It appears that I was wrong about what was causing the problem as I still
get the error. I've moved to using the cloud version as I had thought that
there is a problem with my installation. Ideally I want to take a given
integer and construct a polynomial from its base m expansion for some n.
The code I have to do this is below.
def poly_coeffs(n,m,d):
# Repeatedly subtract powers of m until polynomial expansion is found.
coeffs = []
while n > 0:
c = 0
while (m^d) <= n:
n -= m^d
c += 1
coeffs += [int(c)]
d -= 1
return coeffs
def base_m_poly(n,m,d):
coefficients = poly_coeffs(n,m,d)
deg = d
f = 0
for c in coefficients: # Construct f using coefficients.
f += c*(u^(int(deg)))
deg -= 1
f = R(f) # Make sure f in R.
return f
This code contains the coercion f = R(f) to make sure that I can use the
is_irreducible and factor methods for univariate polynomials. Everything
works fine if called step-by-step as below.
R.<u> = ZZ['u']
S.<u,v> = ZZ['u,v']
f = base_m_poly(1337,36,2); parent(f); f
g = S(f); parent(g)
In this case I get that R is the parent of f and S is the parent of g, as
expected and desired. When I run this as part of a larger function building
towards the number field sieve I get the parent sympy.core.add.Add for g.
The current code for the sieve function is given below.
import time
def nfs(n,b,d,m):
print("n=",str(n),",b=",str(b),",d=",str(d),",m=",str(m))
n_factorization = []
# Start timer.
start = time.time()
iterations = 0
print("Checking primality.")
while miller_rabin(n,10) == "composite" and iterations < b and n > 1:
print("inside main iteration loop")
iterations += 1
# Find polynomial expansion of n.
f = base_m_poly(n,m,d)
# Check irreducibility of f.
if f.is_irreducible():
print("inside main loop")
# Find homogenization of f
g = S(f)
print(parent(g))
if n > 1:
n_factorization += [int(n)]
end = time.time()
print("Total calculation took ", str(end-start), " seconds.")
print("Final factorization:")
print(n_factorization)
The function miller_rabin is given as Python code, could the change to
Python scripting be causing a problem?
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