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RE: Exact real solutions of cubic equations

• To: mathgroup at smc.vnet.net
• Subject: [mg46989] RE: [mg46932] Exact real solutions of cubic equations
• From: JonasB at iui.se
• Date: Fri, 19 Mar 2004 01:35:38 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Thank you all. Within 24 hours I had 10 answers to my question
(ComplexExpand), with pointers to the theory and a bit of history. As a
newcomer to this list, I am impressed.

Jonas

> -----Original Message-----
> From: JonasB at iui.se [mailto:JonasB at iui.se] 
To: mathgroup at smc.vnet.net
> Sent: den 17 mars 2004 01:55
> To: mathgroup at smc.vnet.net
> Subject: [mg46989] [mg46932] Exact real solutions of cubic equations
> 
> 
> Hello,
> 
> I would like to find the _exact_ real roots of some cubic 
> polynomials. Mathematica seems to have problems determining 
> that a root is real
>  
> Solve[1 + a s + b s^2 + s^3 == 0, s]
> 
> results in three complex solutions for a = -4 and b = 3. 
> FullSimplify does not help, either it does nothing or it gets 
> stuck, depending on the values of a and b. I can of course 
> evaluate the solution numerically, but that is not what I 
> want. Does anyone know of a package that can simplify 
> expressions with complex numbers? 
> 
> Jonas
>