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 | 1 | initial version |
You can do the following:
R.<x> = PolynomialRing(QQ)
f = (x^2-2)*(x^2-3)
K.<a> = f.splitting_field()
Note that f.splitting_field() requires a name for the primitive element of the field (a here), which is passed here by using the shorthand notation, as shown in the documentation.
To identify the elements of the splitting field K which correspond to the roots of f you can do e.g.
f.change_ring(K).factor()
or in this case also something like
sqrt(K(3))
| | 2 | No.2 Revision |
You can do the following:
R.<x> = PolynomialRing(QQ)
f = (x^2-2)*(x^2-3)
K.<a> = f.splitting_field()
Note that f.splitting_field() requires a name for the primitive element of the field (a here), which is passed here by using the shorthand notation, as shown in the documentation.
To identify the elements of the splitting field K which correspond to the roots of f you can do e.g.
f.change_ring(K).factor()
f.change_ring(K).roots()
or in this case also something like
sqrt(K(3))
