According to
this test,
sympycore is from 2.5x to 5x faster than Maxima. This is an absolutely fantastic result and also a perfect certificate for Python in scientific computing. Considering that we compare pure Python to LISP.
Ok, this made us excited, so we dugg deeper and ran more benchmarks. But first, let me say a few general remarks. I want a fast CAS (Computer Algebra System) in Python. General CAS, that people use, that is useful, that is easily extensible (!), that is not missing anything, that is comparable to Mathematica and Maple -- and most importantly -- I want it now and I don't care about 30 years horizons (I won't be able to do any serious programming in 30 years anyway). All right. How to do that? Well, many people tried... And failed. The only opensource CAS system, that has any chance of becoming the opensource CAS, in my own opinion, is
Sage. You can read more about my impressions form Sage
here. I am actually only interested in mathematical physics, so basically Sage.calculus. Currently Sage uses Maxima, because Maxima is old, proven, working system and it's reasonably fast and quite reliable, but written in LISP. Some people like LISP. I don't and I find it extremely difficult to extend Maxima. Also even though Maxima is in LISP, it uses it's own language for interacting with the user (well, that's not the way). I like python, so I want to use Python. Sage has written Python wrappers to Maxima, so Sage can do almost everything that Maxima can, plus many other things. Now. But the Sage.calculus has issues.
First, I don't know how to extend the wrappers with some new things, see my
post in the sage-devel for details, it's almost 2 months old with no reaction, which shows that it's a difficult issue (or nonsense:)).
And second, it's slow. For some examples that Sage users have found out, even
SymPy, as it is now, is 7x
faster than Sage and sympycore 23x faster and with the recent speed improvements 40x faster than Sage.
So let's improve Sage.calculus. How? Well, no one knows for sure, but
I believe in my original idea of pure Python CAS (SymPy), possibly with some parts rewritten in C. Fortunately, quite a lot of us believe that this is the way.
What is this sympycore thing? In sympy, we wanted to have something now, instead of tomorrow, so we were adding a lot of features, not looking too much on speed. But then Pearu Peterson came and said, guys, we need speed too. So he rewrote the core (resulting in 10x to 100x speedup) and we moved to the new core. But first, the speed isn't sufficient, and second it destabilized SymPy a lot (there are still some problems with caching and assumptions half a year later). So with the next package of speed improvements, we decided to either port them to the current sympy, or wait until the new core stabilizes enough. So the new new core is called sympycore now, currently it only has the very basic arithmetics (and derivatives and simple integrals), but it's very fast. It's mainly done by Pearu. But for example the latest speed improvement using sexpressions was invented by Fredrik Johansson, another SymPy developer and the author of
mpmath.
OK, let's go back to the benchmarks. First thing we realized is that Pearu was using CLISP 2.41 (2006-10-13) and compiled Maxima by hand in the above timings, but when I tried Maxima in Debian (which is compiled with GNU Common Lisp (GCL) GCL 2.6.8), I got different results, Maxima did beat sympycore.
SymPyCore:
In [5]: %time e=((x+y+z)**100).expand()
CPU times: user 0.57 s, sys: 0.00 s, total: 0.57 s
Wall time: 0.57
In [6]: %time e=((x+y+z)**20 * (y+x)**19).expand()
CPU times: user 0.25 s, sys: 0.00 s, total: 0.25 s
Wall time: 0.25
Maxima:
(%i7) t0:elapsed_real_time ()$ expand ((x+y+z)^100)$ elapsed_real_time ()-t0;
(%o9) 0.41
(%i16) t0:elapsed_real_time ()$ expand ((x + y+z)^20*(x+z)^19)$ elapsed_real_time ()-t0;
(%o18) 0.080000000000005
So when expanding, Maxima is comparable to sympycore (0.41 vs 0.57), but for general arithmetics, Maxima is 3.5x faster. We also compared GiNaC (resp. swiginac):
>>> %time e=((x+y+z)**20 * (y+x)**19).expand()
CPU times: user 0.03 s, sys: 0.00 s, total: 0.03 s
Wall time: 0.03
Then we compared just the (x+y+z)**200:
sympycore:
>>> %time e=((x+y+z)**200).expand()
CPU times: user 1.80 s, sys: 0.06 s, total: 1.86 s
Wall time: 1.92
swiginac:
>>> %time e=((x+y+z)**200).expand()
CPU times: user 0.52 s, sys: 0.02 s, total: 0.53 s
maxima:
(%i41) t0:elapsed_real_time ()$ expand ((x + y+z)^200)$ elapsed_real_time ()-t0;
(%o43) 2.220000000000027
Where GiNaC still wins, but sympycore beats Maxima, but the timings really depend on the algorithm used, sympycore uses Millers algorithm which is the most efficient.
