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MultirationalMap ** Ring -- change the coefficient ring of a multi-rational map

Synopsis

• Operator: **
• Usage:
Phi ** K
• Inputs:
• Phi, , defined over a coefficient ring F
• K, a ring, the new coefficient ring (which must be a field)
• Outputs:
• , a multi-rational map defined over K, obtained by coercing the coefficients of the multi-forms defining Phi into K

Description

It is necessary that all multi-forms in the old coefficient ring F can be automatically coerced into the new coefficient ring K.

 i1 : Phi = inverse first graph rationalMap PP_QQ^(2,2); o1 : MultirationalMap (birational map from PP^5 to 5-dimensional subvariety of PP^5 x PP^5) i2 : describe Phi o2 = multi-rational map consisting of 2 rational maps source variety: PP^5 target variety: 5-dimensional subvariety of PP^5 x PP^5 cut out by 8 hypersurfaces of multi-degree (1,1) base locus: surface in PP^5 cut out by 6 hypersurfaces of degree 2 dominance: true multidegree: {1, 3, 9, 23, 51, 102} degree: 1 degree sequence (map 1/2): [1] degree sequence (map 2/2): [2] coefficient ring: QQ i3 : K = ZZ/65521; i4 : Phi' = Phi ** K; o4 : MultirationalMap (birational map from PP^5 to 5-dimensional subvariety of PP^5 x PP^5) i5 : describe Phi' o5 = multi-rational map consisting of 2 rational maps source variety: PP^5 target variety: 5-dimensional subvariety of PP^5 x PP^5 cut out by 8 hypersurfaces of multi-degree (1,1) base locus: surface in PP^5 cut out by 6 hypersurfaces of degree 2 dominance: true multidegree: {1, 3, 9, 23, 51, 102} degree: 1 degree sequence (map 1/2): [1] degree sequence (map 2/2): [2] coefficient ring: K i6 : Phi'' = Phi ** frac(K[t]); o6 : MultirationalMap (birational map from PP^5 to 5-dimensional subvariety of PP^5 x PP^5) i7 : describe Phi'' o7 = multi-rational map consisting of 2 rational maps source variety: PP^5 target variety: 5-dimensional subvariety of PP^5 x PP^5 cut out by 8 hypersurfaces of multi-degree (1,1) base locus: surface in PP^5 cut out by 6 hypersurfaces of degree 2 dominance: true multidegree: {1, 3, 9, 23, 51, 102} degree: 1 degree sequence (map 1/2): [1] degree sequence (map 2/2): [2] coefficient ring: frac(K[t])