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Macros | Functions
mpr_inout.h File Reference

Go to the source code of this file.

Macros

#define DEFAULT_DIGITS   30
 
#define MPR_DENSE   1
 
#define MPR_SPARSE   2
 

Functions

BOOLEAN nuUResSolve (leftv res, leftv args)
 solve a multipolynomial system using the u-resultant Input ideal must be 0-dimensional and (currRing->N) == IDELEMS(ideal).
 
BOOLEAN nuMPResMat (leftv res, leftv arg1, leftv arg2)
 returns module representing the multipolynomial resultant matrix Arguments 2: ideal i, int k k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky k=1: use resultant matrix of Macaulay (k=0 is default)
 
BOOLEAN nuLagSolve (leftv res, leftv arg1, leftv arg2, leftv arg3)
 find the (complex) roots an univariate polynomial Determines the roots of an univariate polynomial using Laguerres' root-solver.
 
BOOLEAN nuVanderSys (leftv res, leftv arg1, leftv arg2, leftv arg3)
 COMPUTE: polynomial p with values given by v at points p1,..,pN derived from p; more precisely: consider p as point in K^n and v as N elements in K, let p1,..,pN be the points in K^n obtained by evaluating all monomials of degree 0,1,...,N at p in lexicographical order, then the procedure computes the polynomial f satisfying f(pi) = v[i] RETURN: polynomial f of degree d.
 
BOOLEAN loNewtonP (leftv res, leftv arg1)
 compute Newton Polytopes of input polynomials
 
BOOLEAN loSimplex (leftv res, leftv args)
 Implementation of the Simplex Algorithm.
 

Macro Definition Documentation

◆ DEFAULT_DIGITS

#define DEFAULT_DIGITS   30

Definition at line 13 of file mpr_inout.h.

◆ MPR_DENSE

#define MPR_DENSE   1

Definition at line 15 of file mpr_inout.h.

◆ MPR_SPARSE

#define MPR_SPARSE   2

Definition at line 16 of file mpr_inout.h.

Function Documentation

◆ loNewtonP()

BOOLEAN loNewtonP ( leftv  res,
leftv  arg1 
)

compute Newton Polytopes of input polynomials

Definition at line 4547 of file ipshell.cc.

4548{
4549 res->data= (void*)loNewtonPolytope( (ideal)arg1->Data() );
4550 return FALSE;
4551}
#define FALSE
Definition auxiliary.h:96
void * Data()
Definition subexpr.cc:1192
CanonicalForm res
Definition facAbsFact.cc:60
ideal loNewtonPolytope(const ideal id)
Definition mpr_base.cc:3191

◆ loSimplex()

BOOLEAN loSimplex ( leftv  res,
leftv  args 
)

Implementation of the Simplex Algorithm.

For args, see class simplex.

Definition at line 4553 of file ipshell.cc.

