After Distinct degree factorization being merged in this PR, I started working on Equal degree factorization.
Following up from previous example, we had:

x**5 + 10

and

x**10 + x**5 + 1

as distinct degree factors.

Now we run Equal degree factorization on both of the above given polynomial, from x**10 + x**5 + 1

We get:

x**2 + x + 1
x**2 + 3x + 9
x**2 + 4x + 5
x**2 + 5x + 3
x**2 + 9x + 4

And for:

x**5 + 10

We get:

x + 2
x + 6
x + 7
x + 8
x + 10

See that the first one gave degree two factors and the second one gave degree one factors.

I have implemented the algorithm in this PR.
Combining the distinct degree and equal degree factorization, we get the factors of a polynomial in finite field. For factorizing a polynomial in integral fielf we need to convert it to some finite field polynomial, factor it and then lift it back to integral field. This is Hensel’s Lifting, I will write about it in the coming blog posts.

I am sorry that I couldn’t work this week as I was at Robo Cup. Looking forward to a good week ahead.