       Re: Re: Re: sqrt(x^2) = x

• To: mathgroup at smc.vnet.net
• Subject: [mg61226] Re: Re: [mg61189] Re: sqrt(x^2) = x
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 13 Oct 2005 01:39:34 -0400 (EDT)
• Reply-to: hanlonr at cox.net
• Sender: owner-wri-mathgroup at wolfram.com

I over simplified the starting point.  This is a better start

Clear[mySqrt];
mySqrt[a_.*x_^n_?EvenQ]:=
mySqrt[a]*x^(n/2);
mySqrt[a_.*x_^n_?OddQ]:=
mySqrt[a*x]*x^((n-1)/2);
mySqrt[a_*b_]:=
mySqrt[a]*mySqrt[b];
mySqrt[a_?AtomQ]:=
Sqrt[a];

convertSqrt=
Power[x_,Rational[1,2]]:>mySqrt[x];

{Sqrt[x^2],Sqrt[a*x^2],Sqrt[a*x^5],Sqrt[a*Pi*
x^6],Sqrt[Pi*x^5*y^6]}/.convertSqrt

{x, Sqrt[a]*x, Sqrt[a]*x^(5/2), Sqrt[a]*Sqrt[Pi]*x^3,
Sqrt[Pi]*x^(5/2)*y^3}

Bob Hanlon

>
> From: Bob Hanlon <hanlonr at cox.net>
To: mathgroup at smc.vnet.net
> Date: 2005/10/12 Wed AM 09:58:43 EDT
> To: "Francisco Javier" <pacoga at ctv.es>, <mathgroup at smc.vnet.net>
> Subject: [mg61226] Re: [mg61189] Re: sqrt(x^2) = x
>
> Changing the definition of a built-in function is dangerous since it may
have
> unintended side effects. I recommend that you use something like
>
> Clear[mySqrt];
> mySqrt[a_.*x_^2]:=mySqrt[a]*x;
> mySqrt[a_?AtomQ]:=Sqrt[a];
>
> convertSqrt=Power[x_,Rational[1,2]]:>mySqrt[x];
>
> {Sqrt[x^2],Sqrt[a*x^2],Sqrt[Pi*x^2*y^2]}/.convertSqrt
>
> {x, Sqrt[a]*x, Sqrt[Pi]*x*y}
>
>
> Bob Hanlon
>
> >
> > From: "Francisco Javier" <pacoga at ctv.es>
To: mathgroup at smc.vnet.net
> > Date: 2005/10/12 Wed AM 01:42:23 EDT
> > Subject: [mg61226] [mg61189] Re: sqrt(x^2) = x
> >
> > Francisco Javier a formulé ce martes :
> > > Dear all, I am new in this group
> > >
> > > How can I tell Mathematica that I want to simplify all expressions like
> > > Sqrt[x^2] as x, whithout taking into account that x is or not a
> > > positive real number?
> > >
> > > Thank you very much
> >
> > Dear F.Jaccard and Ruth for your answers, but what I really mean has
> > not a such simple solution.
> >
> > I want to "teach" to Mathematica that in next calculations Sqrt[x^2] is
> > equivalent to x,
> >
> > I have tried
> >
> > Unprotect[Sqrt];
> > Sqrt[(x_)^2] := x;
> >
> > This seems works fine then with calculations like
> >
> > Sqrt[y^2]
> > y
> >
> > but it fails with
> >
> > Sqrt[x^2 y^4]
> >
> > or even with
> >
> > Sqrt[x^2 y^4]
> >
> > Any ideas?
> >
> > --
> > ----
> > Francisco Javier García Capitán
> > http://garciacapitan.auna.com
> >
> >
>
>

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