Question

I have written some very simple trial-and-error code in Sage (a computer algebra system written in python where you can use regular python syntax in scripting). The little code snippet creates a polynomial and does some calculations with the coefficients, especially it determines the Groebner basis for the ideal generated by three expressions in the coefficients.

The problem is: This program goes on and eats up all my memory until it’s killed by the kernel. Every iteration consumes only like 200kB, but this memory is never freed again.

Here is the code. The details are not that important and very bulky, therefore left out:

R = PolynomialRing(QQ, 2, 'bc', order='lex')
expr1, expr2, expr3 = ...

for i in range (0,50):
    for j in range(i+1,50):
        for k in range(j+1,50):
            for l in range(k+1,50):
                for m in range(l+1,50):
                    for n in range(m+1,50):
                        poly = (x-i)*(x-j)*(x-k)*(x-l)*(x-m)*(x-n)
                        r = poly.coeffs()

                        p1 = expr1.substitute(r...)
                        p2 = expr2.substitute(r...)
                        p3 = expr3.substitute(r...)

                        I = (p1, p2, p3)*R
                        B = I.groebner_basis()

As far as I understood python’s memory management, the variables in the loop body are freed every so often. Now, it may be a programming problem, an internal python problem or some problem in the Sage routines. I don’t know. Can you spot a problem with my code or is it something else?

Answer 1

The problem doesn’t appear to be your loops (in python2.7, OS-X 10.5.8):

a = 0
for i in range (0,50):
    for j in range(i+1,50):
        for k in range(j+1,50):
            for l in range(k+1,50):
                for m in range(l+1,50):
                    for n in range(m+1,50):
                        a += 1

print( a )

Which takes very little additional memory on both python2.x and python3.x.

And it really doesn’t take all that long to run either:

time python test.py
15890700

real   0m6.015s
user   0m5.940s
sys    0m0.032s

Perhaps something is funky when running with sage? Or maybe it’s something else in your loops that is causing the problem…