polynomial-converter.rd

[index]

# Utility of Conversion of Polynomials

## File Name

- polyomimial-converter.rb

## Methods:

`Algebra::Polynomial.convert_to(ring)`

  Returns the ring converted to ring of Algebra::MPolynomial.

`Algebra::Polynomial#value_on(ring)`

  Returns the ring converted to ring of Algebra::MPolynomial.

  Example:

      require "m-polynomial"
      require "polynomial"

      P = Algebra::Polynomial(Integer, "x", "y", "z")
      x, y, z = P.vars
      f = x**2 + y**2 + z**2 - x*y - y*z - z*x

      MP = P.convert_to(Algebra::MPolynomial)
      p f = f.value_on(MP) #=> z^2 - zy - zx + y^2 - yx + x^2
      x, y, z = MP.vars
      p f == x**2 + y**2 + z**2 - x*y - y*z - z*x #=> true

`Algebra::MPolynomial.convert_to(ring)`

  Returns the ring converted to ring of Algebra::Polynomial

`Algebra::MPolynomial#value_on(ring)`

  Returns the ring converted to ring of Algebra::Polynomial.

  Example:

      require "m-polynomial"
      require "polynomial"

      MP = Algebra::MPolynomial(Integer, "x", "y", "z")
      x, y, z = MP.vars
      f = x**2 + y**2 + z**2 - x*y - y*z - z*x

      P = MP.convert_to(Algebra::Polynomial)
      p f = f.value_on(P) #=> x^2 + (-y - z)x + y^2 - zy + z^2
      x, y, z = P.vars
      p f == x**2 + y**2 + z**2 - x*y - y*z - z*x #=> true