captain's profile - activity

I searched for my question through internet but could not find a clear way to do it. So, how can I find partial sums of the value of the Dedekind zeta function of any number field?

Thank you! Now, I want to define a function as the following:

 f(k,x) = sum( (x+i)^k for i in (1..k))

How can I do that?

R = ZZ['x'] 
x = R.gen()

Under this setup, I define a function like f(x) = 122313*x^23 + 445*x^12 + 2013*x + 2345 of high degree with large coefficients. Then, I define

def h(x):  
return diff(f(x),x)

Then, Sage cannot compute the value of h, like h(5),h(10) etc. It returns 0 somehow. How can I fix this problem and get the values of the function h?

I think I forgot to add " [] " because it works now, my bad.

When I replace QQ with GF(p) I am getting "Object P.is_irreducible not found." error. What is the problem?

A univariate polynomial over the integers

Hi, given a polynomial we can check whether its irreducibility via .is_irreducible() command. I wonder how sage checks it so fast even though the polynomial has large degree with large coefficients?