# 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[0]*z,y=y+pt[1]*z,z=pt[2]*z)
#temp=f(x=x+pt[0]*z,y=y+pt[1]*z,z=pt[2]*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?

I confirm the steady increase. This is not reduced by

`gc.collect()`

. Maybe it is a Singular issue (Singular is used by Sage in case of multivariate polynomials).Maybe http://trac.sagemath.org/ticket/17494 is related. In any case the output of

`get_memory_usage()`

increases too.This is almost certainly a Singular problem. The example is not leaving an undue number python objects around. Furthermore, the symbolic ring can be taken out completely and the problem persists. If you declare:

you can declare the polynomial immediately, and

`x,y,z`

will be actual polynomials. This suggests that sage/singular is currently leaking even on basic polynomial arithmetic . I find it hard to believe that this would go unnoticed in Singular proper, so I expect that this leak has a different origin from the one in #17494.