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facHensel.h File Reference

This file defines functions for Hensel lifting. More...

#include "cf_assert.h"
#include "debug.h"
#include "timing.h"
#include "canonicalform.h"
#include "fac_util.h"

Go to the source code of this file.

Functions

void sortList (CFList &list, const Variable &x)
 sort a list of polynomials by their degree in x. More...
 
void henselLift12 (const CanonicalForm &F, CFList &factors, int l, CFArray &Pi, CFList &diophant, CFMatrix &M, modpk &b, bool sort=true)
 Hensel lift from univariate to bivariate. More...
 
void henselLift12 (const CanonicalForm &F, CFList &factors, int l, CFArray &Pi, CFList &diophant, CFMatrix &M, bool sort=true)
 Hensel lift from univariate to bivariate. More...
 
void henselLiftResume12 (const CanonicalForm &F, CFList &factors, int start, int end, CFArray &Pi, const CFList &diophant, CFMatrix &M, const modpk &b=modpk())
 resume Hensel lift from univariate to bivariate. Assumes factors are lifted to precision Variable (2)^start and lifts them to precision Variable (2)^end More...
 
CFList henselLift23 (const CFList &eval, const CFList &factors, int *l, CFList &diophant, CFArray &Pi, CFMatrix &M)
 Hensel lifting from bivariate to trivariate. More...
 
void henselLiftResume (const CanonicalForm &F, CFList &factors, int start, int end, CFArray &Pi, const CFList &diophant, CFMatrix &M, const CFList &MOD)
 resume Hensel lifting. More...
 
CFList henselLift (const CFList &F, const CFList &factors, const CFList &MOD, CFList &diophant, CFArray &Pi, CFMatrix &M, int lOld, int lNew)
 Hensel lifting. More...
 
CFList henselLift (const CFList &eval, const CFList &factors, int *l, int lLength, bool sort=true)
 Hensel lifting from bivariate to multivariate. More...
 
void nonMonicHenselLift12 (const CanonicalForm &F, CFList &factors, int l, CFArray &Pi, CFList &diophant, CFMatrix &M, const CFArray &LCs, bool sort)
 Hensel lifting from univariate to bivariate, factors need not to be monic. More...
 
CFList nonMonicHenselLift2 (const CFList &eval, const CFList &factors, int *l, int lLength, bool sort, const CFList &LCs1, const CFList &LCs2, const CFArray &Pi, const CFList &diophant, bool &noOneToOne)
 two factor Hensel lifting from bivariate to multivariate, factors need not to be monic More...
 
CFList nonMonicHenselLift (const CFList &eval, const CFList &factors, CFList *const &LCs, CFList &diophant, CFArray &Pi, int *liftBound, int length, bool &noOneToOne)
 Hensel lifting of non monic factors, needs correct leading coefficients of factors and a one to one corresponds between bivariate and multivariate factors to succeed. More...
 

Detailed Description

This file defines functions for Hensel lifting.

ABSTRACT: function are used for bi- and multivariate factorization over finite fields. Described in "Efficient Multivariate Factorization over Finite Fields" by L. Bernardin & M. Monagon and "Algorithms for Computer Algebra" by Geddes, Czapor, Labahn

Author
Martin Lee

Definition in file facHensel.h.

Function Documentation

◆ henselLift() [1/2]

CFList henselLift ( const CFList eval,
const CFList factors,
int *  l,
int  lLength,
bool  sort = true 
)

Hensel lifting from bivariate to multivariate.

Returns
henselLift returns a list of lifted factors
See also
henselLift12(), henselLiftResume12(), henselLift23(), henselLiftResume()
Parameters
[in]evala list of polynomials the last element is a compressed multivariate poly, last but one element equals the last elements modulo its main variable and so on. The first element is a compressed bivariate poly.
[in]factorsbivariate factors, including leading coefficient
[in]llifting bounds
[in]lLengthlength of l
[in]sortsort factors by degree in Variable(1)

Definition at line 1892 of file facHensel.cc.

