Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
On 19 January 2015 at 23:03, mmarco mma...@unizar.es wrote: It is much faster to work with absolute fields instead of towers of extensions: sage: K.sqrt3=QuadraticField(3) sage: F.sqrt5=K.extension(x^2-5) sage: R.a1,a2,a3,a4,a5 = F[] sage: %time _=(a1+a2+a3+sqrt5*a4+sqrt3*a5)^25 CPU times: user 27.4 s, sys: 12 ms, total: 27.4 s Wall time: 27.5 s sage: FF.a=F.absolute_field() sage: fsqrt3=FF(F(sqrt3)) sage: fsqrt5=FF(sqrt5) sage: RR.a1,a2,a3,a4,a5 = FF[] sage: %time _=(a1+a2+a3+fsqrt5*a4+fsqrt3*a5)^25 CPU times: user 1.26 s, sys: 3 ms, total: 1.27 s Wall time: 1.27 s I guess that pari internally follows the second approach. No I don't think so. In gp: ? Mod(x,x^2-3) + Mod(y,y^2-5) %2 = Mod(x + Mod(y, y^2 - 5), x^2 - 3) This can be read as a polynomial in x subject to the side condition that x^2=3, where one of the coefficients is y subject to y^2=5. Before I tried the above I did this: ? Mod(x,x^2-3) + Mod(x,x^2-5) %1 = 0 which is a warning to anyone trying to interface between Sage and Pari/GP! John -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
On 2015-01-20 10:14, John Cremona wrote: ? Mod(x,x^2-3) + Mod(x,x^2-5) %1 = 0 That's a PARI feature: the result would lie in the ring QQ[x]/(x^2-3, x^2-5) = QQ[x]/(1) -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
any idea how to get the number of terms in a better way in Sage?): sage: K.sqrt3 = QuadraticField(3) sage: L.sqrt5 = K.extension(x^2-5) sage: R.a1,a2,a3,a4,a5 = L[] sage: time f = (a1+a2+a3+sqrt5*a4+sqrt3*a5)^18 CPU times: user 2.43 s, sys: 3.94 ms, total: 2.44 s Wall time: 2.44 s sage: len(str(f).split(+)) 7315 You may do len(list(f)). To avoid the creation of the list: sum(1 for _ in f). Some timings: sage: %time len(str(f).split(+)) CPU times: user 8.2 s, sys: 3.14 s, total: 11.3 s Wall time: 12 s 7315 sage: %time len(list(f)) CPU times: user 699 ms, sys: 98.1 ms, total: 797 ms Wall time: 770 ms 7315 sage: %time len(f.monomials()) CPU times: user 127 ms, sys: 13.7 ms, total: 141 ms Wall time: 135 ms 7315 sage: %time sum(1 for _ in f) CPU times: user 69.6 ms, sys: 18.8 ms, total: 88.3 ms Wall time: 85.2 ms 7315 Sébastien -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
It is much faster to work with absolute fields instead of towers of extensions: sage: K.sqrt3=QuadraticField(3) sage: F.sqrt5=K.extension(x^2-5) sage: R.a1,a2,a3,a4,a5 = F[] sage: %time _=(a1+a2+a3+sqrt5*a4+sqrt3*a5)^25 CPU times: user 27.4 s, sys: 12 ms, total: 27.4 s Wall time: 27.5 s sage: FF.a=F.absolute_field() sage: fsqrt3=FF(F(sqrt3)) sage: fsqrt5=FF(sqrt5) sage: RR.a1,a2,a3,a4,a5 = FF[] sage: %time _=(a1+a2+a3+fsqrt5*a4+fsqrt3*a5)^25 CPU times: user 1.26 s, sys: 3 ms, total: 1.27 s Wall time: 1.27 s I guess that pari internally follows the second approach. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
Hi Miguel, On Mon, Jan 19, 2015 at 4:03 PM, mmarco mma...@unizar.es wrote: It is much faster to work with absolute fields instead of towers of extensions: sage: K.sqrt3=QuadraticField(3) sage: F.sqrt5=K.extension(x^2-5) sage: R.a1,a2,a3,a4,a5 = F[] sage: %time _=(a1+a2+a3+sqrt5*a4+sqrt3*a5)^25 CPU times: user 27.4 s, sys: 12 ms, total: 27.4 s Wall time: 27.5 s sage: FF.a=F.absolute_field() sage: fsqrt3=FF(F(sqrt3)) sage: fsqrt5=FF(sqrt5) sage: RR.a1,a2,a3,a4,a5 = FF[] sage: %time _=(a1+a2+a3+fsqrt5*a4+fsqrt3*a5)^25 CPU times: user 1.26 s, sys: 3 ms, total: 1.27 s Wall time: 1.27 s Thanks. I tried it on SMC: sage: K.sqrt3=QuadraticField(3) sage: F.sqrt5=K.extension(x^2-5) sage: R.a1,a2,a3,a4,a5 = F[] sage: %time _=(a1+a2+a3+sqrt5*a4+sqrt3*a5)^18 CPU times: user 2.76 s, sys: 12.5 ms, total: 2.77 s Wall time: 2.77 s sage: len(str(_).split(+)) 7315 sage: FF.a=F.absolute_field() sage: fsqrt3=FF(F(sqrt3)) sage: fsqrt5=FF(sqrt5) sage: RR.a1,a2,a3,a4,a5 = FF[] sage: %time _=(a1+a2+a3+fsqrt5*a4+fsqrt3*a5)^18 CPU times: user 320 ms, sys: 0 ns, total: 320 ms Wall time: 320 ms sage: len(str(_).split(+)) 12430 and your approach returns a wrong number of terms, so something is wrong. But it is quite fast. Ondrej -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
On Monday, January 19, 2015 at 9:27:44 PM UTC-8, Ondřej Čertík wrote: and your approach returns a wrong number of terms, so something is wrong. But it is quite fast. The term count doesn't tell you that. The representation of sqrt3 and sqrt5 doesn't consist of single term expressions: sage: fsqrt3 -1/4*a^3 + 7/2*a sage: fsqrt5 -1/4*a^3 + 9/2*a -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
What is here?
AMD Phenom 3GHz, 8GB RAM, no other big jobs
Since that expression is large, the cache size of the CPU might
significantly impact performance.
Wouldn't that affect any of the following?
│ Sage Version 6.5.beta5, Release Date: 2015-01-05 │
│ Type notebook() for the browser-based notebook interface.│
│ Type help() for help.│
└┘
┏┓
┃ Warning: this is a prerelease version, and it may be unstable. ┃
┗┛
sage: K.sqrt3 = QuadraticField(3)
sage: R.a1,a2,a3,a4,a5 = K[]
sage: timeit((a1+a2+a3+a4+sqrt3*a5)^25)
5 loops, best of 3: 140 ms per loop
sage: a1,a2,a3,a4,a5=var('a1,a2,a3,a4,a5')
sage: timeit(ex=expand((a1+a2+a3+a4+sqrt(3)*a5)^25))
5 loops, best of 3: 5.29 s per loop
I was wrong in the poly(SR) case. That's even slower than SR.expand():
sage: R.a1,a2,a3,a4,a5 = PolynomialRing(SR, 'a1,a2,a3,a4,a5')
sage: %time p=(a1+a2+a3+a4+sqrt(3)*a5)^25
stopped after a minute
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Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
On Sunday, January 18, 2015 at 9:18:53 AM UTC+1, vdelecroix wrote: Your example can be reduced to polynomials sage: K.sqrt3 = QuadraticField(3) sage: R.a1,a2,a3,a4,a5 = K[] sage: timeit((a1+a2+a3+a4+sqrt3*a5)^25) 5 loops, best of 3: 81 ms per loop How do you get this speed? Here it's three orders of magnitude slower. BTW another way is to use polynomials over SR, for about the same speed but without number field restrictions. Regards, -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
On Mon, Jan 19, 2015 at 8:55 AM, Ralf Stephan gtrw...@gmail.com wrote: On Sunday, January 18, 2015 at 9:18:53 AM UTC+1, vdelecroix wrote: Your example can be reduced to polynomials sage: K.sqrt3 = QuadraticField(3) sage: R.a1,a2,a3,a4,a5 = K[] sage: timeit((a1+a2+a3+a4+sqrt3*a5)^25) 5 loops, best of 3: 81 ms per loop How do you get this speed? Here it's three orders of magnitude slower. What is here? When I try it on SageMathCloud it's almost 4 *times* slower, so half of an order of magnitude: https://cloud.sagemath.com/projects/4a5f0542-5873-4eed-a85c-a18c706e8bcd/files/support/2015-01-19-expand-speed.sagews Since that expression is large, the cache size of the CPU might significantly impact performance. William BTW another way is to use polynomials over SR, for about the same speed but without number field restrictions. Regards, -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- William Stein Professor of Mathematics University of Washington http://wstein.org -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
On Mon, Jan 19, 2015 at 9:46 AM, Ralf Stephan gtrw...@gmail.com wrote:
What is here?
