1 | /*****************************************************************************\ |
---|
2 | * Computer Algebra System SINGULAR |
---|
3 | \*****************************************************************************/ |
---|
4 | /** @file facSparseHensel.cc |
---|
5 | * |
---|
6 | * This file implements functions for sparse heuristic Hensel lifting |
---|
7 | * |
---|
8 | * ABSTRACT: "A fast implementation of polynomial factorization" by M. Lucks and |
---|
9 | * "Effective polynomial computation" by R. Zippel |
---|
10 | * |
---|
11 | * @author Martin Lee |
---|
12 | * |
---|
13 | * @internal @version \$Id$ |
---|
14 | * |
---|
15 | **/ |
---|
16 | /*****************************************************************************/ |
---|
17 | |
---|
18 | #include "config.h" |
---|
19 | #include "cf_assert.h" |
---|
20 | #include "facSparseHensel.h" |
---|
21 | #include "cf_algorithm.h" |
---|
22 | #include "cf_gcd_smallp.h" |
---|
23 | #include "facFqFactorize.h" |
---|
24 | |
---|
25 | bool |
---|
26 | LucksWangSparseHeuristic (const CanonicalForm& F, const CFList& factors, |
---|
27 | int level, const CFList& leadingCoeffs, CFList& result) |
---|
28 | { |
---|
29 | CFArray* monoms= new CFArray [factors.length()]; |
---|
30 | int i= 0; |
---|
31 | int num= 0; |
---|
32 | for (CFListIterator iter= factors; iter.hasItem(); iter++, i++) |
---|
33 | { |
---|
34 | monoms[i]= getTerms (iter.getItem()); |
---|
35 | num += monoms [i].size(); |
---|
36 | sort (monoms [i]); |
---|
37 | } |
---|
38 | |
---|
39 | i= 0; |
---|
40 | CFArray* monomsLead= new CFArray [leadingCoeffs.length()]; |
---|
41 | for (CFListIterator iter= leadingCoeffs; iter.hasItem(); iter++, i++) |
---|
42 | { |
---|
43 | monomsLead[i]= getTerms (iter.getItem()); |
---|
44 | sort (monomsLead [i]); |
---|
45 | groupTogether (monomsLead [i], level); |
---|
46 | strip (monomsLead [i], level); |
---|
47 | } |
---|
48 | |
---|
49 | CFArray solution= CFArray (num); |
---|
50 | int k, d, count, j= F.level() + 1; |
---|
51 | num= 0; |
---|
52 | i= 0; |
---|
53 | for (CFListIterator iter= factors; iter.hasItem(); i++, iter++) |
---|
54 | { |
---|
55 | d= degree (iter.getItem(), 1); |
---|
56 | count= 0; |
---|
57 | for (k= 0; k < monoms[i].size(); k++, j++, num++) |
---|
58 | { |
---|
59 | monoms [i][k] *= Variable (j); |
---|
60 | if (degree (monoms[i][k], 1) == d) |
---|
61 | { |
---|
62 | solution[num]= monomsLead [i] [count]; |
---|
63 | count++; |
---|
64 | } |
---|
65 | } |
---|
66 | } |
---|
67 | |
---|
68 | delete [] monomsLead; |
---|
69 | |
---|
70 | CFArray termsF= getTerms (F); |
---|
71 | sort (termsF); |
---|
72 | |
---|
73 | CFList tmp; |
---|
74 | CFArray* stripped2= new CFArray [factors.length()]; |
---|
75 | for (i= factors.length() - 1; i > -1; i--) |
---|
76 | { |
---|
77 | tmp.insert (buildPolyFromArray (monoms [i])); |
---|
78 | strip (monoms[i], stripped2 [i], level); |
---|
79 | } |
---|
80 | delete [] monoms; |
---|
81 | |
---|
82 | CanonicalForm H= prod (tmp); |
---|
83 | CFArray monomsH= getMonoms (H); |
---|
84 | sort (monomsH); |
---|
85 | |
---|
86 | groupTogether (termsF, level); |
---|
87 | groupTogether (monomsH, F.level()); |
---|
88 | |
---|
89 | if (monomsH.size() != termsF.size()) |
---|
90 | { |
---|
91 | delete [] stripped2; |
---|
92 | return false; |
---|
93 | } |
---|
94 | |
---|
95 | CFArray strippedH; |
---|
96 | strip (monomsH, strippedH, level); |