1894{
1895 CFList diophant;
1896 CFList buf= factors;
1897 buf.insert (LC (eval.getFirst(), 1));
1898 if (sort)
1899 sortList (buf, Variable (1));
1900 CFArray Pi;
1901 CFMatrix M= CFMatrix (l[1], factors.length());
1902 CFList result= henselLift23 (eval, buf, l, diophant, Pi, M);
1903 if (eval.length() == 2)
1904 return result;
1905 CFList MOD;
1906 for (int i= 0; i < 2; i++)
1907 MOD.append (power (Variable (i + 2), l[i]));
1909 j++;
1910 CFList bufEval;
1911 bufEval.append (j.getItem());
1912 j++;
1913
1914 for (int i= 2; i < lLength && j.hasItem(); i++, j++)
1915 {
1916 result.insert (LC (bufEval.getFirst(), 1));
1917 bufEval.append (j.getItem());
1918 M= CFMatrix (l[i], factors.length());
1919 result= henselLift (bufEval, result, MOD, diophant, Pi, M, l[i - 1], l[i]);
1920 MOD.append (power (Variable (i + 2), l[i]));
1921 bufEval.removeFirst();
1922 }
1923 return result;
1924}
CanonicalForm power(const CanonicalForm &f, int n)
exponentiation
Matrix< CanonicalForm > CFMatrix
CanonicalForm LC(const CanonicalForm &f)
int l
Definition: cfEzgcd.cc:100
int i
Definition: cfEzgcd.cc:132
T getFirst() const
Definition: ftmpl_list.cc:279
void removeFirst()
Definition: ftmpl_list.cc:287
int length() const
Definition: ftmpl_list.cc:273
void append(const T &)
Definition: ftmpl_list.cc:256
void insert(const T &)
Definition: ftmpl_list.cc:193
factory's class for variables
Definition: factory.h:134
CFList & eval
Definition: facFactorize.cc:47
int j
Definition: facHensel.cc:110
CFList henselLift23(const CFList &eval, const CFList &factors, int *l, CFList &diophant, CFArray &Pi, CFMatrix &M)
Hensel lifting from bivariate to trivariate.
Definition: facHensel.cc:1783
const CanonicalForm & M
Definition: facHensel.cc:97
fq_nmod_t buf
Definition: facHensel.cc:101
CFList henselLift(const CFList &F, const CFList &factors, const CFList &MOD, CFList &diophant, CFArray &Pi, CFMatrix &M, int lOld, int lNew)
Hensel lifting.
Definition: facHensel.cc:1850
CFList result
Definition: facHensel.cc:126
void sortList(CFList &list, const Variable &x)
sort a list of polynomials by their degree in x.
Definition: facHensel.cc:449
void sort(CFArray &A, int l=0)
quick sort A

◆ henselLift() [2/2]

CFList henselLift ( const CFList F,
const CFList factors,
const CFList MOD,
CFList diophant,
CFArray Pi,
CFMatrix M,
int  lOld,
int  lNew 
)

Hensel lifting.

Returns
henselLift returns a list of polynomials lifted to precision F.getLast().mvar()^l_new
See also
henselLift12(), henselLiftResume12(), henselLift23(), henselLiftResume()
Parameters
[in]Ftwo compressed, multivariate polys F and G
[in]factorsmonic multivariate factors including leading coefficient as first element.
[in]MODa list of powers of Variables of level higher than 1
[in,out]diophantresult of multiRecDiophantine()
[in,out]Pistores intermediate results
[in,out]Mstores intermediate results
[in]lOldlifting precision of F.mvar()
[in]lNewlifting precision of G.mvar()

Definition at line 1850 of file facHensel.cc.

