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Re: A question about algebraic numbers using Mathematica
*To*: mathgroup at smc.vnet.net
*Subject*: [mg62799] Re: [mg62762] A question about algebraic numbers using Mathematica
*From*: Daniel Lichtblau <danl at wolfram.com>
*Date*: Mon, 5 Dec 2005 13:41:03 -0500 (EST)
*References*: <200512050837.DAA08323@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Kent Holing wrote:
> I want to find the inverse of 2 - r in Q[r] where r is a root of the equation
> x^4 - 2c x^3 + (c^2 - 2a^2) x^2 + 2a^2 c x - a^2 c^2 = 0 for a, b and c integers.
>
> Can this be done for general a, b and c? (I know how to do it for specific given numerical values of a, b and c.)
>
> Kent Holing
<<Algebra`PolynomialPowerMod`
InputForm[PolynomialPowerMod[2 - x, -1, x,
{x^4 - 2*c*x^3 + (c^2-2*a^2)*x^2 + 2*a^2*c*x - a^2*c^2, 0}]]
Out[5]//InputForm=
PolynomialPowerMod[2 - x, -1, x,
{-(a^2*c^2) + 2*a^2*c*x + (-2*a^2 + c^2)*x^2 - 2*c*x^3 + x^4, 0}]
Daniel Lichtblau
Wolfram Research
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