MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Simplify results

  • To: mathgroup at smc.vnet.net
  • Subject: [mg118300] Re: Simplify results
  • From: Alexei Boulbitch <alexei.boulbitch at iee.lu>
  • Date: Thu, 21 Apr 2011 03:09:25 -0400 (EDT)

Hi, Berthold,


Nothing is really bad. The initial result:

expr = (8 a^2 b^3 (c^2 + 1)^4 - 6 a^3 b^2 (c^2 + 1)^3 +
     14 a^4 b (c^2 + 1)^2)/(4 a^3 b^2 (c^2 + 1)^2 - 10 a^4 b^3 (c^2 + 1)^3)
expr1 = Simplify[expr]


(14 a^4 b (1 + c^2)^2 - 6 a^3 b^2 (1 + c^2)^3 + 8 a^2 b^3 (1 + c^2)^4)/(
4 a^3 b^2 (1 + c^2)^2 - 10 a^4 b^3 (1 + c^2)^3)

(-7 a^2 + 3 a b (1 + c^2) - 4 b^2 (1 + c^2)^2)/(a b (-2 + 5 a b (1 + c^2)))

and your "hand-made" result:

expr2 = (7 a^2 - 3 a b (1 + c^2) +
     4 b^2 (1 + c^2)^2)/(a b (2 - 5 a b (1 + c^2)))


(7 a^2 - 3 a b (1 + c^2) + 4 b^2 (1 + c^2)^2)/(a b (2 - 5 a b (1 + c^2)))

differ from one another by multiplication by -1 both in the Numerator and in the Denominator. They are in fact equal to one another


Numerator[expr1]
Numerator[expr2]

-7 a^2 + 3 a b (1 + c^2) - 4 b^2 (1 + c^2)^2

7 a^2 - 3 a b (1 + c^2) + 4 b^2 (1 + c^2)^2

Denominator[expr1]
Denominator[expr2]


a b (-2 + 5 a b (1 + c^2))

a b (2 - 5 a b (1 + c^2))

It is probably obvious now.
Let us also make a general check:

expr1 = expr2 // Simplify

True

and numerically:

expr1 /. {a ->  1, b ->  2, c ->  3}
expr2 /. {a ->  1, b ->  2, c ->  3}

-(221/28)

-(221/28)


Have fun. Alexei



Hi,

This might be a silly question, so please bear with me, but I have been
scratching my head about it for some time now.

Is there a particular reason why Mathematica (8.01) simplifies the following
fraction reversing the signs in the result:

IN:

Simplify[(8a^2b^3(c^2+1)^4-6a^3b^2(c^2+1)^3+14a^4b
(c^2+1)^2)/(4a^3b^2(c^2+1)^2-10a^4b^3(c^2+1)^3)]

OUT:

(-7 a^2+3 a b (1+c^2)-4 b^2 (1+c^2)^2)/(a b (-2+5 a b (1+c^2)))

Reducing the fraction by hand gives me:

(7 a^2-3 a b (1+c^2)+4 b^2 (1+c^2)^2)/(a b (2-5 a b (1+c^2)))

Thanks

Berthold

-- 

Berthold Hamburger - Cellist/Spain

Email: behambu at artinso.com

http://www.artinso.com

http://www.astronomy.artinso.com

-- 
Alexei Boulbitch, Dr. habil.
Senior Scientist
Material Development

IEE S.A.
ZAE Weiergewan
11, rue Edmond Reuter
L-5326 CONTERN
Luxembourg

Tel: +352 2454 2566
Fax: +352 2454 3566
Mobile: +49 (0) 151 52 40 66 44

e-mail: alexei.boulbitch at iee.lu

www.iee.lu

--

This e-mail may contain trade secrets or privileged, undisclosed or
otherwise confidential information. If you are not the intended
recipient and have received this e-mail in error, you are hereby
notified that any review, copying or distribution of it is strictly
prohibited. Please inform us immediately and destroy the original
transmittal from your system. Thank you for your co-operation.



  • Prev by Date: Re: Converting list of subscripted variables into an array
  • Next by Date: Re: SortBy + Sort Strings with apo.marks + CharacterCode
  • Previous by thread: Re: Simplify results
  • Next by thread: Re: Simplify results