High memory usage when substituting variables
I need to make a lot of variable substitutions in multivariate polynomials. However, I only need to store one polynomial at a time and I only need to make one substitution at a time. Nonetheless sage uses a lot of memory. This memory is not freed until sage is killed.
Here is a small example:
var("x y z") # A polynomial in three variables (The Trott quartic): poly=12^2*(x^4+y^4)-15^2*(x^2+y^2)*z^2+350*x^2*y^2+9^2*z^4 poly=poly.polynomial(ZZ) pnt=[1,2,3] # Makes a certain variable subsitution, defined by pt, n times. def test_subs(f,pt,n): for i in xrange(n): temp=f.substitute(x=x+pt*z,y=y+pt*z,z=pt*z) #temp=f(x=x+pt*z,y=y+pt*z,z=pt*z) #This also uses a lot of memory.
When i run
test_subs(poly,pnt,100000) I can see the memory usage ticking up from around 1% up to nearly 2%. if I then run the function again the ticking starts at 2%, and so on. In the real problem I have my program eventually fills up all memory and then crashes.
Can you see why this is happening and do you know how to prevent it from happening?