4554{
4555 if ( !(rField_is_long_R(currRing)) )
4556 {
4557 WerrorS("Ground field not implemented!");
4558 return TRUE;
4559 }
4560
4561 simplex * LP;
4562 matrix m;
4563
4564 leftv v= args;
4565 if ( v->Typ() != MATRIX_CMD ) // 1: matrix
4566 return TRUE;
4567 else
4568 m= (matrix)(v->CopyD());
4569
4570 LP = new simplex(MATROWS(m),MATCOLS(m));
4571 LP->mapFromMatrix(m);
4572
4573 v= v->next;
4574 if ( v->Typ() != INT_CMD ) // 2: m = number of constraints
4575 return TRUE;
4576 else
4577 LP->m= (int)(long)(v->Data());
4578
4579 v= v->next;
4580 if ( v->Typ() != INT_CMD ) // 3: n = number of variables
4581 return TRUE;
4582 else
4583 LP->n= (int)(long)(v->Data());
4584
4585 v= v->next;
4586 if ( v->Typ() != INT_CMD ) // 4: m1 = number of <= constraints
4587 return TRUE;
4588 else
4589 LP->m1= (int)(long)(v->Data());
4590
4591 v= v->next;
4592 if ( v->Typ() != INT_CMD ) // 5: m2 = number of >= constraints
4593 return TRUE;
4594 else
4595 LP->m2= (int)(long)(v->Data());
4596
4597 v= v->next;
4598 if ( v->Typ() != INT_CMD ) // 6: m3 = number of == constraints
4599 return TRUE;
4600 else
4601 LP->m3= (int)(long)(v->Data());
4602
4603#ifdef mprDEBUG_PROT
4604 Print("m (constraints) %d\n",LP->m);
4605 Print("n (columns) %d\n",LP->n);
4606 Print("m1 (<=) %d\n",LP->m1);
4607 Print("m2 (>=) %d\n",LP->m2);
4608 Print("m3 (==) %d\n",LP->m3);
4609#endif
4610
4611 LP->compute();
4612
4613 lists lres= (lists)omAlloc( sizeof(slists) );
4614 lres->Init( 6 );
4615
4616 lres->m[0].rtyp= MATRIX_CMD; // output matrix
4617 lres->m[0].data=(void*)LP->mapToMatrix(m);
4618
4619 lres->m[1].rtyp= INT_CMD; // found a solution?
4620 lres->m[1].data=(void*)(long)LP->icase;
4621
4622 lres->m[2].rtyp= INTVEC_CMD;
4623 lres->m[2].data=(void*)LP->posvToIV();
4624
4625 lres->m[3].rtyp= INTVEC_CMD;
4626 lres->m[3].data=(void*)LP->zrovToIV();
4627
4628 lres->m[4].rtyp= INT_CMD;
4629 lres->m[4].data=(void*)(long)LP->m;
4630
4631 lres->m[5].rtyp= INT_CMD;
4632 lres->m[5].data=(void*)(long)LP->n;
4633
4634 res->data= (void*)lres;
4635
4636 return FALSE;
4637}
#define TRUE
Definition auxiliary.h:100
int m
Definition cfEzgcd.cc:128
Variable next() const
Definition factory.h:146
Linear Programming / Linear Optimization using Simplex - Algorithm.
intvec * zrovToIV()
BOOLEAN mapFromMatrix(matrix m)
void compute()
matrix mapToMatrix(matrix m)
intvec * posvToIV()
Class used for (list of) interpreter objects.
Definition subexpr.h:83
Definition lists.h:24
#define Print
Definition emacs.cc:80
const Variable & v
< [in] a sqrfree bivariate poly
Definition facBivar.h:39
void WerrorS(const char *s)
Definition feFopen.cc:24
@ MATRIX_CMD
Definition grammar.cc:287
ip_smatrix * matrix
Definition matpol.h:43
#define MATROWS(i)
Definition matpol.h:26
#define MATCOLS(i)
Definition matpol.h:27
slists * lists
#define omAlloc(size)
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition polys.cc:13
static BOOLEAN rField_is_long_R(const ring r)
Definition ring.h:547
@ INTVEC_CMD
Definition tok.h:101
@ INT_CMD
Definition tok.h:96

◆ nuLagSolve()

BOOLEAN nuLagSolve ( leftv  res,
leftv  arg1,
leftv  arg2,
leftv  arg3 
)

find the (complex) roots an univariate polynomial Determines the roots of an univariate polynomial using Laguerres' root-solver.

Good for polynomials with low and middle degree (<40). Arguments 3: poly arg1 , int arg2 , int arg3 arg2>0: defines precision of fractional part if ground field is Q arg3: number of iterations for approximation of roots (default=2) Returns a list of all (complex) roots of the polynomial arg1

Definition at line 4662 of file ipshell.cc.

