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# WeightedRationalMap -- the class of all weighted-rational maps

## Description

A weighted-rational map is a rational map between weighted-projective varieties. It can be defined using the functions rationalMap and multirationalMap, just like (multi-)rational maps.

 i1 : K = ZZ/65521; i2 : X = PP_K(1,1,3); o2 : ProjectiveVariety, PP(1,1,3) i3 : Y = PP_K(4,5); o3 : ProjectiveVariety, PP(4,5) i4 : f = rationalMap(ring X,ring Y,{random(4,ring X),random(5,ring X)}) o4 = -- rational map -- source: Proj(K[p , p , p ],Degrees=>{{1}, {1}, {3}}) 0 1 2 target: Proj(K[p , p ],Degrees=>{{4}, {5}}) 0 1 defining forms: { 4 3 2 2 3 4 - 32646p - 28377p p + 26433p p - 29566p p + 26696p + 3783p p + 8570p p , 0 0 1 0 1 0 1 1 0 2 1 2 5 4 3 2 2 3 4 5 2 2 16659p + 8444p p - 11230p p - 22394p p + 23752p p + 5071p - 8214p p - 30100p p p + 25800p p 0 0 1 0 1 0 1 0 1 1 0 2 0 1 2 1 2 } o4 : WeightedHomogeneousRationalMap (rational map from PP(1,1,3) to PP(4,5)) i5 : F = multirationalMap f; o5 : WeightedRationalMap (rational map from X to Y)

Note that rationalMap(RingMap) and rationalMap(Matrix) return a raw type of rational map (just like it happens with the multi-rational maps). You can always apply multirationalMap to the output and convert to the raw type using toRationalMap. Alternatively, you can proceed as follows:

 i6 : M = matrix f o6 = | -32646p_0^4-28377p_0^3p_1+26433p_0^2p_1^2-29566p_0p_1^3+26696p_1^4+ ------------------------------------------------------------------------ 3783p_0p_2+8570p_1p_2 16659p_0^5+8444p_0^4p_1-11230p_0^3p_1^2-22394p_0^ ------------------------------------------------------------------------ 2p_1^3+23752p_0p_1^4+5071p_1^5-8214p_0^2p_2-30100p_0p_1p_2+25800p_1^2p_2 ------------------------------------------------------------------------ | 1 2 o6 : Matrix (K[p ..p ]) <-- (K[p ..p ]) 0 2 0 2 i7 : rationalMap {M} o7 = multi-rational map consisting of one single rational map source variety: PP(1,1,3) target variety: PP(4,5) o7 : WeightedRationalMap (rational map from X to PP(4,5)) i8 : rationalMap {f} o8 = F o8 : WeightedRationalMap (rational map from X to Y)

## Caveat

This class is currently experimental and under development.