# Tagged Questions

Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.

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### Advice for Mathematica as Mathematician's Aid

I use Mathematica mainly as an aid in symbolic attacks on problems, usually intermediate or harder and often number theoretic. While Reduce, ...
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### What is the difference between a few simplification techniques?

I am trying to understand the difference between Refine, Simplify and FullSimplify, and when ...
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### Why does Simplify ignore an assumption?

Here is the example: Simplify[x + y, x + y == a] Simplify[x + y, x + y == 5] Mathematica 9 output: x+y 5 I expect the ...
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### Can I simplify an expression into form which uses my own definitions?

This seems like a simple thing to do, but I couldn't find anything relevant from Mathematica documentation. So suppose I have an expression: a*b/(a + a*Cos[a/b]) ...
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### Why doesn't Mathematica simplify a square root of an expression that equals a square of a positive real?

When I try and simplify this expression: ...
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### Using Simplify on a consistent system returns False

Bug introduced in 8.0 and fixed in 10.3. It's late, but am I missing something here? Why should two independent equations, which together are consistent, ...
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### What are the default TransformationFunctions used in Simplify and FullSimplify?

If I do Simplify[(c^3 - s^3)^2 - (s^3 + c^3)^2, TransformationFunctions -> Automatic] (i.e. a verbose version of default behaviour), what transformation ...
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### Why does this happen with FullSimplify? [duplicate]

It is stated at the Wolfram Documentation Center (FullSimplify/Possible Issues) that: Why and when this could happen? How to avoid it? Any patterns? Edit: As pointed out in the comments, this ...
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### Simplify expressions with Log

How can I get Mathematica to simplify the following expression n Log[a] + m Log[b] - m Log[a + b] - n Log[a + b] into ...
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### Why does Simplify[b-a] give -a+b and not b-a?

Simplify[b - a] results in -a + b. I prefer b - a, which is a bit simpler (3 symbols instead ...
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Mathematica provide Algebraic Manipulate palette for simplifying expression. But the palette window will always stay on top, which is quite annoying. Is is ...
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### How to deduce a generator formula for a polynomial sequence?

Consider a polynomial sequence $\{p_n\}$ generated by some (simple) rule:  \begin{array}{l} p_1(x)=x \\ p_2(x)=2 x-x^2 \\ p_3(x)= x^3-3 x^2+3 x \\ p_4(x)=-x^4+4 x^3-6 x^2+4 x \\ p_5(x)= x^5-5 x^4+...
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### How to simplify -a*z+a*z to 0 where “a” is an expression

Consider the following: a = 1+(x+y+z+u)^10000 (* Out[57]= 1+(u+x+y+z)^10000 *) e = -a*z+a*z (* Out[59]= z (-1-(u+x+y+z)^10000)+z (1+(u+x+y+z)^10000) *) How can ...
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### How to get FullSimplify to fully simplify my expression with custom complexity function?

To simplify based on the visual complexity of an expression (i.e. the complexity of the function as displayed in the notebook instead of the internal form, which in some cases may be substantially ...
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### Why is this evaluation halved when adding units?

Why does this strange behavior occur when dealing with units and quantities? ...
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### FullSimplify does freaky things with approximate Gaussians [duplicate]

I was playing around with Vitaliy Kaurov's neat answer to this question, and found something a bit unusual: ...
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### Simplify and Sqrt, inconsistent behavior?

I have encountered some problems when using Simplify with expressions containing a square root and isolated a following test case ...
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### How to prevent simplification?

I have a question about the concept of simplification. I want to explain it with an example. When I write $4/8$ in mathematica, output is 1/2. How can I return ...