AMD Phenom 3GHz, 8GB RAM, no other big jobs
Since that expression is large, the cache size of the CPU might
significantly impact performance.
Wouldn't that affect any of the following?
│ Sage Version 6.5.beta5, Release Date: 2015-01-05 │
│ Type notebook() for the browser-based notebook interface.│
│ Type help() for help.│
└┘
┏┓
┃ Warning: this is a prerelease version, and it may be unstable. ┃
┗┛
sage: K.sqrt3 = QuadraticField(3)
sage: R.a1,a2,a3,a4,a5 = K[]
sage: timeit((a1+a2+a3+a4+sqrt3*a5)^25)
5 loops, best of 3: 140 ms per loop
sage: a1,a2,a3,a4,a5=var('a1,a2,a3,a4,a5')
sage: timeit(ex=expand((a1+a2+a3+a4+sqrt(3)*a5)^25))
5 loops, best of 3: 5.29 s per loop
That expand above is probably the problem. When you evaluate
(a1+a2+a3+a4+sqrt3*a5)^25
it is *already* expanded. Doing an additional expand isn't necessary.
It should be ano-op. In fact,
sage: timeit(ex=expand((a1+a2+a3+a4+sqrt(3)*a5)^25))
5 loops, best of 3: 5.29 s per loop
should take the same time as the previous line and without the
assignment it *does*:
sage: timeit(expand((a1+a2+a3+a4+sqrt3*a5)^25))
FAST
But with the assignment it takes way longer. Hence I suspect some
issue with memory management... no clue though.
I was wrong in the poly(SR) case. That's even slower than SR.expand():
sage: R.a1,a2,a3,a4,a5 = PolynomialRing(SR, 'a1,a2,a3,a4,a5')
sage: %time p=(a1+a2+a3+a4+sqrt(3)*a5)^25
stopped after a minute
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Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
On Mon, Jan 19, 2015 at 11:19 AM, Ondřej Čertík ondrej.cer...@gmail.com wrote: Hi Vincent, On Sun, Jan 18, 2015 at 10:06 AM, Vincent Delecroix 20100.delecr...@gmail.com wrote: Hi, 2015-01-18 18:03 UTC+01:00, Ondřej Čertík ondrej.cer...@gmail.com: Can you invent an example, that can't be converted to polynomials? Perhaps (a1+a2+a3+sqrt(5)*a4+sqrt(3)*a5)^25? Still doable. You need to involve log, exp, cos or similar transcendental functions. Can you show me how to do that? I tried: sage: K.sqrt3 = QuadraticField(3) sage: K.sqrt5 = QuadraticField(5) sage: R.a1,a2,a3,a4,a5 = K[] sage: time f = (a1+a2+a3+sqrt5*a4+sqrt3*a5)^25 But I got: TypeError: unsupported operand parent(s) for '*': 'Number Field in sqrt3 with defining polynomial x^2 - 3' and 'Multivariate Polynomial Ring in a1, a2 , a3, a4, a5 over Number Field in sqrt5 with defining polynomial x^2 - 5' Full stacktrace here: https://gist.github.com/certik/a7f2434820f8dbf890b9 I think I figured it out: sage: K.sqrt3 = QuadraticField(3) sage: L.sqrt5 = K.extension(x^2-5) sage: R.a1,a2,a3,a4,a5 = L[] sage: time f = (a1+a2+a3+sqrt5*a4+sqrt3*a5)^18 CPU times: user 2.43 s, sys: 3.94 ms, total: 2.44 s Wall time: 2.44 s (I did smaller exponent so that it finishes.) Ondrej -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
