Waldek, Ralf, Although as I said, I do not like to call the map x+->[x,x] a "coercion" (and it's associated "retraction") I have problems justifying denying it formally. It seems to satisfy all the requirements as I understand them. (We've discussed the requirements previously and there are some relevant pages on the Axiom wiki.) I think that
if R has SetCategory then FullyRetractableTo R is true under our normal understanding of these terms and FullyRetractableTo(R) exports coerce:R->%. Also as Ralf points out there are other reasons why this coercion appears when R has even more structure (such as a Ring). I think it would be difficult to avoid this. Perhaps there should be something else to obstruct the formation of this unexpected product. Gaby commented in the OpenAxiom thread on this subject that he thought the problem might be overloading of *. Does it make sense to use the symbol * to denote mulitiplication of a Matrix by a row vector (DirectProduct)? Regards, Bill Page. On Sat, Jun 12, 2010 at 7:50 AM, Waldek Hebisch <[email protected]> wrote: > Bill Page wrote: >> Ralf, >> >> I think that the map >> >> coerce : Fraction Polynomial Complex Integer -> % >> >> which is apparently x+-> [x,x] >> >> in >> >> )sh DirectProduct(2,Fraction Polynomial Complex Integer) >> >> should not be called a coercion. > > Good spot. AFAICS that coercion is defined because we have > > if R has SetCategory then FullyRetractableTo R > > in DirectProductCategory. IMHO this does not make sense. > But before removing it one have to fix a few places in algebra > (at least retract in SquareMatrix) where the retraction from direct > product to scalars is used. > > -- > Waldek Hebisch > [email protected] > > -- > You received this message because you are subscribed to the Google Groups > "FriCAS - computer algebra system" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/fricas-devel?hl=en. > > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en.
