# shortcuts -- Some convenient shortcuts for multi-rational maps consisting of a single rational map

## Synopsis

• Usage:
rationalMap X <==> multirationalMap {rationalMap ideal X}
rationalMap(X,a) <==> multirationalMap {rationalMap(ideal X,a)}
rationalMap(X,a,b) <==> multirationalMap {rationalMap(ideal X,a,b)}
multirationalMap f <==> multirationalMap {f}
• Inputs:
 i1 : X = PP_QQ^(1,3); o1 : ProjectiveVariety, curve in PP^3 i2 : a = 4, b = 2; i3 : phi = rationalMap X; o3 : MultirationalMap (rational map from PP^3 to PP^2) i4 : assert(phi <==> multirationalMap {rationalMap ideal X}) i5 : phi = rationalMap(X,a); o5 : MultirationalMap (rational map from PP^3 to PP^21) i6 : assert(phi <==> multirationalMap {rationalMap(ideal X,a)}) i7 : phi = rationalMap(X,a,b); o7 : MultirationalMap (rational map from PP^3 to PP^5) i8 : assert(phi <==> multirationalMap {rationalMap(ideal X,a,b)})

If you want to consider $X$ as a subvariety of another multi-projective variety $Y$, you may use the command X_Y. For instance, rationalMap(X_Y,a) returns the rational map from $Y$ defined by a basis of the linear system $|H^0(Y,\mathcal{I}_{X\subseteq Y}(a))|$ (basically, this is equivalent to trim((rationalMap(X,a))|Y)).

 i9 : Y = random(3,X); o9 : ProjectiveVariety, surface in PP^3 i10 : rationalMap(X_Y,a); o10 : MultirationalMap (rational map from Y to PP^17) i11 : rationalMap X_Y; o11 : MultirationalMap (rational map from Y to PP^2)