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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 4558 of file ipshell.cc.

4559{
4560 res->data= (void*)loNewtonPolytope( (ideal)arg1->Data() );
4561 return FALSE;
4562}
#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 4564 of file ipshell.cc.

4565{
4566 if ( !(rField_is_long_R(currRing)) )
4567 {
4568 WerrorS("Ground field not implemented!");
4569 return TRUE;
4570 }
4571
4572 simplex * LP;
4573 matrix m;
4574
4575 leftv v= args;
4576 if ( v->Typ() != MATRIX_CMD ) // 1: matrix
4577 return TRUE;
4578 else
4579 m= (matrix)(v->CopyD());
4580
4581 LP = new simplex(MATROWS(m),MATCOLS(m));
4582 LP->mapFromMatrix(m);
4583
4584 v= v->next;
4585 if ( v->Typ() != INT_CMD ) // 2: m = number of constraints
4586 return TRUE;
4587 else
4588 LP->m= (int)(long)(v->Data());
4589
4590 v= v->next;
4591 if ( v->Typ() != INT_CMD ) // 3: n = number of variables
4592 return TRUE;
4593 else
4594 LP->n= (int)(long)(v->Data());
4595
4596 v= v->next;
4597 if ( v->Typ() != INT_CMD ) // 4: m1 = number of <= constraints
4598 return TRUE;
4599 else
4600 LP->m1= (int)(long)(v->Data());
4601
4602 v= v->next;
4603 if ( v->Typ() != INT_CMD ) // 5: m2 = number of >= constraints
4604 return TRUE;
4605 else
4606 LP->m2= (int)(long)(v->Data());
4607
4608 v= v->next;
4609 if ( v->Typ() != INT_CMD ) // 6: m3 = number of == constraints
4610 return TRUE;
4611 else
4612 LP->m3= (int)(long)(v->Data());
4613
4614#ifdef mprDEBUG_PROT
4615 Print("m (constraints) %d\n",LP->m);
4616 Print("n (columns) %d\n",LP->n);
4617 Print("m1 (<=) %d\n",LP->m1);
4618 Print("m2 (>=) %d\n",LP->m2);
4619 Print("m3 (==) %d\n",LP->m3);
4620#endif
4621
4622 LP->compute();
4623
4624 lists lres= (lists)omAlloc( sizeof(slists) );
4625 lres->Init( 6 );
4626
4627 lres->m[0].rtyp= MATRIX_CMD; // output matrix
4628 lres->m[0].data=(void*)LP->mapToMatrix(m);
4629
4630 lres->m[1].rtyp= INT_CMD; // found a solution?
4631 lres->m[1].data=(void*)(long)LP->icase;
4632
4633 lres->m[2].rtyp= INTVEC_CMD;
4634 lres->m[2].data=(void*)LP->posvToIV();
4635
4636 lres->m[3].rtyp= INTVEC_CMD;
4637 lres->m[3].data=(void*)LP->zrovToIV();
4638
4639 lres->m[4].rtyp= INT_CMD;
4640 lres->m[4].data=(void*)(long)LP->m;
4641
4642 lres->m[5].rtyp= INT_CMD;
4643 lres->m[5].data=(void*)(long)LP->n;
4644
4645 res->data= (void*)lres;
4646
4647 return FALSE;
4648}
#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 4673 of file ipshell.cc.

