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
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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
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i3 : time CSM(I,Method=>DirectCompletInt)
-- used 1.94541 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
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i4 : time CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2})
-- used 1.82277 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
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The object IndsOfSmooth is a symbol.