1852{
1853 diophant= multiRecDiophantine (F.getFirst(), factors, diophant, MOD, lOld);
1854 int k= 0;
1855 CFArray bufFactors= CFArray (factors.length());
1856 for (CFListIterator i= factors; i.hasItem(); i++, k++)
1857 {
1858 if (k == 0)
1859 bufFactors[k]= LC (F.getLast(), 1);
1860 else
1861 bufFactors[k]= i.getItem();
1862 }
1863 CFList buf= factors;
1864 buf.removeFirst();
1865 buf.insert (LC (F.getLast(), 1));
1867 i++;
1868 Variable y= F.getLast().mvar();
1869 Variable x= F.getFirst().mvar();
1870 CanonicalForm xToLOld= power (x, lOld);
1871 Pi [0]= mod (Pi[0], xToLOld);
1872 M (1, 1)= Pi [0];
1873 k= 1;
1874 if (i.hasItem())
1875 i++;
1876 for (; i.hasItem(); i++, k++)
1877 {
1878 Pi [k]= mod (Pi [k], xToLOld);
1879 M (1, k + 1)= Pi [k];
1880 }
1881
1882 for (int d= 1; d < lNew; d++)
1883 henselStep (F.getLast(), buf, bufFactors, diophant, M, Pi, d, MOD);
1884 CFList result;
1885 for (k= 1; k < factors.length(); k++)
1886 result.append (bufFactors[k]);
1887 return result;
1888}
Array< CanonicalForm > CFArray
int k
Definition: cfEzgcd.cc:99
factory's main class
Definition: canonicalform.h:86
Variable mvar() const
mvar() returns the main variable of CO or Variable() if CO is in a base domain.
T getLast() const
Definition: ftmpl_list.cc:309
const CanonicalForm int const CFList const Variable & y
Definition: facAbsFact.cc:53
Variable x
Definition: facHensel.cc:127
static int mod(const CFList &L, const CanonicalForm &p)
Definition: facHensel.cc:252
CFList multiRecDiophantine(const CanonicalForm &F, const CFList &factors, const CFList &recResult, const CFList &M, int d)
Definition: facHensel.cc:1468
static void henselStep(const CanonicalForm &F, const CFList &factors, CFArray &bufFactors, const CFList &diophant, CFMatrix &M, CFArray &Pi, int j, const CFList &MOD)
Definition: facHensel.cc:1557

◆ henselLift12() [1/2]

void henselLift12 ( const CanonicalForm F,
CFList factors,
int  l,
CFArray Pi,
CFList diophant,
CFMatrix M,
bool  sort = true 
)

Hensel lift from univariate to bivariate.

See also
henselLiftResume12(), henselLift23(), henselLiftResume(), henselLift()
Parameters
[in]Fcompressed, bivariate poly
[in,out]factorsmonic univariate factors of F, including leading coefficient as first element. Returns monic lifted factors without the leading coefficient
[in]llifting precision
[in,out]Pistores intermediate results
[in,out]diophantresult of diophantine()
[in,out]Mstores intermediate results
[in]sortsort factors by degree in Variable(1)

Definition at line 1332 of file facHensel.cc.

1334{
1335 modpk dummy= modpk();
1336 henselLift12 (F, factors, l, Pi, diophant, M, dummy, sort);
1337}
class to do operations mod p^k for int's p and k
Definition: fac_util.h:23
return modpk(p, k)
void henselLift12(const CanonicalForm &F, CFList &factors, int l, CFArray &Pi, CFList &diophant, CFMatrix &M, modpk &b, bool sort)
Hensel lift from univariate to bivariate.
Definition: facHensel.cc:1272

◆ henselLift12() [2/2]

void henselLift12 ( const CanonicalForm F,
CFList factors,
int  l,
CFArray Pi,
CFList diophant,
CFMatrix M,
modpk b,
bool  sort = true 
)

Hensel lift from univariate to bivariate.

See also
henselLiftResume12(), henselLift23(), henselLiftResume(), henselLift()
Parameters
[in]Fcompressed, bivariate poly
[in,out]factorsmonic univariate factors of F, including leading coefficient as first element. Returns monic lifted factors without the leading coefficient
[in]llifting precision
[in,out]Pistores intermediate results
[in,out]diophantresult of diophantine()
[in,out]Mstores intermediate results
[in]bcoeff bound
[in]sortsort factors by degree in Variable(1)

Definition at line 1272 of file facHensel.cc.

