4 added 16 characters in body

My question is related to this one: http://mathoverflow.net/questions/22923/computing-the-galois-group-of-a-polynomial.

I was wondering if there is a faster algorithm just to compute the order of the group rather than the group itself.

Also, has anybody compared the performance of GAP and Magma in computing Galois groups? I just heard Magma is very good at it.

I asked this question because I encounter every so often new bug with Magma's implementation and I wanted to see if I can implement something similar. But at this time I'm just interested in the exponent at the first place. This is the last annoying error that I get for basically any deg 5 poly that has Gal group $S_5$.

k := FiniteField(2);
kx<x> := RationalFunctionField(k);
kxbyb<y> := PolynomialRing(kx);
MinP :=  y^5 + y + x^2 + x;
print GaloisGroup(MinP);


The result is:

Runtime error: too much looping


Which I don't understand what it means (Magma Ver 2.16-8).

To be more clear, my ultimate goal is to check a lot of polynomials and throw out those with $S_n$ Gal group and focus on those which are not such. As you see even an upper bound over the exponent is enough for me.

3 Clarify the goal of the computation

My question is related to this one: http://mathoverflow.net/questions/22923/computing-the-galois-group-of-a-polynomial.

I was wondering if there is a faster algorithm just to compute the order of the group rather than the group itself.

Also, has anybody compared the performance of GAP and Magma in computing Galois groups? I just heard Magma is very good at it.

I asked this question because I encounter every so often new bug with Magma's implementation and I wanted to see if I can implement something similar. But at this time I'm just interested in the exponent at the first place. This is the last annoying error that I get for basically any deg 5 poly that has Gal group $S_5$.

k := FiniteField(2);

kx := RationalFunctionField(k);

kxbyb := PolynomialRing(kx);

MinP := y^5 + y + x^2 + x;

print GaloisGroup(MinP);

The result is:

Runtime error: too much looping

Which I don't understand what it means (Magma Ver 2.16-8).

To be more clear, my ultimate goal is to check a lot of polynomials and throw out those with $S_n$ Gal group and focus on those which are not such. As you see even an upper bound over the exponent is enough for me.

2 Added Magma code

My question is related to this one: http://mathoverflow.net/questions/22923/computing-the-galois-group-of-a-polynomial.

I was wondering if there is a faster algorithm just to compute the order of the group rather than the group itself.

Also, has anybody compared the performance of GAP and Magma in computing Galois groups? I just heard Magma is very good at it.

More also,

I asked this is my first time here, question because I encounter every so often new bug with Magma's implementation and I wanted to see if I can implement something similar. But at this time I'm not following some of just interested in the protocols correctly please correct meexponent at the first place. This is the last annoying error that I get for basically any deg 5 poly that has Gal group $S_5$.

k := FiniteField(2);

kx := RationalFunctionField(k);

kxbyb := PolynomialRing(kx);

MinP := y^5 + y + x^2 + x;

print GaloisGroup(MinP);

The result is:

Runtime error: too much looping

Which I don't understand what it means (Magma Ver 2.16-8).

1