# OrderingFunctions(dim, S)¶

This package provides ordering functions on vectors which are suitable parameters for OrderedDirectProduct.

pureLex: (Vector S, Vector S) -> Boolean

pureLex(v1, v2) return true if the vector v1 is less than the vector v2 in the lexicographic ordering.

reverseLex: (Vector S, Vector S) -> Boolean

reverseLex(v1, v2) return true if the vector v1 is less than the vector v2 in the ordering which is total degree refined by the reverse lexicographic ordering.

totalLex: (Vector S, Vector S) -> Boolean

totalLex(v1, v2) return true if the vector v1 is less than the vector v2 in the ordering which is total degree refined by lexicographic ordering.