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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 4565 of file ipshell.cc.

4566{
4567 res->data= (void*)loNewtonPolytope( (ideal)arg1->Data() );
4568 return FALSE;
4569}
#define FALSE
Definition auxiliary.h:96
void * Data()
Definition subexpr.cc:1173
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 4571 of file ipshell.cc.

4572{
4573 if ( !(rField_is_long_R(currRing)) )
4574 {
4575 WerrorS("Ground field not implemented!");
4576 return TRUE;
4577 }
4578
4579 simplex * LP;
4580 matrix m;
4581
4582 leftv v= args;
4583 if ( v->Typ() != MATRIX_CMD ) // 1: matrix
4584 return TRUE;
4585 else
4586 m= (matrix)(v->CopyD());
4587
4588 LP = new simplex(MATROWS(m),MATCOLS(m));
4589 LP->mapFromMatrix(m);
4590
4591 v= v->next;
4592 if ( v->Typ() != INT_CMD ) // 2: m = number of constraints
4593 return TRUE;
4594 else
4595 LP->m= (int)(long)(v->Data());
4596
4597 v= v->next;
4598 if ( v->Typ() != INT_CMD ) // 3: n = number of variables
4599 return TRUE;
4600 else
4601 LP->n= (int)(long)(v->Data());
4602
4603 v= v->next;
4604 if ( v->Typ() != INT_CMD ) // 4: m1 = number of <= constraints
4605 return TRUE;
4606 else
4607 LP->m1= (int)(long)(v->Data());
4608
4609 v= v->next;
4610 if ( v->Typ() != INT_CMD ) // 5: m2 = number of >= constraints
4611 return TRUE;
4612 else
4613 LP->m2= (int)(long)(v->Data());
4614
4615 v= v->next;
4616 if ( v->Typ() != INT_CMD ) // 6: m3 = number of == constraints
4617 return TRUE;
4618 else
4619 LP->m3= (int)(long)(v->Data());
4620
4621#ifdef mprDEBUG_PROT
4622 Print("m (constraints) %d\n",LP->m);
4623 Print("n (columns) %d\n",LP->n);
4624 Print("m1 (<=) %d\n",LP->m1);
4625 Print("m2 (>=) %d\n",LP->m2);
4626 Print("m3 (==) %d\n",LP->m3);
4627#endif
4628
4629 LP->compute();
4630
4631 lists lres= (lists)omAlloc( sizeof(slists) );
4632 lres->Init( 6 );
4633
4634 lres->m[0].rtyp= MATRIX_CMD; // output matrix
4635 lres->m[0].data=(void*)LP->mapToMatrix(m);
4636
4637 lres->m[1].rtyp= INT_CMD; // found a solution?
4638 lres->m[1].data=(void*)(long)LP->icase;
4639
4640 lres->m[2].rtyp= INTVEC_CMD;
4641 lres->m[2].data=(void*)LP->posvToIV();
4642
4643 lres->m[3].rtyp= INTVEC_CMD;
4644 lres->m[3].data=(void*)LP->zrovToIV();
4645
4646 lres->m[4].rtyp= INT_CMD;
4647 lres->m[4].data=(void*)(long)LP->m;
4648
4649 lres->m[5].rtyp= INT_CMD;
4650 lres->m[5].data=(void*)(long)LP->n;
4651
4652 res->data= (void*)lres;
4653
4654 return FALSE;
4655}
#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:286
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 4680 of file ipshell.cc.

