31 if (termsF.
size() > threshold)
41 num += monoms [
i].
size();
50 sort (monomsLead [i]);
52 strip (monomsLead [i], level);
63 for (k= 0; k < monoms[
i].
size(); k++, j++, num++)
66 if (
degree (monoms[i][k], 1) == d)
78 for (i= factors.
length() - 1; i > -1; i--)
81 strip (monoms[i], stripped2 [i], level);
98 strip (monomsH, strippedH, level);
100 strip (termsF, strippedF, level);
102 if (!
isEqual (strippedH, strippedF))
109 CFArray startingSolution= solution;
124 if (!
merge (solution, newSolution))
128 if (
isEqual (startingSolution, solution))
135 for (i= 0; i < factors.
length(); i++)
137 k= stripped2[
i].
size();
139 for (j= 0; j <
k; j++, num++)
141 if (solution [num].
isZero())
143 factor += solution [
num]*stripped2[
i][
j];
145 result.append (factor);
149 if (result.length() > 0)
164 for (i= 0; i <
j; i++)
165 storeFactors [i]=
new CFArray* [2];
173 for (i= 1; i <
j; i++)
183 evaluation.
getLast(), uniFactors);
184 for (i= j - 1; i > 0; i--)
195 eval[i], uniFactors);
199 tmp=
normalize (biFactors, normalizingFactors[0]);
201 storeFactors [0] [1]=
evaluate (storeFactors [0] [0], minFactorsLength,
203 for (i= j - 1; i > 0; i--)
205 tmp=
normalize (moreBiFactors [i-1], normalizingFactors [i]);
207 storeFactors [
i] [1]=
evaluate (storeFactors [i] [0], minFactorsLength,
212 int k,
l,
m, mm,
count, sizeOfUniFactors= 0;
213 int*** seperator=
new int** [
j];
216 for (i= 0; i <
j; i++)
217 seperator [i]=
new int* [minFactorsLength];
220 for (i= 0; i <
j; i++)
223 for (l= 0; l < storeFactors [
i][0][
k].
size() - 1; l++)
225 if (
degree (storeFactors[i][0][k][l], x) <
226 degree (storeFactors[i][0][k][l+1], x))
230 sizeOfUniFactors=
count;
231 else if (sizeOfUniFactors != count)
233 for (m= 0; m <
j; m++)
235 delete [] storeFactors [
m] [0];
236 delete [] storeFactors [
m] [1];
237 delete [] storeFactors [
m];
238 for (mm= 0; mm <
k; mm++)
239 delete [] seperator [m][mm];
240 delete [] seperator [
m];
242 delete [] storeFactors;
244 delete [] normalizingFactors;
247 seperator [
i][
k]=
new int [count + 3];
248 seperator [
i][
k][0]= count + 1;
249 seperator [
i][
k][1]= 0;
251 for (l= 0; l < storeFactors [
i][0][
k].
size() - 1; l++)
253 if (
degree (storeFactors[i][0][k][l], x) <
254 degree (storeFactors[i][0][k][l+1], x))
267 int maxTerms, n, index1, index2, mmm,
found, columns, oneCount;
273 sizeOfUniFactors= seperator [0][
k][0];
274 for (n= 1; n <= sizeOfUniFactors; n++)
279 for (i= j - 1; i >= 0; i--)
281 if (maxTerms < seperator[i][k][n+1]-seperator[i][k][n])
283 maxTerms= seperator[
i][
k][n + 1]-seperator[
i][
k][n];
287 for (i= j - 1; i >= 0; i--)
291 columns += seperator [
i][
k][n+1]-seperator[
i][
k][n];
293 mat=
new int *[maxTerms];
295 for (m= seperator[index1][k][n]; m < seperator[index1][
k][n+1]; m++, mm++)
297 tmp1= storeFactors [index1][1][
k][
m];
298 mat[mm]=
new int [columns];
299 for (i= 0; i < columns; i++)
302 for (i= j - 1; i >= 0; i--)
307 if ((found=
search (storeFactors[i][1][k], tmp1,
308 seperator[i][k][n], seperator[i][k][n+1])) >= 0)
309 mat[mm][index2 + found - seperator [
i][
k][n]]= 1;
310 index2 += seperator [
i][
k][n+1]-seperator[
i][
k][n];
315 for (i= j - 1; i >= 0; i--)
320 for (mm= 0; mm < seperator [
i][
k][n + 1] - seperator [
i][
k][n]; mm++)
322 for (m= 0; m < maxTerms; m++)
324 if (mat[m][mm+index2] == 1)
328 if (oneCount == seperator [i][k][n+1]-seperator[i][k][n] - 1)
330 for (mm= 0; mm < seperator [
i][
k][n+1]-seperator[
i][
k][n]; mm++)
333 for (m= 0; m < maxTerms; m++)
334 if (mat[m][mm+index2] == 1)
338 for (m= 0; m < maxTerms; m++)
341 for (mmm= 0; mmm < seperator[
i][
k][n+1]-seperator[
i][
k][n]; mmm++)
343 if (mat[m][mmm+index2] == 1)
348 mat[
m][mm+index2]= 1;
352 index2 += seperator [
i][
k][n+1] - seperator [
i][
k][n];
357 for (m= seperator[index1][k][n]; m < seperator[index1][
k][n+1]; m++, mm++)
359 tmp1= storeFactors [index1][0][
k][
m];
361 for (i= j - 1; i > -1; i--)
365 for (mmm= 0; mmm < seperator [
i][
k][n+1]-seperator[
i][
k][n]; mmm++)
