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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.

See also

For the programmer

The object WeightedRationalMap is a type, with ancestor classes MultirationalMap < MutableHashTable < HashTable < Thing.