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Re: Simplify results

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Hi Alexei and all,

Thank you so much for the clarifications!

Best regards

Berthold Hamburger

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http://www.astronomy.artinso.com

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-----Original Message-----
From: Alexei Boulbitch [mailto:alexei.boulbitch@iee.lu]
Sent: mi=E9rcoles, 20 de abril de 2011 9:19
Subject: Re:  Simplify results

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

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Berthold Hamburger - Cellist/Spain

Email: behambu at artinso.com

http://www.artinso.com

http://www.astronomy.artinso.com

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Re: Simplify results "Berthold Hamburger" <b-hamburger@artinso.com> - 2011-04-21 07:11 +0000

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