---|
97 | CFArray strippedF; |
---|
98 | strip (termsF, strippedF, level); |
---|
99 | |
---|
100 | if (!isEqual (strippedH, strippedF)) |
---|
101 | { |
---|
102 | delete [] stripped2; |
---|
103 | return false; |
---|
104 | } |
---|
105 | |
---|
106 | CFArray A= getEquations (monomsH, termsF); |
---|
107 | CFArray newSolution= CFArray (solution.size()); |
---|
108 | do |
---|
109 | { |
---|
110 | evaluate (A, solution, F.level() + 1); |
---|
111 | if (isZero (A)) |
---|
112 | break; |
---|
113 | if (!simplify (A, newSolution, F.level() + 1)) |
---|
114 | { |
---|
115 | delete [] stripped2; |
---|
116 | return false; |
---|
117 | } |
---|
118 | if (isZero (newSolution)) |
---|
119 | { |
---|
120 | delete [] stripped2; |
---|
121 | return false; |
---|
122 | } |
---|
123 | if (!merge (solution, newSolution)) |
---|
124 | { |
---|
125 | delete [] stripped2; |
---|
126 | return false; |
---|
127 | } |
---|
128 | } while (1); |
---|
129 | |
---|
130 | |
---|
131 | result= CFList(); |
---|
132 | CanonicalForm factor; |
---|
133 | num= 0; |
---|
134 | for (i= 0; i < factors.length(); i++) |
---|
135 | { |
---|
136 | k= stripped2[i].size(); |
---|
137 | factor= 0; |
---|
138 | for (j= 0; j < k; j++, num++) |
---|
139 | factor += solution [num]*stripped2[i][j]; |
---|
140 | result.append (factor); |
---|
141 | } |
---|
142 | |
---|
143 | delete [] stripped2; |
---|
144 | return true; |
---|
145 | } |
---|
146 | |
---|
147 | CFList |
---|
148 | sparseHeuristic (const CanonicalForm& A, const CFList& biFactors, |
---|
149 | CFList*& moreBiFactors, const CFList& evaluation, |
---|
150 | int minFactorsLength) |
---|
151 | { |
---|
152 | int j= A.level() - 1; |
---|
153 | int i; |
---|
154 | |
---|
155 | //initialize storage |
---|
156 | CFArray *** storeFactors= new CFArray** [j]; |
---|
157 | for (i= 0; i < j; i++) |
---|
158 | storeFactors [i]= new CFArray* [2]; |
---|
159 | |
---|
160 | CFArray eval= CFArray (j); |
---|
161 | i= j - 1; |
---|
162 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++,i--) |
---|
163 | eval[i]= iter.getItem(); |
---|
164 | storeFactors [0] [0]= new CFArray [minFactorsLength]; |
---|
165 | storeFactors [0] [1]= new CFArray [minFactorsLength]; |
---|
166 | for (i= 1; i < j; i++) |
---|
167 | { |
---|
168 | storeFactors[i] [0]= new CFArray [minFactorsLength]; |
---|
169 | storeFactors[i] [1]= new CFArray [minFactorsLength]; |
---|
170 | } |
---|
171 | // |
---|
172 | |
---|
173 | CFList * normalizingFactors= new CFList [j]; |
---|
174 | CFList uniFactors; |
---|
175 | normalizingFactors [0]= findNormalizingFactor1 (biFactors, |
---|
176 | evaluation.getLast(), uniFactors); |
---|
177 | for (i= j - 1; i > 0; i--) |
---|
178 | { |
---|
179 | if (moreBiFactors[i-1].length() != minFactorsLength) |
---|
180 | { |
---|
181 | moreBiFactors[i-1]= |
---|
182 | recombination (moreBiFactors [i-1], uniFactors, 1, |
---|
183 | moreBiFactors[i-1].length()-uniFactors.length()+1, |
---|
184 | eval[i], Variable (i + 2) |
---|
185 | ); |
---|
186 | } |
---|
187 | normalizingFactors [i]= findNormalizingFactor2 (moreBiFactors [i - 1], |
---|
188 | eval[i], uniFactors); |
---|
189 | } |
---|
190 | |
---|
191 | CFList tmp; |
---|
192 | tmp= normalize (biFactors, normalizingFactors[0]); |
---|
193 | getTerms2 (tmp, storeFactors [0] [0]); |
---|
194 | storeFactors [0] [1]= evaluate (storeFactors [0] [0], minFactorsLength, |
