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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 4549 of file ipshell.cc.

4550{
4551 res->data= (void*)loNewtonPolytope( (ideal)arg1->Data() );
4552 return FALSE;
4553}
#define FALSE
Definition auxiliary.h:97
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 4555 of file ipshell.cc.

4556{
4557 if ( !(rField_is_long_R(currRing)) )
4558 {
4559 WerrorS("Ground field not implemented!");
4560 return TRUE;
4561 }
4562
4563 simplex * LP;
4564 matrix m;
4565
4566 leftv v= args;
4567 if ( v->Typ() != MATRIX_CMD ) // 1: matrix
4568 return TRUE;
4569 else
4570 m= (matrix)(v->CopyD());
4571
4572 LP = new simplex(MATROWS(m),MATCOLS(m));
4573 LP->mapFromMatrix(m);
4574
4575 v= v->next;
4576 if ( v->Typ() != INT_CMD ) // 2: m = number of constraints
4577 return TRUE;
4578 else
4579 LP->m= (int)(long)(v->Data());
4580
4581 v= v->next;
4582 if ( v->Typ() != INT_CMD ) // 3: n = number of variables
4583 return TRUE;
4584 else
4585 LP->n= (int)(long)(v->Data());
4586
4587 v= v->next;
4588 if ( v->Typ() != INT_CMD ) // 4: m1 = number of <= constraints
4589 return TRUE;
4590 else
4591 LP->m1= (int)(long)(v->Data());
4592
4593 v= v->next;
4594 if ( v->Typ() != INT_CMD ) // 5: m2 = number of >= constraints
4595 return TRUE;
4596 else
4597 LP->m2= (int)(long)(v->Data());
4598
4599 v= v->next;
4600 if ( v->Typ() != INT_CMD ) // 6: m3 = number of == constraints
4601 return TRUE;
4602 else
4603 LP->m3= (int)(long)(v->Data());
4604
4605#ifdef mprDEBUG_PROT
4606 Print("m (constraints) %d\n",LP->m);
4607 Print("n (columns) %d\n",LP->n);
4608 Print("m1 (<=) %d\n",LP->m1);
4609 Print("m2 (>=) %d\n",LP->m2);
4610 Print("m3 (==) %d\n",LP->m3);
4611#endif
4612
4613 LP->compute();
4614
4615 lists lres= (lists)omAlloc( sizeof(slists) );
4616 lres->Init( 6 );
4617
4618 lres->m[0].rtyp= MATRIX_CMD; // output matrix
4619 lres->m[0].data=(void*)LP->mapToMatrix(m);
4620
4621 lres->m[1].rtyp= INT_CMD; // found a solution?
4622 lres->m[1].data=(void*)(long)LP->icase;
4623
4624 lres->m[2].rtyp= INTVEC_CMD;
4625 lres->m[2].data=(void*)LP->posvToIV();
4626
4627 lres->m[3].rtyp= INTVEC_CMD;
4628 lres->m[3].data=(void*)LP->zrovToIV();
4629
4630 lres->m[4].rtyp= INT_CMD;
4631 lres->m[4].data=(void*)(long)LP->m;
4632
4633 lres->m[5].rtyp= INT_CMD;
4634 lres->m[5].data=(void*)(long)LP->n;
4635
4636 res->data= (void*)lres;
4637
4638 return FALSE;
4639}
#define TRUE
Definition auxiliary.h:101
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 4664 of file ipshell.cc.

