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/*
* app_padic.cpp
*
* Created on: Dec 1, 2010
* Author: anders
*/
#include "printer.h"
#include "parser.h"
#include "gfanapplication.h"
#include "division.h"
#include "log.h"
#include "polyhedralcone.h"
#include "padic.h"
#include <ostream>
using namespace std;
class PAdicApplication : public GFanApplication
{
IntegerOption primeOption;
SimpleOption gbOption;
SimpleOption initialOption;
SimpleOption gComplexOption;
SimpleOption gPolyhedronOption;
SimpleOption listOption;
public:
const char *helpText()
{
return "This program is an experimental implementation of p-adic Groebner bases as proposed by Diane Maclagan.\n"
"Several operations are supported by specifying the appropriate option:\n"
" (1) computation of Groebner basis with respect to a given vector (tiebroken lexicographically),\n"
" (2) computation of the p-adic initial ideal,\n"
" (3) computation of the p-adic Groebner complex as defined by Maclagan and Sturmfels,\n"
" (4) computation of a single polyhedron of the p-adic Groebner complex.\n"
"The input ideal should be an ideal of the polynomial ring with coefficient field Q. The valuation is specified with the option -p. The ideal MUST BE HOMOGENEOUS (in a positive grading).\n"
"Since gfan can only handle fans and not polyhedral complexes in general, what is computed as the Groebner complex is actually the \"fan over\" the complex - in other words, the first coordinate is supposed to be 1 in the output fan.\n"
"Similarly, the weight vectors must be specified in an homogeneous way, for example by adding an additional 1 entry as first coordinate. (If fractions are needed, use the entry as a common denominator.) "
"NOTE: This program is experimental and expected to change behaviour in future releases, so don't write your SAGE and M2 interfaces just yet. In particular this program uses the tropical minimum-convention!!\n";
}
PAdicApplication():
primeOption("-p","Defines the prime used for the valuation.",2),
gbOption("--groebnerBasis","Asks the program to compute a marked Groebner basis with respect to a weight vector (tie-broken lexicographically).\n"
"The input order is: Ring ideal vector.\n"),
initialOption("--initialIdeal","Asks the program to compute an initial ideal with respect to a vector. "
"The input order is: Ring ideal vector.\n"),
gComplexOption("--groebnerComplex","Asks the program to compute the p-adic Groebner complex. \n "
"The input order is: Ring ideal.\n"),
gPolyhedronOption("--groebnerPolyhedron","Asks the program to compute a single polyhedron of the Groebner complex containing the specified vector in its relative interior. The output is stored as a fan. "
"The input order is: Ring ideal vector."),
listOption("-m","For the operations taking a vector as input, read in a list of vectors instead, and perform the operation for each vector in the list.")
{
registerOptions();
}
const char *name()
{
return "_padic";
}
int main()
{
if(gbOption.getValue()+initialOption.getValue()+gComplexOption.getValue()+gPolyhedronOption.getValue()!=1)
{
debug<<"WRONG COMBINATION OF COMMAND LINE OPTIONS\n";
assert(0);
}
LexicographicTermOrder tieBreaker;
FileParser P(Stdin);
int prime=primeOption.getValue();
PolynomialSet a=P.parsePolynomialSetWithRing();
int n=a.getRing().getNumberOfVariables();
if(gComplexOption.getValue())
{
SymmetryGroup G(n+1);
SymmetricTargetFanBuilder target(n+1,G);
PAdicGroebnerFanTraverser traverser(a,prime);
symmetricTraverse(traverser,target);
AsciiPrinter Q(Stdout);
target.getFanRef().printWithIndices(&Q,
FPF_default);
}
else
{
IntegerVectorList omegas;
if(listOption.getValue())
omegas=P.parseIntegerVectorList();
else
omegas.push_back(P.parseIntegerVector());
for(IntegerVectorList::const_iterator i=omegas.begin();i!=omegas.end();i++)
{
if(i->size()!=a.getRing().getNumberOfVariables()+1)
{
debug<<"ERROR: The number of entries of the weight vector is not one higher than the number of variables in the ring.\n";
assert(0);
}
if(gbOption.getValue())
{
//debug<<"P-ADIC GROEBNER BASIS:\n";
pAdicBuchberger(a,prime,*i,tieBreaker);
pout<<a.getRing()<<a;
}
else if(initialOption.getValue())
{
pAdicBuchberger(a,prime,*i,tieBreaker);
PolynomialRing ZModPZRing=residuePolynomialRing(a.getRing(), prime);
// debug<<"P-ADIC INITIAL IDEAL:\n";
pout<<ZModPZRing;
pout<<pAdicInitialForms(ZModPZRing,a,prime,*i);
}
// PolynomialRing ZModPZRing=residuePolynomialRing(a.getRing(), prime);
// debug<<"P-ADIC INITIAL IDEAL:\n";
// debug<<ZModPZRing;
// debug<<pAdicInitialForms(ZModPZRing,a,prime,*i);
// debug<<"P-ADIC INITIAL TERMS:\n";
// debug<<ZModPZRing;
// debug<<pAdicInitialTerms(ZModPZRing,a,prime,omega,tieBreaker);
// debug<<"AUTOREDUCED:\n";
// pAdicAutoReduce(a,prime,omega,tieBreaker);
// debug<<a;
else if(gPolyhedronOption.getValue())
{
pAdicBuchberger(a,prime,*i,tieBreaker);
IntegerVectorList inequalities=normalPolyhedralInequalities(a,prime,*i,tieBreaker);
inequalities.push_back(IntegerVector::standardVector(n+1,0));
IntegerVectorList empty;
PolyhedralCone C(inequalities,empty,n+1);
C=C.faceContaining(*i);
C.canonicalize();
PolyhedralFan F(C.ambientDimension());
F.insert(C);
F.printWithIndices(&pout,
FPF_default);
// pout<<C;
}
/* debug<<"GROEBNER POLYHEDRON:\n";
IntegerVectorList inequalities=normalPolyhedralInequalities(a,prime,omega,tieBreaker);
inequalities.push_back(IntegerVector::standardVector(n+1,0));
IntegerVectorList empty;
PolyhedralCone C(inequalities,empty,n+1);
debug<<C;
debug<<"RAYS:\n";
debug<<C.extremeRays();
*/
}
}
return 0;
}
};
static PAdicApplication theApplication;
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