On Fri, 3 Nov 2006, William Stein wrote: > > On Fri, 03 Nov 2006 09:54:14 -0800, Robert Bradshaw > <[EMAIL PROTECTED]> wrote: >> I think the problem here is that it _assumes_ that x and y commute, >> which is not the only option. >> >> I am still looking for a convincing reason that >> >> sage: (1/2) * Matrix(ZZ, 2, 2, [1,2,3,4]) >> >> should not give >> >> [1/2 1] >> [3/2 2] >> >> in MatrixSpace(QQ, 2, 2). Maybe it's just the cleanliness/ >> implementation of the coercion rules. > > In this case there could be a clean coercion rule. E.g., > > Try standard rules. If they fail, then: > > (1) Check if the base ring of the parent of the left hand > side coerces to the parent of the right hand side. > > (2) Check if the base ring of the right hand side coerces > to the parent of the left hand side. > > If exactly one of (1) and (2) succeeds, say (2), then: > > (a) Compute the base extension of the right hand side > to the parent of the parent of the left hand side. > (b) Do the algebra multiply. > > If both succeed, it's ambiguous -- throw an error. > > With your > > (1/2) * Matrix(ZZ, 2, 2, [1,2,3,4]) > > example this gives what you want. > > With your > > (1/2) * (x^2 + 1) > > with x in ZZ['x'] this also gives what you want. > > With > > x * y > > with x in ZZ['x'] and y in ZZ['y'] this gives *ambiguous* > and throws an error. > > What do you think? > > -- William >
This is exactly what I was thinking of before I started about generalizing to other rings. I think this could be rephrased recursively to handle cases like 1/2 * ZZ[x][y]. Robert > > --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
