IndsOfSmooth

Description

The option IndsOfSmooth is only used by the commands CSM, and Euler in combination with the option Method=>DirectCompletInt. When used this option may allow the user to speed up the computation by telling giving the method a list of indices for the generators of the input ideal that, when taken together, define a smooth subscheme of the ambient space. This option will be ignored otherwise.

i1 : R = MultiProjCoordRing({2,2})

o1 = R

o1 : PolynomialRing

i2 : I=ideal(R_0*R_1*R_3-R_0^2*R_3,random({0,1},R),random({1,2},R));

o2 : Ideal of R

i3 : time CSM(I,Method=>DirectCompletInt)
 -- used 2.71111s (cpu); 1.36119s (thread); 0s (gc)

       2 2     2         2
o3 = 2h h  + 2h h  + 5h h
       1 2     1 2     1 2

     ZZ[h ..h ]
         1   2
o3 : ----------
        3   3
      (h , h )
        1   2

i4 : time CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2})
 -- used 2.6941s (cpu); 1.30631s (thread); 0s (gc)

       2 2     2         2
o4 = 2h h  + 2h h  + 5h h
       1 2     1 2     1 2

     ZZ[h ..h ]
         1   2
o4 : ----------
        3   3
      (h , h )
        1   2

Functions with optional argument named IndsOfSmooth:

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

For the programmer

The object IndsOfSmooth is a symbol.

The source of this document is in CharacteristicClasses.m2:2445:0.