So then we tried a fair comparison: compare expanding x * y where x and y are expanded powers (to make more terms):
sympycore:
>>> from sympy import *
>>> x,y,z=map(Symbol,'xyz')
>>> xx=((x+y+z)**20).expand()
>>> yy=((x+y+z)**21).expand()
>>> %time e=(xx*yy).expand()
CPU times: user 2.21 s, sys: 0.10 s, total: 2.32 s
Wall time: 2.31
swiginac:
>>> xx=((x+y+z)**20).expand()
>>> yy=((x+y+z)**21).expand()
>>> %time e=(xx*yy).expand()
CPU times: user 0.30 s, sys: 0.00 s, total: 0.30 s
Wall time: 0.30
maxima:
(%i44) xx:expand((x+y+z)^20)$
(%i45) yy:expand((x+y+z)^21)$
(%i46) t0:elapsed_real_time ()$ expand (xx*yy)$ elapsed_real_time ()-t0;
(%o48) 0.57999999999993
So, sympycore is 7x slower than swiginac and 3x slower than maxima. We are still using pure Python, so that's very promising.
When using sexpr functions directly then 3*(a*x+..) is 4-5x faster than Maxima in Debian/Ubuntu. So, the headline of this post is justified. :)
ConclusionLet's build the car. Sage has the most features and it is the most complete car. It has issues, some wheels need to be improved (Sage.calculus). Let's change them then. Maybe SymPy could be the new wheel, maybe not, we'll see. SymPy is quite a reasonable car for calculus (it has plotting, it has exports to latex, nice, simple but powerfull command line with ipython and all those bells and whistles and it can also be used as a regular python library). But it also has issues, one wheel should be improved. That's the sympycore project.
All those smaller and smaller wheels show, that this is indeed the way to go, but very important thing is to put them back in the car. I.e. sympycore back to sympy and sympy back to Sage and integrate them well. While also leaving them as separate modules, so that users, that only need one particular wheel, can use them.
"Day Two Downers" be damned, Sarah's powering along like a freight train.
Neither of us had a terribly fantastic night's sleep. Her chest drain is
attached to this big box thing that has some sort of water seal in it, and
with the suction going through it, it bubbles and makes noise like a massive
aquarium. But she did get some sleep, and said she felt better this morning
for it.
The doctor came by at 8am, and took the incision dressing off, and we got
our first good look at it. It's big (i.e. long). It runs from about the top
of her breastbone to the bottom of her sternum. 20cm at my estimation. She
said that she thought the chest tube could come out today, and sure enough
it came out at about 12:30pm. They also took her urinary catheter out at
that time, so now all she's hooked up to is oxygen. Her blood sugar levels
were acceptable at breakfast time.
Oh, the reason the incision ran so high was because they elected to do the
bypass attachment to an artery in her neck, rather than further around the
aorta, because the tissue was fragile and they didn't want to risk a
dissection. Not doing the bypass in the aorta also left them the option of
removing some of the transcending arch if they determined it still ended up
being necessary.
Sarah got up and had breakfast in a chair again, and was generally feeling
pretty mobile. She moved between the chair and a wheelchair (and back) when
they came to get her for another x-ray, without requiring any assistance.
She took her first walk around the ward at 11am. I'd popped home for a
shower and to check on the cats, and so I missed it.
Doctor Miller dropped in at around 12:30pm to see how she was doing, and
that was good as Sarah got a chance to talk directly to him about how the
procedure had gone. He was very positive and said she could put this whole
thing behind her now.
At 2pm, she went for another walk, this time sans two thirds of the tubes
from her first walk, and got in and out of bed unassisted.
She took her last walk of the day at 4pm.
Apparently her blood sugar is still on the high side, but within the range
that they don't feel the need to give her insulin. Her chest is apparently
looking better on the x-ray they took this morning. They took a second one
after they removed the chest drain, but we haven't heard anything about how
that looks yet.
She's continuing to do extremely well, most of this less than 48 hours out
of surgery.
I haven't blogged since last year :-D so a "Happy New Year!" is required.
I finally found some time over Christmas to solve the
It's noon now and half the attendees or so the day hasn't really begun. Sure, some people here at the 
Some small portable MP3 players also allow reproducing images and videos (does anyone know why they call them MP4 players?), but they need the latter to be in some funny format called SMV (for devices with SigmaTel chipset. Other devices use different formats, such as 
The second in the Vampire Earth series by E. E. Knight, this
book has our protagonist moving to the next step in the genetically
augmented hunter clans of the human resistance. Well written,
though the next stage of the character development would require
the people to actually get into some relationships. Apart from
that, the series is moving well along, with other team members
being brought into the fold.