Hello Ondrej, For such questions of Sage usage, it is better to discuss on ask.sagemath.org or sage-support. You can also deal with all algebraic numbers at once with QQbar sage: sqrt3 = QQbar(sqrt(3)) sage: sqrt5 = QQbar(sqrt(5)) But then polynomials over QQbar are much slower. Vincent 2015-01-19 19:24 UTC+01:00, Ondřej Čertík ondrej.cer...@gmail.com: On Mon, Jan 19, 2015 at 11:19 AM, Ondřej Čertík ondrej.cer...@gmail.com wrote: Hi Vincent, On Sun, Jan 18, 2015 at 10:06 AM, Vincent Delecroix 20100.delecr...@gmail.com wrote: Hi, 2015-01-18 18:03 UTC+01:00, Ondřej Čertík ondrej.cer...@gmail.com: Can you invent an example, that can't be converted to polynomials? Perhaps (a1+a2+a3+sqrt(5)*a4+sqrt(3)*a5)^25? Still doable. You need to involve log, exp, cos or similar transcendental functions. Can you show me how to do that? I tried: sage: K.sqrt3 = QuadraticField(3) sage: K.sqrt5 = QuadraticField(5) sage: R.a1,a2,a3,a4,a5 = K[] sage: time f = (a1+a2+a3+sqrt5*a4+sqrt3*a5)^25 But I got: TypeError: unsupported operand parent(s) for '*': 'Number Field in sqrt3 with defining polynomial x^2 - 3' and 'Multivariate Polynomial Ring in a1, a2 , a3, a4, a5 over Number Field in sqrt5 with defining polynomial x^2 - 5' Full stacktrace here: https://gist.github.com/certik/a7f2434820f8dbf890b9 I think I figured it out: sage: K.sqrt3 = QuadraticField(3) sage: L.sqrt5 = K.extension(x^2-5) sage: R.a1,a2,a3,a4,a5 = L[] sage: time f = (a1+a2+a3+sqrt5*a4+sqrt3*a5)^18 CPU times: user 2.43 s, sys: 3.94 ms, total: 2.44 s Wall time: 2.44 s (I did smaller exponent so that it finishes.) Ondrej -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
Hi Vincent,
On Mon, Jan 19, 2015 at 11:30 AM, Vincent Delecroix
20100.delecr...@gmail.com wrote:
Hello Ondrej,
For such questions of Sage usage, it is better to discuss on
ask.sagemath.org or sage-support.
You can also deal with all algebraic numbers at once with QQbar
sage: sqrt3 = QQbar(sqrt(3))
sage: sqrt5 = QQbar(sqrt(5))
But then polynomials over QQbar are much slower.
Thanks, I'll ask there the next time. Since I started the thread here,
I'll keep it here so that everything is in one place.