4665{
4666 poly gls;
4667 gls= (poly)(arg1->Data());
4668 int howclean= (int)(long)arg3->Data();
4669
4670 if ( gls == NULL || pIsConstant( gls ) )
4671 {
4672 WerrorS("Input polynomial is constant!");
4673 return TRUE;
4674 }
4675
4677 {
4678 int* r=Zp_roots(gls, currRing);
4679 lists rlist;
4680 rlist= (lists)omAlloc( sizeof(slists) );
4681 rlist->Init( r[0] );
4682 for(int i=r[0];i>0;i--)
4683 {
4684 rlist->m[i-1].data=n_Init(r[i],currRing->cf);
4685 rlist->m[i-1].rtyp=NUMBER_CMD;
4686 }
4687 omFree(r);
4688 res->data=rlist;
4689 res->rtyp= LIST_CMD;
4690 return FALSE;
4691 }
4692 if ( !(rField_is_R(currRing) ||
4696 {
4697 WerrorS("Ground field not implemented!");
4698 return TRUE;
4699 }
4700
4703 {
4704 unsigned long int ii = (unsigned long int)arg2->Data();
4706 }
4707
4708 int ldummy;
4709 int deg= currRing->pLDeg( gls, &ldummy, currRing );
4710 int i,vpos=0;
4711 poly piter;
4712 lists elist;
4713
4714 elist= (lists)omAlloc( sizeof(slists) );
4715 elist->Init( 0 );
4716
4717 if ( rVar(currRing) > 1 )
4718 {
4719 piter= gls;
4720 for ( i= 1; i <= rVar(currRing); i++ )
4721 if ( pGetExp( piter, i ) )
4722 {
4723 vpos= i;
4724 break;
4725 }
4726 while ( piter )
4727 {
4728 for ( i= 1; i <= rVar(currRing); i++ )
4729 if ( (vpos != i) && (pGetExp( piter, i ) != 0) )
4730 {
4731 WerrorS("The input polynomial must be univariate!");
4732 return TRUE;
4733 }
4734 pIter( piter );
4735 }
4736 }
4737
4738 rootContainer * roots= new rootContainer();
4739 number * pcoeffs= (number *)omAlloc( (deg+1) * sizeof( number ) );
4740 piter= gls;
4741 for ( i= deg; i >= 0; i-- )
4742 {
4743 if ( piter && pTotaldegree(piter) == i )
4744 {
4745 pcoeffs[i]= nCopy( pGetCoeff( piter ) );
4746 //nPrint( pcoeffs[i] );PrintS(" ");
4747 pIter( piter );
4748 }
4749 else
4750 {
4751 pcoeffs[i]= nInit(0);
4752 }
4753 }
4754
4755#ifdef mprDEBUG_PROT
4756 for (i=deg; i >= 0; i--)
4757 {
4758 nPrint( pcoeffs[i] );PrintS(" ");
4759 }
4760 PrintLn();
4761#endif
4762
4763 roots->fillContainer( pcoeffs, NULL, 1, deg, rootContainer::onepoly, 1 );
4764 roots->solver( howclean );
4765
4766 int elem= roots->getAnzRoots();
4767 char *dummy;
4768 int j;
4769
4770 lists rlist;
4771 rlist= (lists)omAlloc( sizeof(slists) );
4772 rlist->Init( elem );
4773
4775 {
4776 for ( j= 0; j < elem; j++ )
4777 {
4778 rlist->m[j].rtyp=NUMBER_CMD;
4779 rlist->m[j].data=(void *)nCopy((number)(roots->getRoot(j)));
4780 //rlist->m[j].data=(void *)(number)(roots->getRoot(j));
4781 }
4782 }
4783 else
4784 {
4785 for ( j= 0; j < elem; j++ )
4786 {
4787 dummy = complexToStr( (*roots)[j], gmp_output_digits, currRing->cf );
4788 rlist->m[j].rtyp=STRING_CMD;
4789 rlist->m[j].data=(void *)dummy;
4790 }
4791 }
4792
4793 elist->Clean();
4794 //omFreeSize( (ADDRESS) elist, sizeof(slists) );
4795
4796 // this is (via fillContainer) the same data as in root
4797 //for ( i= deg; i >= 0; i-- ) nDelete( &pcoeffs[i] );
4798 //omFreeSize( (ADDRESS) pcoeffs, (deg+1) * sizeof( number ) );
4799
4800 delete roots;
4801
4802 res->data= (void*)rlist;
4803
4804 return FALSE;
4805}
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 4641 of file ipshell.cc.

4642{
4643 ideal gls = (ideal)(arg1->Data());
4644 int imtype= (int)(long)arg2->Data();
4645
4647
4648 // check input ideal ( = polynomial system )
4649 if ( mprIdealCheck( gls, arg1->Name(), mtype, true ) != mprOk )
4650 {
4651 return TRUE;
4652 }
4653
4654 uResultant *resMat= new uResultant( gls, mtype, false );
4655 if (resMat!=NULL)
4656 {
4657 res->rtyp = MODUL_CMD;
4658 res->data= (void*)resMat->accessResMat()->getMatrix();
4659 if (!errorreported) delete resMat;
4660 }
4661 return errorreported;
4662}
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 4908 of file ipshell.cc.