1274{
1275 if (sort)
1276 sortList (factors, Variable (1));
1277 Pi= CFArray (factors.length() - 1);
1278 CFListIterator j= factors;
1279 diophant= diophantine (F[0], F, factors, b);
1280 CanonicalForm bufF= F;
1281 if (getCharacteristic() == 0 && b.getp() != 0)
1282 {
1283 Variable v;
1284 bool hasAlgVar= hasFirstAlgVar (F, v);
1285 for (CFListIterator i= factors; i.hasItem() && !hasAlgVar; i++)
1286 hasAlgVar= hasFirstAlgVar (i.getItem(), v);
1287 Variable w;
1288 bool hasAlgVar2= false;
1289 for (CFListIterator i= diophant; i.hasItem() && !hasAlgVar2; i++)
1290 hasAlgVar2= hasFirstAlgVar (i.getItem(), w);
1291 if (hasAlgVar && hasAlgVar2 && v!=w)
1292 {
1293 bufF= replacevar (bufF, v, w);
1294 for (CFListIterator i= factors; i.hasItem(); i++)
1295 i.getItem()= replacevar (i.getItem(), v, w);
1296 }
1297 }
1298
1299 DEBOUTLN (cerr, "diophant= " << diophant);
1300 j++;
1301 Pi [0]= mulNTL (j.getItem(), mod (factors.getFirst(), F.mvar()), b);
1302 M (1, 1)= Pi [0];
1303 int i= 1;
1304 if (j.hasItem())
1305 j++;
1306 for (; j.hasItem(); j++, i++)
1307 {
1308 Pi [i]= mulNTL (Pi [i - 1], j.getItem(), b);
1309 M (1, i + 1)= Pi [i];
1310 }
1311 CFArray bufFactors= CFArray (factors.length());
1312 i= 0;
1313 for (CFListIterator k= factors; k.hasItem(); i++, k++)
1314 {
1315 if (i == 0)
1316 bufFactors[i]= mod (k.getItem(), F.mvar());
1317 else
1318 bufFactors[i]= k.getItem();
1319 }
1320 for (i= 1; i < l; i++)
1321 henselStep12 (bufF, factors, bufFactors, diophant, M, Pi, i, b);
1322
1323 CFListIterator k= factors;
1324 for (i= 0; i < factors.length (); i++, k++)
1325 k.getItem()= bufFactors[i];
1326 factors.removeFirst();
1327}
bool hasFirstAlgVar(const CanonicalForm &f, Variable &a)
check if poly f contains an algebraic variable a
Definition: cf_ops.cc:679
int FACTORY_PUBLIC getCharacteristic()
Definition: cf_char.cc:70
CanonicalForm b
Definition: cfModGcd.cc:4105
#define DEBOUTLN(stream, objects)
Definition: debug.h:49
const CanonicalForm & w
Definition: facAbsFact.cc:51
int hasAlgVar(const CanonicalForm &f, const Variable &v)
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:39
CFList diophantine(const CanonicalForm &F, const CFList &factors)
Definition: facHensel.cc:1060
static CFList replacevar(const CFList &L, const Variable &a, const Variable &b)
Definition: facHensel.cc:289
void henselStep12(const CanonicalForm &F, const CFList &factors, CFArray &bufFactors, const CFList &diophant, CFMatrix &M, CFArray &Pi, int j, const modpk &b)
Definition: facHensel.cc:1068
CanonicalForm mulNTL(const CanonicalForm &F, const CanonicalForm &G, const modpk &b)
multiplication of univariate polys using FLINT/NTL over F_p, F_q, Z/p^k, Z/p^k[t]/(f),...
Definition: facMul.cc:411

◆ henselLift23()

CFList henselLift23 ( const CFList eval,
const CFList factors,
int *  l,
CFList diophant,
CFArray Pi,
CFMatrix M 
)

Hensel lifting from bivariate to trivariate.

Returns
henselLift23 returns a list of polynomials lifted to precision Variable (3)^l[1]
See also
henselLift12(), henselLiftResume12(), henselLiftResume(), henselLift()
Parameters
[in]evalcontains compressed, bivariate as first element and trivariate one as second element
[in]factorsmonic bivariate factors, including leading coefficient as first element.
[in]ll[0]: precision of bivariate lifting, l[1] as above
[in,out]diophantreturns the result of biDiophantine()
[in,out]Pistores intermediate results
[in,out]Mstores intermediate results

Definition at line 1783 of file facHensel.cc.