---|
195 | evaluation.getLast(), Variable (2)); |
---|
196 | for (i= j - 1; i > 0; i--) |
---|
197 | { |
---|
198 | tmp= normalize (moreBiFactors [i-1], normalizingFactors [i]); |
---|
199 | getTerms2 (tmp, storeFactors [i] [0]); |
---|
200 | storeFactors [i] [1]= evaluate (storeFactors [i] [0], minFactorsLength, |
---|
201 | eval[i], Variable (i + 2)); |
---|
202 | } |
---|
203 | |
---|
204 | |
---|
205 | int k, l, m, mm, count, sizeOfUniFactors= 0; |
---|
206 | int*** seperator= new int** [j]; |
---|
207 | Variable x= Variable (1); |
---|
208 | |
---|
209 | for (i= 0; i < j; i++) |
---|
210 | seperator [i]= new int* [minFactorsLength]; |
---|
211 | for (k= 0; k < minFactorsLength; k++) |
---|
212 | { |
---|
213 | for (i= 0; i < j; i++) |
---|
214 | { |
---|
215 | count= 0; |
---|
216 | for (l= 0; l < storeFactors [i][0][k].size() - 1; l++) |
---|
217 | { |
---|
218 | if (degree (storeFactors[i][0][k][l], x) < |
---|
219 | degree (storeFactors[i][0][k][l+1], x)) |
---|
220 | count++; |
---|
221 | } |
---|
222 | if (i == 0) |
---|
223 | sizeOfUniFactors= count; |
---|
224 | else if (sizeOfUniFactors != count) |
---|
225 | { |
---|
226 | for (m= 0; m < j; m++) |
---|
227 | { |
---|
228 | delete [] storeFactors [m] [0]; |
---|
229 | delete [] storeFactors [m] [1]; |
---|
230 | delete [] storeFactors [m]; |
---|
231 | for (mm= 0; mm < k; mm++) |
---|
232 | delete [] seperator [m][mm]; |
---|
233 | delete [] seperator [m]; |
---|
234 | } |
---|
235 | delete [] storeFactors; |
---|
236 | delete [] seperator; |
---|
237 | return CFList(); |
---|
238 | } |
---|
239 | seperator [i][k]= new int [count + 3]; |
---|
240 | seperator [i][k][0]= count + 1; |
---|
241 | seperator [i][k][1]= 0; |
---|
242 | count= 2; |
---|
243 | for (l= 0; l < storeFactors [i][0][k].size() - 1; l++) |
---|
244 | { |
---|
245 | if (degree (storeFactors[i][0][k][l], x) < |
---|
246 | degree (storeFactors[i][0][k][l+1], x)) |
---|
247 | { |
---|
248 | seperator[i][k][count]=l + 1; |
---|
249 | count++; |
---|
250 | } |
---|
251 | } |
---|
252 | seperator [i][k][count]= storeFactors[i][0][k].size(); |
---|
253 | } |
---|
254 | } |
---|
255 | |
---|
256 | CanonicalForm tmp1, factor, quot; |
---|
257 | CanonicalForm B= A; |
---|
258 | CFList result; |
---|
259 | int maxTerms, n, index1, index2, mmm, found, columns, oneCount; |
---|
260 | int ** mat; |
---|
261 | |
---|
262 | for (k= 0; k < minFactorsLength; k++) |
---|
263 | { |
---|
264 | factor= 0; |
---|
265 | sizeOfUniFactors= seperator [0][k][0]; |
---|
266 | for (n= 1; n <= sizeOfUniFactors; n++) |
---|
267 | { |
---|
268 | columns= 0; |
---|
269 | maxTerms= 1; |
---|
270 | index1= j - 1; |
---|
271 | for (i= j - 1; i >= 0; i--) |
---|
272 | { |
---|
273 | if (maxTerms < seperator[i][k][n+1]-seperator[i][k][n]) |
---|
274 | { |
---|
275 | maxTerms= seperator[i][k][n + 1]-seperator[i][k][n]; |
---|
276 | index1= i; |
---|
277 | } |
---|
278 | } |
---|
279 | for (i= j - 1; i >= 0; i--) |
---|
280 | { |
---|
281 | if (i == index1) |
---|
282 | continue; |
---|
283 | columns += seperator [i][k][n+1]-seperator[i][k][n]; |
---|
284 | } |
---|
285 | mat= new int *[maxTerms]; |
---|
286 | mm= 0; |
---|
287 | for (m= seperator[index1][k][n]; m < seperator[index1][k][n+1]; m++, mm++) |
---|
288 | { |
---|
289 | tmp1= storeFactors [index1][1][k][m]; |
---|
290 | mat[mm]= new int [columns]; |
---|
291 | for (i= 0; i < columns; i++) |
