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# 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 2.24297s (cpu); 1.19223s (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 2.20527s (cpu); 1.147s (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 /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CharacteristicClasses.m2:2482:0.