I agree with your proposed terminology for term, coefficient and monomial. Though I would only have used the word "monomial" for a polynomial algebra when thought of as a module, otherwise just "generator" or similar.
John 2010/1/13 Jason Bandlow <jband...@gmail.com>: > 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 > > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > >
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