4681{
4682 poly gls;
4683 gls= (poly)(arg1->Data());
4684 int howclean= (int)(long)arg3->Data();
4685
4686 if ( gls == NULL || pIsConstant( gls ) )
4687 {
4688 WerrorS("Input polynomial is constant!");
4689 return TRUE;
4690 }
4691
4693 {
4694 int* r=Zp_roots(gls, currRing);
4695 lists rlist;
4696 rlist= (lists)omAlloc( sizeof(slists) );
4697 rlist->Init( r[0] );
4698 for(int i=r[0];i>0;i--)
4699 {
4700 rlist->m[i-1].data=n_Init(r[i],currRing->cf);
4701 rlist->m[i-1].rtyp=NUMBER_CMD;
4702 }
4703 omFree(r);
4704 res->data=rlist;
4705 res->rtyp= LIST_CMD;
4706 return FALSE;
4707 }
4708 if ( !(rField_is_R(currRing) ||
4712 {
4713 WerrorS("Ground field not implemented!");
4714 return TRUE;
4715 }
4716
4719 {
4720 unsigned long int ii = (unsigned long int)arg2->Data();
4722 }
4723
4724 int ldummy;
4725 int deg= currRing->pLDeg( gls, &ldummy, currRing );
4726 int i,vpos=0;
4727 poly piter;
4728 lists elist;
4729
4730 elist= (lists)omAlloc( sizeof(slists) );
4731 elist->Init( 0 );
4732
4733 if ( rVar(currRing) > 1 )
4734 {
4735 piter= gls;
4736 for ( i= 1; i <= rVar(currRing); i++ )
4737 if ( pGetExp( piter, i ) )
4738 {
4739 vpos= i;
4740 break;
4741 }
4742 while ( piter )
4743 {
4744 for ( i= 1; i <= rVar(currRing); i++ )
4745 if ( (vpos != i) && (pGetExp( piter, i ) != 0) )
4746 {
4747 WerrorS("The input polynomial must be univariate!");
4748 return TRUE;
4749 }
4750 pIter( piter );
4751 }
4752 }
4753
4754 rootContainer * roots= new rootContainer();
4755 number * pcoeffs= (number *)omAlloc( (deg+1) * sizeof( number ) );
4756 piter= gls;
4757 for ( i= deg; i >= 0; i-- )
4758 {
4759 if ( piter && pTotaldegree(piter) == i )
4760 {
4761 pcoeffs[i]= nCopy( pGetCoeff( piter ) );
4762 //nPrint( pcoeffs[i] );PrintS(" ");
4763 pIter( piter );
4764 }
4765 else
4766 {
4767 pcoeffs[i]= nInit(0);
4768 }
4769 }
4770
4771#ifdef mprDEBUG_PROT
4772 for (i=deg; i >= 0; i--)
4773 {
4774 nPrint( pcoeffs[i] );PrintS(" ");
4775 }
4776 PrintLn();
4777#endif
4778
4779 roots->fillContainer( pcoeffs, NULL, 1, deg, rootContainer::onepoly, 1 );
4780 roots->solver( howclean );
4781
4782 int elem= roots->getAnzRoots();
4783 char *dummy;
4784 int j;
4785
4786 lists rlist;
4787 rlist= (lists)omAlloc( sizeof(slists) );
4788 rlist->Init( elem );
4789
4791 {
4792 for ( j= 0; j < elem; j++ )
4793 {
4794 rlist->m[j].rtyp=NUMBER_CMD;
4795 rlist->m[j].data=(void *)nCopy((number)(roots->getRoot(j)));
4796 //rlist->m[j].data=(void *)(number)(roots->getRoot(j));
4797 }
4798 }
4799 else
4800 {
4801 for ( j= 0; j < elem; j++ )
4802 {
4803 dummy = complexToStr( (*roots)[j], gmp_output_digits, currRing->cf );
4804 rlist->m[j].rtyp=STRING_CMD;
4805 rlist->m[j].data=(void *)dummy;
4806 }
4807 }
4808
4809 elist->Clean();
4810 //omFreeSize( (ADDRESS) elist, sizeof(slists) );
4811
4812 // this is (via fillContainer) the same data as in root
4813 //for ( i= deg; i >= 0; i-- ) nDelete( &pcoeffs[i] );
4814 //omFreeSize( (ADDRESS) pcoeffs, (deg+1) * sizeof( number ) );
4815
4816 delete roots;
4817
4818 res->data= (void*)rlist;
4819
4820 return FALSE;
4821}
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:535
int j
Definition facHensel.cc:110
@ NUMBER_CMD
Definition grammar.cc:288
#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:185

◆ 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 4657 of file ipshell.cc.

4658{
4659 ideal gls = (ideal)(arg1->Data());
4660 int imtype= (int)(long)arg2->Data();
4661
4663
4664 // check input ideal ( = polynomial system )
4665 if ( mprIdealCheck( gls, arg1->Name(), mtype, true ) != mprOk )
4666 {
4667 return TRUE;
4668 }
4669
4670 uResultant *resMat= new uResultant( gls, mtype, false );
4671 if (resMat!=NULL)
4672 {
4673 res->rtyp = MODUL_CMD;
4674 res->data= (void*)resMat->accessResMat()->getMatrix();
4675 if (!errorreported) delete resMat;
4676 }
4677 return errorreported;
4678}
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:287
@ 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 4924 of file ipshell.cc.

