substitute(Path,Ring) -- changes the coefficient ring of a path

• Function: substitute

• Usage:

  Y = substitute(X,R)

• Inputs:
  • X, an instance of the type Path,
  • R, a ring, an algebra over the coefficient ring of the polynomials defining X;
• Outputs:
  • Y, an instance of the type Path, a path with the same pieces as X but whose coordinate functions are now polynomials with coefficients in R;

i1 : R = QQ[t];

i2 : X = polyPath({t,t^2})

o2 = Path in 2-dimensional space with 1 polynomial segment:

           2
     {{t, t }}

o2 : Path

i3 : coefficientRing X

o3 = QQ

o3 : Ring

i4 : A = QQ[a];

i5 : Y = substitute(X,A)

o5 = Path in 2-dimensional space with 1 polynomial segment:

           2
     {{t, t }}

o5 : Path

i6 : coefficientRing Y

o6 = A

o6 : PolynomialRing