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isLexIdeal -- determine whether an ideal is a lexicographic ideal

Synopsis

Description

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 first checks to see that I is a monomial ideal. If not, it returns false. If so, isLexIdeal computes bases of R/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 : Q=R/ideal(a^3,b^3,a*c^2);
i6 : isLexIdeal ideal(a^2*b,a^2*c)

o6 = true
i7 : isLexIdeal ideal(a^2*b,a*b^2)

o7 = false

See also

Ways to use isLexIdeal :