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

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7
votes
2answers
545 views

Simplifying the derivative of $|x|$

Context In[855]:= D[Abs[x], x] /. x -> 1 Out[855]= Derivative[1][Abs][1] In[856]:= D[x, x] /. x -> 1 Out[856]= 1 Question Why is ...
5
votes
2answers
114 views

FullSimplify inconsistent

I'm having problems using FullSimplify to simplify a differential equation. The expression is simplifying just as I would like when I express a variable ...
5
votes
3answers
331 views

Removing Abs from Abs[a + Exp[I*c]b]^2

Title says it all. Mathematica produces sometimes expressions of the form Abs[a + Exp[I*c]b]^2 where all three quantities a, b and c are positive real numbers. ...
4
votes
1answer
124 views

Mathematica rule to express exponentials as multiplication

I'm sorry if this has been asked before, but it is a very simple question and I would imagine it shouldn't be terribly hard for someone that knows to answer. I'm essentially trying to tell ...
4
votes
2answers
248 views

Simplifying the trace of a matrix expression

I have a long expression involving matrices that I derived using the NCAlgebra package. Can I simplify the trace of the expression? For example, say b is a scalar ...
4
votes
1answer
343 views

Checking if an expression is equal to zero

I have 6 points in $\mathbb R^3$ as follows: ...
3
votes
2answers
234 views

Simplifying expressions involving Sum

I am trying to use Mathematica to simplify a symbolic expression involving Sum. Particularly, I define a sum via ...
3
votes
1answer
1k views

Remove annoying Conjugate

Here is an expression ...
2
votes
2answers
138 views

Transform Piecewise[] into sum of indicators

I'm interested in transforming a piecewise defined function into a sum of indicator functions, ultimately with the aim to be better able to integrate them. As an example I would like to transform the ...
2
votes
2answers
418 views

How to expand a general expression in cross and dot product in Mathematica

I am looking for a way to simply the general expression in cross product and dot product with general vectors. I got a help in How do I simplify a vector expression? but soon I find that it doesn't ...
0
votes
1answer
216 views

Avoid trigonometric simplifications?

When evaluating the expression Sinh[x]^2 + Cosh[x]^2 // FullSimplify I get Cosh[2 x] That is indeed a simplification, but ...
-7
votes
1answer
101 views

Simplify looks ugly [closed]

I use Simplify mostly to make expressions look neat. However, Mathematica often does not produce expression in, what I consider, the optimal way. Look at this: ...
8
votes
2answers
320 views

How can I get $(r^{1/x})^x$ to simplify to $r$?

Simplify and FullSimplify do not simplify this kind of expression: $(r^\frac{1}{x})^x$. Consider ...
7
votes
4answers
270 views

How to make Mathematica simplify $\cos[(i + j + k)\pi]$ to $(-1)^{i+j+k}$?

We know that: $$ \cos\left[(i+j+k)\pi\right] = (-1)^{i+j+k} $$ for $i, j, k$ being positive integers. In Mathematica I've tried: ...
7
votes
1answer
655 views

Simplify an expression containing NonCommutativeMultiply

How does mathematica evaluate the following expression to zero: ...
6
votes
1answer
663 views

Properly Force Mathematica to Simplify Log Expressions/Rules

I want to be able to expand $\log(x^n e^x) = n \log(x) +x$: FullSimplify[Log[x^n Exp[x]], x > 0 && Element[n, Integers] && n > 1] yields ...
6
votes
1answer
537 views

How to Simplify equations over a Ring with Mathematica?

For example, when we work over a ring, the equation x^3=0 does not imply x^2=0 or x=0, but ...
6
votes
1answer
150 views

How to reduce expressions with complex coefficients in the form of a+0.*I

I'm trying to get an eigenvalue equation in Mathematica, and the result is an expression with coefficients of the form a + 0. I. For example, Is there any clever ...
5
votes
1answer
161 views

Simplification of integrals depending on a parameter [duplicate]

Assuming[Element[n, Integers], Integrate[Sin[x]*Sin[n*x],{x,0,Pi}]] returns 0, which is obviously wrong for n=1. ...
5
votes
2answers
422 views

Replacements/Substitutions in Mathematica

I am a new user of Mathematica and have some questions about the simplifications of calculated expressions. I am unable to attach an image of the session, but my Mathematica commands are: ...
4
votes
1answer
159 views

How to find the most compact form of an equation

I would like to know whether there is any general approach to obtain the most compact form of an equation with Mathematica. I used to believe that the ...
3
votes
1answer
170 views

Strange behavior of Reduce with a cubic equation

This equation: $(\frac{-a}{x})^2=\sqrt{\frac{1}{x}}$ at $a > 0$ and $x > 0$ has a clear solution $x=a^{4/3}$, doesn't it? However, ...
3
votes
2answers
364 views

Combining and separating sums

How can I combine or separate sums in Mathematica in the way that Together or Expand work for rational expressions´╝č For ...
3
votes
2answers
324 views

a problem about simplifing conjugate

the situation is as follows ...
3
votes
1answer
481 views

Don't simplify an expression

I have an expression that I want Mathematica to fully expand without any simplification afterwards. I want the output to look like the following example. ...
3
votes
2answers
261 views
2
votes
1answer
133 views

Why FullSimplify doesn't work here?

Since the emphasis of this question is on finding a workaround, I decided to post this question with an emphasis on the explanation of the behavior of Mathematica. The Bessel function satisfies the ...
1
vote
1answer
167 views

Normalization of eigenvectors

I am trying to normalize the following vector in Mathematica with the Normalize command. $$(-1+2\cot[x]\csc[x]+2\csc[x]^2,\;2^\frac{1}{2} (1+\cos[x])\csc[x],\; ...
1
vote
1answer
88 views

Simplifying using assumptions

Is there a way to simplify the following equation (-p(a-x)((a-b)P(b-x)+Q(b+x)(a-b+2x))+q(a+x)(-(a-b)Q(b+x)+P(b-x)(-a +b+2x)))/((b-x)(-a + x)(a+x)(b+x)) assuming ...
1
vote
2answers
128 views

Show Simplified Directives [closed]

Is there a way to force Mathematica to convert an already rendered Graphic to the simplified Directive form of that Graphic. Background: I am currently editing Graphics using Drawing Tools and then ...
1
vote
2answers
177 views

Set all instances of Exp[-x_] to zero?

To simplify a huge expression efficiently, which involves a variable in a bunch of exponential functions going to infinity, I have tried to substitute ...
0
votes
2answers
109 views

Expand 2f[x] to f[x]+f[x] (Simplify sums of ArcTan)

I'm trying to simplify an expression with sums of ArcTan, for which I've written a transformation rule that works for simple sums, so that ...
0
votes
0answers
57 views

Inconsistent behavior of Assuming[] in combination with Simplify[]

The following integral gives the correct result ...
0
votes
1answer
155 views

Reduce Cannot Solve Complicated Function

As per the answer to this question: SolveAlways rejects inequality, I tried the following commands: ...
0
votes
3answers
162 views

Conjugate and simplify

I want to get a cosine from taking the real part of a complex exponential: $cos(x) = Re(exp(i x))$. What I do in Mathematica is ...
0
votes
1answer
161 views

Simplify expressions that contain full derivatives

The best way to show what I want is by giving an example: How to go from ...
0
votes
2answers
435 views

Simplifying a trigonometric equation to obtain specific terms

When I try to solve the non-homogeneous differential equation ...