I have questions about coercion rules for finite fields. 1. Let F1 and F2 be two finite fields of order q, x1 in F1, x2 in F2. Do the planned on coercion rules imply that x1+x2 is defined? I assume so, since there probably is a coercion map F1 -> F2 (and F2->F1). The problem is that x1+x2 != x2+x1
2. Let F1 subset F2 be two finite fields of order q, x1 in F1, x2 in F2. Consider the sum x2+x1+x2. The sum x2+(x1+x2) makes sense but the sum (x2+x1)+x2 does not (assuming that there is no coercion F2->F1). 3. Does 0 coerce into any other finite field? In other words, does F2(0)+F1(0) make sense? +++++++++++++++++++++++++++++++++++++++++ David Harvey wrote: > On Oct 28, 2006, at 8:23 PM, William Stein wrote: > > >> What are the rules for algebras going to be? >> >> Suppose R and S are commutative rings (for simplicity) and M and N are >> R modules and K is an S-module. >> >> Choose x in M and y in N. Then coerce should work exactly as before. >> All the _coerce_ maps are R-module homomorphisms, etc., and there >> is nothing new going on here. Next assume that z in K. To do x + z, >> we have to worry about base rings. >> >> PROPOSED RULE: Suppose there is a coerce map (of rings!) R --> S. >> Then to compute x+z we first compute Z = M.base_extend(S), which is an >> S-module >> such that _coerce_ on elements of M gives elements of Z in the >> natural way. >> We are now do the add >> Z._coerce_(x) + z >> using the usual rules. >> > > This sounds good to me. > > >> Next, consider multiplication. Suppose in addition that M, N, and >> K are >> all >> algebras. Suppose that x in M and z in K. Multiplication should >> work in >> exactly the same way as addition above. >> > > [...] > > Also sounds good. > > I'm a bit worried about ambiguous situations arising, although I > can't think of any specific examples. If both objects are module > elements (or algebra elements) then everything's ok I think. I'm more > worried about multiplying a ring element by an algebra element; it > feels like it might be possible to get an ambiguous situation where > you don't know whether to coerce yourself towards a scalar > multiplication or an algebra multiplication. > > David > > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