So if you agree that I did things correctly, let's compare timings
(and lengths of expressions --- any idea how to get the number of
terms in a better way in Sage?):
sage: K.sqrt3 = QuadraticField(3)
sage: L.sqrt5 = K.extension(x^2-5)
sage: R.a1,a2,a3,a4,a5 = L[]
sage: time f = (a1+a2+a3+sqrt5*a4+sqrt3*a5)^18
CPU times: user 2.43 s, sys: 3.94 ms, total: 2.44 s
Wall time: 2.44 s
sage: len(str(f).split(+))
7315
Now compare this to CSymPy:
In [1]: from csympy import *
In [2]: var('a1 a2 a3 a4 a5 a6 a7')
Out[2]: (a1, a2, a3, a4, a5, a6, a7)
In [3]: %time f = ((a1+a2+a3+sqrt(5)*a4+sqrt(3)*a5)**18).expand()
CPU times: user 125 ms, sys: 7.73 ms, total: 133 ms
Wall time: 133 ms
In [4]: len(f.args)
Out[4]: 7315
You can also compare this to Sage symbolics (which should use the same
algorithm as CSymPy):
sage: var('a1 a2 a3 a4 a5 a6 a7')
(a1, a2, a3, a4, a5, a6, a7)
sage: %time f = ((a1+a2+a3+sqrt(5)*a4+sqrt(3)*a5)**18).expand()
CPU times: user 4.98 s, sys: 76.4 ms, total: 5.05 s
Wall time: 4.95 s
sage: len(f.operands())
7315
Which is also very slow.
I will try this in ginac directly, as that's what pynac is forked
from, maybe it's just the Python overhead. Also, I will carefully
check that we don't have a bug in csympy.
Ondrej
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Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
Hi Vincent, On Sun, Jan 18, 2015 at 10:06 AM, Vincent Delecroix 20100.delecr...@gmail.com wrote: Hi, 2015-01-18 18:03 UTC+01:00, Ondřej Čertík ondrej.cer...@gmail.com: Can you invent an example, that can't be converted to polynomials? Perhaps (a1+a2+a3+sqrt(5)*a4+sqrt(3)*a5)^25? Still doable. You need to involve log, exp, cos or similar transcendental functions. Can you show me how to do that? I tried: sage: K.sqrt3 = QuadraticField(3) sage: K.sqrt5 = QuadraticField(5) sage: R.a1,a2,a3,a4,a5 = K[] sage: time f = (a1+a2+a3+sqrt5*a4+sqrt3*a5)^25 But I got: TypeError: unsupported operand parent(s) for '*': 'Number Field in sqrt3 with defining polynomial x^2 - 3' and 'Multivariate Polynomial Ring in a1, a2 , a3, a4, a5 over Number Field in sqrt5 with defining polynomial x^2 - 5' Full stacktrace here: https://gist.github.com/certik/a7f2434820f8dbf890b9 Ondrej -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
On Monday, January 19, 2015 at 9:46:47 AM UTC-8, Ralf Stephan wrote: What is here? AMD Phenom 3GHz, 8GB RAM, no other big jobs On Intel(R) Core(TM) i7-2600 CPU @ 3.40GHz I'm getting the same times as Vincent. That's on 6.5beta4 or 5. The difference you're reporting is very large. You might want to check your sage build. Or otherwise sell your timing results to Intel to finance the purchase of another computer. I was wrong in the poly(SR) case. That's even slower than SR.expand(): sage: R.a1,a2,a3,a4,a5 = PolynomialRing(SR, 'a1,a2,a3,a4,a5') sage: %time p=(a1+a2+a3+a4+sqrt(3)*a5)^25 stopped after a minute Yes, I would expect that SR is *much* slower for computing in Q(sqrt(3)) than PARI is: sage: K.sqrt3 = QuadraticField(3) sage: s=sqrt(3) sage: %timeit (sqrt3+1)^25 10 loops, best of 3: 5.32 µs per loop sage: %timeit ((s+1)^25).expand() 100 loops, best of 3: 5.85 ms per loop -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
