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MathGroup Archive 2001

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Re: Q: Factor with Polynominals?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26784] Re: Q: Factor with Polynominals?
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Wed, 24 Jan 2001 04:18:30 -0500 (EST)
  • References: <943d4e$chm@smc.vnet.net> <9461cq$gaa@smc.vnet.net> <948rc8$kku@smc.vnet.net> <94gqbh$qsj@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Here is a technique that works, with little thought, for both of the
examples given so far in this thread.

poly = (x^2 + y^2)^4 + y (x^2 + y^2) + y;
poly2 = 3 x^2 + 3 y^2 + x + y^3 + y x^2;


tf[u___ + a_ b_ + v___ + a_ c_ + w___] := u + a(b + c) + v + w;
tf[z_] := z;


fs = FullSimplify[poly, TransformationFunctions -> {Automatic, tf},
ComplexityFunction -> (Length[#] &)
]

y + (x^2 + y^2)*(y + (x^2 + y^2)^3)


fs = FullSimplify[poly2, TransformationFunctions -> {Automatic, tf},
ComplexityFunction -> (Length[#] &)
]

x + (3 + y)*(x^2 + y^2)

--
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

"Allan Hayes" <hay at haystack.demon.co.uk> wrote in message
news:94gqbh$qsj at smc.vnet.net...
> Robert
>
> poly = Expand[(x^2 + y^2)^4 + y (x^2 + y^2) + y];
>
> We can help FullSimplify (please check in HelpBrowser)
>
> rules = {x^2 + y^2 -> v};
>
> tf[u_] := u /. rules;
>
> fs = FullSimplify[poly, TransformationFunctions -> {Automatic, tf},
>     ComplexityFunction -> Length
>     ]
>
> y + v*(v^3 + y)
>
> % /. Reverse /@ rules
>
> y + (x^2 + y^2)*(y + (x^2 + y^2)^3)
>
> You might find the the Horner package useful:
>
> Algebra`Horner`
>
> --
> Allan
> ---------------------
> Allan Hayes
> Mathematica Training and Consulting
> Leicester UK
> www.haystack.demon.co.uk
> hay at haystack.demon.co.uk
> Voice: +44 (0)116 271 4198
> Fax: +44 (0)870 164 0565
>
> "Robert" <robert.schuerhuber at gmx.at> wrote in message
> news:948rc8$kku at smc.vnet.net...
> > thanks for this solution, it works very well in some cases.
> >
> > but unfortunately this is not exactly the solution i was looking for,
> maybe i
> > stated the problem unprecise:
> >
> > i'd like to single out a polynomial from an other (longer polynomial),
> e.g.
> >
> > Expand[(x^2 + y^2)^4 + y (x^2 + y^2)+y]
> >
> > yields
> >
> > y+x^2 y+y^3+(x^2+y^2)^4
> >
> > with the method suggested by you.
> >
> > but i would like to get
> >
> > (x^2+y^2) ((x^2+y^2)^3 + y) + y,
> >
> > therefore in this example i'd like to single out the polynomial x^2+y^2.
> >
> > is there a way to do this?
> >
> > thanks, robert
> >
> >
>
>
>




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