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# trim(MultirationalMap) -- trim the target of a multi-rational map

## Synopsis

• Function: trim
• Usage:
trim Phi
• Inputs:
• Phi, , from $X$ to $\mathbb{P}^{k_1}\times\cdots\times\mathbb{P}^{k_n}$
• Optional inputs:
• Outputs:
• , from $X$ to $\mathbb{P}^{s_1}\times\cdots\times\mathbb{P}^{s_n}$, with $s_i\leq k_i$, which is isomorphic to the original map, but whose image is not contained in any hypersurface of multidegree $(d_1,\ldots,d_n)$ with $\sum_{i=1}^n d_i = 1$

## Description

 i1 : K = ZZ/33331; C = PP_K^(1,4); -- rational normal quartic curve o2 : ProjectiveVariety, curve in PP^4 i3 : Phi = rationalMap C; -- map defined by the quadrics through C o3 : MultirationalMap (rational map from PP^4 to PP^5) i4 : Q = random(2,C); -- random quadric hypersurface through C o4 : ProjectiveVariety, hypersurface in PP^4 i5 : Phi = Phi|Q; o5 : MultirationalMap (rational map from Q to PP^5) i6 : image Phi o6 = threefold in PP^5 cut out by 2 hypersurfaces of degrees 1^1 2^1 o6 : ProjectiveVariety, threefold in PP^5 i7 : Psi = trim Phi; o7 : MultirationalMap (rational map from Q to PP^4) i8 : image Psi o8 = hypersurface in PP^4 defined by a form of degree 2 o8 : ProjectiveVariety, hypersurface in PP^4 i9 : Phi || Phi || Psi; o9 : MultirationalMap (rational map from Q x Q x Q to PP^5 x PP^5 x PP^4) i10 : image oo o10 = 9-dimensional subvariety of PP^5 x PP^5 x PP^4 cut out by 5 hypersurfaces of multi-degrees (0,0,2)^1 (0,1,0)^1 (0,2,0)^1 (1,0,0)^1 (2,0,0)^1 o10 : ProjectiveVariety, 9-dimensional subvariety of PP^5 x PP^5 x PP^4 i11 : trim (Phi || Phi || Psi); o11 : MultirationalMap (rational map from Q x Q x Q to PP^4 x PP^4 x PP^4) i12 : image oo o12 = 9-dimensional subvariety of PP^4 x PP^4 x PP^4 cut out by 3 hypersurfaces of multi-degrees (0,0,2)^1 (0,2,0)^1 (2,0,0)^1 o12 : ProjectiveVariety, 9-dimensional subvariety of PP^4 x PP^4 x PP^4