On Sat, Oct 13, 2012 at 07:09:33AM +0000, Simon King wrote:
> By the way, did you think about a construction functor for the new
> parents? If I understand correctly, you have some algorithmic procedure
> A that you apply to some basic data (a root) R. Hence, it would not be
> totally absurd to have an AlgorithmicClosure functor F(A), such that
> F(A) applied to R returns the associated RecursiveSet. The existence of
> a construction functor would support the construction of coerce maps -
> *IF* one is able to guess the priority of F(A) (i.e., would one first
> apply F(A) or another functor in a pushout?) and how it merges/commutes
> with other functors - both would depend on the mathematical properties of A.
>
> That's a pretty big "if". So, perhaps having construction functors would
> be unfeasible. But perhaps you have ideas of how to make it work.
Interesting. On a similar note, in MuPAD-Combinat, we had things
like:
M.monoid_closure(generators) (based on TransitiveIdeal)
G.group_closure(generators) (based on TranstivieIdeal; of
course for permutation/matrix
groups we should do better)
V.module_closure(generators, operators)
A.algebra_closure(generators) (based on the above)
C.coalgebra_closure(generators)
K.kac_algebra_closure(generators)
We need to implement those and think along the way about a nice
functorial approach if there is one!
Hmm, the above suggests to have S.set_closure(generators, operators)
as idiom for TransitiveIdeal ? The inconvenient is that we need to
have a set S under hand.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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