initial.cc File Reference

#include "kernel/ideals.h"
#include "polys/monomials/p_polys.h"
#include "gfanlib/gfanlib.h"

Go to the source code of this file.

Functions
long	wDeg (const poly p, const ring r, const gfan::ZVector &w)
	various functions to compute the initial form of polynomials and ideals More...
gfan::ZVector	WDeg (const poly p, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W)
	Returns the weighted multidegree of the leading term of p with respect to (w,W). More...
poly	initial (const poly p, const ring r, const gfan::ZVector &w)
	Returns the initial form of p with respect to w. More...
ideal	initial (const ideal I, const ring r, const gfan::ZVector &w)
	Returns the initial form of I with respect to w. More...
poly	initial (const poly p, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W)
	Returns the initial form of p with respect to w and W. More...
ideal	initial (const ideal I, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W)
	Returns the initial form of I with respect to w and W. More...
void	initial (poly *pStar, const ring r, const gfan::ZVector &w)
	Stores the initial form of *pStar with respect to w in pStar. More...
void	initial (ideal *IStar, const ring r, const gfan::ZVector &w)
	Stores the initial form of *IStar with respect to w in IStar. More...
void	initial (poly *pStar, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W)
	Stores the initial form of *pStar with respect to w and W in pStar. More...
void	initial (ideal *IStar, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W)
	Stores the initial form of *IStar with respect to w and W in IStar. More...

Function Documentation

initial() [1/8]

ideal initial	(	const ideal	I,
		const ring	r,
		const gfan::ZVector &	w
	)

Returns the initial form of I with respect to w.

Definition at line 58 of file initial.cc.

{
  int k = IDELEMS(I); ideal inI = idInit(k);
  for (int i=0; i<k; i++)
    inI->m[i] = initial(I->m[i],r,w);
  return inI;
}

initial() [2/8]

ideal initial	(	const ideal	I,
		const ring	r,
		const gfan::ZVector &	w,
		const gfan::ZMatrix &	W
	)

Returns the initial form of I with respect to w and W.

Definition at line 94 of file initial.cc.

{
  int k = IDELEMS(I); ideal inI = idInit(k);
  for (int i=0; i<k; i++)
    inI->m[i] = initial(I->m[i],r,w,W);
  return inI;
}

initial() [3/8]

poly initial	(	const poly	p,
		const ring	r,
		const gfan::ZVector &	w
	)

Returns the initial form of p with respect to w.

Definition at line 30 of file initial.cc.

{
  if (p==NULL)
    return NULL;
 
  poly q0 = p_Head(p,r);
  poly q1 = q0;
  long d = wDeg(p,r,w);
  for (poly currentTerm = p->next; currentTerm; pIter(currentTerm))
  {
    long e = wDeg(currentTerm,r,w);
    if (d<e)
    {
      p_Delete(&q0,r);
      q0 = p_Head(currentTerm,r);
      q1 = q0;
      d = e;
    }
    else
      if (e==d)
      {
        pNext(q1) = p_Head(currentTerm,r);
        pIter(q1);
      }
  }
  return q0;
}

initial() [4/8]

poly initial	(	const poly	p,
		const ring	r,
		const gfan::ZVector &	w,
		const gfan::ZMatrix &	W
	)

Returns the initial form of p with respect to w and W.

Definition at line 66 of file initial.cc.

{
  if (p==NULL)
    return NULL;
 
  poly q0 = p_Head(p,r);
  poly q1 = q0;
  gfan::ZVector d = WDeg(p,r,w,W);
  for (poly currentTerm = p->next; currentTerm; pIter(currentTerm))
  {
    gfan::ZVector e = WDeg(currentTerm,r,w,W);
    if (d<e)
    {
      p_Delete(&q0,r);
      q0 = p_Head(p,r);
      q1 = q0;
      d = e;
    }
    else
      if (d==e)
      {
        pNext(q1) = p_Head(currentTerm,r);
        pIter(q1);
      }
  }
  return q0;
}

initial() [5/8]

void initial	(	ideal *	IStar,
		const ring	r,
		const gfan::ZVector &	w
	)

Stores the initial form of *IStar with respect to w in IStar.

