Hi,
I was wondering what the fastest way is to do this benchmark in Sage:
┌────────────────────────────────────────────────────────────────────┐
│ Sage Version 6.4, Release Date: 2014-11-14 │
│ Enhanced for SageMathCloud. │
└────────────────────────────────────────────────────────────────────┘
sage: var('a1 a2 a3 a4 a5 a6 a7')
(a1, a2, a3, a4, a5, a6, a7)
sage: time f = expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
CPU times: user 9.02 s, sys: 281 ms, total: 9.3 s
Wall time: 8.91 s
sage: len(f.operands())
23751
I took the "Expanding a Symbolic Expression" from
http://www.sagemath.org/tour-benchmarks.html, but made it shorter and
added sqrt(3) in there. I tried to use the polynomials way, i.e.
R.<a1,a2,a3,a4,a5,a6,a7> = QQ[], but that didn't expand it at all. The
above is using SMC.
On my slow laptop, using our CSymPy library
(https://github.com/sympy/csympy), written in C++, I get:
In [4]: time f = ((a1+a2+a3+a4+sqrt(3)*a5)**25).expand()
CPU times: user 201 ms, sys: 23.9 ms, total: 225 ms
Wall time: 226 ms
In [5]: len(f.args)
Out[5]: 23751
Which is almost 40x faster.
Essentially I am wondering, if there is any software in Sage that can
do this faster. In other words, whether this is a good benchmark to
test general symbolic manipulation, that cannot be trivially converted
to a polynomial manipulation (for which there are great libraries out
there, that one should just call).
Ondrej
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