Hello all, I'm currently working on enriching the ModulesWithBasis Category in Sage, and I have a question about what to call things. Namely, when given a sum of generators with coefficients, what is a 'term' and what is a 'monomial'. (Typically, I am asking for leading/trailing terms/monomials). I would like to make the following definitions: Given a QQ-module with basis B[0], B[1] and an element
f = 3*B[0] + 2*B[1] I would have f.leading_term() == 3*B[0] f.leading_coefficient() == 3 f.leading_monomial() == B[0] This is consistent with what I found in the doc of sage.rings.polynomial.toy_d_basis: The notion of 'term' and 'monomial' in [BW93]_ is swapped from the notion of those words in Sage (or the other way around, however you prefer it). In Sage a term is a monomial multiplied by a coefficient, while in [BW93]_ a monomial is a term multiplied by a coefficient. Also, what is called LM (the leading monomial) in Sage is called HT (the head term) in [BW93]_. Singular and Magma seem to agree with Sage. MuPAD uses the opposite convention. Both show up in the literature. Is everyone OK with term = coefficient * monomial ? Does anyone know of a part of Sage that is currently not consistent with this? Thanks, Jason
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