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CharacteristicClasses :: IndsOfSmooth

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 1.57345 seconds

       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 1.27822 seconds

       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 :

For the programmer

The object IndsOfSmooth is a symbol.