My Project
|
This file provides functions to factorize polynomials over alg. More...
#include "config.h"
#include "cf_assert.h"
#include "debug.h"
#include "cf_generator.h"
#include "cf_iter.h"
#include "cf_util.h"
#include "cf_algorithm.h"
#include "templates/ftmpl_functions.h"
#include "cf_map.h"
#include "cfModResultant.h"
#include "cfCharSets.h"
#include "facAlgFunc.h"
#include "facAlgFuncUtil.h"
Go to the source code of this file.
Functions | |
void | out_cf (const char *s1, const CanonicalForm &f, const char *s2) |
cf_algorithm.cc - simple mathematical algorithms. More... | |
CanonicalForm | alg_content (const CanonicalForm &f, const CFList &as) |
CanonicalForm | alg_gcd (const CanonicalForm &fff, const CanonicalForm &ggg, const CFList &as) |
static CanonicalForm | resultante (const CanonicalForm &f, const CanonicalForm &g, const Variable &v) |
static CFFList | norm (const CanonicalForm &f, const CanonicalForm &PPalpha, CFGenerator &myrandom, CanonicalForm &s, CanonicalForm &g, CanonicalForm &R, bool proof) |
compute the norm R of f over PPalpha, g= f (x-s*alpha) if proof==true, R is squarefree and if in addition getCharacteristic() > 0 the squarefree factors of R are returned. Based on Trager's sqrf_norm algorithm. More... | |
static CFFList | sqrfNorm (const CanonicalForm &f, const CanonicalForm &PPalpha, const Variable &Extension, CanonicalForm &s, CanonicalForm &g, CanonicalForm &R) |
see norm, R is guaranteed to be squarefree Based on Trager's sqrf_norm algorithm. More... | |
static CFList | simpleExtension (CFList &backSubst, const CFList &Astar, const Variable &Extension, bool &isFunctionField, CanonicalForm &R) |
static CFFList | Trager (const CanonicalForm &F, const CFList &Astar, const Variable &vminpoly, const CFList &as, bool isFunctionField) |
Trager's algorithm, i.e. convert to one field extension and factorize over this field extension. More... | |
CFList | mapIntoPIE (CFFList &varsMapLevel, CanonicalForm &lcmVars, const CFList &AS) |
map elements in AS into a PIE and record where the variables are mapped to in varsMapLevel, i.e varsMapLevel contains a list of pairs of variables and integers such that More... | |
CFFList | SteelTrager (const CanonicalForm &f, const CFList &AS) |
algorithm of A. Steel described in "Conquering Inseparability: Primary
decomposition and multivariate factorization over algebraic function fields
of positive characteristic" with the following modifications: we use characteristic sets in IdealOverSubfield and Trager's primitive element algorithm instead of FGLM More... | |
CFFList | facAlgFunc2 (const CanonicalForm &f, const CFList &as) |
factorize a polynomial that is irreducible over the ground field modulo an extension given by an irreducible characteristic set More... | |
CFFList | facAlgFunc (const CanonicalForm &f, const CFList &as) |
factorize a polynomial modulo an extension given by an irreducible characteristic set More... | |
This file provides functions to factorize polynomials over alg.
function fields
ABSTRACT: Descriptions can be found in B. Trager "Algebraic Factoring and Rational Function Integration" and A. Steel "Conquering Inseparability: Primary decomposition and multivariate factorization over algebraic function fields of positive characteristic"
Definition in file facAlgFunc.cc.
CanonicalForm alg_content | ( | const CanonicalForm & | f, |
const CFList & | as | ||
) |
Definition at line 42 of file facAlgFunc.cc.
CanonicalForm alg_gcd | ( | const CanonicalForm & | fff, |
const CanonicalForm & | ggg, | ||
const CFList & | as | ||
) |
Definition at line 61 of file facAlgFunc.cc.
CFFList facAlgFunc | ( | const CanonicalForm & | f, |
const CFList & | as | ||
) |
factorize a polynomial modulo an extension given by an irreducible characteristic set
factorize a polynomial f modulo an extension given by an irreducible characteristic set as, f is assumed to be integral, i.e. , and each element of as is assumed to be integral as well. must be either or .
[in] | f | univariate poly |
[in] | as | irreducible characteristic set |
Definition at line 1043 of file facAlgFunc.cc.
CFFList facAlgFunc2 | ( | const CanonicalForm & | f, |
const CFList & | as | ||
) |
factorize a polynomial that is irreducible over the ground field modulo an extension given by an irreducible characteristic set
factorize a polynomial f that is irreducible over the ground field modulo an extension given by an irreducible characteristic set as, f is assumed to be integral, i.e. , and each element of as is assumed to be integral as well. must be either or .
[in] | f | univariate poly |
[in] | as | irreducible characteristic set |
Definition at line 905 of file facAlgFunc.cc.
CFList mapIntoPIE | ( | CFFList & | varsMapLevel, |
CanonicalForm & | lcmVars, | ||
const CFList & | AS | ||
) |
map elements in AS into a PIE and record where the variables are mapped to in varsMapLevel, i.e varsMapLevel contains a list of pairs of variables and integers such that
Definition at line 609 of file facAlgFunc.cc.
|
static |
compute the norm R of f over PPalpha, g= f (x-s*alpha) if proof==true, R is squarefree and if in addition getCharacteristic() > 0 the squarefree factors of R are returned. Based on Trager's sqrf_norm algorithm.
Definition at line 206 of file facAlgFunc.cc.
void out_cf | ( | const char * | s1, |
const CanonicalForm & | f, | ||
const char * | s2 | ||
) |
cf_algorithm.cc - simple mathematical algorithms.
Hierarchy: mathematical algorithms on canonical forms
A "mathematical" algorithm is an algorithm which calculates some mathematical function in contrast to a "structural" algorithm which gives structural information on polynomials.
Compare these functions to the functions in ‘cf_ops.cc’, which are structural algorithms.
Definition at line 99 of file cf_factor.cc.
|
static |
Definition at line 179 of file facAlgFunc.cc.
|
static |
Definition at line 313 of file facAlgFunc.cc.
|
static |
see norm, R is guaranteed to be squarefree Based on Trager's sqrf_norm algorithm.
Definition at line 287 of file facAlgFunc.cc.
CFFList SteelTrager | ( | const CanonicalForm & | f, |
const CFList & | AS | ||
) |
algorithm of A. Steel described in "Conquering Inseparability: Primary decomposition and multivariate factorization over algebraic function fields of positive characteristic" with the following modifications: we use characteristic sets in IdealOverSubfield and Trager's primitive element algorithm instead of FGLM
Definition at line 759 of file facAlgFunc.cc.
|
static |
Trager's algorithm, i.e. convert to one field extension and factorize over this field extension.
Definition at line 430 of file facAlgFunc.cc.