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MathGroup Archive 2000

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Re: Manipulating Equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25096] Re: Manipulating Equations
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Fri, 8 Sep 2000 03:00:42 -0400 (EDT)
  • References: <8p9jfa$1gm@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Laurent,

For polynomial equations with rational or integral coefficients we can use

sol = InequalitySolve[{x^2 - y^2 == 1, x y == 1, x > 0, y > 0}, {x, y}]

x == Root[-1 - #1^2 + #1^4 & , 2] &&
 y == Root[-1 + #1^2 + #1^4 & , 2]


rad=ToRadicals[sol]

x == Sqrt[1/2 + Sqrt[5]/2] && y == Sqrt[-1/2 + Sqrt[5]/2]


{ToRules[rad]}

{{x -> Sqrt[1/2 + Sqrt[5]/2],
  y -> Sqrt[-1/2 + Sqrt[5]/2]}}

If sol cannot be expressed in radicals we can get numerical values

N[sol]

x == 1.272019649514069 && y == 0.7861513777574233

If the coefficients are symbolic then the problem is much harder.

Assumptions with Simplify and FullSimplify are dealt with in the Help
Browser. But note that if you have several simultaneous assumptions then
they must be in a list  {a>0, b>0} or logically combined a>0&&b>0.

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Laurent CHUSSEAU" <chusseau at univ-montp2.fr> wrote in message
news:8p9jfa$1gm at smc.vnet.net...
> First excuse my question which is probably easy to answer for the
high-level
> Mathematica users that you are.
> I have to simultaneously solve equations corresponding to a physical
> problem. Therefore most of my variables have a meaning only if they are
real
> and positive. How can I say to Mathematica that it has to reject solutions
> not corresponding to these cases, and furthermore how to declare these
> variables so that their particular nature is used by Simplify or
> FullSimplify.
> Thanks in advance
>
>




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