On Dec 1, 2008, at 5:11 AM, Stan Schymanski wrote:
> Hi Robert,
>
> I wasn't aware of the real() function; pretty cool. I tried it out
> myself in the above example and found an error. Not sure whether this
> is an error in the real() function or in simplify_full. I suspect the
> latter. Could you comment on this? I would also be very interested in
> a way of defining symbolic variables such that they can only be real.
> Is this only possible by doing assume(omgo,'real')?
Yes.
sage: assume(x, 'real')
sage: x.imag()
0
Are you saying you would like to pass in a domain when creating the
variables? Something like
sage: var('omega', domain=RR)
> Here is the error I found. The result given by omgo.simplify_full
> ().real() is different to the one obtained by omgo.factor().
Currently we're using maxima as a back end for all the calculus
operations. This is probably due to maxima's simplifications being
lax with branch cuts, similar to
-1 = sqrt(-1)^2 = sqrt(-1) * sqrt(-1) "=" sqrt(-1 * -1) = sqrt(1) = 1
> Thanks for your help!
You're welcome.
- Robert
>
> ----------------------------------------------------------------------
> | Sage Version 3.2, Release Date: 2008-11-20 |
> | Type notebook() for the GUI, and license() for information. |
> ----------------------------------------------------------------------
>
> sage: var('omgo zr ys cz')
> (omgo, zr, ys, cz)
> sage: omgo = (sqrt(-zr^2 + 2*ys*zr + (2*cz - zr)^2 - 2*ys*(2*cz - zr))
> + 2*zr- 2*cz)/(2*zr - 2*cz)
> sage: assume(cz>ys,cz>zr)
> sage: omgo.factor()
> (zr + sqrt(cz - ys)*sqrt(cz - zr) - cz)/(zr - cz)
> sage: omgo.simplify_full().real()
> (zr - sqrt(cz - ys)*sqrt(cz - zr) - cz)/(zr - cz)
>
> On Nov 28, 9:14 am, Robert Bradshaw <[EMAIL PROTECTED]>
> wrote:
>> On Nov 27, 2008, at 6:58 AM, [EMAIL PROTECTED] wrote:
>>
>>> Hello,
>>
>>> the example below shows that a complex number ( i think the "I"
>>> stands
>>> for it ? ) appears by doing a simplify_full. Is there a way to
>>> prevent
>>> this and to get output in real number format?
>>
>>> sage: var('omgo zr ys cz')
>>> sage: eqomgo = omgo == (sqrt(2*ys - 2*cz)*sqrt(2*zr - 2*cz))/(2*zr -
>>> 2*cz)
>>> sage: eqomgo.rhs().simplify_full()
>>> I*sqrt(cz - ys)/sqrt(zr - cz)
>>
>> Is ys assumed to be larger than cz? What about zr and cz? You can use
>> the assume command
>>
>> sage: assume(ys > cz)
>> sage: assume(zr > cz)
>>
>> Then do
>>
>> sage: sage: eqomgo.rhs().simplify_full().real()
>> -sqrt(ys - cz)/sqrt(zr - cz)
>>
>> - Robert
> >
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