4674{
4675 poly gls;
4676 gls= (poly)(arg1->Data());
4677 int howclean= (int)(long)arg3->Data();
4678
4679 if ( gls == NULL || pIsConstant( gls ) )
4680 {
4681 WerrorS("Input polynomial is constant!");
4682 return TRUE;
4683 }
4684
4686 {
4687 int* r=Zp_roots(gls, currRing);
4688 lists rlist;
4689 rlist= (lists)omAlloc( sizeof(slists) );
4690 rlist->Init( r[0] );
4691 for(int i=r[0];i>0;i--)
4692 {
4693 rlist->m[i-1].data=n_Init(r[i],currRing->cf);
4694 rlist->m[i-1].rtyp=NUMBER_CMD;
4695 }
4696 omFree(r);
4697 res->data=rlist;
4698 res->rtyp= LIST_CMD;
4699 return FALSE;
4700 }
4701 if ( !(rField_is_R(currRing) ||
4705 {
4706 WerrorS("Ground field not implemented!");
4707 return TRUE;
4708 }
4709
4712 {
4713 unsigned long int ii = (unsigned long int)arg2->Data();
4715 }
4716
4717 int ldummy;
4718 int deg= currRing->pLDeg( gls, &ldummy, currRing );
4719 int i,vpos=0;
4720 poly piter;
4721 lists elist;
4722
4723 elist= (lists)omAlloc( sizeof(slists) );
4724 elist->Init( 0 );
4725
4726 if ( rVar(currRing) > 1 )
4727 {
4728 piter= gls;
4729 for ( i= 1; i <= rVar(currRing); i++ )
4730 if ( pGetExp( piter, i ) )
4731 {
4732 vpos= i;
4733 break;
4734 }
4735 while ( piter )
4736 {
4737 for ( i= 1; i <= rVar(currRing); i++ )
4738 if ( (vpos != i) && (pGetExp( piter, i ) != 0) )
4739 {
4740 WerrorS("The input polynomial must be univariate!");
4741 return TRUE;
4742 }
4743 pIter( piter );
4744 }
4745 }
4746
4747 rootContainer * roots= new rootContainer();
4748 number * pcoeffs= (number *)omAlloc( (deg+1) * sizeof( number ) );
4749 piter= gls;
4750 for ( i= deg; i >= 0; i-- )
4751 {
4752 if ( piter && pTotaldegree(piter) == i )
4753 {
4754 pcoeffs[i]= nCopy( pGetCoeff( piter ) );
4755 //nPrint( pcoeffs[i] );PrintS(" ");
4756 pIter( piter );
4757 }
4758 else
4759 {
4760 pcoeffs[i]= nInit(0);
4761 }
4762 }
4763
4764#ifdef mprDEBUG_PROT
4765 for (i=deg; i >= 0; i--)
4766 {
4767 nPrint( pcoeffs[i] );PrintS(" ");
4768 }
4769 PrintLn();
4770#endif
4771
4772 roots->fillContainer( pcoeffs, NULL, 1, deg, rootContainer::onepoly, 1 );
4773 roots->solver( howclean );
4774
4775 int elem= roots->getAnzRoots();
4776 char *dummy;
4777 int j;
4778
4779 lists rlist;
4780 rlist= (lists)omAlloc( sizeof(slists) );
4781 rlist->Init( elem );
4782
4784 {
4785 for ( j= 0; j < elem; j++ )
4786 {
4787 rlist->m[j].rtyp=NUMBER_CMD;
4788 rlist->m[j].data=(void *)nCopy((number)(roots->getRoot(j)));
4789 //rlist->m[j].data=(void *)(number)(roots->getRoot(j));
4790 }
4791 }
4792 else
4793 {
4794 for ( j= 0; j < elem; j++ )
4795 {
4796 dummy = complexToStr( (*roots)[j], gmp_output_digits, currRing->cf );
4797 rlist->m[j].rtyp=STRING_CMD;
4798 rlist->m[j].data=(void *)dummy;
4799 }
4800 }
4801
4802 elist->Clean();
4803 //omFreeSize( (ADDRESS) elist, sizeof(slists) );
4804
4805 // this is (via fillContainer) the same data as in root
4806 //for ( i= deg; i >= 0; i-- ) nDelete( &pcoeffs[i] );
4807 //omFreeSize( (ADDRESS) pcoeffs, (deg+1) * sizeof( number ) );
4808
4809 delete roots;
4810
4811 res->data= (void*)rlist;
4812
4813 return FALSE;
4814}
int i
Definition cfEzgcd.cc:132
int * Zp_roots(poly p, const ring r)
Definition clapsing.cc:2188
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 initalized 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 4650 of file ipshell.cc.

4651{
4652 ideal gls = (ideal)(arg1->Data());
4653 int imtype= (int)(long)arg2->Data();
4654
4656
4657 // check input ideal ( = polynomial system )
4658 if ( mprIdealCheck( gls, arg1->Name(), mtype, true ) != mprOk )
4659 {
4660 return TRUE;
4661 }
4662
4663 uResultant *resMat= new uResultant( gls, mtype, false );
4664 if (resMat!=NULL)
4665 {
4666 res->rtyp = MODUL_CMD;
4667 res->data= (void*)resMat->accessResMat()->getMatrix();
4668 if (!errorreported) delete resMat;
4669 }
4670 return errorreported;
4671}
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 4917 of file ipshell.cc.

