truncate

truncate (i,M) -- yields the submodule of M consisting of all elements of degrees >= i. If i is a multi-degree, then this yields the submodule generated by all elements of degree exactly i, together with all generators which have a higher primary degree than that of i.

The degree i may be a multi-degree, represented as a list of integers. The ring of M should be a (quotient of a) polynomial ring, where the coefficient ring, k, is a field.

Caveat: if the degrees of the variables are not all one, then there is currently a bug in the routine: some generators of higher degree than i may be duplicated in the generator list

     i1 = R = ZZ/101[a..c]
     
     o1 = R
     
     o1 : PolynomialRing

     i2 = truncate(2,R^1)
     
     o2 = image | a2 ab ac b2 bc c2 |
     
                                    1
          R - module, submodule of R

     i3 = truncate(2, ideal(a,b,c^3)/ideal(a^2,b^2,c^4))
     
     o3 = subquotient(| c3 bc ab ac |,| b2 a2 c4 |)
     
                                      1
          R - module, subquotient of R

     i4 = S = ZZ/101[x,y,z,Degrees=>{{1,3},{1,4},{1,-1}}]
     
     o4 = S
     
     o4 : PolynomialRing

     i5 = truncate({7,24}, S^1 ++ S^{{-8,-20}})
     
     o5 = image | x4y3 0 |
                | 0    1 |
     
                                    2
          S - module, submodule of S

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