4925{
4926 leftv v= args;
4927
4928 ideal gls;
4929 int imtype;
4930 int howclean;
4931
4932 // get ideal
4933 if ( v->Typ() != IDEAL_CMD )
4934 return TRUE;
4935 else gls= (ideal)(v->Data());
4936 v= v->next;
4937
4938 // get resultant matrix type to use (0,1)
4939 if ( v->Typ() != INT_CMD )
4940 return TRUE;
4941 else imtype= (int)(long)v->Data();
4942 v= v->next;
4943
4944 if (imtype==0)
4945 {
4946 ideal test_id=idInit(1,1);
4947 int j;
4948 for(j=IDELEMS(gls)-1;j>=0;j--)
4949 {
4950 if (gls->m[j]!=NULL)
4951 {
4952 test_id->m[0]=gls->m[j];
4954 if (dummy_w!=NULL)
4955 {
4956 WerrorS("Newton polytope not of expected dimension");
4957 delete dummy_w;
4958 return TRUE;
4959 }
4960 }
4961 }
4962 }
4963
4964 // get and set precision in digits ( > 0 )
4965 if ( v->Typ() != INT_CMD )
4966 return TRUE;
4967 else if ( !(rField_is_R(currRing) || rField_is_long_R(currRing) || \
4969 {
4970 unsigned long int ii=(unsigned long int)v->Data();
4972 }
4973 v= v->next;
4974
4975 // get interpolation steps (0,1,2)
4976 if ( v->Typ() != INT_CMD )
4977 return TRUE;
4978 else howclean= (int)(long)v->Data();
4979
4981 int i,count;
4983 number smv= NULL;
4985
4986 //emptylist= (lists)omAlloc( sizeof(slists) );
4987 //emptylist->Init( 0 );
4988
4989 //res->rtyp = LIST_CMD;
4990 //res->data= (void *)emptylist;
4991
4992 // check input ideal ( = polynomial system )
4993 if ( mprIdealCheck( gls, args->Name(), mtype ) != mprOk )
4994 {
4995 return TRUE;
4996 }
4997
4998 uResultant * ures;
5002
5003 // main task 1: setup of resultant matrix
5004 ures= new uResultant( gls, mtype );
5005 if ( ures->accessResMat()->initState() != resMatrixBase::ready )
5006 {
5007 WerrorS("Error occurred during matrix setup!");
5008 return TRUE;
5009 }
5010
5011 // if dense resultant, check if minor nonsingular
5013 {
5014 smv= ures->accessResMat()->getSubDet();
5015#ifdef mprDEBUG_PROT
5016 PrintS("// Determinant of submatrix: ");nPrint(smv);PrintLn();
5017#endif
5018 if ( nIsZero(smv) )
5019 {
5020 WerrorS("Unsuitable input ideal: Minor of resultant matrix is singular!");
5021 return TRUE;
5022 }
5023 }
5024
5025 // main task 2: Interpolate specialized resultant polynomials
5026 if ( interpolate_det )
5027 iproots= ures->interpolateDenseSP( false, smv );
5028 else
5029 iproots= ures->specializeInU( false, smv );
5030
5031 // main task 3: Interpolate specialized resultant polynomials
5032 if ( interpolate_det )
5033 muiproots= ures->interpolateDenseSP( true, smv );
5034 else
5035 muiproots= ures->specializeInU( true, smv );
5036
5037#ifdef mprDEBUG_PROT
5038 int c= iproots[0]->getAnzElems();
5039 for (i=0; i < c; i++) pWrite(iproots[i]->getPoly());
5040 c= muiproots[0]->getAnzElems();
5041 for (i=0; i < c; i++) pWrite(muiproots[i]->getPoly());
5042#endif
5043
5044 // main task 4: Compute roots of specialized polys and match them up
5045 arranger= new rootArranger( iproots, muiproots, howclean );
5046 arranger->solve_all();
5047
5048 // get list of roots
5049 if ( arranger->success() )
5050 {
5051 arranger->arrange();
5053 }
5054 else
5055 {
5056 WerrorS("Solver was unable to find any roots!");
5057 return TRUE;
5058 }
5059
5060 // free everything
5061 count= iproots[0]->getAnzElems();
5062 for (i=0; i < count; i++) delete iproots[i];
5063 omFreeSize( (ADDRESS) iproots, count * sizeof(rootContainer*) );
5064 count= muiproots[0]->getAnzElems();
5065 for (i=0; i < count; i++) delete muiproots[i];
5067
5068 delete ures;
5069 delete arranger;
5070 if (smv!=NULL) nDelete( &smv );
5071
5072 res->data= (void *)listofroots;
5073
5074 //emptylist->Clean();
5075 // omFreeSize( (ADDRESS) emptylist, sizeof(slists) );
5076
5077 return FALSE;
5078}
int BOOLEAN
Definition auxiliary.h:87
@ denseResMat
Definition mpr_base.h:65
@ IDEAL_CMD
Definition grammar.cc:284
lists listOfRoots(rootArranger *self, const unsigned int oprec)
Definition ipshell.cc:5081
#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:59
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 4823 of file ipshell.cc.

