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.
i1 : R = ZZ/32749[x_0..x_6] o1 = R o1 : PolynomialRing |
i2 : I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3); o2 : Ideal of R |
i3 : time CSM I
-- used 1.44229 seconds
5 4 3
o3 = 12h + 10h + 6h
1 1 1
ZZ[h ]
1
o3 : ------
7
h
1
|
i4 : time CSM(I,Method=>DirectCompleteInt)
-- used 0.306481 seconds
5 4 3
o4 = 12h + 10h + 6h
1 1 1
ZZ[h ]
1
o4 : ------
7
h
1
|
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.