4918{
4919 leftv v= args;
4920
4921 ideal gls;
4922 int imtype;
4923 int howclean;
4924
4925 // get ideal
4926 if ( v->Typ() != IDEAL_CMD )
4927 return TRUE;
4928 else gls= (ideal)(v->Data());
4929 v= v->next;
4930
4931 // get resultant matrix type to use (0,1)
4932 if ( v->Typ() != INT_CMD )
4933 return TRUE;
4934 else imtype= (int)(long)v->Data();
4935 v= v->next;
4936
4937 if (imtype==0)
4938 {
4939 ideal test_id=idInit(1,1);
4940 int j;
4941 for(j=IDELEMS(gls)-1;j>=0;j--)
4942 {
4943 if (gls->m[j]!=NULL)
4944 {
4945 test_id->m[0]=gls->m[j];
4947 if (dummy_w!=NULL)
4948 {
4949 WerrorS("Newton polytope not of expected dimension");
4950 delete dummy_w;
4951 return TRUE;
4952 }
4953 }
4954 }
4955 }
4956
4957 // get and set precision in digits ( > 0 )
4958 if ( v->Typ() != INT_CMD )
4959 return TRUE;
4960 else if ( !(rField_is_R(currRing) || rField_is_long_R(currRing) || \
4962 {
4963 unsigned long int ii=(unsigned long int)v->Data();
4965 }
4966 v= v->next;
4967
4968 // get interpolation steps (0,1,2)
4969 if ( v->Typ() != INT_CMD )
4970 return TRUE;
4971 else howclean= (int)(long)v->Data();
4972
4974 int i,count;
4976 number smv= NULL;
4978
4979 //emptylist= (lists)omAlloc( sizeof(slists) );
4980 //emptylist->Init( 0 );
4981
4982 //res->rtyp = LIST_CMD;
4983 //res->data= (void *)emptylist;
4984
4985 // check input ideal ( = polynomial system )
4986 if ( mprIdealCheck( gls, args->Name(), mtype ) != mprOk )
4987 {
4988 return TRUE;
4989 }
4990
4991 uResultant * ures;
4995
4996 // main task 1: setup of resultant matrix
4997 ures= new uResultant( gls, mtype );
4998 if ( ures->accessResMat()->initState() != resMatrixBase::ready )
4999 {
5000 WerrorS("Error occurred during matrix setup!");
5001 return TRUE;
5002 }
5003
5004 // if dense resultant, check if minor nonsingular
5006 {
5007 smv= ures->accessResMat()->getSubDet();
5008#ifdef mprDEBUG_PROT
5009 PrintS("// Determinant of submatrix: ");nPrint(smv);PrintLn();
5010#endif
5011 if ( nIsZero(smv) )
5012 {
5013 WerrorS("Unsuitable input ideal: Minor of resultant matrix is singular!");
5014 return TRUE;
5015 }
5016 }
5017
5018 // main task 2: Interpolate specialized resultant polynomials
5019 if ( interpolate_det )
5020 iproots= ures->interpolateDenseSP( false, smv );
5021 else
5022 iproots= ures->specializeInU( false, smv );
5023
5024 // main task 3: Interpolate specialized resultant polynomials
5025 if ( interpolate_det )
5026 muiproots= ures->interpolateDenseSP( true, smv );
5027 else
5028 muiproots= ures->specializeInU( true, smv );
5029
5030#ifdef mprDEBUG_PROT
5031 int c= iproots[0]->getAnzElems();
5032 for (i=0; i < c; i++) pWrite(iproots[i]->getPoly());
5033 c= muiproots[0]->getAnzElems();
5034 for (i=0; i < c; i++) pWrite(muiproots[i]->getPoly());
5035#endif
5036
5037 // main task 4: Compute roots of specialized polys and match them up
5038 arranger= new rootArranger( iproots, muiproots, howclean );
5039 arranger->solve_all();
5040
5041 // get list of roots
5042 if ( arranger->success() )
5043 {
5044 arranger->arrange();
5046 }
5047 else
5048 {
5049 WerrorS("Solver was unable to find any roots!");
5050 return TRUE;
5051 }
5052
5053 // free everything
5054 count= iproots[0]->getAnzElems();
5055 for (i=0; i < count; i++) delete iproots[i];
5056 omFreeSize( (ADDRESS) iproots, count * sizeof(rootContainer*) );
5057 count= muiproots[0]->getAnzElems();
5058 for (i=0; i < count; i++) delete muiproots[i];
5060
5061 delete ures;
5062 delete arranger;
5063 if (smv!=NULL) nDelete( &smv );
5064
5065 res->data= (void *)listofroots;
5066
5067 //emptylist->Clean();
5068 // omFreeSize( (ADDRESS) emptylist, sizeof(slists) );
5069
5070 return FALSE;
5071}
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:5074
#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 4816 of file ipshell.cc.

