# Method

## Description

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.

## Functions with optional argument named Method :

• CSM(...,Method=>...) (missing documentation)
• Euler(...,Method=>...) (missing documentation)

## For the programmer

The object Method is .