[Maxima-discuss] trigrat with fractional powers WAS trigrat crashes

[Stavros M. (Σ. Μ. <mac...@al...>]

I don't think trigrat is very useful for fractional powers.

Consider the simplest example, trigrat(sin(x)^(1/2).  This returns

(sqrt(2)*%i*(sin(2*x)^2+cos(2*x)^2-2*cos(2*x)+1)^(1/4)*
sin((atan2(cos(2*x)-1,-sin(2*x))-atan2(sin(x),cos(x))+%pi)/2)+
sqrt(2)*(sin(2*x)^2+cos(2*x)^2-2*cos(2*x)+1)^(1/4)*
cos((atan2(cos(2*x)-1,-sin(2*x))-atan2(sin(x),cos(x))+%pi)/2))/2

Is that useful for anything? Note for example the subexpressions

     sin(2*x)^2+cos(2*x)^2   (identically 1)
     atan2(sin(x),cos(x))  probably should be treated as x

etc.

I doubt trigrat was even *designed* to be useful for this case.

If something more powerful than ratsimp is wanted, perhaps a useful choice
would be radcan(exponentialize(logarc(expr))).  But don't blame me if
that's a bad idea ... just a suggested thing to try.

          -s



On Thu, Jul 31, 2014 at 5:50 PM, Stavros Macrakis (Σταῦρος Μακράκης) <
mac...@al...> wrote:

> a) What do you mean by "seems to be crashing"? Does Maxima give an error
> message? Does the process coredump? Or does it just run for a very long
> time?
>
> b) Why are you using trigrat to compare expressions? trigrat expands
> expressions enormously. For example, trigrat(1/(sin(x)^(9/2)+1) is 173,754
> characters long. I am not surprised that calling trigrat on larger
> expressions might take a long time.
>
> c) In your particular example, you don't need any trig simplifications at
> all. lhs(ex)-rhs(ex) => 0. Why use a nuclear bomb when you can use a
> nail-file?
>
> d) I'm not even sure that trigrat is any better at canonicalizing
> expressions than other approaches. For example, trigrat sometimes produces
> things like atan2(sin(x),cos(x)).
>
> e) For checking expressions that don't have parameters for equality,
> taylor can be very valuable. There must be some way of determining how many
> terms of a taylor series must be zero to prove that the expression is zero
> for some classes of expression, but I don't know it....
>
> f) If you really thing trigrat is what you need, at least use
> is(equal(trigrat(a-b),0)) rather than is(trigrat(a=b)). There's a good
> chance in the former case that cancellations will happen, while in the
> latter, you are forcing trigrat to expand even if there will ultimately be
> cancellations.
>
>
>
> On Thu, Jul 31, 2014 at 4:38 PM, Max Cohen <ma...@so...> wrote:
>
>>  Hello,
>>
>> I use trigrat to compare expressions with trigonometry in them. When I do
>> is(trigrat(((diff((7) /(4 +(sin(x))^((5)/2)),x)=( - ( (( ( 35 * cos(x) )
>> * (sin(x)^(3/2)) )/( 2 * (( (sin(x)^(5/2)) + 4 )^2) )) ) )))));
>>
>> maxima seems to be crashing. However, if I interrupt maxima and run the
>> same command again, it does answer!?
>> This looks to me like a bug in maxima?
>>
>> Also, maybe related, the following takes a very long time on my machine:
>> (trigrat(radcan((4*sin(%pi*93/180)/sin(%pi*65/180)))));
>>
>> I'm on ubuntu, sbcl.
>>
>> regards,
>>
>> Max  <http://sowiso.com/en/blog/>
>>
>>
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