4663{
4664 poly gls;
4665 gls= (poly)(arg1->Data());
4666 int howclean= (int)(long)arg3->Data();
4667
4668 if ( gls == NULL || pIsConstant( gls ) )
4669 {
4670 WerrorS("Input polynomial is constant!");
4671 return TRUE;
4672 }
4673
4675 {
4676 int* r=Zp_roots(gls, currRing);
4677 lists rlist;
4678 rlist= (lists)omAlloc( sizeof(slists) );
4679 rlist->Init( r[0] );
4680 for(int i=r[0];i>0;i--)
4681 {
4682 rlist->m[i-1].data=n_Init(r[i],currRing->cf);
4683 rlist->m[i-1].rtyp=NUMBER_CMD;
4684 }
4685 omFree(r);
4686 res->data=rlist;
4687 res->rtyp= LIST_CMD;
4688 return FALSE;
4689 }
4690 if ( !(rField_is_R(currRing) ||
4694 {
4695 WerrorS("Ground field not implemented!");
4696 return TRUE;
4697 }
4698
4701 {
4702 unsigned long int ii = (unsigned long int)arg2->Data();
4704 }
4705
4706 int ldummy;
4707 int deg= currRing->pLDeg( gls, &ldummy, currRing );
4708 int i,vpos=0;
4709 poly piter;
4710 lists elist;
4711
4712 elist= (lists)omAlloc( sizeof(slists) );
4713 elist->Init( 0 );
4714
4715 if ( rVar(currRing) > 1 )
4716 {
4717 piter= gls;
4718 for ( i= 1; i <= rVar(currRing); i++ )
4719 if ( pGetExp( piter, i ) )
4720 {
4721 vpos= i;
4722 break;
4723 }
4724 while ( piter )
4725 {
4726 for ( i= 1; i <= rVar(currRing); i++ )
4727 if ( (vpos != i) && (pGetExp( piter, i ) != 0) )
4728 {
4729 WerrorS("The input polynomial must be univariate!");
4730 return TRUE;
4731 }
4732 pIter( piter );
4733 }
4734 }
4735
4736 rootContainer * roots= new rootContainer();
4737 number * pcoeffs= (number *)omAlloc( (deg+1) * sizeof( number ) );
4738 piter= gls;
4739 for ( i= deg; i >= 0; i-- )
4740 {
4741 if ( piter && pTotaldegree(piter) == i )
4742 {
4743 pcoeffs[i]= nCopy( pGetCoeff( piter ) );
4744 //nPrint( pcoeffs[i] );PrintS(" ");
4745 pIter( piter );
4746 }
4747 else
4748 {
4749 pcoeffs[i]= nInit(0);
4750 }
4751 }
4752
4753#ifdef mprDEBUG_PROT
4754 for (i=deg; i >= 0; i--)
4755 {
4756 nPrint( pcoeffs[i] );PrintS(" ");
4757 }
4758 PrintLn();
4759#endif
4760
4761 roots->fillContainer( pcoeffs, NULL, 1, deg, rootContainer::onepoly, 1 );
4762 roots->solver( howclean );
4763
4764 int elem= roots->getAnzRoots();
4765 char *dummy;
4766 int j;
4767
4768 lists rlist;
4769 rlist= (lists)omAlloc( sizeof(slists) );
4770 rlist->Init( elem );
4771
4773 {
4774 for ( j= 0; j < elem; j++ )
4775 {
4776 rlist->m[j].rtyp=NUMBER_CMD;
4777 rlist->m[j].data=(void *)nCopy((number)(roots->getRoot(j)));
4778 //rlist->m[j].data=(void *)(number)(roots->getRoot(j));
4779 }
4780 }
4781 else
4782 {
4783 for ( j= 0; j < elem; j++ )
4784 {
4785 dummy = complexToStr( (*roots)[j], gmp_output_digits, currRing->cf );
4786 rlist->m[j].rtyp=STRING_CMD;
4787 rlist->m[j].data=(void *)dummy;
4788 }
4789 }
4790
4791 elist->Clean();
4792 //omFreeSize( (ADDRESS) elist, sizeof(slists) );
4793
4794 // this is (via fillContainer) the same data as in root
4795 //for ( i= deg; i >= 0; i-- ) nDelete( &pcoeffs[i] );
4796 //omFreeSize( (ADDRESS) pcoeffs, (deg+1) * sizeof( number ) );
4797
4798 delete roots;
4799
4800 res->data= (void*)rlist;
4801
4802 return FALSE;
4803}
int i
Definition cfEzgcd.cc:132
int * Zp_roots(poly p, const ring r)
Definition clapsing.cc:2190
complex root finder for univariate polynomials based on laguers algorithm
Definition mpr_numeric.h:66
gmp_complex * getRoot(const int i)
Definition mpr_numeric.h:88
void fillContainer(number *_coeffs, number *_ievpoint, const int _var, const int _tdg, const rootType _rt, const int _anz)
int getAnzRoots()
Definition mpr_numeric.h:97
bool solver(const int polishmode=PM_NONE)
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
Definition coeffs.h:539
int j
Definition facHensel.cc:110
@ NUMBER_CMD
Definition grammar.cc:289
#define pIter(p)
Definition monomials.h:37
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition monomials.h:44
EXTERN_VAR size_t gmp_output_digits
Definition mpr_base.h:115
char * complexToStr(gmp_complex &c, const unsigned int oprec, const coeffs src)
void setGMPFloatDigits(size_t digits, size_t rest)
Set size of mantissa digits - the number of output digits (basis 10) the size of mantissa consists of...
#define nCopy(n)
Definition numbers.h:15
#define nPrint(a)
only for debug, over any initialized currRing
Definition numbers.h:46
#define nInit(i)
Definition numbers.h:24
#define omFree(addr)
#define NULL
Definition omList.c:12
static long pTotaldegree(poly p)
Definition polys.h:282
#define pIsConstant(p)
like above, except that Comp must be 0
Definition polys.h:238
#define pGetExp(p, i)
Exponent.
Definition polys.h:41
void PrintS(const char *s)
Definition reporter.cc:284
void PrintLn()
Definition reporter.cc:310
static BOOLEAN rField_is_R(const ring r)
Definition ring.h:523
static BOOLEAN rField_is_Zp(const ring r)
Definition ring.h:505
static BOOLEAN rField_is_long_C(const ring r)
Definition ring.h:550
static BOOLEAN rField_is_Q(const ring r)
Definition ring.h:511
static short rVar(const ring r)
#define rVar(r) (r->N)
Definition ring.h:597
@ LIST_CMD
Definition tok.h:118
@ STRING_CMD
Definition tok.h:187