Definition at line 141 of file initial.cc.

{
  ideal I = *IStar;
  int k = IDELEMS(I);
  for (int i=0; i<k; i++)
    initial(&I->m[i],r,w);
  return;
}

initial() [6/8]

void initial	(	ideal *	IStar,
		const ring	r,
		const gfan::ZVector &	w,
		const gfan::ZMatrix &	W
	)

Stores the initial form of *IStar with respect to w and W in IStar.

Definition at line 189 of file initial.cc.

{
  ideal I = *IStar;
  int k = IDELEMS(I);
  for (int i=0; i<k; i++)
    initial(&I->m[i],r,w,W);
  return;
}

initial() [7/8]

void initial	(	poly *	pStar,
		const ring	r,
		const gfan::ZVector &	w
	)

Stores the initial form of *pStar with respect to w in pStar.

Definition at line 102 of file initial.cc.

{
  poly p = *pStar;
  if (p==NULL)
    return;
 
  long d = wDeg(p,r,w);
  poly q0 = p;
  poly q1 = q0;
  pNext(q1) = NULL;
  pIter(p);
 
  while(p)
  {
    long e = wDeg(p,r,w);
    if (d<e)
    {
      p_Delete(&q0,r);
      q0 = p;
      q1 = q0;
      pNext(q1) = NULL;
      d = e;
      pIter(p);
    }
    else
      if (e==d)
      {
        pNext(q1) = p;
        pIter(q1);
        pNext(q1) = NULL;
        pIter(p);
      }
      else
        p = p_LmDeleteAndNext(p,r);
  }
  pStar = &q0;
  return;
}

initial() [8/8]

void initial	(	poly *	pStar,
		const ring	r,
		const gfan::ZVector &	w,
		const gfan::ZMatrix &	W
	)

Stores the initial form of *pStar with respect to w and W in pStar.

Definition at line 150 of file initial.cc.

{
  poly p = *pStar;
  if (p==NULL)
    return;
 
  gfan::ZVector d = WDeg(p,r,w,W);
  poly q0 = p;
  poly q1 = q0;
  pNext(q1) = NULL;
  pIter(p);
 
  while(p)
  {
    gfan::ZVector e = WDeg(p,r,w,W);
    if (d<e)
    {
      p_Delete(&q0,r);
      q0 = p;
      q1 = q0;
      pNext(q1) = NULL;
      d = e;
      pIter(p);
    }
    else
      if (d==e)
      {
        pNext(q1) = p;
        pIter(q1);
        pNext(q1) = NULL;
        pIter(p);
      }
      else
        p = p_LmDeleteAndNext(p,r);
  }
  pStar = &q0;
  return;
}

wDeg()

long wDeg	(	const poly	p,
		const ring	r,
		const gfan::ZVector &	w
	)

various functions to compute the initial form of polynomials and ideals

Returns the weighted degree of the leading term of p with respect to w

Definition at line 6 of file initial.cc.

{
  long d=0;
  for (unsigned i=0; i<w.size(); i++)
  {
    if (!w[i].fitsInInt())
    {
      WerrorS("wDeg: overflow in weight vector");
      throw 0; // weightOverflow;
    }
    d += p_GetExp(p,i+1,r)*w[i].toInt();
  }
  return d;
}

WDeg()

gfan::ZVector WDeg	(	const poly	p,
		const ring	r,
		const gfan::ZVector &	w,
		const gfan::ZMatrix &	W
	)

Returns the weighted multidegree of the leading term of p with respect to (w,W).

The weighted multidegree is a vector of length one higher than the column vectors of W. The first entry is the weighted degree with respect to w and the i+1st entry is the weighted degree with respect to the i-th row vector of W.

Definition at line 21 of file initial.cc.

{
  gfan::ZVector d = gfan::ZVector(W.getHeight()+1);
  d[0] = wDeg(p,r,w);
  for (int i=0; i<W.getHeight(); i++)
    d[i+1] = wDeg(p,r,W[i]);
  return d;
}