366 if (mat[mm][mmm+index2] == 1)
367 tmp1=
patch (tmp1, storeFactors[i][0][k][seperator[i][k][n]+mmm],
369 index2 += seperator [
i][
k][n+1]-seperator[
i][
k][n];
374 for (m= 0; m < maxTerms; m++)
392 for (i= 0; i <
j; i++)
394 delete [] storeFactors [
i] [0];
395 delete [] storeFactors [
i] [1];
396 delete [] storeFactors [
i];
398 delete [] seperator [i][k];
399 delete [] seperator [
i];
402 delete [] storeFactors;
403 delete [] normalizingFactors;
int status int void size_t count
CFList findNormalizingFactor1(const CFList &biFactors, const CanonicalForm &evalPoint, CFList &uniFactors)
find normalizing factors for biFactors and build monic univariate factors from biFactors ...
CFArray getBiTerms(const CanonicalForm &F, int threshold)
get terms of F where F is considered a bivariate poly in Variable(1), Variable (2) ...
static poly normalize(poly next_p, ideal add_generators, syStrategy syzstr, int *g_l, int *p_l, int crit_comp)
int ** merge(int **points1, int sizePoints1, int **points2, int sizePoints2, int &sizeResult)
factory's class for variables
CFList int & minFactorsLength
[in,out] minimal length of bivariate factors
CanonicalForm buildPolyFromArray(const CFArray &A)
build a poly from entries in A
const CanonicalForm int const CFList & evaluation
int LucksWangSparseHeuristic(const CanonicalForm &F, const CFList &factors, int level, const CFList &leadingCoeffs, CFList &result)
sparse heuristic lifting by Wang and Lucks
This file provides functions for factorizing a multivariate polynomial over , or GF...
CanonicalForm simplify(const CanonicalForm &A, int level)
simplify A if possible, i.e. A consists of 2 terms and contains only one variable of level greater or...
CanonicalForm patch(const CanonicalForm &F1, const CanonicalForm &F2, const CanonicalForm &eval)
patch together F1 and F2 and normalize by a power of eval F1 and F2 are assumed to be bivariate with ...
This file provides functions for sparse heuristic Hensel lifting.
CFArray getMonoms(const CanonicalForm &F)
extract monomials of F, parts in algebraic variable are considered coefficients
void groupTogether(CFArray &A, int level)
group together elements in A, where entries in A are put together if they coincide up to level level ...
int search(const CFArray &A, const CanonicalForm &F, int i, int j)
search for F in A between index i and j
CFArray evaluate(const CFArray &A, const CFList &evalPoints)
CFList recombination(const CFList &factors1, const CFList &factors2, int s, int thres, const CanonicalForm &evalPoint, const Variable &x)
recombination of bivariate factors factors1 s. t. the result evaluated at evalPoint coincides with fa...
declarations of higher level algorithms.
void strip(CFArray &F, CFArray &G, int level)
strip off those parts of entries in F whose level is less than or equal than level and store the stri...
CFArray getEquations(const CFArray &A, const CFArray &B)
get equations for LucksWangSparseHeuristic
CFArray getTerms2(const CanonicalForm &F)
get terms of F wrt. Variable (1)
bool isEqual(int *a, int *b, int lower, int upper)
bool fdivides(const CanonicalForm &f, const CanonicalForm &g)
bool fdivides ( const CanonicalForm & f, const CanonicalForm & g )
CFList sparseHeuristic(const CanonicalForm &A, const CFList &biFactors, CFList *&moreBiFactors, const CFList &evaluation, int minFactorsLength)
sparse heuristic which patches together bivariate factors of A wrt. different second variables by the...
void getTerms(const CanonicalForm &f, const CanonicalForm &t, CFList &result)
get_Terms: Split the polynomial in the containing terms.
static BOOLEAN length(leftv result, leftv arg)
bool isZero(const CFArray &A)
checks if entries of A are zero
modular and sparse modular GCD algorithms over finite fields and Z.
void sort(CFArray &A, int l=0)
quick sort A
CFList findNormalizingFactor2(CFList &biFactors, const CanonicalForm &evalPoint, const CFList &uniFactors)
find normalizing factors for biFactors and sort biFactors s.t. the returned biFactors evaluated at ev...