4817{
4818 int i;
4819 ideal p,w;
4820 p= (ideal)arg1->Data();
4821 w= (ideal)arg2->Data();
4822
4823 // w[0] = f(p^0)
4824 // w[1] = f(p^1)
4825 // ...
4826 // p can be a vector of numbers (multivariate polynom)
4827 // or one number (univariate polynom)
4828 // tdg = deg(f)
4829
4830 int n= IDELEMS( p );
4831 int m= IDELEMS( w );
4832 int tdg= (int)(long)arg3->Data();
4833
4834 res->data= (void*)NULL;
4835
4836 // check the input
4837 if ( tdg < 1 )
4838 {
4839 WerrorS("Last input parameter must be > 0!");
4840 return TRUE;
4841 }
4842 if ( n != rVar(currRing) )
4843 {
4844 Werror("Size of first input ideal must be equal to %d!",rVar(currRing));
4845 return TRUE;
4846 }
4847 if ( m != (int)pow((double)tdg+1,(double)n) )
4848 {
4849 Werror("Size of second input ideal must be equal to %d!",
4850 (int)pow((double)tdg+1,(double)n));
4851 return TRUE;
4852 }
4853 if ( !(rField_is_Q(currRing) /* ||
4854 rField_is_R() || rField_is_long_R() ||
4855 rField_is_long_C()*/ ) )
4856 {
4857 WerrorS("Ground field not implemented!");
4858 return TRUE;
4859 }
4860
4861 number tmp;
4862 number *pevpoint= (number *)omAlloc( n * sizeof( number ) );
4863 for ( i= 0; i < n; i++ )
4864 {
4865 pevpoint[i]=nInit(0);
4866 if ( (p->m)[i] )
4867 {
4868 tmp = pGetCoeff( (p->m)[i] );
4869 if ( nIsZero(tmp) || nIsOne(tmp) || nIsMOne(tmp) )
4870 {
4871 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4872 WerrorS("Elements of first input ideal must not be equal to -1, 0, 1!");
4873 return TRUE;
4874 }
4875 } else tmp= NULL;
4876 if ( !nIsZero(tmp) )
4877 {
4878 if ( !pIsConstant((p->m)[i]))
4879 {
4880 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4881 WerrorS("Elements of first input ideal must be numbers!");
4882 return TRUE;
4883 }
4884 pevpoint[i]= nCopy( tmp );
4885 }
4886 }
4887
4888 number *wresults= (number *)omAlloc( m * sizeof( number ) );
4889 for ( i= 0; i < m; i++ )
4890 {
4891 wresults[i]= nInit(0);
4892 if ( (w->m)[i] && !nIsZero(pGetCoeff((w->m)[i])) )
4893 {
4894 if ( !pIsConstant((w->m)[i]))
4895 {
4896 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4897 omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4898 WerrorS("Elements of second input ideal must be numbers!");
4899 return TRUE;
4900 }
4901 wresults[i]= nCopy(pGetCoeff((w->m)[i]));
4902 }
4903 }
4904
4905 vandermonde vm( m, n, tdg, pevpoint, FALSE );
4906 number *ncpoly= vm.interpolateDense( wresults );
4907 // do not free ncpoly[]!!
4908 poly rpoly= vm.numvec2poly( ncpoly );
4909
4910 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4911 omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4912
4913 res->data= (void*)rpoly;
4914 return FALSE;
4915}
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