On Mon, Jan 19, 2015 at 10:32 AM, Nils Bruin nbr...@sfu.ca wrote: On Monday, January 19, 2015 at 9:46:47 AM UTC-8, Ralf Stephan wrote: What is here? AMD Phenom 3GHz, 8GB RAM, no other big jobs On Intel(R) Core(TM) i7-2600 CPU @ 3.40GHz I'm getting the same times as Vincent. That's on 6.5beta4 or 5. The difference you're reporting is very large. You might want to check your sage build. Or otherwise sell your timing results to Intel to finance the purchase of another computer. Nils, did you specifically try this **exact input**?? sage: timeit(ex=expand((a1+a2+a3+a4+sqrt(3)*a5)^25)) 5 loops, best of 3: 5.29 s per loop I was wrong in the poly(SR) case. That's even slower than SR.expand(): sage: R.a1,a2,a3,a4,a5 = PolynomialRing(SR, 'a1,a2,a3,a4,a5') sage: %time p=(a1+a2+a3+a4+sqrt(3)*a5)^25 stopped after a minute Yes, I would expect that SR is *much* slower for computing in Q(sqrt(3)) than PARI is: sage: K.sqrt3 = QuadraticField(3) sage: s=sqrt(3) sage: %timeit (sqrt3+1)^25 10 loops, best of 3: 5.32 µs per loop sage: %timeit ((s+1)^25).expand() 100 loops, best of 3: 5.85 ms per loop -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- William Stein Professor of Mathematics University of Washington http://wstein.org -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
On Monday, January 19, 2015 at 10:35:42 AM UTC-8, William wrote: Nils, did you specifically try this **exact input**?? Full session: sage: sage: K.sqrt3 = QuadraticField(3) sage: sage: R.a1,a2,a3,a4,a5 = K[] sage: sage: timeit((a1+a2+a3+a4+sqrt3*a5)^25) 5 loops, best of 3: 79.9 ms per loop sage: sage: timeit(ex=(a1+a2+a3+a4+sqrt3*a5)^25) 5 loops, best of 3: 80.4 ms per loop sage: sage: timeit(ex=expand((a1+a2+a3+a4+sqrt3*a5)^25)) 5 loops, best of 3: 80.5 ms per loop sage: sage: timeit(expand((a1+a2+a3+a4+sqrt3*a5)^25)) 5 loops, best of 3: 79.6 ms per loop version: commit b1287e75962a2dc590f1fa22acc90a4e53383aab Merge: 99ec4cc 106f5d4 Author: Jeroen Demeyer Date: Mon Jan 12 13:51:07 2015 +0100 Merge branch 'ticket/17561' into ticket/10513 Conflicts: src/sage/modules/free_module_element.pyx commit 106f5d41398794b13a6a683236cf219d49602312 Author: Jeroen Demeyer Date: Sat Jan 3 11:04:51 2015 +0100 Minor improvements in FreeModuleElement_generic_sparse.__init__ commit 99ec4cc13099658e0bc762a6e8d230c3956c7150 Author: Peter Bruin Date: Sat Jan 3 09:40:54 2015 +0100 Trac 10513: revert a change in try...except commit df0fb69e1aa9ab205e35b98ad6d97d0c67b889af Author: Jeroen Demeyer Date: Mon Dec 29 09:19:24 2014 +0100 Declare types of _entries commit 5bf671225b38a8efd55a662a8c967767ac85c7db Author: Volker Braun Date: Sun Dec 21 22:47:26 2014 +0100 Updated Sage version to 6.5.beta4 -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
The computation in pari (directed from Sage): sage: x=pari(x) sage: y=pari(y) sage: sqrt3=pari(Mod)(x, x^2-3) sage: sqrt5=pari(Mod)(y, y^2-5) sage: a1=pari(a1) sage: a2=pari(a2) sage: a3=pari(a3) sage: a4=pari(a4) sage: a5=pari(a5) sage: time f = (a1+a2+a3+sqrt5*a4+sqrt3*a5)**18 CPU times: user 148 ms, sys: 0 ns, total: 148 ms Wall time: 146 ms sage: len(str(f).split(+)) 7315 But in pari, it is not very elegant to see as there is no real support for polynomials over several variables. My conclusion is that generic polynomials in Sage are very slow! Vincent 2015-01-19 19:53 UTC+01:00, William Stein wst...