1785{
1786 CFList buf= factors;
1787 int k= 0;
1788 int liftBoundBivar= l[k];
1789 diophant= biDiophantine (eval.getFirst(), buf, liftBoundBivar);
1790 CFList MOD;
1791 MOD.append (power (Variable (2), liftBoundBivar));
1792 CFArray bufFactors= CFArray (factors.length());
1793 k= 0;
1795 j++;
1796 buf.removeFirst();
1797 buf.insert (LC (j.getItem(), 1));
1798 for (CFListIterator i= buf; i.hasItem(); i++, k++)
1799 bufFactors[k]= i.getItem();
1800 Pi= CFArray (factors.length() - 1);
1802 i++;
1803 Variable y= j.getItem().mvar();
1804 Pi [0]= mulMod (i.getItem(), mod (buf.getFirst(), y), MOD);
1805 M (1, 1)= Pi [0];
1806 k= 1;
1807 if (i.hasItem())
1808 i++;
1809 for (; i.hasItem(); i++, k++)
1810 {
1811 Pi [k]= mulMod (Pi [k - 1], i.getItem(), MOD);
1812 M (1, k + 1)= Pi [k];
1813 }
1814
1815 for (int d= 1; d < l[1]; d++)
1816 henselStep (j.getItem(), buf, bufFactors, diophant, M, Pi, d, MOD);
1817 CFList result;
1818 for (k= 1; k < factors.length(); k++)
1819 result.append (bufFactors[k]);
1820 return result;
1821}
CFList biDiophantine(const CanonicalForm &F, const CFList &factors, int d)
Definition: facHensel.cc:1367
CanonicalForm mulMod(const CanonicalForm &A, const CanonicalForm &B, const CFList &MOD)
Karatsuba style modular multiplication for multivariate polynomials.
Definition: facMul.cc:3080

◆ henselLiftResume()

void henselLiftResume ( const CanonicalForm F,
CFList factors,
int  start,
int  end,
CFArray Pi,
const CFList diophant,
CFMatrix M,
const CFList MOD 
)

resume Hensel lifting.

See also
henselLift12(), henselLiftResume12(), henselLift23(), henselLift()
Parameters
[in]Fcompressed, multivariate poly
[in,out]factorsmonic multivariate factors lifted to precision F.mvar()^start, including leading coefficient as first element. Returns factors lifted to precision F.mvar()^end
[in]startstarting precision
[in]endend precision
[in,out]Pistores intermediate results
[in]diophantresult of multiRecDiophantine()
[in,out]Mstores intermediate results
[in]MODa list of powers of Variables of level higher than 1

Definition at line 1825 of file facHensel.cc.

1828{
1829 CFArray bufFactors= CFArray (factors.length());
1830 int i= 0;
1831 CanonicalForm xToStart= power (F.mvar(), start);
1832 for (CFListIterator k= factors; k.hasItem(); k++, i++)
1833 {
1834 if (i == 0)
1835 bufFactors[i]= mod (k.getItem(), xToStart);
1836 else
1837 bufFactors[i]= k.getItem();
1838 }
1839 for (i= start; i < end; i++)
1840 henselStep (F, factors, bufFactors, diophant, M, Pi, i, MOD);
1841
1842 CFListIterator k= factors;
1843 for (i= 0; i < factors.length(); k++, i++)
1844 k.getItem()= bufFactors [i];
1845 factors.removeFirst();
1846 return;
1847}

◆ henselLiftResume12()

void henselLiftResume12 ( const CanonicalForm F,
CFList factors,
int  start,
int  end,
CFArray Pi,
const CFList diophant,
CFMatrix M,
const modpk b = modpk() 
)

resume Hensel lift from univariate to bivariate. Assumes factors are lifted to precision Variable (2)^start and lifts them to precision Variable (2)^end

See also
henselLift12(), henselLift23(), henselLiftResume(), henselLift()
Parameters
[in]Fcompressed, bivariate poly
[in,out]factorsmonic factors of F, lifted to precision start, including leading coefficient as first element. Returns monic lifted factors without the leading coefficient
[in]startstarting precision
[in]endend precision
[in,out]Pistores intermediate results
[in]diophantresult of diophantine
[in,out]Mstores intermediate results
[in]bcoeff bound

Definition at line 1341 of file facHensel.cc.

1344{
1345 CFArray bufFactors= CFArray (factors.length());
1346 int i= 0;
1347 CanonicalForm xToStart= power (F.mvar(), start);
1348 for (CFListIterator k= factors; k.hasItem(); k++, i++)
1349 {
1350 if (i == 0)
1351 bufFactors[i]= mod (k.getItem(), xToStart);
1352 else
1353 bufFactors[i]= k.getItem();
1354 }
1355 for (i= start; i < end; i++)
1356 henselStep12 (F, factors, bufFactors, diophant, M, Pi, i, b);
1357
1358 CFListIterator k= factors;
1359 for (i= 0; i < factors.length(); k++, i++)
1360 k.getItem()= bufFactors [i];
1361 factors.removeFirst();
1362 return;
1363}

◆ nonMonicHenselLift()

CFList nonMonicHenselLift ( const CFList eval,
const CFList factors,
CFList *const LCs,
CFList diophant,
CFArray Pi,
int *  liftBound,
int  length,
bool &  noOneToOne 
)

Hensel lifting of non monic factors, needs correct leading coefficients of factors and a one to one corresponds between bivariate and multivariate factors to succeed.

