On Sat, Oct 31, 2009 at 12:53 PM, <leh...@bayou.uni-linz.ac.at> wrote: > > On Sat, Oct 31, 2009 at 10:30:31AM -0400, Bill Page wrote: >> Do you think we can define exactly what it should mean? > I don't understand this question.
What does the following recursive definition mean? >> Coalgebra(R : CommutativeRing, RR : TensorPowerCategory(R, %)): Category == _ >> Module(R) with >> coproduct : % -> RR >> Specifically, if you specify that a domain satisfies this category what does RR represent? It appears that the domain is somehow recursive since we cannot know what is this domain unless we know what is RR. We cannot know what is RR unless we first know what is the domain. So the meaning is not immediately clear to me. I wonder how you and Bertfried interpret this definition? >> My questions was intended to ask why you considered this "too rigid". > because I do not know how to define > tensor: (TensorPower(m,M),TensorPower(n,M)) -> TensorPower(m+n,M) > without a lot of typing. The same decision apparently was made > with Matrix and Vector. I think the appropriate mode for Tensor is not Matrix (which has a clear and simple category) but rather SquareMatrix. See especially the definition: SquareMatrixCategory(ndim,R,Row,Col): Category == Definition where ndim : NonNegativeInteger R : Ring Row : DirectProductCategory(ndim,R) Col : DirectProductCategory(ndim,R) > ... Regards, Bill Page. --~--~---------~--~----~------------~-------~--~----~ 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 fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
