RationalMap ** Ring -- change the coefficient ring of a rational map

i1 : QQ[vars(0..5)]

o1 = QQ[a..f]

o1 : PolynomialRing

i2 : phi = rationalMap {e^2-d*f, c*e-b*f, c*d-b*e, c^2-a*f, b*c-a*e, b^2-a*d}

o2 = -- rational map --
     source: Proj(QQ[a, b, c, d, e, f])
     target: Proj(QQ[a, b, c, d, e, f])
     defining forms: {
                       2
                      e  - d*f,
                      
                      c*e - b*f,
                      
                      c*d - b*e,
                      
                       2
                      c  - a*f,
                      
                      b*c - a*e,
                      
                       2
                      b  - a*d
                     }

o2 : RationalMap (quadratic rational map from PP^5 to PP^5)

i3 : K = ZZ/65521;

i4 : phi ** K

o4 = -- rational map --
     source: Proj(K[a, b, c, d, e, f])
     target: Proj(K[a, b, c, d, e, f])
     defining forms: {
                       2
                      e  - d*f,
                      
                      c*e - b*f,
                      
                      c*d - b*e,
                      
                       2
                      c  - a*f,
                      
                      b*c - a*e,
                      
                       2
                      b  - a*d
                     }

o4 : RationalMap (quadratic rational map from PP^5 to PP^5)

i5 : phi ** frac(K[t])

o5 = -- rational map --
     source: Proj(frac(K[t])[a, b, c, d, e, f])
     target: Proj(frac(K[t])[a, b, c, d, e, f])
     defining forms: {
                       2
                      e  - d*f,
                      
                      c*e - b*f,
                      
                      c*d - b*e,
                      
                       2
                      c  - a*f,
                      
                      b*c - a*e,
                      
                       2
                      b  - a*d
                     }

o5 : RationalMap (quadratic rational map from PP^5 to PP^5)