Re: [Reduce-algebra-developers] is this a bug?

[Alan B. <ala...@gm...>]

Hi Rudolf,

Yes, you may use either TPS or TAYLOR packages to expand an expression 
as a power series.

Either, I think, will do equally well for your problem.  The main 
difference for the user is that tps (which I developed) calculates an 
extendible power series using  simulated lazy evaluation.   By default 
terms up to sixth order are calculated and displayed although this limit 
can be altered by the function PSEXPLIM with an integer argument.  You 
can also truncate a power sereis expansion to produce a polynomial (or a 
rational function if the order of the series is negative) using the 
function PSTRUNCATE.

The main advantage of the lazy evaluation scheme is that if you decide 
you want (say) the 20th term of the power series just calculated with (say)

ps(some-exp,x,0);

You issue a call

psterm(ws, 20);

The series will be extended automatically up to the 20th term and the 
required term output.

With the taylor package one would need to do

taylor(some-exp, x, 0, 6);

To see the 20th term you would need to recalculate the whole series from 
the start with a call such as

taylor(some-exp, x, 0, 20);

Admittedly with modern machines being so fast, this is not a big penalty 
unless, of course, some-exp is very complicated.

The extendible nature of the series is also very useful in examples such as

s1 := ps(cos x-cosh x, x, 0);

s2:=ps(sin x -sinh x, x,0);

s1/s2;   % power quotient calculated automatically and displayed 
correctly to SIXTH order

Getting the same effect with TAYLOR is a little more complicated.

However, TAYLOR is usually faster and uses less store than TPS on many 
problems.

Actually the name TPS is misleading, it originally stood for truncated 
power series. The PS package was developed from an earlier TPS  package 
written by Julian Padget which did use truncated series, but the 
algorithms and data structures were extendd to allow the automatic 
extension of the series.  Somehow Julian and I never got around to 
changing the name of the package!

Regards
Alan Barnes

On 20/02/2018 14:43, Rudolf Sykora wrote:
> Dear Arthur,
>
> On 20 February 2018 at 14:39, Arthur Norman <ac...@ca...> wrote:
>> Apologies if my previous message was too brief. The weight/wtlevel stuff
>> rather expects to be applying to polynomials and you can see that it it
>> looks as sqrt(-delta^2+epsilion^2) it is liable to map that onto
>> sqrt(epsilon^2) before considering much more.
> thanks for more information.
> So, in my case, I should have used the 'tps' package,
> not the weight/wtlevel. I thought the weight would do the
> expansion, which it does not.
>
> Thanks once more,
>
> Ruda
>
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