4824{
4825 int i;
4826 ideal p,w;
4827 p= (ideal)arg1->Data();
4828 w= (ideal)arg2->Data();
4829
4830 // w[0] = f(p^0)
4831 // w[1] = f(p^1)
4832 // ...
4833 // p can be a vector of numbers (multivariate polynom)
4834 // or one number (univariate polynom)
4835 // tdg = deg(f)
4836
4837 int n= IDELEMS( p );
4838 int m= IDELEMS( w );
4839 int tdg= (int)(long)arg3->Data();
4840
4841 res->data= (void*)NULL;
4842
4843 // check the input
4844 if ( tdg < 1 )
4845 {
4846 WerrorS("Last input parameter must be > 0!");
4847 return TRUE;
4848 }
4849 if ( n != rVar(currRing) )
4850 {
4851 Werror("Size of first input ideal must be equal to %d!",rVar(currRing));
4852 return TRUE;
4853 }
4854 if ( m != (int)pow((double)tdg+1,(double)n) )
4855 {
4856 Werror("Size of second input ideal must be equal to %d!",
4857 (int)pow((double)tdg+1,(double)n));
4858 return TRUE;
4859 }
4860 if ( !(rField_is_Q(currRing) /* ||
4861 rField_is_R() || rField_is_long_R() ||
4862 rField_is_long_C()*/ ) )
4863 {
4864 WerrorS("Ground field not implemented!");
4865 return TRUE;
4866 }
4867
4868 number tmp;
4869 number *pevpoint= (number *)omAlloc( n * sizeof( number ) );
4870 for ( i= 0; i < n; i++ )
4871 {
4872 pevpoint[i]=nInit(0);
4873 if ( (p->m)[i] )
4874 {
4875 tmp = pGetCoeff( (p->m)[i] );
4876 if ( nIsZero(tmp) || nIsOne(tmp) || nIsMOne(tmp) )
4877 {
4878 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4879 WerrorS("Elements of first input ideal must not be equal to -1, 0, 1!");
4880 return TRUE;
4881 }
4882 } else tmp= NULL;
4883 if ( !nIsZero(tmp) )
4884 {
4885 if ( !pIsConstant((p->m)[i]))
4886 {
4887 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4888 WerrorS("Elements of first input ideal must be numbers!");
4889 return TRUE;
4890 }
4891 pevpoint[i]= nCopy( tmp );
4892 }
4893 }
4894
4895 number *wresults= (number *)omAlloc( m * sizeof( number ) );
4896 for ( i= 0; i < m; i++ )
4897 {
4898 wresults[i]= nInit(0);
4899 if ( (w->m)[i] && !nIsZero(pGetCoeff((w->m)[i])) )
4900 {
4901 if ( !pIsConstant((w->m)[i]))
4902 {
4903 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4904 omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4905 WerrorS("Elements of second input ideal must be numbers!");
4906 return TRUE;
4907 }
4908 wresults[i]= nCopy(pGetCoeff((w->m)[i]));
4909 }
4910 }
4911
4912 vandermonde vm( m, n, tdg, pevpoint, FALSE );
4913 number *ncpoly= vm.interpolateDense( wresults );
4914 // do not free ncpoly[]!!
4915 poly rpoly= vm.numvec2poly( ncpoly );
4916
4917 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4918 omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4919
4920 res->data= (void*)rpoly;
4921 return FALSE;
4922}
Rational pow(const Rational &a, int e)
Definition GMPrat.cc:411
int p
Definition cfModGcd.cc:4079
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