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(solution) Use a resolvent for A 3 to produce algebraic numbers α that generate Fix( A 3 ) over Q for the


Use a resolvent for A 3 to produce algebraic numbers α that generate Fix( A 3 ) over Q for the following polynomials p with Galois group S 3 and A 3 . (1) X 3 + 3 X + 1; (2) X 3 + X 2 + 1; (3) X 3 − 20; (4) X 3 + 2 X 2 − 5 X + 1. Indicate α by its minimal polynomial, or, if requested, by an arithmetic combination of the roots of p .

 


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Sep 13, 2020

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