◆ nuMPResMat()

BOOLEAN nuMPResMat ( leftv  res,
leftv  arg1,
leftv  arg2 
)

returns module representing the multipolynomial resultant matrix Arguments 2: ideal i, int k k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky k=1: use resultant matrix of Macaulay (k=0 is default)

Definition at line 4639 of file ipshell.cc.

4640{
4641 ideal gls = (ideal)(arg1->Data());
4642 int imtype= (int)(long)arg2->Data();
4643
4645
4646 // check input ideal ( = polynomial system )
4647 if ( mprIdealCheck( gls, arg1->Name(), mtype, true ) != mprOk )
4648 {
4649 return TRUE;
4650 }
4651
4652 uResultant *resMat= new uResultant( gls, mtype, false );
4653 if (resMat!=NULL)
4654 {
4655 res->rtyp = MODUL_CMD;
4656 res->data= (void*)resMat->accessResMat()->getMatrix();
4657 if (!errorreported) delete resMat;
4658 }
4659 return errorreported;
4660}
virtual ideal getMatrix()
Definition mpr_base.h:31
const char * Name()
Definition subexpr.h:120
Base class for solving 0-dim poly systems using u-resultant.
Definition mpr_base.h:63
resMatrixBase * accessResMat()
Definition mpr_base.h:78
VAR short errorreported
Definition feFopen.cc:23
@ MODUL_CMD
Definition grammar.cc:288
@ mprOk
Definition mpr_base.h:98
uResultant::resMatType determineMType(int imtype)
mprState mprIdealCheck(const ideal theIdeal, const char *name, uResultant::resMatType mtype, BOOLEAN rmatrix=false)

◆ nuUResSolve()

BOOLEAN nuUResSolve ( leftv  res,
leftv  args 
)

solve a multipolynomial system using the u-resultant Input ideal must be 0-dimensional and (currRing->N) == IDELEMS(ideal).

Resultant method can be MPR_DENSE, which uses Macaulay Resultant (good for dense homogeneous polynoms) or MPR_SPARSE, which uses Sparse Resultant (Gelfand, Kapranov, Zelevinsky). Arguments 4: ideal i, int k, int l, int m k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky k=1: use resultant matrix of Macaulay (k=0 is default) l>0: defines precision of fractional part if ground field is Q m=0,1,2: number of iterations for approximation of roots (default=2) Returns a list containing the roots of the system.

Definition at line 4906 of file ipshell.cc.

