Go to the source code of this file.
|
matrix | divisionDiscardingRemainder (const poly f, const ideal G, const ring r) |
| Computes a division discarding remainder of f with respect to G. More...
|
|
matrix | divisionDiscardingRemainder (const ideal F, const ideal G, const ring r) |
| Computes a division discarding remainder of F with respect to G. More...
|
|
poly | witness (const poly m, const ideal I, const ideal inI, const ring r) |
| Let w be the uppermost weight vector in the matrix defining the ordering on r. More...
|
|
ideal | witness (const ideal inI, const ideal J, const ring r) |
| Computes witnesses in J for inI Given inI={h1,...,hl} and J={g1,...,gk} two sets of polynomials in r, returns a set I={f1,...,fl} of <g1,...,gk> such that in_w(fj)=hj for all j=1,...,l, where w denotes the uppoermost weight vector in the matrix defining the ordering on r. More...
|
|
BOOLEAN | dwrDebug (leftv res, leftv args) |
|
BOOLEAN | witnessDebug (leftv res, leftv args) |
|
§ divisionDiscardingRemainder() [1/2]
Computes a division discarding remainder of f with respect to G.
Given f a polynomial and G={g1,...,gk} a set of polynomials in r, returns a matrix Q=(q1,...,qk) over r such that f = q1*g1+...+qk*gk+s is a determinate division with remainder s.
Definition at line 9 of file witness.cc.
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
void rChangeCurrRing(ring r)
ideal idInit(int idsize, int rank)
initialise an ideal / module
matrix id_Module2formatedMatrix(ideal mod, int rows, int cols, const ring R)
ideal idLift(ideal mod, ideal submod, ideal *rest, BOOLEAN goodShape, BOOLEAN isSB, BOOLEAN divide, matrix *unit)
§ divisionDiscardingRemainder() [2/2]
Computes a division discarding remainder of F with respect to G.
Given F={f1,...,fl} and G={g1,...,gk} two sets of polynomials in r, returns a matrix Q=(qij) i=1,..,k j=1,...,l over r such that fj = q1j*g1+...+qkj*gk+sj is a determinate division with remainder sj for all j=1,...,l.
Definition at line 21 of file witness.cc.
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
void mp_Delete(matrix *a, const ring r)
void rChangeCurrRing(ring r)
matrix id_Module2formatedMatrix(ideal mod, int rows, int cols, const ring R)
ideal idLift(ideal mod, ideal submod, ideal *rest, BOOLEAN goodShape, BOOLEAN isSB, BOOLEAN divide, matrix *unit)
§ dwrDebug()
Definition at line 73 of file witness.cc.
77 ideal F = (ideal) u->
CopyD();
78 ideal
G = (ideal) v->
CopyD();
85 res->
data = (
char*) Q;
matrix divisionDiscardingRemainder(const poly f, const ideal G, const ring r)
Computes a division discarding remainder of f with respect to G.
Class used for (list of) interpreter objects.
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
const Variable & v
< [in] a sqrfree bivariate poly
§ witness() [1/2]
Let w be the uppermost weight vector in the matrix defining the ordering on r.
Let I be a Groebner basis of an ideal in r, inI its initial form with respect w. Given an w-homogeneous element m of inI, computes a witness g of m in I, i.e. g in I such that in_w(g)=m.
Definition at line 34 of file witness.cc.
42 for (
int i=1;
i<
k;
i++)
matrix divisionDiscardingRemainder(const poly f, const ideal G, const ring r)
Computes a division discarding remainder of f with respect to G.
static poly p_Copy(poly p, const ring r)
returns a copy of p
void mp_Delete(matrix *a, const ring r)
static poly p_Add_q(poly p, poly q, const ring r)
static poly p_Mult_q(poly p, poly q, const ring r)
§ witness() [2/2]
Computes witnesses in J for inI Given inI={h1,...,hl} and J={g1,...,gk} two sets of polynomials in r, returns a set I={f1,...,fl} of <g1,...,gk> such that in_w(fj)=hj for all j=1,...,l, where w denotes the uppoermost weight vector in the matrix defining the ordering on r.
Assumes that hj is an element of <in_w(g1),...,in_w(gk)>
Definition at line 52 of file witness.cc.
57 ideal NFinI =
kNF(J,
r->qideal,inI);
63 for (
int i=0;
i<
k;
i++)
poly kNF(ideal F, ideal Q, poly p, int syzComp, int lazyReduce)
static poly p_Copy(poly p, const ring r)
returns a copy of p
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
void rChangeCurrRing(ring r)
ideal idInit(int idsize, int rank)
initialise an ideal / module
static poly p_Neg(poly p, const ring r)
static poly p_Add_q(poly p, poly q, const ring r)
§ witnessDebug()
Definition at line 89 of file witness.cc.
99 ideal inI = (ideal) u->
CopyD();
100 ideal J = (ideal) v->
CopyD();
105 res->
data = (
char*) I;
Class used for (list of) interpreter objects.
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
const Variable & v
< [in] a sqrfree bivariate poly
poly witness(const poly m, const ideal I, const ideal inI, const ring r)
Let w be the uppermost weight vector in the matrix defining the ordering on r.