Given an ideal I in a ring R that is either a polynomial ring or a quotient of a polynomial ring by a monomial ideal, isLexIdeal computes bases of I in each degree up through the maximum degree of a minimal generator of I to determine whether I is a lexicographic ideal in R.
i1 : R=ZZ/32003[a..c]; |
i2 : isLexIdeal lexIdeal(R,{1,3,4,3,1}) o2 = true |
i3 : isLexIdeal ideal(a^3-a^2*b) o3 = false |
i4 : isLexIdeal ideal(a^3,a^2*b) o4 = true |
i5 : isLexIdeal ideal(a^3,a^2*b,a^3-a^2*b) --not given as a monomial ideal but still a lex ideal o5 = true |
i6 : Q=R/ideal(a^3,b^3,a*c^2); |
i7 : isLexIdeal ideal(a^2*b,a^2*c) o7 = true |
i8 : isLexIdeal ideal(a^2*b,a*b^2) o8 = false |
The object isLexIdeal is a method function.