Returns
nonMonicHenselLift returns a list of lifted factors such that prod (factors) == eval.getLast() if there is a one to one correspondence
Parameters
[in]evala list of polys the last element is a compressed multivariate poly, last but one element equals the last elements modulo its main variable and so on. The first element is a compressed poly in 3 variables
[in]factorsa list of bivariate factors
[in]LCsleading coefficients, evaluated in the same way as eval
[in,out]diophantsolution of univariate diophantine equation
[in,out]Pibuffer intermediate results
[in]liftBoundlifting bounds
[in]lengthlength of lifting bounds
[in,out]noOneToOnecheck for one to one correspondence

Definition at line 2938 of file facHensel.cc.

2942{
2943 CFList bufDiophant= diophant;
2944 CFList buf= factors;
2945 CFArray bufPi= Pi;
2946 CFMatrix M= CFMatrix (liftBound[1], factors.length() - 1);
2947 int k= 0;
2948
2949 TIMING_START (hensel23);
2950 CFList result=
2951 nonMonicHenselLift23 (eval.getFirst(), factors, LCs [0], diophant, bufPi,
2952 liftBound[1], liftBound[0], noOneToOne);
2953 TIMING_END_AND_PRINT (hensel23, "time for 23: ");
2954
2955 if (noOneToOne)
2956 return CFList();
2957
2958 if (eval.length() == 1)
2959 return result;
2960
2961 k++;
2962 CFList MOD;
2963 for (int i= 0; i < 2; i++)
2964 MOD.append (power (Variable (i + 2), liftBound[i]));
2965
2967 CFList bufEval;
2968 bufEval.append (j.getItem());
2969 j++;
2970
2971 for (int i= 2; i <= length && j.hasItem(); i++, j++, k++)
2972 {
2973 bufEval.append (j.getItem());
2974 M= CFMatrix (liftBound[i], factors.length() - 1);
2975 TIMING_START (hensel);
2976 result= nonMonicHenselLift (bufEval, result, LCs [i-1], diophant, bufPi, M,
2977 liftBound[i-1], liftBound[i], MOD, noOneToOne);
2978 TIMING_END_AND_PRINT (hensel, "time for further hensel: ");
2979 if (noOneToOne)
2980 return result;
2981 MOD.append (power (Variable (i + 2), liftBound[i]));
2982 bufEval.removeFirst();
2983 }
2984
2985 return result;
2986}
List< CanonicalForm > CFList
TIMING_END_AND_PRINT(fac_alg_resultant, "time to compute resultant0: ")
TIMING_START(fac_alg_resultant)
CFList nonMonicHenselLift(const CFList &F, const CFList &factors, const CFList &LCs, CFList &diophant, CFArray &Pi, CFMatrix &M, int lOld, int &lNew, const CFList &MOD, bool &noOneToOne)
Definition: facHensel.cc:2853
CFList nonMonicHenselLift23(const CanonicalForm &F, const CFList &factors, const CFList &LCs, CFList &diophant, CFArray &Pi, int liftBound, int bivarLiftBound, bool &bad)
Definition: facHensel.cc:2749
static BOOLEAN length(leftv result, leftv arg)
Definition: interval.cc:257

◆ nonMonicHenselLift12()

void nonMonicHenselLift12 ( const CanonicalForm F,
CFList factors,
int  l,
CFArray Pi,
CFList diophant,
CFMatrix M,
const CFArray LCs,
bool  sort 
)

Hensel lifting from univariate to bivariate, factors need not to be monic.

Parameters
[in]Fa bivariate poly
[in,out]factorsa list of univariate polys lifted factors
[in]llift bound
[in,out]Pistores intermediate results
[in,out]diophantresult of diophantine
[in,out]Mstores intermediate results
[in]LCsleading coefficients
[in]sortif true factors are sorted by their degree

Definition at line 2152 of file facHensel.cc.

