="$\textstyle\parbox{\pboxargslen}{\em f \/}$"> [<EM>FUNCTION</EM>]
1523<BLOCKQUOTE>
1524Divide a non<MATH CLASS="INLINE">
1525-
1526</MATH>zero polynomial by the coefficient at the highest
1527power. </BLOCKQUOTE><H4><A NAME="SECTION0001200840000000000000">
1528<I>ratpoly<MATH CLASS="INLINE">
1529-
1530</MATH>resultant</I></A>
1531</H4>
1532<P><IMG WIDTH="469" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1533 SRC="img187.gif"
1534 ALT="$\textstyle\parbox{\pboxargslen}{\em f g \/}$"> [<EM>FUNCTION</EM>]
1535<BLOCKQUOTE>
1536Return the resultant of polynomials F and G.</BLOCKQUOTE><H4><A NAME="SECTION0001200850000000000000">
1537<I>deg</I></A>
1538</H4>
1539<P><IMG WIDTH="587" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
1540 SRC="img209.gif"
1541 ALT="$\textstyle\parbox{\pboxargslen}{\em s \/}$"> [<EM>FUNCTION</EM>]
1542<BLOCKQUOTE>
1543 </BLOCKQUOTE><H4><A NAME="SECTION0001200860000000000000">
1544<I>lead</I></A>
1545</H4>
1546<P><IMG WIDTH="587" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
1547 SRC="img209.gif"
1548 ALT="$\textstyle\parbox{\pboxargslen}{\em s \/}$"> [<EM>FUNCTION</EM>]
1549<BLOCKQUOTE>
1550 </BLOCKQUOTE><H4><A NAME="SECTION0001200870000000000000">
1551<I>ratpoly<MATH CLASS="INLINE">
1552-
1553</MATH>discriminant</I></A>
1554</H4>
1555<P><IMG WIDTH="466" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
1556 SRC="img210.gif"
1557 ALT="$\textstyle\parbox{\pboxargslen}{\em p {\sf \&aux} (l (deg p)) \/}$"> [<EM>FUNCTION</EM>]
1558<BLOCKQUOTE>
1559The discriminant of a polynomial P.</BLOCKQUOTE><H4><A NAME="SECTION0001200880000000000000">
1560<I>ratpoly<MATH CLASS="INLINE">
1561-
1562</MATH>print</I></A>
1563</H4>
1564<P><IMG WIDTH="518" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
1565 SRC="img211.gif"
1566 ALT="$\textstyle\parbox{\pboxargslen}{\em p vars {\sf \&optional} (stream t) (beg t) (p$-$orig p) \/}$"> [<EM>FUNCTION</EM>]
1567<BLOCKQUOTE>
1568 </BLOCKQUOTE><H4><A NAME="SECTION0001200890000000000000">
1569<I>poly<MATH CLASS="INLINE">
1570-
1571</MATH>to<MATH CLASS="INLINE">
1572-
1573</MATH>ratpoly</I></A>
1574</H4>
1575<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1576 SRC="img80.gif"
1577 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1578<BLOCKQUOTE>
1579 </BLOCKQUOTE><H4><A NAME="SECTION0001200900000000000000">
1580<I>poly<MATH CLASS="INLINE">
1581-
1582</MATH>to<MATH CLASS="INLINE">
1583-
1584</MATH>poly1</I></A>
1585</H4>
1586<P><IMG WIDTH="505" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
1587 SRC="img212.gif"
1588 ALT="$\textstyle\parbox{\pboxargslen}{\em p {\sf \&aux} (htab (make$-$hash$-$table)) q \/}$"> [<EM>FUNCTION</EM>]
1589<BLOCKQUOTE>
1590 </BLOCKQUOTE><H4><A NAME="SECTION0001200910000000000000">
1591<I>poly1<MATH CLASS="INLINE">
1592-
1593</MATH>to<MATH CLASS="INLINE">
1594-
1595</MATH>ratpoly</I></A>
1596</H4>
1597<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1598 SRC="img80.gif"
1599 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1600<BLOCKQUOTE>
1601 </BLOCKQUOTE><H4><A NAME="SECTION0001200920000000000000">
1602<I>ratpoly<MATH CLASS="INLINE">
1603-
1604</MATH>to<MATH CLASS="INLINE">
1605-
1606</MATH>poly1</I></A>
1607</H4>
1608<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1609 SRC="img80.gif"
1610 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1611<BLOCKQUOTE>
1612Convert every coefficient of ratpoly to polynomial if possible</BLOCKQUOTE><H4><A NAME="SECTION0001200930000000000000">
1613<I>poly1<MATH CLASS="INLINE">
1614-
1615</MATH>to<MATH CLASS="INLINE">
1616-
1617</MATH>poly</I></A>
1618</H4>
1619<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1620 SRC="img80.gif"
1621 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1622<BLOCKQUOTE>
1623Convert a ratpoly, whose coeffs have been converted to poly,
1624into a poly structure, i.e. tack in powers of first variable.</BLOCKQUOTE><H4><A NAME="SECTION0001200940000000000000">
1625<I>ratpoly<MATH CLASS="INLINE">
1626-
1627</MATH>to<MATH CLASS="INLINE">
1628-
1629</MATH>poly</I></A>
1630</H4>
1631<P><IMG WIDTH="538" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1632 SRC="img80.gif"
1633 ALT="$\textstyle\parbox{\pboxargslen}{\em p \/}$"> [<EM>FUNCTION</EM>]
1634<BLOCKQUOTE>
1635 </BLOCKQUOTE><H4><A NAME="SECTION0001200950000000000000">
