This routine returns an irredundant primary decomposition for the ideal
I. The specific algorithm used varies depending on the characteristics of the ideal, and can also be specified using the optional argument
Strategy. In all cases, the radical of each entry of the output is equal to the corresponding entry of the output of
associatedPrimes.
Primary decompositions algorithms are very sensitive to their input. Some algorithms work very well on certain classes of ideals, but poorly on other classes. If this function seems to be taking too long, try another algorithm (using
primaryDecomposition(..., Strategy => ...)).
R = QQ[a..i]; |
I = permanents(2,genericMatrix(R,a,3,3)) |
C = primaryDecomposition I; |
I == intersect C |
#C |
Recall that
List / Function applies a function to each element of a list, returning the results as a list. This is often useful with lists of ideals, such as the list
C of primary components.
C/toString/print; |
C/codim |
C/degree |
The corresponding list of associated prime ideals is cached in
I.cache#"AssociatedPrimes", and can be obtained by using
associatedPrimes(Ideal).
associatedPrimes I / print; |