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# RAT Tally -- rational map defined by an effective divisor

## Synopsis

• Operator: SPACE
• Usage:
H D
check H D
• Inputs:
• H, , the hom-set of rational maps between two varieties X and Y
• D, , a multiset of pure codimension 1 subschemes of $X$ with no embedded components; so that D is interpreted as an effective divisor on $X$
• Outputs:
• , the rational map defined by the complete linear system $|D|$

## Description

This is another way of calling rationalMap(MultiprojectiveVariety,Tally).

 i1 : X = random(3,0_(PP_(ZZ/5)^2)); o1 : ProjectiveVariety, curve in PP^2 i2 : Y = PP_(ZZ/5)^4; o2 : ProjectiveVariety, PP^4 i3 : H = Hom(X,Y); o3 : Hom(X,Y) i4 : D = tally toList(5:point X) o4 = Tally{point of coordinates [1, -1, 1] => 5} o4 : Tally i5 : H D o5 = multi-rational map consisting of one single rational map source variety: curve in PP^2 defined by a form of degree 3 target variety: PP^4 o5 : MultirationalMap (rational map from X to Y) i6 : show oo o6 = -- multi-rational map -- ZZ source: subvariety of Proj(--[x , x , x ]) defined by 5 0 1 2 { 3 2 3 2 2 2 2 3 x + x x + x + 2x x - 2x x - x x + x x + x 0 0 1 1 0 2 1 2 0 2 1 2 2 } ZZ target: Proj(--[x , x , x , x , x ]) 5 0 1 2 3 4 -- rational map 1/1 -- map 1/1, one of its representatives: { 2 2 2 2 3 2 2 3 2 3 4 4 5 x x x - 2x x x - x x + x x + 2x x + 2x x - x x - x , 0 1 2 0 1 2 1 2 0 2 1 2 0 2 1 2 2 3 2 2 3 2 3 4 x x x + x x x - x x - 2x x x + x x , 0 1 2 0 1 2 1 2 0 1 2 1 2 2 2 2 3 2 3 4 5 x x x + x x - x x - 2x x + x , 0 1 2 0 2 1 2 0 2 2 2 2 4 2 2 3 2 3 4 x x x + x x + 2x x x - x x - x x x + 2x x , 0 1 2 1 2 0 1 2 1 2 0 1 2 1 2 2 2 3 2 2 3 2 3 4 5 x x x + x x + 2x x - x x - x x + 2x 0 1 2 1 2 0 2 1 2 0 2 2 }