1636<I>poly<MATH CLASS="INLINE">
1637-
1638</MATH>resultant</I></A>
1639</H4>
1640<P><IMG WIDTH="469" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1641 SRC="img187.gif"
1642 ALT="$\textstyle\parbox{\pboxargslen}{\em f g \/}$"> [<EM>FUNCTION</EM>]
1643<BLOCKQUOTE>
1644Calculate resultant of F and G given in poly i.e. alist
1645representation. </BLOCKQUOTE><H4><A NAME="SECTION0001200960000000000000">
1646<I>term*</I></A>
1647</H4>
1648<P><IMG WIDTH="571" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
1649 SRC="img213.gif"
1650 ALT="$\textstyle\parbox{\pboxargslen}{\em term1 term2 {\sf \&optional} (ring *coefficient$-$ring*) \/}$"> [<EM>FUNCTION</EM>]
1651<BLOCKQUOTE>
1652 </BLOCKQUOTE><H4><A NAME="SECTION0001200970000000000000">
1653<I>term/</I></A>
1654</H4>
1655<P><IMG WIDTH="571" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
1656 SRC="img213.gif"
1657 ALT="$\textstyle\parbox{\pboxargslen}{\em term1 term2 {\sf \&optional} (ring *coefficient$-$ring*) \/}$"> [<EM>FUNCTION</EM>]
1658<BLOCKQUOTE>
1659 </BLOCKQUOTE><H4><A NAME="SECTION0001200980000000000000">
1660<I>monom<MATH CLASS="INLINE">
1661-
1662</MATH>times<MATH CLASS="INLINE">
1663-
1664</MATH>term</I></A>
1665</H4>
1666<P><IMG WIDTH="465" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1667 SRC="img214.gif"
1668 ALT="$\textstyle\parbox{\pboxargslen}{\em m term \/}$"> [<EM>FUNCTION</EM>]
1669<BLOCKQUOTE>
1670 </BLOCKQUOTE><H4><A NAME="SECTION0001200990000000000000">
1671<I>term<MATH CLASS="INLINE">
1672-
1673</MATH>divides<MATH CLASS="INLINE">
1674-
1675</MATH>p</I></A>
1676</H4>
1677<P><IMG WIDTH="498" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1678 SRC="img215.gif"
1679 ALT="$\textstyle\parbox{\pboxargslen}{\em term1 term2 \/}$"> [<EM>FUNCTION</EM>]
1680<BLOCKQUOTE>
1681 </BLOCKQUOTE><H4><A NAME="SECTION00012001000000000000000">
1682<I>term<MATH CLASS="INLINE">
1683-
1684</MATH>monom</I></A>
1685</H4>
1686<P><IMG WIDTH="558" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1687 SRC="img216.gif"
1688 ALT="$\textstyle\parbox{\pboxargslen}{\em term \/}$"> [<EM>MACRO</EM>]
1689<BLOCKQUOTE>
1690 </BLOCKQUOTE><H4><A NAME="SECTION00012001010000000000000">
1691<I>term<MATH CLASS="INLINE">
1692-
1693</MATH>coefficient</I></A>
1694</H4>
1695<P><IMG WIDTH="558" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1696 SRC="img216.gif"
1697 ALT="$\textstyle\parbox{\pboxargslen}{\em term \/}$"> [<EM>MACRO</EM>]
1698<BLOCKQUOTE>
1699 </BLOCKQUOTE><H4><A NAME="SECTION00012001020000000000000">
1700<I>(setf term<MATH CLASS="INLINE">
1701-
1702</MATH>monom)</I></A>
1703</H4>
1704<P><IMG WIDTH="414" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
1705 SRC="img217.gif"
1706 ALT="$\textstyle\parbox{\pboxargslen}{\em monom \/}$"> [<EM>SETF MAPPING</EM>]
1707<BLOCKQUOTE>
1708 </BLOCKQUOTE><H4><A NAME="SECTION00012001030000000000000">
1709<I>(setf term<MATH CLASS="INLINE">
1710-
1711</MATH>coefficient)</I></A>
1712</H4>
1713<P><IMG WIDTH="395" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
1714 SRC="img218.gif"
1715 ALT="$\textstyle\parbox{\pboxargslen}{\em coefficient \/}$"> [<EM>SETF MAPPING</EM>]
1716<BLOCKQUOTE>
1717 </BLOCKQUOTE><H4><A NAME="SECTION00012001040000000000000">
1718<I>xgcd</I></A>
1719</H4>
1720<P><IMG WIDTH="580" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
1721 SRC="img219.gif"
1722 ALT="$\textstyle\parbox{\pboxargslen}{\em x y \/}$"> [<EM>FUNCTION</EM>]
1723<BLOCKQUOTE>
1724Extended gcd; the call
1725 (xgcd X Y)
1726returns a multiple value list:
1727<MATH CLASS="INLINE">
1728-
1729</MATH> GCD
1730<MATH CLASS="INLINE">
1731-
1732</MATH> U,V such that they solve the equation
1733 GCD=U*X+V*Y
1734<MATH CLASS="INLINE">
1735-
1736</MATH> U1,V1 such that
1737 LCM=U1*X=V1*Y (up to the sign).</BLOCKQUOTE>
1738<P><HR>
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1752<BR>
1753<B> Next:</B> <A NAME="tex2html1095"
1754 HREF="node13.html">All examples produced by</A>
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1758 HREF="node11.html">The Parser Package</A>
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1760<ADDRESS>
1761<I>Marek Rychlik</I>
1762<BR><I>3/21/1998</I>
1763</ADDRESS>
1764</BODY>
1765</HTML>
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