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I have many huge algebraic expressions such as:

$\frac{8Y}{1+x}-\frac{(1-Y)}{x}+\frac{Kx(1+5x)^{3/5}}{2}$

where $\ Y=\dfrac{Kx(1+x)^{n+2}}{(n+4)(1+5x)^{2/5}}+\dfrac{7-10x-x^2}{7(1+x)^2}+\dfrac{Ax}{(1+5x)^{2/5}(1+x)^2}\ $ and $A,n$ are constants.

To simplify these expressions by hand is taking me a lot of time and there is also the danger of making a mistake. I am looking for a free software on the internet using which I can simplify these expressions. Does anyone have any recommendations?

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    just another doubt i just got, cant matlab be used? ( i know author is asking for a free software)2012-01-02

3 Answers 3

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Try WolframAlpha, http://www.wolframalpha.com/. It is free on the internet. But another one you can also try which is very easy to use is Maple. I cannot tell if it is free.

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    @Shahab you are right, and I think Python as well. Try http://www.sagenb.org/. I think is very easy to use, but you can always download free materials from the internet.2012-01-02
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Note that if you set $\rm\ z = (5x+1)^{1/5}\ $ then your computations reduce to rational function arithmetic combined with the rewrite rule $\rm\: z^5\ \to\ 5x+1\ $ with the following expressions

$\frac{8Y}{1+x}-\frac{(1-Y)}{x}+\frac{Kxz^3}{2}$

where $\ Y\ =\ \dfrac{Kx(1+x)^{n+2}}{(n+4)z^2}+\dfrac{7-10x-x^2}{7(1+x)^2}+\dfrac{Ax}{(z(1+x))^2}\ $ and $A,n$ are constants.

This is so simple that it can be done by hand. When using computer algebra systems you need to be sure that they can effectively compute with algebraic functions, or that they can effectively handle said rewrite rule implementing this simple special case. For example, in Macsyma (or Maxima, e.g. in Sage) one may use $\rm\:radcan\:$ (RADical CANonicalize) or, alternatively, set $\rm\:algebraic:true\:$ and do $\rm\:tellrat(\:z^5 =\: 5*x+1)\ $ and then employ the $\rm\:rat\:$ function to normalize such "rational" expressions.

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    @Yrogirg Yes, I am aware of that (I was a lead developer of Macsyma).2012-05-25
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The most popular open-source symbolic math software is Maxima: http://maxima.sourceforge.net/ It's pretty sophisticated. You could also check out sage, yacas, and axiom.

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    You can use Maxima inside of Sage, as well as many other features that are not in Maxima.2012-01-02