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#include "dimension.h"
#include "printer.h"
#include "parser.h"
#include "gfanapplication.h"
#include "division.h"
#include "field_rationals.h"
class SturmSequenceApplication : public GFanApplication
{
SimpleOption evaluateOption;
public:
bool includeInDefaultInstallation()
{
return false;
}
const char *helpText()
{
return "Given a polynomial this program computes the Sturm sequence of polynomials as defined in Sturm's Theorem.\n";
}
SturmSequenceApplication():
evaluateOption("-e","Evaluate the sequence in a set of points given in a vector. (Only integer vectors are supported at the moment).")
{
registerOptions();
}
const char *name()
{
return "_sturmsequence";
}
int main()
{
FileParser P(Stdin);
Polynomial f1=P.parsePolynomialWithRing();
Polynomial f2=f1.derivative();
PolynomialRing theRing=f1.getRing();
PolynomialSet result(theRing);
result.push_back(f1);
while(!f2.isZero())
{
result.push_back(f2);
PolynomialSet g(theRing);
Polynomial temp=f2;
g.push_back(f2);
g.markAndScale(LexicographicTermOrder());
f2=(f1-f1)-division(f1,g,LexicographicTermOrder());
f1=temp;
}
AsciiPrinter(Stdout).printPolynomialSet(result);
if(evaluateOption.getValue())
{
IntegerVector v=P.parseIntegerVector();
for(int i=0;i<v.size();i++)
{
FieldElement x=Q.zHomomorphism(v[i]);
AsciiPrinter(Stdout).printString("Evaluating in ");
AsciiPrinter(Stdout).printFieldElement(x);
AsciiPrinter(Stdout).printNewLine();
for(PolynomialSet::const_iterator j=result.begin();j!=result.end();j++)
{
AsciiPrinter(Stdout).printFieldElement(j->evaluate(x));
AsciiPrinter(Stdout).printNewLine();
}
}
}
return 0;
}
};
static SturmSequenceApplication theApplication;
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