truncate -- truncate the module at a specified degree

truncate -- truncate the module at a specified degree

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];

i2 : truncate(2,R^1)



o2 = image | a2 ab ac b2 bc c2 |



                             1

o2 : 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 |, | a2 b2 c4 |)



                               1

o3 : R-module, subquotient of R

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

i5 : truncate({7,24}, S^1 ++ S^{{-8,-20}})



o5 = image {0, 0}  | x4y3 0 |

           {8, 20} | 0    1 |



                             2

o5 : S-module, submodule of S

Ways to use truncate :

truncate(List,Ideal)

truncate(List,Module)

truncate(ZZ,Ideal)

truncate(ZZ,Module)