2155{
2156 if (sort)
2157 sortList (factors, Variable (1));
2158 Pi= CFArray (factors.length() - 2);
2159 CFList bufFactors2= factors;
2160 bufFactors2.removeFirst();
2161 diophant= diophantine (F[0], bufFactors2);
2162 DEBOUTLN (cerr, "diophant= " << diophant);
2163
2164 CFArray bufFactors= CFArray (bufFactors2.length());
2165 int i= 0;
2166 for (CFListIterator k= bufFactors2; k.hasItem(); i++, k++)
2167 bufFactors[i]= replaceLc (k.getItem(), LCs [i]);
2168
2169 Variable x= F.mvar();
2170 if (degree (bufFactors[0], x) > 0 && degree (bufFactors [1], x) > 0)
2171 {
2172 M (1, 1)= mulNTL (bufFactors [0] [0], bufFactors[1] [0]);
2173 Pi [0]= M (1, 1) + (mulNTL (bufFactors [0] [1], bufFactors[1] [0]) +
2174 mulNTL (bufFactors [0] [0], bufFactors [1] [1]))*x;
2175 }
2176 else if (degree (bufFactors[0], x) > 0)
2177 {
2178 M (1, 1)= mulNTL (bufFactors [0] [0], bufFactors[1]);
2179 Pi [0]= M (1, 1) +
2180 mulNTL (bufFactors [0] [1], bufFactors[1])*x;
2181 }
2182 else if (degree (bufFactors[1], x) > 0)
2183 {
2184 M (1, 1)= mulNTL (bufFactors [0], bufFactors[1] [0]);
2185 Pi [0]= M (1, 1) +
2186 mulNTL (bufFactors [0], bufFactors[1] [1])*x;
2187 }
2188 else
2189 {
2190 M (1, 1)= mulNTL (bufFactors [0], bufFactors[1]);
2191 Pi [0]= M (1, 1);
2192 }
2193
2194 for (i= 1; i < Pi.size(); i++)
2195 {
2196 if (degree (Pi[i-1], x) > 0 && degree (bufFactors [i+1], x) > 0)
2197 {
2198 M (1,i+1)= mulNTL (Pi[i-1] [0], bufFactors[i+1] [0]);
2199 Pi [i]= M (1,i+1) + (mulNTL (Pi[i-1] [1], bufFactors[i+1] [0]) +
2200 mulNTL (Pi[i-1] [0], bufFactors [i+1] [1]))*x;
2201 }
2202 else if (degree (Pi[i-1], x) > 0)
2203 {
2204 M (1,i+1)= mulNTL (Pi[i-1] [0], bufFactors [i+1]);
2205 Pi [i]= M(1,i+1) + mulNTL (Pi[i-1] [1], bufFactors[i+1])*x;
2206 }
2207 else if (degree (bufFactors[i+1], x) > 0)
2208 {
2209 M (1,i+1)= mulNTL (Pi[i-1], bufFactors [i+1] [0]);
2210 Pi [i]= M (1,i+1) + mulNTL (Pi[i-1], bufFactors[i+1] [1])*x;
2211 }
2212 else
2213 {
2214 M (1,i+1)= mulNTL (Pi [i-1], bufFactors [i+1]);
2215 Pi [i]= M (1,i+1);
2216 }
2217 }
2218
2219 for (i= 1; i < l; i++)
2220 nonMonicHenselStep12 (F, bufFactors2, bufFactors, diophant, M, Pi, i, LCs);
2221
2222 factors= CFList();
2223 for (i= 0; i < bufFactors.size(); i++)
2224 factors.append (bufFactors[i]);
2225 return;
2226}
int degree(const CanonicalForm &f)
int size() const
Definition: ftmpl_array.cc:92
void nonMonicHenselStep12(const CanonicalForm &F, const CFList &factors, CFArray &bufFactors, const CFList &diophant, CFMatrix &M, CFArray &Pi, int j, const CFArray &)
Definition: facHensel.cc:1930
CanonicalForm replaceLc(const CanonicalForm &f, const CanonicalForm &c)
Definition: fac_util.cc:90

◆ nonMonicHenselLift2()