@gmail.com: On Mon, Jan 19, 2015 at 10:47 AM, Nils Bruin nbr...@sfu.ca wrote: Nils, did you specifically try this **exact input**?? Full session: sage: sage: K.sqrt3 = QuadraticField(3) sage: sage: R.a1,a2,a3,a4,a5 = K[] sage: sage: timeit((a1+a2+a3+a4+sqrt3*a5)^25) 5 loops, best of 3: 79.9 ms per loop sage: sage: timeit(ex=(a1+a2+a3+a4+sqrt3*a5)^25) 5 loops, best of 3: 80.4 ms per loop sage: sage: timeit(ex=expand((a1+a2+a3+a4+sqrt3*a5)^25)) 5 loops, best of 3: 80.5 ms per loop sage: sage: timeit(expand((a1+a2+a3+a4+sqrt3*a5)^25)) 5 loops, best of 3: 79.6 ms per loop version: Thanks. I tried again and found that timeit(ex=expand((a1+a2+a3+a4+sqrt3*a5)^25)) is (of course) the same speed as timeit((a1+a2+a3+a4+sqrt3*a5)^25) in my tests.(I was in a spouse-induced hurry before.) William commit b1287e75962a2dc590f1fa22acc90a4e53383aab Merge: 99ec4cc 106f5d4 Author: Jeroen Demeyer Date: Mon Jan 12 13:51:07 2015 +0100 Merge branch 'ticket/17561' into ticket/10513 Conflicts: src/sage/modules/free_module_element.pyx commit 106f5d41398794b13a6a683236cf219d49602312 Author: Jeroen Demeyer Date: Sat Jan 3 11:04:51 2015 +0100 Minor improvements in FreeModuleElement_generic_sparse.__init__ commit 99ec4cc13099658e0bc762a6e8d230c3956c7150 Author: Peter Bruin Date: Sat Jan 3 09:40:54 2015 +0100 Trac 10513: revert a change in try...except commit df0fb69e1aa9ab205e35b98ad6d97d0c67b889af Author: Jeroen Demeyer Date: Mon Dec 29 09:19:24 2014 +0100 Declare types of _entries commit 5bf671225b38a8efd55a662a8c967767ac85c7db Author: Volker Braun Date: Sun Dec 21 22:47:26 2014 +0100 Updated Sage version to 6.5.beta4 -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- William Stein Professor of Mathematics University of Washington http://wstein.org -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
Your example can be reduced to polynomials
sage: K.sqrt3 = QuadraticField(3)
sage: R.a1,a2,a3,a4,a5 = K[]
sage: timeit((a1+a2+a3+a4+sqrt3*a5)^25)
5 loops, best of 3: 81 ms per loop
(And just for completeness, the symbolic expansion on my laptop took 4.54s)
Vincent
2015-01-18 7:26 UTC+01:00, Ondřej Čertík ondrej.cer...@gmail.com:
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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Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
Hi, 2015-01-18 18:03 UTC+01:00, Ondřej Čertík ondrej.cer...@gmail.com: Can you invent an example, that can't be converted to polynomials? Perhaps (a1+a2+a3+sqrt(5)*a4+sqrt(3)*a5)^25? Still doable. You need to involve log, exp, cos or similar transcendental functions. Vincent -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
Hi Vincent, On Sun, Jan 18, 2015 at 1:18 AM, Vincent Delecroix 20100.delecr...@gmail.com wrote: Your example can be reduced to polynomials sage: K.sqrt3 = QuadraticField(3) sage: R.a1,a2,a3,a4,a5 = K[] sage: timeit((a1+a2+a3+a4+sqrt3*a5)^25) 5 loops, best of 3: 81 ms per loop That's cool, I wasn't aware you can do that. Thanks. Can you invent an example, that can't be converted to polynomials? Perhaps (a1+a2+a3+sqrt(5)*a4+sqrt(3)*a5)^25? Ondrej -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] The fastest way to expand((a1+a2+a3+a4+sqrt(3)*a5)^25)
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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