Ask Your Question
0

irreducibility using factor function()

asked 2017-10-08 00:27:24 +0100

updated 2017-10-08 15:37:00 +0100

tmonteil gravatar image

Consider the polynomial p=x^3-3*x+4. Use the factor() function to determine if p is irreducible over:

a. finite field Z_5

b. the rationals

c. the complex numbers

edit retag flag offensive close merge delete

Comments

This looks like homework. Please always mention the own effort to make sage compute something on the way. Here, a possibility to proceed - for each field - would be to construct the corresponding field, the ring of polynomials over it, then define $p$ over this field, finally ask for the factorization. For instance:

sage: F = GF(5)
sage: F.<x> = PolynomialRing( F )    # or F[] for short, but criptic.
sage: factor( x^3 - 3*x + 4 )
x^3 + 2*x + 4

Which is the code for the other two fields? (Of course, we can already decide...)

dan_fulea gravatar imagedan_fulea ( 2017-10-08 09:53:51 +0100 )edit

1 Answer

Sort by ยป oldest newest most voted
0

answered 2017-10-11 07:48:46 +0100

this post is marked as community wiki

This post is a wiki. Anyone with karma >750 is welcome to improve it.

sage: R.<x> = IntegerModRing(5)[] sage: k = x^3 -3*x + 4 sage: K = k.factor(); K sage: k.is_irreducible()

b. the rationals

sage: R.<x> = CC[] sage: p = x^3 -3*x + 4 sage: P = p.factor(); P sage: p.is_irreducible()

c. the complex numbers

sage: R.<x> = CC[] sage: p = x^3 -3*x + 4 sage: P = p.factor(); P sage: p.is_irreducible()

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2017-10-08 00:27:24 +0100

Seen: 640 times

Last updated: Oct 08 '17