4907{
4908 leftv v= args;
4909
4910 ideal gls;
4911 int imtype;
4912 int howclean;
4913
4914 // get ideal
4915 if ( v->Typ() != IDEAL_CMD )
4916 return TRUE;
4917 else gls= (ideal)(v->Data());
4918 v= v->next;
4919
4920 // get resultant matrix type to use (0,1)
4921 if ( v->Typ() != INT_CMD )
4922 return TRUE;
4923 else imtype= (int)(long)v->Data();
4924 v= v->next;
4925
4926 if (imtype==0)
4927 {
4928 ideal test_id=idInit(1,1);
4929 int j;
4930 for(j=IDELEMS(gls)-1;j>=0;j--)
4931 {
4932 if (gls->m[j]!=NULL)
4933 {
4934 test_id->m[0]=gls->m[j];
4936 if (dummy_w!=NULL)
4937 {
4938 WerrorS("Newton polytope not of expected dimension");
4939 delete dummy_w;
4940 return TRUE;
4941 }
4942 }
4943 }
4944 }
4945
4946 // get and set precision in digits ( > 0 )
4947 if ( v->Typ() != INT_CMD )
4948 return TRUE;
4949 else if ( !(rField_is_R(currRing) || rField_is_long_R(currRing) || \
4951 {
4952 unsigned long int ii=(unsigned long int)v->Data();
4954 }
4955 v= v->next;
4956
4957 // get interpolation steps (0,1,2)
4958 if ( v->Typ() != INT_CMD )
4959 return TRUE;
4960 else howclean= (int)(long)v->Data();
4961
4963 int i,count;
4965 number smv= NULL;
4967
4968 //emptylist= (lists)omAlloc( sizeof(slists) );
4969 //emptylist->Init( 0 );
4970
4971 //res->rtyp = LIST_CMD;
4972 //res->data= (void *)emptylist;
4973
4974 // check input ideal ( = polynomial system )
4975 if ( mprIdealCheck( gls, args->Name(), mtype ) != mprOk )
4976 {
4977 return TRUE;
4978 }
4979
4980 uResultant * ures;
4984
4985 // main task 1: setup of resultant matrix
4986 ures= new uResultant( gls, mtype );
4987 if ( ures->accessResMat()->initState() != resMatrixBase::ready )
4988 {
4989 WerrorS("Error occurred during matrix setup!");
4990 return TRUE;
4991 }
4992
4993 // if dense resultant, check if minor nonsingular
4995 {
4996 smv= ures->accessResMat()->getSubDet();
4997#ifdef mprDEBUG_PROT
4998 PrintS("// Determinant of submatrix: ");nPrint(smv);PrintLn();
4999#endif
5000 if ( nIsZero(smv) )
5001 {
5002 WerrorS("Unsuitable input ideal: Minor of resultant matrix is singular!");
5003 return TRUE;
5004 }
5005 }
5006
5007 // main task 2: Interpolate specialized resultant polynomials
5008 if ( interpolate_det )
5009 iproots= ures->interpolateDenseSP( false, smv );
5010 else
5011 iproots= ures->specializeInU( false, smv );
5012
5013 // main task 3: Interpolate specialized resultant polynomials
5014 if ( interpolate_det )
5015 muiproots= ures->interpolateDenseSP( true, smv );
5016 else
5017 muiproots= ures->specializeInU( true, smv );
5018
5019#ifdef mprDEBUG_PROT
5020 int c= iproots[0]->getAnzElems();
5021 for (i=0; i < c; i++) pWrite(iproots[i]->getPoly());
5022 c= muiproots[0]->getAnzElems();
5023 for (i=0; i < c; i++) pWrite(muiproots[i]->getPoly());
5024#endif
5025
5026 // main task 4: Compute roots of specialized polys and match them up
5027 arranger= new rootArranger( iproots, muiproots, howclean );
5028 arranger->solve_all();
5029
5030 // get list of roots
5031 if ( arranger->success() )
5032 {
5033 arranger->arrange();
5035 }
5036 else
5037 {
5038 WerrorS("Solver was unable to find any roots!");
5039 return TRUE;
5040 }
5041
5042 // free everything
5043 count= iproots[0]->getAnzElems();
5044 for (i=0; i < count; i++) delete iproots[i];
5045 omFreeSize( (ADDRESS) iproots, count * sizeof(rootContainer*) );
5046 count= muiproots[0]->getAnzElems();
5047 for (i=0; i < count; i++) delete muiproots[i];
5049
5050 delete ures;
5051 delete arranger;
5052 if (smv!=NULL) nDelete( &smv );
5053
5054 res->data= (void *)listofroots;
5055
5056 //emptylist->Clean();
5057 // omFreeSize( (ADDRESS) emptylist, sizeof(slists) );
5058
5059 return FALSE;
5060}
int BOOLEAN
Definition auxiliary.h:87
@ denseResMat
Definition mpr_base.h:65
@ IDEAL_CMD
Definition grammar.cc:285
lists listOfRoots(rootArranger *self, const unsigned int oprec)
Definition ipshell.cc:5063
#define nDelete(n)
Definition numbers.h:16
#define nIsZero(n)
Definition numbers.h:19
#define omFreeSize(addr, size)
void pWrite(poly p)
Definition polys.h:308
int status int void size_t count
Definition si_signals.h:69
ideal idInit(int idsize, int rank)
initialise an ideal / module
intvec * id_QHomWeight(ideal id, const ring r)
#define IDELEMS(i)

◆ nuVanderSys()

BOOLEAN nuVanderSys ( leftv  res,
leftv  arg1,
leftv  arg2,
leftv  arg3 
)

COMPUTE: polynomial p with values given by v at points p1,..,pN derived from p; more precisely: consider p as point in K^n and v as N elements in K, let p1,..,pN be the points in K^n obtained by evaluating all monomials of degree 0,1,...,N at p in lexicographical order, then the procedure computes the polynomial f satisfying f(pi) = v[i] RETURN: polynomial f of degree d.

