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 1.45549s (cpu); 0.814824s (thread); 0s (gc)

        5      4     3
o3 = 12h  + 10h  + 6h
        1      1     1

     ZZ[h ]
         1
o3 : ------
        7
       h
        1

i4 : time CSM(I,Method=>DirectCompleteInt)
 -- used 0.256302s (cpu); 0.162912s (thread); 0s (gc)

        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=>...) -- see CSM -- The Chern-Schwartz-MacPherson class
Euler(...,Method=>...) (missing documentation)

For the programmer

The object Method is a symbol.