---|
292 | mat[mm][i]= 0; |
---|
293 | index2= 0; |
---|
294 | for (i= j - 1; i >= 0; i--) |
---|
295 | { |
---|
296 | if (i == index1) |
---|
297 | continue; |
---|
298 | found= -1; |
---|
299 | if ((found= search (storeFactors[i][1][k], tmp1, |
---|
300 | seperator[i][k][n], seperator[i][k][n+1])) >= 0) |
---|
301 | mat[mm][index2 + found - seperator [i][k][n]]= 1; |
---|
302 | index2 += seperator [i][k][n+1]-seperator[i][k][n]; |
---|
303 | } |
---|
304 | } |
---|
305 | |
---|
306 | index2= 0; |
---|
307 | for (i= j - 1; i >= 0; i--) |
---|
308 | { |
---|
309 | if (i == index1) |
---|
310 | continue; |
---|
311 | oneCount= 0; |
---|
312 | for (mm= 0; mm < seperator [i][k][n + 1] - seperator [i][k][n]; mm++) |
---|
313 | { |
---|
314 | for (m= 0; m < maxTerms; m++) |
---|
315 | { |
---|
316 | if (mat[m][mm+index2] == 1) |
---|
317 | oneCount++; |
---|
318 | } |
---|
319 | } |
---|
320 | if (oneCount == seperator [i][k][n+1]-seperator[i][k][n] - 1) |
---|
321 | { |
---|
322 | for (mm= 0; mm < seperator [i][k][n+1]-seperator[i][k][n]; mm++) |
---|
323 | { |
---|
324 | oneCount= 0; |
---|
325 | for (m= 0; m < maxTerms; m++) |
---|
326 | if (mat[m][mm+index2] == 1) |
---|
327 | oneCount++; |
---|
328 | if (oneCount > 0) |
---|
329 | continue; |
---|
330 | for (m= 0; m < maxTerms; m++) |
---|
331 | { |
---|
332 | oneCount= 0; |
---|
333 | for (mmm= 0; mmm < seperator[i][k][n+1]-seperator[i][k][n]; mmm++) |
---|
334 | { |
---|
335 | if (mat[m][mmm+index2] == 1) |
---|
336 | oneCount++; |
---|
337 | } |
---|
338 | if (oneCount > 0) |
---|
339 | continue; |
---|
340 | mat[m][mm+index2]= 1; |
---|
341 | } |
---|
342 | } |
---|
343 | } |
---|
344 | index2 += seperator [i][k][n+1] - seperator [i][k][n]; |
---|
345 | } |
---|
346 | |
---|
347 | //read off solution |
---|
348 | mm= 0; |
---|
349 | for (m= seperator[index1][k][n]; m < seperator[index1][k][n+1]; m++, mm++) |
---|
350 | { |
---|
351 | tmp1= storeFactors [index1][0][k][m]; |
---|
352 | index2= 0; |
---|
353 | for (i= j - 1; i > -1; i--) |
---|
354 | { |
---|
355 | if (i == index1) |
---|
356 | continue; |
---|
357 | for (mmm= 0; mmm < seperator [i][k][n+1]-seperator[i][k][n]; mmm++) |
---|
358 | if (mat[mm][mmm+index2] == 1) |
---|
359 | tmp1= patch (tmp1, storeFactors[i][0][k][seperator[i][k][n]+mmm], |
---|
360 | eval[i]); |
---|
361 | index2 += seperator [i][k][n+1]-seperator[i][k][n]; |
---|
362 | } |
---|
363 | factor += tmp1; |
---|
364 | } |
---|
365 | |
---|
366 | for (m= 0; m < maxTerms; m++) |
---|
367 | delete [] mat [m]; |
---|
368 | delete [] mat; |
---|
369 | } |
---|
370 | |
---|
371 | if (fdivides (factor, B, quot)) |
---|
372 | { |
---|
373 | result.append (factor); |
---|
374 | B= quot; |
---|
375 | if (result.length() == biFactors.length() - 1) |
---|
376 | { |
---|
377 | result.append (quot); |
---|
378 | break; |
---|
379 | } |
---|
380 | } |
---|
381 | } |
---|
382 | |
---|
383 | //delete |
---|
384 | for (i= 0; i < j; i++) |
---|
385 | { |
---|
386 | delete [] storeFactors [i] [0]; |
---|
387 | delete [] storeFactors [i] [1]; |
---|
388 | delete [] storeFactors [i]; |
---|
389 | for (k= 0; k < minFactorsLength; k++) |
---|
390 | delete [] seperator [i][k]; |
---|
391 | delete [] seperator [i]; |
---|
392 | } |
---|
393 | delete [] seperator; |
---|
394 | delete [] storeFactors; |
---|
395 | // |
---|
396 | |
---|
397 | return result; |
---|
398 | } |
---|