Definition at line 4805 of file ipshell.cc.

4806{
4807 int i;
4808 ideal p,w;
4809 p= (ideal)arg1->Data();
4810 w= (ideal)arg2->Data();
4811
4812 // w[0] = f(p^0)
4813 // w[1] = f(p^1)
4814 // ...
4815 // p can be a vector of numbers (multivariate polynom)
4816 // or one number (univariate polynom)
4817 // tdg = deg(f)
4818
4819 int n= IDELEMS( p );
4820 int m= IDELEMS( w );
4821 int tdg= (int)(long)arg3->Data();
4822
4823 res->data= (void*)NULL;
4824
4825 // check the input
4826 if ( tdg < 1 )
4827 {
4828 WerrorS("Last input parameter must be > 0!");
4829 return TRUE;
4830 }
4831 if ( n != rVar(currRing) )
4832 {
4833 Werror("Size of first input ideal must be equal to %d!",rVar(currRing));
4834 return TRUE;
4835 }
4836 if ( m != (int)pow((double)tdg+1,(double)n) )
4837 {
4838 Werror("Size of second input ideal must be equal to %d!",
4839 (int)pow((double)tdg+1,(double)n));
4840 return TRUE;
4841 }
4842 if ( !(rField_is_Q(currRing) /* ||
4843 rField_is_R() || rField_is_long_R() ||
4844 rField_is_long_C()*/ ) )
4845 {
4846 WerrorS("Ground field not implemented!");
4847 return TRUE;
4848 }
4849
4850 number tmp;
4851 number *pevpoint= (number *)omAlloc( n * sizeof( number ) );
4852 for ( i= 0; i < n; i++ )
4853 {
4854 pevpoint[i]=nInit(0);
4855 if ( (p->m)[i] )
4856 {
4857 tmp = pGetCoeff( (p->m)[i] );
4858 if ( nIsZero(tmp) || nIsOne(tmp) || nIsMOne(tmp) )
4859 {
4860 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4861 WerrorS("Elements of first input ideal must not be equal to -1, 0, 1!");
4862 return TRUE;
4863 }
4864 } else tmp= NULL;
4865 if ( !nIsZero(tmp) )
4866 {
4867 if ( !pIsConstant((p->m)[i]))
4868 {
4869 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4870 WerrorS("Elements of first input ideal must be numbers!");
4871 return TRUE;
4872 }
4873 pevpoint[i]= nCopy( tmp );
4874 }
4875 }
4876
4877 number *wresults= (number *)omAlloc( m * sizeof( number ) );
4878 for ( i= 0; i < m; i++ )
4879 {
4880 wresults[i]= nInit(0);
4881 if ( (w->m)[i] && !nIsZero(pGetCoeff((w->m)[i])) )
4882 {
4883 if ( !pIsConstant((w->m)[i]))
4884 {
4885 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4886 omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4887 WerrorS("Elements of second input ideal must be numbers!");
4888 return TRUE;
4889 }
4890 wresults[i]= nCopy(pGetCoeff((w->m)[i]));
4891 }
4892 }
4893
4894 vandermonde vm( m, n, tdg, pevpoint, FALSE );
4895 number *ncpoly= vm.interpolateDense( wresults );
4896 // do not free ncpoly[]!!
4897 poly rpoly= vm.numvec2poly( ncpoly );
4898
4899 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4900 omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4901
4902 res->data= (void*)rpoly;
4903 return FALSE;
4904}
Rational pow(const Rational &a, int e)
Definition GMPrat.cc:411
int p
Definition cfModGcd.cc:4086
vandermonde system solver for interpolating polynomials from their values
Definition mpr_numeric.h:29
const CanonicalForm & w
Definition facAbsFact.cc:51
#define nIsMOne(n)
Definition numbers.h:26
#define nIsOne(n)
Definition numbers.h:25
void Werror(const char *fmt,...)
Definition reporter.cc:189