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MathGroup Archive 1999

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Re: Real roots and other assumptions...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20028] Re: Real roots and other assumptions...
  • From: Adam Strzebonski <adams at wolfram.com>
  • Date: Sat, 25 Sep 1999 02:40:52 -0400
  • Organization: Wolfram Reasearch, Inc
  • References: <7s3p1u$ck5@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In Mathematica 3 (univariate case only) and 
Mathematica 4 (multivariate polynomials too)
you can use InequalitySolve. 

In[1]:= <<Algebra`InequalitySolve`
 
In[2]:= InequalitySolve[(x-1)(x^2+1)==0, x]
Out[2]= x == 1

It will return a description of the real solution set
in terms of equations and inequalities. If you are 
solving univariate equations you can get the solutions 
in terms of replacement rules by using ToRules.

In[3]:= {ToRules[%]}
Out[3]= {{x -> 1}} 

In the multivariate case description of real solutions 
of equations may require using inequalities, and 
inequalities do not translate into replacement rules.
                                                             
In[4]:= InequalitySolve[x^2+y^2==1, {x, y}]
 
Out[4]= x == -1 && y == 0 || -1 < x < 1 &&
 
                       2                    2
>     (y == -Sqrt[1 - x ] || y == Sqrt[1 - x ]) || x == 1 && y == 0


Best Regards,

Adam Strzebonski
Wolfram Research

             
Janus Wesenberg wrote:
> 
> Hi,
> I keep encountering problems of the following type when using mathematica:
> I want to solve some equation(s) under some assumptions about the unknown(s),
> e.g. find the real roots of (x-1)(x^2+1).
> I've tried Solve[{Im[x]==0,(x-1)(x^2+1)==0},x]] for the above problem, but that
> doesn't get me anywhere.
> 
> Is there a general way to let Mathematica know about such additional bounds as
> non-complexness etc? -- if so I would be happy to know it!
> 
> Janus Wesenberg
> Student of Physics.
> 
> PS. I'm using Mathematica from a HP-UX 10 system, and the notebook interface
> have grave difficulties handling large expressions (they scrambled to complete
> nonsense). The local system administrator just says "Use the text access", but
> does anyone know how to make the notebook interface work?


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