Actually, I was wrong about calculations within the rectform being done in
floating-point here. In particular, %pi is not expanded to a float.
Rectform should probably take numer into account here to make it more
efficient. Or maybe the simplifier should always use the numeric form of
symbolic constants like %e, %pi, etc. when they are combined with floats,
e.g. 2.0*%pi => 6.28, not 2.0*%pi.
-s
On Sun, Feb 24, 2013 at 12:33 PM, Stavros Macrakis <macrakis at alum.mit.edu>wrote:
> To put a numerical expression in a+b*%i form, use
>
> block([numer:true],float(rectform(subst([a=1,b=2,...],expr))))
>
> or
>
> ev(float(rectform(expr)),numer,a=1,b=2,...).
>
> These ensures that calculations *within *the rectform are done in
> floating-point, not symbolic form, which can be *much* faster that
> something like float(rectform(expr)) on large expressions because it avoids
> unnecessary intermediate-expression expansion.
>
> Both of these solutions seem unnecessarily complicated. There have been
> proposals to treat complex numbers as single numbers, rather than
> expressions involving numbers, but as far as I know, no one has
> demonstrated a comprehensive solution along those lines (that handles
> complex rationals, complex bfloats, etc. uniformly).
>
> You may be wondering what the 'float' is for if we already have
> numer:true. That is to catch the edge case where expr is a simple integer:
> ev(3,numer) => 3, not 3.0.
>
> -s
>
> On Sun, Feb 24, 2013 at 10:33 AM, Henry Baker <hbaker1 at pipeline.com>wrote:
>
>> What is the preferred way to convert the results of
>> solve(z^3+b*z^2+c*z+d,z), where b,c,d are complex floating point numbers,
>> and z is a complex variable, into floating point?
>>
>> numer doesn't always do it.
>>
>> expand doesn't always do it.
>>
>> rectform doesn't always do it.
>>
>> radcan doesn't do it.
>>
>> I keep getting expt(...) forms in my display that I can't always get rid
>> of.
>>
>> These are all _constant_ numerical numbers, so there ought to be a way to
>> force numerical evaluation.
>>
>>
>