On Tue, 2008-06-10 at 12:56 -0700, Carl Witty wrote:
> On Jun 10, 10:44 am, polo0691 <[EMAIL PROTECTED]> wrote:
> > Thanks for creating sage! I can really see how useful sage could be
> > for engineering purposes. I've been playing around with sage for a
> > couple of days and I have had trouble with the following:
> >
> > 1) simplifying equations with exponents:
> >
> > sage: var('vgs vt n')
> > (vgs, vt, n)
> > sage: f = (vgs - vt)^n
> > sage: f^(1/n)
> > ((vgs - vt)^n)^(1/n)
> > sage: f^(1/n).simplify()
> > ((vgs - vt)^n)^(1/n)
> >
> > It doesn't seem to easily simplify the exponent. I'm guessing it
> > is a limitation of the CAS engine used. I also tried the same test
> > case on YACAS and it didn't seem to want to simplify the exponent
> > either.
>
> I'm not surprised this doesn't simplify: there's no consistent
> definition for exponentiation that lets you safely apply the
> simplification you want. To pick a simple case, over the reals,
> squaring followed by square root gives the absolute value:
>
> sage: ((-2)^2)^(1/2)
> 2
Sometimes you can use 'assume' to get the behavior you want, however. In
this case, for example:
sage: var('vgs vt n')
(vgs, vt, n)
sage: f = (vgs - vt)^n
sage: assume(vgs > vt)
sage: f^(1/n)
vgs - vt
sage: forget()
sage: f^(1/n)
((vgs - vt)^n)^(1/n)
sage:
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