That looks very nice!

New syntax is certainly a step ahead for Maple.

Such things would be much easier to do in Python though.

Alec

That looks very nice!

New syntax is certainly a step ahead for Maple.

Such things would be much easier to do in Python though.

Alec

you use $ in some strange way, with backquotes and parentheses. What if you used it in a normal way, [$1..2000000] ? That's 4 characters less of typing, and I'm not sure whether I can type 4 characters in 0.3 sec, or not. So the total time, including typing, would be less even if the timings are the same.

Alec

you use $ in some strange way, with backquotes and parentheses. What if you used it in a normal way, [$1..2000000] ? That's 4 characters less of typing, and I'm not sure whether I can type 4 characters in 0.3 sec, or not. So the total time, including typing, would be less even if the timings are the same.

Alec

Just wasn't sure about the order of the arguments. Is seq now preferred to $?

Alec

Just wasn't sure about the order of the arguments. Is seq now preferred to $?

Alec

And here are the SAGE calculations for the updated list of values:

sage: a=[11269, 11566, 12376, 12430, 12700, 12754, 15013, 17589, 17797, 18181, 18421, 18453, 18549, 18597, 18885, 18949, 18997, 20865, 21531, 21721, 21963, 22683, 23421, 23457, 23547, 23691, 23729, 23853, 24015, 24087, 24231, 24339, 24519, 24591, 24627, 24681, 24825, 24933, 25005, 25023, 25059, 25185, 25293, 27020]
sage: b=map(number_of_partitions,a)
sage: print map(lambda n: n%100, b)
[50, 48, 86, 95, 91, 45, 81, 90, 83, 54, 77, 59, 0, 15, 35, 0, 12, 88, 94, 79, 14, 63, 68, 44, 28, 33, 5, 61, 74, 69, 6, 45, 15, 55, 18, 7, 6, 34, 0, 1, 40, 80, 1, 13]
 

Alec

1. Neil J. A. Sloane updated the sequence to include Maple 12.
2. Richard Mathar did the exhaustive search up to 27020 and the complete list of the values of the sequence in this range is

11269, 11566, 12376, 12430, 12700, 12754, 15013, 17589, 17797, 18181, 18421, 18453, 18549, 18597, 18885, 18949, 18997, 20865, 21531, 21721, 21963, 22683, 23421, 23457, 23547, 23691, 23729, 23853, 24015, 24087, 24231, 24339, 24519, 24591, 24627, 24681, 24825, 24933, 25005, 25023, 25059, 25185, 25293, 27020

Alec

I would also add testing for Ramanujan congruences - they can be used only for some n, but for those n they would add some confidence that the answer is correct, and it is easy to test them.

Alec

Also, it is interesting to compare timings. Here is the timing in SAGE:

sage: a=[ 11269, 11566, 12376, 12430, 12700, 12754, 15013, 17589, 17797, 18181, 18421, 18453, 18549, 18597, 18885, 18949, 18997, 101269, 501269 ]

sage: time b=[number_of_partitions(n) for n in a]
CPU times: user 0.15 s, sys: 0.00 s, total: 0.15 s
Wall time: 0.15
 

Here are the correct last 2 digits for those who is interested,

sage: for n in b: print n%100,
....:
50 48 86 95 91 45 81 90 83 54 77 59 0 15 35 0 12 65 25
 

The last 2 terms which are terms of the sequence, but not necessarily the next terms, were added by Robert Gerbicz.

One more timing:

sage: time c=number_of_partitions(10^9)
CPU times: user 35.38 s, sys: 0.00 s, total: 35.38 s
Wall time: 35.38
 

I wonder how long it would take Maple to calculate that.

Alec

Cerainly I don't have the copyright on the original. The translation is a different story. The online Google translator is just a tool. The copyright belongs to the person using that tool and not to the tool host if that was what you implied. The same as, for instance, if somebody get a result using Maple, then the copyright on that result belongs to him (or to her) and not to Maplesoft.

Actually, I like the translation given by Google. It looks like a poetry, and not only using the definition of a poem as "series of lines of various lengths printed in the middle of the page". Perhaps (or, maybe, certainly) it is not as impressive as its German original is, but it has its own charm.

I hope that I still have the copyright of the translation, and not Mapleprimes.

Alec

Still, it seems as if the existence of the Navier-Stokes equations solutions is an interesting unsolved problem only for mathematicians. I might be wrong, but I get an impression that physicists that I know don't care much about that. They seem to be more interested in finding solutions independently of whether they exist or not, or maybe even more if the solutions don't exist. They develop their own methods to finding solutions that mathematicians think don't exist - using renormalization (in some other situations), for example, that still doesn't have a solid mathematical foundation in some (or maybe most) cases.

Alec

Just came home, opened few boxes trying to find Stewart's Calculus, and didn't find it yet. We are preparing for moving and many things are already packed.

Actually, that doesn't seem to matter. Few things became clear at the moment.

First, that even if Maple can be used to reproduce some of manual calculations necessary to do the calculations of partial derivatives, it can't be done straitforward using double diff commands, so it is not usable in class (especially since I stopped using Maple in my classes anyway.)

Second, Maplesoft seems to be not keeping track of old bugs reports - otherwise my bug report would be found in the database. As far as I recall, it was resolved as "works as designed".

An additional note - the function should be defined as it is defined in the Wikipedia - as a piecewice function equal to 0 at 0 and given by the formula otherwise. That doesn't actually matter and shouldn't change anything in the derivatives calculation - this is just the way that should be used by students.

Alec

That's an interesting question. I don't have Mathematica currently installed - it was installed on my old computer that crashed and during system restore did clean restore (quite unexpectable for me) erasing everything that I had there (3 years of work), including both Mathematica and Maple. But I know where the Mathematica's disc is, so I can install it on this computer that I am using now. For Maple, I have no idea where my Maple 10 discs are. Also, I'll try SAGE later - the basic calculus functionality there is provided through Maxima, and it has an access to Axiom as well.

Alec