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Re: Radicals simplify

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106418] Re: Radicals simplify
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Tue, 12 Jan 2010 04:47:32 -0500 (EST)

On 1/11/10 at 6:52 PM, fracix at hotmail.com (francix) wrote:

>Thank you all for your answer.

>I understand your explanations, but I have the impression that in
>this case Mathematica uses numbers in a different way from letters.

>If I do Simplify[2 Sqrt[2] + 4 Sqrt[2]]  I get

>6 Sqrt[2]

You needn't use Simplify to get this result since,

In[7]:= 2 Sqrt[2] + 4 Sqrt[2]

Out[7]= 6*Sqrt[2]

>or

>Simplify[5 Sqrt[50] + 6 Sqrt[18]]  I get

>43 Sqrt[2]

In this case too,

In[8]:= 5 Sqrt[50] + 6 Sqrt[18]

Out[8]= 43*Sqrt[2]

Once you provide exact values Mathematica simply evaluates the
expression and Simplify has nothing to do. The difference is
with a variable which does not yet have an assigned value,
Mathematica cannot evaluate the expression to a specific result.
In that case, Simplify does have something to do but does it
according to the LeafCount for the expression. That is, there
are not separate rules for numbers and variables. Mathematica
always attempts to evaluate any expression. If that expression
consists of algebraic operations on numbers, the result of the
evaluation will be what you are looking for. But the evaluator
cannot do the same for variables that do not have assigned values.

>Simplify[5 Sqrt[x^3] + 6 x Sqrt[x], x >= 0] I get

>11 x^(3/2)  instead of  11 x Sqrt[x]

Here

In[9]:= LeafCount[11 x^(3/2)]

Out[9]= 7

In[10]:= LeafCount[11 x Sqrt[x]]

Out[10]= 7

That is from Mathematica's perspective each of these is equally
simple. Although not explicitly stated in the documentation as
far as I know, I believe Simplify only returns the expression
modified when it can find a form with a smaller leaf count value.

>As you know the last one is the result normally found in Algebra books.

>So, there is no solution?

If your goal is to obtain the same expression you see in a text,
that often cannot be achieved easily using default behavior of
Mathematica. In order for Mathematica to do things like
Simplify, it needs to have a formal definition of what a simpler
expression is and that likely involves writing the expression in
some canonical way which may not be the same as what is shown in
texts. You can usually manipulate expression to be the same as
what you see in texts, but this often means a fairly solid
understanding of how Mathematic works and using things like
HoldForm to prevent Mathematica from doing further evaluation
once an expression is in the desired form.



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