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

## Synopsis

• Operator: **
• Usage:
phi ** K
• Inputs:
• phi, , defined over a coefficient ring F
• K, a ring, the new coefficient ring (which must be a field)
• Outputs:
• , a rational map defined over K, obtained by coercing the coefficients of the forms defining phi into K

## Description

It is necessary that all forms in the old coefficient ring F can be automatically coerced into the new coefficient ring K.

 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)