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### How is "is_irreducible" function implemented in SAGE

Dear community,

Suppose I have a polynomial $g$ over a finite field $\mathbb{F}_q[x]$. Then we can check whether $g$ is irreducible by using the following command

g.is_irreducible()

I did not know about this method until recently. Previously, I just factorized g and counted the number of factors. If this number is 1, then g is irreducible. I compared the running time of my method and the above built-in method. I learned the latter is much faster (which makes sense). That leads me to wonder whether which method is used to implement is_irreducible. For example, some search on the internet suggests that Rabin's algorithm is a popular one. Is it true that Rabin's algorithm is implemented on Sage? For the record, I am using the paid version of Cocalc.

Best wishes, Tung

### How is "is_irreducible" function implemented in SAGE

Dear community,

Suppose I have a polynomial $g$ over a finite field $\mathbb{F}_q[x]$. Then we can check whether $g$ is irreducible by using the following command

g.is_irreducible()

I did not know about this method until recently. Previously, I just factorized g and counted the number of factors. If this number is 1, then g is irreducible. I compared the running time of my method and the above built-in method. I learned that the latter method is much faster (which makes sense). That leads me to wonder whether which method is used to implement is_irreducible. For example, some search on the internet suggests that Rabin's algorithm is a popular one. Is it true that Rabin's algorithm is implemented on Sage? For the record, I am using the paid version of Cocalc.