4909{
4910 leftv v= args;
4911
4912 ideal gls;
4913 int imtype;
4914 int howclean;
4915
4916 // get ideal
4917 if ( v->Typ() != IDEAL_CMD )
4918 return TRUE;
4919 else gls= (ideal)(v->Data());
4920 v= v->next;
4921
4922 // get resultant matrix type to use (0,1)
4923 if ( v->Typ() != INT_CMD )
4924 return TRUE;
4925 else imtype= (int)(long)v->Data();
4926 v= v->next;
4927
4928 if (imtype==0)
4929 {
4930 ideal test_id=idInit(1,1);
4931 int j;
4932 for(j=IDELEMS(gls)-1;j>=0;j--)
4933 {
4934 if (gls->m[j]!=NULL)
4935 {
4936 test_id->m[0]=gls->m[j];
4938 if (dummy_w!=NULL)
4939 {
4940 WerrorS("Newton polytope not of expected dimension");
4941 delete dummy_w;
4942 return TRUE;
4943 }
4944 }
4945 }
4946 }
4947
4948 // get and set precision in digits ( > 0 )
4949 if ( v->Typ() != INT_CMD )
4950 return TRUE;
4951 else if ( !(rField_is_R(currRing) || rField_is_long_R(currRing) || \
4953 {
4954 unsigned long int ii=(unsigned long int)v->Data();
4956 }
4957 v= v->next;
4958
4959 // get interpolation steps (0,1,2)
4960 if ( v->Typ() != INT_CMD )
4961 return TRUE;
4962 else howclean= (int)(long)v->Data();
4963
4965 int i,count;
4967 number smv= NULL;
4969
4970 //emptylist= (lists)omAlloc( sizeof(slists) );
4971 //emptylist->Init( 0 );
4972
4973 //res->rtyp = LIST_CMD;
4974 //res->data= (void *)emptylist;
4975
4976 // check input ideal ( = polynomial system )
4977 if ( mprIdealCheck( gls, args->Name(), mtype ) != mprOk )
4978 {
4979 return TRUE;
4980 }
4981
4982 uResultant * ures;
4986
4987 // main task 1: setup of resultant matrix
4988 ures= new uResultant( gls, mtype );
4989 if ( ures->accessResMat()->initState() != resMatrixBase::ready )
4990 {
4991 WerrorS("Error occurred during matrix setup!");
4992 return TRUE;
4993 }
4994
4995 // if dense resultant, check if minor nonsingular
4997 {
4998 smv= ures->accessResMat()->getSubDet();
4999#ifdef mprDEBUG_PROT
5000 PrintS("// Determinant of submatrix: ");nPrint(smv);PrintLn();
5001#endif
5002 if ( nIsZero(smv) )
5003 {
5004 WerrorS("Unsuitable input ideal: Minor of resultant matrix is singular!");
5005 return TRUE;
5006 }
5007 }
5008
5009 // main task 2: Interpolate specialized resultant polynomials
5010 if ( interpolate_det )
5011 iproots= ures->interpolateDenseSP( false, smv );
5012 else
5013 iproots= ures->specializeInU( false, smv );
5014
5015 // main task 3: Interpolate specialized resultant polynomials
5016 if ( interpolate_det )
5017 muiproots= ures->interpolateDenseSP( true, smv );
5018 else
5019 muiproots= ures->specializeInU( true, smv );
5020
5021#ifdef mprDEBUG_PROT
5022 int c= iproots[0]->getAnzElems();
5023 for (i=0; i < c; i++) pWrite(iproots[i]->getPoly());
5024 c= muiproots[0]->getAnzElems();
5025 for (i=0; i < c; i++) pWrite(muiproots[i]->getPoly());
5026#endif
5027
5028 // main task 4: Compute roots of specialized polys and match them up
5029 arranger= new rootArranger( iproots, muiproots, howclean );
5030 arranger->solve_all();
5031
5032 // get list of roots
5033 if ( arranger->success() )
5034 {
5035 arranger->arrange();
5037 }
5038 else
5039 {
5040 WerrorS("Solver was unable to find any roots!");
5041 return TRUE;
5042 }
5043
5044 // free everything
5045 count= iproots[0]->getAnzElems();
5046 for (i=0; i < count; i++) delete iproots[i];
5047 omFreeSize( (ADDRESS) iproots, count * sizeof(rootContainer*) );
5048 count= muiproots[0]->getAnzElems();
5049 for (i=0; i < count; i++) delete muiproots[i];
5051
5052 delete ures;
5053 delete arranger;
5054 if (smv!=NULL) nDelete( &smv );
5055
5056 res->data= (void *)listofroots;
5057
5058 //emptylist->Clean();
5059 // omFreeSize( (ADDRESS) emptylist, sizeof(slists) );
5060
5061 return FALSE;
5062}
int BOOLEAN
Definition auxiliary.h:88
@ denseResMat
Definition mpr_base.h:65
@ IDEAL_CMD
Definition grammar.cc:285
lists listOfRoots(rootArranger *self, const unsigned int oprec)
Definition ipshell.cc:5065
#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 4807 of file ipshell.cc.

