# applying the script to running over variables-(write to file/read from file?)

As I am new in programming with SAGE, I wonder whether anyone can help me in this topic which I think is a matter of writing results to a file first, and then taking them from there.

In particular, I have a command like this;

n = 11
K = GF(4,'a')
R = PolynomialRing(GF(4,'a'),"x")
x = R.gen()
a = K.gen()

v = [1,0,0,0,1,1,1,0,0,0,1]
R(v)
f = x^n-R(v)
S = R.quotient(f, 'y')
y = S.gen()


In the later steps I am using this v as a list of coefficients of a polynomial. And I do some algebra on them. But I want this v to run over all possible 11-length vectors over the finite field K as I defined. And I want to get the results for each v separately.

How can I write a program that will do this for me?

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The corresponding vector space is K^n. Then you can just

for v in K^n:
# whatever...

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Now, ok to get v's from there but then below there is an algebraic process, for example, it will take each v and apply some procedure and get a result for this v. I want the results listed for each v at the end of the process.:(. Do you want an iteration through all variations of [0,1] of length 10?

V = Tuples([0,1],10)
for v in V:
print v

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Actually, since I am working on GF(4) the elements are 0,1,a,a+1