On 07/12/2011 06:11 PM, robin hankin wrote:
> Hi.
>
>
> The psi function is defined over the entire complex plane.
>
> But sage doesn't seem to know anything about its properties.
>
> For example, I happen to know that psi(1-z) == pi/tan(pi*z) + psi(z)
>
> So I would expect the following sage command:
>
> sage: (psi(1-z)- psi(z)-pi/tan(pi*z)).full_simplify()
>
> [complicated expression deleted].
>
>
> to give zero.
>
> How do I tell sage to simplify this expression?
>
Slight non-sequitur: is there an easy-to-express notion of which is the
simpler of two expressions in Sage? For example, the way that I'd go
about adding a simplification for this is the following pseudo-code:
def simplify_psi(expr):
for v in expr.variables():
if v is complex:
# Try to substitute one psi expression for the other.
simple_expr = expr.subs({psi(1-v): pi/tan(pi*v) + psi(v)})
# Return the answer if the substitution did any good.
if simple_expr <simpler than> expr:
return simple_expr
else:
return expr
But generally this transformation would make the expression more
complex. In a few cases, it would wind up simpler; but, how do we tell
which we've just done?
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