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isLexIdeal -- determine whether an ideal is a lexicographic ideal



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

See also

Ways to use isLexIdeal :

For the programmer

The object isLexIdeal is a method function.