CFList nonMonicHenselLift2 ( const CFList eval,
const CFList factors,
int *  l,
int  lLength,
bool  sort,
const CFList LCs1,
const CFList LCs2,
const CFArray Pi,
const CFList diophant,
bool &  noOneToOne 
)

two factor Hensel lifting from bivariate to multivariate, factors need not to be monic

Returns
henselLift122 returns a list of lifted factors
Parameters
[in]evala list of polynomials the last element is a compressed multivariate poly, last but one element equals the last elements modulo its main variable and so on. The first element is a compressed bivariate poly.
[in]factorsbivariate factors
[in]llift bounds
[in]lLengthlength of l
[in]sortif true factors are sorted by their degree in Variable(1)
[in]LCs1a list of evaluated LC of first factor
[in]LCs2a list of evaluated LC of second factor
[in]Piintermediate result
[in]diophantresult of diophantine
[in,out]noOneToOnecheck for one to one correspondence

Definition at line 2695 of file facHensel.cc.

2698{
2699 CFList bufDiophant= diophant;
2700 CFList buf= factors;
2701 if (sort)
2702 sortList (buf, Variable (1));
2703 CFArray bufPi= Pi;
2704 CFMatrix M= CFMatrix (l[1], factors.length());
2705 CFList result=
2706 nonMonicHenselLift232(eval, buf, l, bufDiophant, bufPi, M, LCs1, LCs2, bad);
2707 if (bad)
2708 return CFList();
2709
2710 if (eval.length() == 2)
2711 return result;
2712 CFList MOD;
2713 for (int i= 0; i < 2; i++)
2714 MOD.append (power (Variable (i + 2), l[i]));
2716 j++;
2717 CFList bufEval;
2718 bufEval.append (j.getItem());
2719 j++;
2720 CFListIterator jj= LCs1;
2721 CFListIterator jjj= LCs2;
2722 CFList bufLCs1, bufLCs2;
2723 jj++, jjj++;
2724 bufLCs1.append (jj.getItem());
2725 bufLCs2.append (jjj.getItem());
2726 jj++, jjj++;
2727
2728 for (int i= 2; i < lLength && j.hasItem(); i++, j++, jj++, jjj++)
2729 {
2730 bufEval.append (j.getItem());
2731 bufLCs1.append (jj.getItem());
2732 bufLCs2.append (jjj.getItem());
2733 M= CFMatrix (l[i], factors.length());
2734 result= nonMonicHenselLift2 (bufEval, result, MOD, bufDiophant, bufPi, M,
2735 l[i - 1], l[i], bufLCs1, bufLCs2, bad);
2736 if (bad)
2737 return CFList();
2738 MOD.append (power (Variable (i + 2), l[i]));
2739 bufEval.removeFirst();
2740 bufLCs1.removeFirst();
2741 bufLCs2.removeFirst();
2742 }
2743 return result;
2744}
T & getItem() const
Definition: ftmpl_list.cc:431
bool bad
Definition: facFactorize.cc:64
CFList nonMonicHenselLift2(const CFList &F, const CFList &factors, const CFList &MOD, CFList &diophant, CFArray &Pi, CFMatrix &M, int lOld, int &lNew, const CFList &LCs1, const CFList &LCs2, bool &bad)
Definition: facHensel.cc:2630
CFList nonMonicHenselLift232(const CFList &eval, const CFList &factors, int *l, CFList &diophant, CFArray &Pi, CFMatrix &M, const CFList &LCs1, const CFList &LCs2, bool &bad)
Definition: facHensel.cc:2566

◆ sortList()

void sortList ( CFList list,
const Variable x 
)

sort a list of polynomials by their degree in x.

Parameters
[in,out]listlist of polys, sorted list
[in]xsome Variable

Definition at line 449 of file facHensel.cc.

450{
451 int l= 1;
452 int k= 1;
455 for (CFListIterator i= list; l <= list.length(); i++, l++)
456 {
457 for (CFListIterator j= list; k <= list.length() - l; k++)
458 {
459 m= j;
460 m++;
461 if (degree (j.getItem(), x) > degree (m.getItem(), x))
462 {
463 buf= m.getItem();
464 m.getItem()= j.getItem();
465 j.getItem()= buf;
466 j++;
467 j.getItem()= m.getItem();
468 }
469 else
470 j++;
471 }
472 k= 1;
473 }
474}
int m
Definition: cfEzgcd.cc:128