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isLPP -- determine whether an ideal is an LPP ideal



Given an ideal I in a polynomial ring R, isLPP checks that I is Artinian and that the power sequence is weakly increasing. Then isLPP computes bases of R/I in each degree up through the maximum degree of a minimal generator of I to determine whether I is an LPP ideal in R.

i1 : R=ZZ/32003[a..c];
i2 : isLPP LPP(R,{1,3,4,3,2},{2,2,4})

o2 = true
i3 : isLPP ideal(a^3,b^3,c^3,a^2*b,a^2*c,a*b^2*c^2)

o3 = true
i4 : isLPP ideal(a^3,b^4) --not Artinian since no power of c

o4 = false
i5 : isLPP ideal(a^3,b^4,c^3) --powers not weakly increasing

o5 = false
i6 : isLPP ideal(a^3,b^3,c^3,a^2*b,a*b^2)

o6 = false

See also

Ways to use isLPP :

For the programmer

The object isLPP is a method function.