Substituting numeric one in symbolic expression gives symbolic one

[zimmermann6]

consider the following in Sage 5.8:

sage: u(n) = n^100 / 100^n; u(1.)
1/100

This is inconsistent with:

sage: n=1.; n^100 / 100^n
0.0100000000000000

and with:

sage: v = lambda(n): n^100 / 100^n; v(1.)
0.0100000000000000

and:

sage: def w(n): return n^100 / 100^n       
sage: w(1.) 
0.0100000000000000

CC: @mezzarobba @burcin

Component: basic arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/14326

[zimmermann6]

comment:2

Jeroen, do you have an idea who to include in cc to help isolate this?

Paul

[kcrisman]

comment:7

Wow, this is weird. Here is a much simpler example.

sage: w(n) = n
sage: w(1.)
1.00000000000000
sage: w(n) = n^2
sage: w(1.)
1

In fact, even

sage: (x^2).subs(x=1.)
1

works. Yuck.

Somehow the custom power method is not doing its job when you substitute . But I don't see an obvious place in Ginac where this would get screwed up...

Aha.

sage: z = x^2
sage: z.subs(x=1.)
1
sage: z.subs(x=2.)
4.00000000000000

Because one does get treated differently. Though

sage: z = x
sage: z.subs(x=1.)
1.00000000000000

so it also has something to do with the coercion that happens in the power method for symbolic expressions.