parzan's profile - activity

After playing with it a bit more, I realized that sage has this too:

sage: f.taylor(q,oo,2)
4/q + 12/q^2 + 1

So I consider the case closed (except for that fact that series should have done the same?)

That's not what had in mind (an infinite sum), but using your approach this does work:

sage: f.maxima_methods().taylor(q,oo,2)

4/q + 12/q^2 + 1

It seems that the most efficient method is A.apply_map(ZZ,ZZ) (in terms of running time).

Note this will not work if you have non-integers in the matrix, then you can use A.apply_map(int,ZZ) or A.apply_map(round,ZZ) to round the entries.

It seems that implicit_plot is not happy about receiving a list of functions. You can do this:

F2=sum([implicit_plot(y^2 - x^2 -c ==0, (x,-5,5), (y,-5,5), color="blue" ) for c in [-5..5]])

which should work for the purpose of displaying or saving the plot.

I'm trying to expand $(q + 1)/(q - 3)$ at $q=\infty$. This doesn't work:

sage: f=(q + 1)/(q - 3)
sage: f.series(q==infinity,3)
Order(-Infinity)

This also doesn't:

sage: f.subs(q==1/q).series(q==0,3).subs(q==1/q)
-1/2/q - 1/2

(the value is wrong, it should be 1 as $q$ goes to infinity, not $-1/2$).

This works:

sage: f.subs(q==1/q).simplify_rational().series(q==0,3).subs(q==1/q)
4/q + 12/q^2 + 1

But is not very friendly. Any ideas?

I am trying to migrate some code from GAP to sage, and the overhead for calls to GAP procedures is enormous. Here is an example:

----------------------------------------------------------------------
| Sage Version 4.6.2, Release Date: 2011-02-25                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: def test1():
....:     for x in xrange(100): gap.eval('G:=Group([(1,2,3)])')
....:     
sage: def test2():
....:     gap.eval('for x in [1..100] do G:=Group([(1,2,3)]);od')
....:     
sage: timeit('test1()')
5 loops, best of 3: 810 ms per loop
sage: timeit('test2()')
25 loops, best of 3: 12.6 ms per loop

Is there anything I am doing wrong?

I tried some profiling, which indicated that most of the time is consumed by "select.select".

Any help will be most welcome.

Jacobi showed that a prime $p$ has $8(p+1)$ decompositions as a sum of four squares. sage.rings.arith.four_squares computes one such decomposition. Is there a way to compute all of them?

Some options:

sage: print 'A=',A
A= 10
sage: print 'A='+`A`
A=10
sage: print 'A=%03d'%A
A=010

See here: http://ask.sagemath.org/question/1144... and here: http://ask.sagemath.org/question/605/...

Quoting from DSM's answer:

"False" doesn't necessarily mean false, it might only mean "Sage couldn't figure out how to prove it was true.

How is this?

sage: dim=4                                
sage: F = PolynomialRing(QQ, dim,'X')      
sage: I = F.ideal([x*y for x,y in tuples(F.gens(),2)])
sage: pol = [I.reduce(F.random_element()) for i in range(dim)]
sage: pol
[-3*X2, -39/2*X1 - 1/18*X2, -1/10*X0 - 3*X1 - X2 - 1/5*X3, X2 + 6*X3]
sage: matrix(dim,lambda i,j:pol[i].coefficient(F.gen(j)))
[    0     0    -3     0]
[    0 -39/2 -1/18     0]
[-1/10    -3    -1  -1/5]
[    0     0     1     6]

Note the order of actions is not the one you would have expected (I think):

sage: ((3^3)^3)^3
7625597484987
sage: 3^(3^(3^3))
---------------------------------------------------------------------------
RuntimeError: exponent must be at most 2147483647

In general if x % 1 fails (for x which is real) you can try RR(x) % 1 or RR(x).frac().

Note also that %1 and .frac() are different:

sage: RR(sqrt(3)) % 1
-0.267949192431123
sage: RR(sqrt(3)).frac()
0.732050807568877

I guess you want the latter. Actually %1 is a bit weird:

sage: [RR((2*k+1)/2)%1 for k in range(10)]
[0.500000000000000, -0.500000000000000, 0.500000000000000, -0.500000000000000, 0.500000000000000, -0.500000000000000, 0.500000000000000, -0.500000000000000, 0.500000000000000, -0.500000000000000]

Did you really use y=x.real_part ? You need y=x.real_part()

This is based on http://www.imagemagick.org/Usage/anim... . Naturally, you need imagemagick installed.

Say you created pic1.gif and pic2.gif, with the same number of frames:

sage: animate([sin(x + float(k)) for k in srange(0,2*pi,0.3)],xmin=0, xmax=2*pi, figsize=[2,1]).save('pic1.gif')
sage: animate([cos(x + float(k)) for k in srange(0,2*pi,0.3)],xmin=0, xmax=2*pi, figsize=[2,1]).save('pic2.gif')

Download and make executable the scripts here and here. Execute the following, changing NUM_FRAMES to the number of frames (21 here, look at the files generated by gif2anim if you are not sure):

gif2anim -c pic1.gif 
gif2anim -c pic2.gif 
for i in `seq -f '%03g' 1 NUM_FRAMES`; do convert pic1_$i.gif pic2_$i.gif -append pic3_$i.gif; done
anim2gif -c -g -b pic3 pic1.anim

You should have pic3.gif with the two animation vertically stacked. If you change -append to +append you get them side by side.