# RationalMap ! -- calculates every possible thing

## Synopsis

• Operator: !
• Usage:
phi!
• Inputs:
• phi,
• Outputs:
• , the same rational map phi

## Description

This method (mainly used for tests) applies almost all the deterministic methods that are available.

 i1 : QQ[x_0..x_5]; phi = rationalMap {x_4^2-x_3*x_5,x_2*x_4-x_1*x_5,x_2*x_3-x_1*x_4,x_2^2-x_0*x_5,x_1*x_2-x_0*x_4,x_1^2-x_0*x_3}; o2 : RationalMap (quadratic rational map from PP^5 to PP^5) i3 : describe phi o3 = rational map defined by forms of degree 2 source variety: PP^5 target variety: PP^5 coefficient ring: QQ i4 : time phi! ; -- used 0.237926 seconds o4 : RationalMap (Cremona transformation of PP^5 of type (2,2)) i5 : describe phi o5 = rational map defined by forms of degree 2 source variety: PP^5 target variety: PP^5 dominance: true birationality: true (the inverse map is already calculated) projective degrees: {1, 2, 4, 4, 2, 1} number of minimal representatives: 1 dimension base locus: 2 degree base locus: 4 coefficient ring: QQ i6 : QQ[x_0..x_4]; phi = rationalMap {-x_1^2+x_0*x_2,-x_1*x_2+x_0*x_3,-x_2^2+x_1*x_3,-x_1*x_3+x_0*x_4,-x_2*x_3+x_1*x_4,-x_3^2+x_2*x_4}; o7 : RationalMap (quadratic rational map from PP^4 to PP^5) i8 : describe phi o8 = rational map defined by forms of degree 2 source variety: PP^4 target variety: PP^5 coefficient ring: QQ i9 : time phi! ; -- used 0.122964 seconds o9 : RationalMap (quadratic rational map from PP^4 to PP^5) i10 : describe phi o10 = rational map defined by forms of degree 2 source variety: PP^4 target variety: PP^5 image: smooth quadric hypersurface in PP^5 dominance: false birationality: false degree of map: 1 projective degrees: {1, 2, 4, 4, 2} number of minimal representatives: 1 dimension base locus: 1 degree base locus: 4 coefficient ring: QQ