# substitute(RationalMap,PolynomialRing,PolynomialRing) -- substitute the ambient projective spaces of source and target

## Synopsis

• Function: substitute
• Usage:
sub(phi,R,S)
• Inputs:
• phi, , $\phi:X\subseteq\mathbb{P}^n\dashrightarrow Y\subseteq\mathbb{P}^m$
• R, , the coordinate ring of $\mathbb{P}^n$
• S, , the coordinate ring of $\mathbb{P}^m$
• Outputs:

## Description

 i1 : ZZ/3331[vars(0..5)]; 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 -- ZZ source: Proj(----[a, b, c, d, e, f]) 3331 ZZ target: Proj(----[a, b, c, d, e, f]) 3331 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 : R = ZZ/3331[x_0..x_5], S = ZZ/3331[y_0..y_5]; i4 : sub(phi,R,S) o4 = -- rational map -- ZZ source: Proj(----[x , x , x , x , x , x ]) 3331 0 1 2 3 4 5 ZZ target: Proj(----[y , y , y , y , y , y ]) 3331 0 1 2 3 4 5 defining forms: { 2 x - x x , 4 3 5 x x - x x , 2 4 1 5 x x - x x , 2 3 1 4 2 x - x x , 2 0 5 x x - x x , 1 2 0 4 2 x - x x 1 0 3 } o4 : RationalMap (quadratic rational map from PP^5 to PP^5)