math/polynomial-derivative.cpp

Computes the first and second derivative of the given polynomial P (in one variable).

See also:

dgtal_mpolynomial_sec2_5 and Input and output for multivariate polynomials

$ ./examples/math/polynomial-derivative "1+x+x^2-3*x^4"
P(X_0)   = (1 + 1 X_0 + 1 X_0^2 + -3 X_0^4)
P'(X_0)  = (1 + 2 X_0 + -12 X_0^3)
P''(X_0) = (2 + -36 X_0^2)
$ ./examples/math/polynomial-derivative "(2 + -36 X_0^2)"
P(X_0)   = (2 + -36 X_0^2)
P'(X_0)  = -72 X_0
P''(X_0) = -72

#include <iostream>
#include <string>
#include <sstream>
#include "DGtal/math/MPolynomial.h"
#include "DGtal/io/readers/MPolynomialReader.h"


using namespace DGtal;


void usage( int, char** argv )
{
  std::cerr << "Usage: " << argv[ 0 ] << " <P>" << std::endl;
  std::cerr << "\t - computes the first and second derivative of the given polynomial P (in one variable)." << std::endl;
}

int main( int argc, char** argv )
{
  if ( argc < 2 )
    {
      usage( argc, argv );
      return 1;
    }

  typedef double Ring;
  typedef MPolynomial<1, Ring> MyPolynomial;

  std::string polynomialString( argv[ 1 ] );
  std::istringstream polynomialIStream( polynomialString );
  MyPolynomial P;
  polynomialIStream >> P;
  MyPolynomial P1 = derivative<0>( P );
  MyPolynomial P2 = derivative<0>( P1 );
  std::cout << "P(X_0)   = " << P << std::endl;
  std::cout << "P'(X_0)  = " << P1 << std::endl;
  std::cout << "P''(X_0) = " << P2 << std::endl;
  return 0;
}