The option Method is only used by the commands CSM and Euler and only in combination with CompMethod=>ProjectiveDegree. The Method InclusionExclusion will always be used with CompMethod PnResidual or bertini. When the input ideal is a complete intersection one may, potentially, speed up the computation by setting Method=> DirectCompleteInt. The option Method is only used by the commands CSM and Euler and only in combination with CompMethod=>ProjectiveDegree. The Method InclusionExclusion will always be used with CompMethod PnResidual or bertini.
R = ZZ/32749[x_0..x_6] |
I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3); |
time CSM I |
time CSM(I,Method=>DirectCompleteInt) |
When using the DirectCompleteInt method one may potentially further speed up computation time by specifying what subset of the generators of the input ideal define a smooth subscheme (if this is known), see IndsOfSmooth.