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D.5.1.1 RiemannRochBN

Procedure from library brillnoether.lib (see brillnoether_lib).

Usage:
RiemannRochBN(C,I,J); ideal C, ideal I, ideal J

Assume:
C is a homogeneous ideal defining a projective curve. If C is a non-planar curve, then C is assumed to be
nonsingular. This assumption is not checked.
The ideals I and J represent a
a divisor D on C.

Return:
A vector space basis of the Riemann-Roch space of D,
stored in a list RRBasis. The list RRBasis contains a list IH and a form F. The vector space basis of L(D)
consists of all rational functions G/F, where G is an element of IH.

Example:
 
LIB "brillnoether.lib";
==> Welcome to polymake version
==> Copyright (c) 1997-2015
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
ring R = 0,(x,y,z),dp;
poly f = y^2+x^2-1;
f = homog(f,z);
ideal C = f;
ideal P1 = x,y-z;
ideal P2 = x^2+y^2,z;
ideal I = intersect(P1^3,P2^2);
ideal P3 = x+z,y;
ideal J = P3^2;
RiemannRochBN(C,I,J);
==> [1]:
==>    _[1]=65y2z2-81xz3-81z4
==>    _[2]=65xyz2+63xz3+65yz3+63z4
==>    _[3]=65y3z-81xyz2-81yz3
==>    _[4]=65xy2z-81x2z2-81xz3
==>    _[5]=65y4-81xy2z-81y2z2
==>    _[6]=65xy3-81x2yz-81xyz2
==> [2]:
==>    8xyz2-y2z2-8xz3+2yz3-z4