4808{
4809 int i;
4810 ideal p,w;
4811 p= (ideal)arg1->Data();
4812 w= (ideal)arg2->Data();
4813
4814 // w[0] = f(p^0)
4815 // w[1] = f(p^1)
4816 // ...
4817 // p can be a vector of numbers (multivariate polynom)
4818 // or one number (univariate polynom)
4819 // tdg = deg(f)
4820
4821 int n= IDELEMS( p );
4822 int m= IDELEMS( w );
4823 int tdg= (int)(long)arg3->Data();
4824
4825 res->data= (void*)NULL;
4826
4827 // check the input
4828 if ( tdg < 1 )
4829 {
4830 WerrorS("Last input parameter must be > 0!");
4831 return TRUE;
4832 }
4833 if ( n != rVar(currRing) )
4834 {
4835 Werror("Size of first input ideal must be equal to %d!",rVar(currRing));
4836 return TRUE;
4837 }
4838 if ( m != (int)pow((double)tdg+1,(double)n) )
4839 {
4840 Werror("Size of second input ideal must be equal to %d!",
4841 (int)pow((double)tdg+1,(double)n));
4842 return TRUE;
4843 }
4844 if ( !(rField_is_Q(currRing) /* ||
4845 rField_is_R() || rField_is_long_R() ||
4846 rField_is_long_C()*/ ) )
4847 {
4848 WerrorS("Ground field not implemented!");
4849 return TRUE;
4850 }
4851
4852 number tmp;
4853 number *pevpoint= (number *)omAlloc( n * sizeof( number ) );
4854 for ( i= 0; i < n; i++ )
4855 {
4856 pevpoint[i]=nInit(0);
4857 if ( (p->m)[i] )
4858 {
4859 tmp = pGetCoeff( (p->m)[i] );
4860 if ( nIsZero(tmp) || nIsOne(tmp) || nIsMOne(tmp) )
4861 {
4862 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4863 WerrorS("Elements of first input ideal must not be equal to -1, 0, 1!");
4864 return TRUE;
4865 }
4866 } else tmp= NULL;
4867 if ( !nIsZero(tmp) )
4868 {
4869 if ( !pIsConstant((p->m)[i]))
4870 {
4871 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4872 WerrorS("Elements of first input ideal must be numbers!");
4873 return TRUE;
4874 }
4875 pevpoint[i]= nCopy( tmp );
4876 }
4877 }
4878
4879 number *wresults= (number *)omAlloc( m * sizeof( number ) );
4880 for ( i= 0; i < m; i++ )
4881 {
4882 wresults[i]= nInit(0);
4883 if ( (w->m)[i] && !nIsZero(pGetCoeff((w->m)[i])) )
4884 {
4885 if ( !pIsConstant((w->m)[i]))
4886 {
4887 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4888 omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4889 WerrorS("Elements of second input ideal must be numbers!");
4890 return TRUE;
4891 }
4892 wresults[i]= nCopy(pGetCoeff((w->m)[i]));
4893 }
4894 }
4895
4896 vandermonde vm( m, n, tdg, pevpoint, FALSE );
4897 number *ncpoly= vm.interpolateDense( wresults );
4898 // do not free ncpoly[]!!
4899 poly rpoly= vm.numvec2poly( ncpoly );
4900
4901 omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4902 omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4903
4904 res->data= (void*)rpoly;
4905 return FALSE;
4906}
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