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Algebraic Simplification Problem

Posted 9 years ago

Hello,

My son and I are beginners using Wolfram Mathematica and we are trying to figure out why the input here doesn't get simplified to x**4 -3 Thank you very much.

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POSTED BY: Wolfgang Baeck
4 Replies
Posted 9 years ago

I forgot to mention that there exists another way of obtaining -3 + x^4 from your initial expression.

You can use the function Expand as

In:= Expand[x y^2/x^-3*(x y^-2/(x (y^2)^0) - 3 y^-2/x^4)]
Out= -3 + x^4

The inverse function of Expand is Factor.

In:= 1 + 2 x + x^2
Out= 1 + 2 x + x^2

In:= Factor[1 + 2 x + x^2]
Out:= (1 + x)^2

Here also, one can use Simplify to obtain the same result

In:= Simplify[1 + 2 x + x^2]
Out= (1 + x)^2

You will find in this tutorial other Wolfram Language functions that may be of use for transforming algebraic expressions.

Regards, Xavier

POSTED BY: Xavier Roy
Posted 9 years ago

Hello Xavier,

Sorry for misspelling your name.

Wolfgang

POSTED BY: Wolfgang Baeck
Posted 9 years ago

Hello Xaver,

Thank you very much. I noticed later that there is a bar showing up after an evaluation with the option "Simplify" on it which returned the desired result. I thank you for the explanation of why it operates the way it does. It was just puzzling to me. So much to learn, so little time.

Wolfgang

POSTED BY: Wolfgang Baeck
Posted 9 years ago

Hello Wolfgang,

By default Mathematica only performs a "small" set of transformations on expressions. To get the result you want, you can use the function Simplify.

In:= Simplify[x y^2/x^-3*(x y^-2/(x (y^2)^0) - 3 y^-2/x^4)]
Out= -3 + x^4

Simplify performs several transformations on expressions and returns the simplest form. For more complex expressions, it can happen that Simplify will not lead to the result sought. In such cases, one can use the function FullSimplify. With the latter, a larger number of transformations will be tried. For instance for an expression with the Euler Gamma function:

In:= Simplify[x Gamma[x]]    
Out= x Gamma[x]

In:= FullSimplify[x Gamma[x]]
Out= Gamma[1 + x]
POSTED BY: Xavier Roy
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