implement substitute for monoids #598
Description
On 9/5/07, Joel B. Mohler <[email protected]> wrote:
\> Yes, so I found FreeMonoid after sending my first e-mail and was testing it
> out. I think I may have found something that is not implemented:
>
> sage: a=FreeMonoid(1,'a').0
> sage: a*a
> a^2
> sage: a.substitute(5)
> a # should be 5?
> sage: a.substitute(a=5)
> a # should be 5?
>
> I would have expected those last two results to be 5 -- am I missing
> something?
The whole "substitute" architecture was implemented in SAGE
long after monoids were implemented. So you'll have to implement
monoid substitution.
> I guess substituting isn't an entirely common operation for free
> monoids, but it seems to be a sensibly defined operation. Then again, maybe
> not:
>
> sage: M.<x,y> = FreeMonoid(2)
> sage: (x*y).substitute(x=1)
> x*y # I would think that this is 1*y
>
> I find that result unsatisfactory as well, but I sure don't have a good idea
> about what ring (?) the result '1*y' would be a part of.
Just do the arithmetic. All monoids have a 1 by definition, so 1*y is just "y"
in that monoid.
William
Component: basic arithmetic
Author: Mike Hansen
Reviewer: Paul Zimmermann
Merged: sage-4.4.alpha0
Issue created by migration from https://trac.sagemath.org/ticket/598