Jason Bandlow's profile - activity

After changing a file and running the doctests, I'm getting:

sage -t  "devel/sage-trac/sage/combinat/sf/hall_littlewood.py"
*** *** Error: TIMED OUT! PROCESS KILLED! *** ***

 [360.2 s]
----------------------------------------------------------------------
The following tests failed:

sage -t  "devel/sage-trac/sage/combinat/sf/hall_littlewood.py" # Time out
Total time for all tests: 360.3 seconds

Is there an easy way to find out which test it was running when the timeout occurred? Or, equivalently, which tests did pass successfully?

When you write pi.n(digits=3), you do not get the rational number 314/100. What you get is a floating point number $x$ with a guarantee that $|\pi - x| \le 0.01$ (I believe this number also "knows" how many digits you care about; that's why print shows exactly 3 digits). Because floating point numbers are internally stored in base 2, it is impossible to represent 314/100 exactly.

I'm not sure I understand your question. Are you talking about pre-defining things you might want to use; for example, in your init.sage file? If you're not, I don't know what you mean, since Python will complain about any symbol it doesn't recognize, and I don't believe there is a way to change that. (I could be wrong, though.)

Since $n$ and $k$ are both bounded, you can try something like this:

sage: var('a b c d n k')
sage: nmin = ceil(1080/90); nmax = floor(2000/60)
sage: kmin = ceil(1000/70); kmax = floor(1920/40)
sage: constraints = [a >= 80, b >= 1000, c >= 20, d >= 40, a + b <= 2000, c + d <= 90]
sage: result = []
sage: for nn in [nmin..nmax]:
....:     for kk in [kmin..kmax]:
....:         result.append( solve(constraints +  [n==nn, k==kk, a+b==n*(c+d), b==k*d], (a,b,c,d,n,k)))

I think this will take some time to run, but it should get you all the solutions you want.

For eqn1, there is an obvious upper and lower bound for n, and for each choice of n in this range, you will have 1 equation in four unknowns to determine a,b,c,d (in addition to the constraints). Once you decide on b, you can choose k freely, and this will determine e. What sort of answer are you hoping to get?

To add to the diversity of answers here, another valid approach is to add a single line to what you already have:

f(x)=x^2
g(x)=x*f(x)
k=var('k')
sum(g(k),k,0,4)

This will return 100. The point is that you can use this syntax to sum the values of a proper function, but not arbitrary Python expressions.

I'm not sure I understand why your example doesn't work, but here is a workaround:

sage: var('a b x')
sage: f = function('foo',x)
sage: g(x) = a*foo(x) + b*foo(x)^2
sage: h = g.diff(x)
sage: bar(x) = a*x + b
sage: h.substitute_function(foo, bar)
2*(a*x + b)*a*b + a^2

Here is one solution:

sage: [p for p in [0..100] if is_prime(p) and (p%6)==1]
[7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97]

For more documentation on this, look for list comprehensions in your favorite Python documentation.

You're welcome! In fact, lists won't work as keys. Look up 'mutable' vs. 'immutable' in connection with Python to understand why.

If I correctly understand your question, dictionaries can do this. You just need to use tuples as keys. Example:

sage: m = {} # an empty dictionary
sage: m[('Cathy', 19)] = '555-1212'
sage: m[('Cathy', 19)]
'555-1212'

To slightly elaborate on John's comment, "CombinatorialFreeModule" allows you to specify an arbitrary comparison function on the elements. Here is a sample doctest from sage.categories.modules_with_basis :

            sage: X = CombinatorialFreeModule(QQ, [1, 2, 3]); X.rename("X")
            sage: x = 3*X.monomial(1) + 2*X.monomial(2) + X.monomial(3)
            sage: x.leading_monomial()
            B[3]
            sage: def cmp(x,y): return y-x
            sage: x.leading_monomial(cmp=cmp)
            B[1]

Here is some code for this:

for n in [2..100]:
    print n,': (',len(n.prime_factors()), sum(a.is_idempotent() for a in Zmod(n)),')'

For a fixed n, len(n.prime_factors()) gives the number of prime factors of n and sum(a.is_idempotent() for a in Zmod(n)) gives the number of idempotents.

See also OrderedSetPartitions, which may be helpful.

Probably not what you're looking for, but the best I could do:

sage: sqrt(m^2).simplify_full()
1/2*abs(sin(theta))

I don't think that what you want is available directly in sage, although there may be some tricks available depending on exactly what you want to do. I don't have time to go into more depth right now, but please post this question to the Google Group: sage-combinat-devel. There are a lot of people (including me!) who read that, who would be interested in getting this kind of functionality into sage.

This was the key. I did not have libpng installed. I installed it, re-compiled r with sage -f, and everything works. Thanks for your help, everyone!

Thanks, I'll try this.

(This should maybe be a comment, but I'm posting as an answer for better formatting.) I just discovered the following:

sage: r.eval('capabilities("png")')
'  png \nFALSE '
sage: r.eval('capabilities("X11")')
' X11 \nTRUE '

So apparently, I have X11 support, but not PNG support. Does that suggest anything that I might be able to do?

I don't think we've discussed this before (maybe that was Jason Grout?). The file /usr/include/X11/Xwindows.h is present on my system; I'll try at some point to take a look at the spkg-install in more detail and see if I can't figure out what is failing. Thanks for pointing out the Trac ticket!