Sage: Ticket #22201: Further series speed improvements
https://trac.sagemath.org/ticket/22201
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This is a followup on <a class="closed ticket" href="https://trac.sagemath.org/ticket/14878" title="#14878: defect: Doctest fix for: very slow taylor expansion for composite functions (closed: fixed)">#14878</a>. There, the GiNaC series code was improved speedwise in many holonomic cases. However, there is still the possibilty of huge slowdown in the other holonomic cases, and of course in all non-holonomic and multivariate cases. Moreover it appears Maxima is actually faster with composite expressions of this type.
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<p>
So, it makes sense to completely abandon the original GiNaC series code, and use Pynac useries with Maxima as fallback.
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Example where Maxima is faster than GiNaC:
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<pre class="wiki">sage: f=5/(e^(1/256*z*(sqrt(5) + I*sqrt(2*sqrt(5) + 10) - 1)^4) + e^(1/64*z*(sqrt(5) + I*sqrt(2*sqrt(5) + 10) - 1)^3) + e^(1/16*z*(sqrt(5) + I*sqrt(2*sqrt(5) + 10) - 1)^2) + e^(1/4*z*(sqrt(5) + I*sqrt(2*sqrt(5) + 10) - 1)) + e^z)
sage: %time _=f.series(z,20)
CPU times: user 6.88 s, sys: 99.7 ms, total: 6.98 s
Wall time: 6.79 s
sage: %time _=f.taylor(z,0,20)
CPU times: user 600 ms, sys: 19.6 ms, total: 620 ms
Wall time: 619 ms
</pre>en-usSagehttps://trac.sagemath.org/chrome/site/logo_sagemath_trac.png
https://trac.sagemath.org/ticket/22201
Trac 1.2