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brunoh
brunoh
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I usually find it difficult to check irreducibility of polynomials in $K[[X,Y]]$ ($K$ zero characteristic and algebraically closed). Does anyone know about generic methods that can be used ? And especially of ones that can be applied to polynomials like $XY-(X+Y)(X^2+Y^2)$ (I found it reducible by using Hensel's lemma after a suitable change of variable, if I did not make mistake).

I usually find it difficult to check irreducibility of polynomials in $K[[X,Y]]$ ($K$ zero characteristic and algebraically closed). Does anyone know about generic methods that can be used ? And especially of ones that can be applied to polynomials like $XY-(X+Y)(X^2+Y^2)$ (I found it reducible by using Hensel's lemma after a suitable change of variable, if I did not make mistake).

I usually find it difficult to check irreducibility of polynomials in $K[[X,Y]]$ ($K$ algebraically closed). Does anyone know about generic methods that can be used ? And especially of ones that can be applied to polynomials like $XY-(X+Y)(X^2+Y^2)$ (I found it reducible by using Hensel's lemma after a suitable change of variable, if I did not make mistake).

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brunoh
brunoh
  • 1.1k
  • 1
  • 12
  • 29

Generic methods to check irreducibility of polynomials in $K[[X,Y]]$

I usually find it difficult to check irreducibility of polynomials in $K[[X,Y]]$ ($K$ zero characteristic and algebraically closed). Does anyone know about generic methods that can be used ? And especially of ones that can be applied to polynomials like $XY-(X+Y)(X^2+Y^2)$ (I found it reducible by using Hensel's lemma after a suitable change of variable, if I did not make mistake).