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When such computation is fast, it depends on some optimized library, and that one depends on the type of polynomials. If you do:

sage: R.<x> = QQ[]
sage: P = R.random_element()
sage: P.is_irreducible??

You will see that flint is used.

If you do the same by replacing QQ with GF(2), you will see that the gf2x library is used but for GF(p) with p>2, the nmod_poly_is_irreducible function is used and that one relies on flint as well, and so on.

So, you have to see the source of those upstream programs to see which algorithm they are using.

When such computation is fast, it depends on some optimized library, and that one depends on the type of polynomials. If you do:

sage: R.<x> = QQ[]
sage: P = R.random_element()
sage: P.is_irreducible??

You will see that flint is used.

If you do the same by replacing QQ with GF(2), you will see that the gf2x library is used but for GF(p) with p>2, the nmod_poly_is_irreducible function is used and that one relies on flint as well, well. If you have polynomials over ZZ, then you will see that the factor method is used, and there you will see that pari is used when the degree of the polyomial is between 30 and 300, and ntl is used otherwise, and so on.

So, you have to see the source of those upstream programs to see which algorithm they are using.

When such computation is fast, it depends on some optimized library, and that one depends on the type of polynomials. If you do:

sage: R.<x> = QQ[]
sage: P = R.random_element()
sage: P.is_irreducible??

You will see that flint is used.

If you do the same by replacing QQ with GF(2), you will see that the gf2x library is used but for GF(p) with p>2, the nmod_poly_is_irreducible function is used and that one relies on flint as well. If you have polynomials over ZZ, then you will see that the factor method is used, and there you will see that pari is used when the degree of the polyomial is between 30 and 300, and ntl is used otherwise, and so on.

So, you have to see the source of those upstream programs to see which algorithm and optimizations they are using.

When such computation is fast, it depends on some optimized library, and that one depends on the type of polynomials. If you do:

sage: R.<x> = QQ[]
sage: P = R.random_element()
sage: P.is_irreducible??

You will see that flint is used.

If you do the same by replacing QQ with GF(2), you will see that the gf2x library is used but for GF(p) with p>2, the nmod_poly_is_irreducible function is used and that one relies on flint as well. If you have polynomials over ZZ, then you will see that the factor method is used, and there you will see that pari is used when the degree of the polyomial is between 30 and 300, and ntl is used otherwise, and so on.

So, you have to see the source of those the corresponding upstream programs program to see which algorithm and optimizations they are using.

When such computation is fast, it depends on some optimized library, library (note that Sage can be seen as a bundle of optimized libraries behind a uniform Python interface), and that one depends on the type of polynomials. If you do:

sage: R.<x> = QQ[]
sage: P = R.random_element()
sage: P.is_irreducible??

You will see that flint is used.

If you do the same by replacing QQ with GF(2), you will see that the gf2x library is used but for GF(p) with p>2, the nmod_poly_is_irreducible function is used and that one relies on flint as well. If you have polynomials over ZZ, then you will see that the factor method is used, and there you will see that pari is used when the degree of the polyomial is between 30 and 300, and ntl is used otherwise, and so on.

So, you have to see the source of the corresponding upstream program to see which algorithm and optimizations they are using.