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

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8
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2answers
252 views

How to simplify an expression with special functions to zero

The following is a well-known Bessel function identity: $$J_{-n}(z)=(-1)^n J_n(z),\qquad n\in\mathbb Z$$ To check this, I used the following code and the result is as what I expected. ...
8
votes
2answers
210 views

How to reduce the number of operations needed to evaluate an expression? [duplicate]

For some numerical calculations in C++ I have, for example, this complicated expression to evaluate. Given as Mathematica input, in its original form it is ...
8
votes
4answers
7k views

Factoring polynomials to factors involving complex coefficients

I've run into some problems using Factor on polynomials with complex coefficient factors. Reading the documentation it looks like it only factors over the ...
8
votes
1answer
188 views

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 ...
8
votes
3answers
653 views

FullSimplify does not work on this expression with no unknowns

I can't reproduce this simple example from Habrat, 2010 ("Mathematica : a Problem-Centered Approach"). It is supposed to demonstrate the functionality of ...
8
votes
1answer
191 views

Expanding derivatives of hypergeometric functions

Sometimes Mathematica expresses results of integration or summation in terms of symbolic derivatives of Hypergeometric2F1 function, and cannot further simplify ...
8
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1answer
252 views

Simplify with TransformationFunctions, Bug?

I want to use custom transformation functions in Simplify, but mathematica does not seem to use them properly. Consider the following ...
8
votes
1answer
694 views

Why doesn't FullSimplify get rid of the common factor in this expression?

FullSimplify does not get rid of the z factor in the following expression: ...
8
votes
1answer
1k views

Assumptions on unknown functions

I'm trying to do analytic calculations in a quantum mechanic harmonic oscillator basis. Specifically I want to be able to evaluate functions of the many particle density. I define the following ...
8
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0answers
326 views

Faster simplification of linear combinations of some specific functions

After some profiling I've found that my program spends most of its time in the simplification step. The program uses my simplification function many times (over different data). My calculation is not ...
7
votes
4answers
3k views

Checking if two trigonometric expressions are equal

Say I have two trigonometric expressions which are a bit complicated. Is there a quick way to check if they reduce to the same thing (that they are equal) using Mathematica? I was solving this: $y'' ...
7
votes
5answers
923 views

How to cancel a common term from numerator and denominator?

What mathematica commands are needed to simplify $\frac{x+n x^m}{x(1+x)}$ to $\frac{1+n x^{m-1}}{(1+x)}$ ? ...
7
votes
4answers
439 views

Counting multiplications (complexity function)

I'm trying to count the number of times multiplication appears in an expression (for the purpose of constructing a ComplexityFunction that would help me simplify a terrible algebraic expression for ...
7
votes
2answers
2k views

Fourier Transform of a Step Function

I'm trying to obtain the form of a sinc function that I know I'm supposed to get in Mathematica. I'm doing this because I intend to do a lot with Fourier transforms (FT) and I'd like to know I'm not ...
7
votes
3answers
228 views

Why does Mathematica not seem to know that $i^x$ cannot be equal to $0$?

I am experiencing a curious behaviour of Simplify when handling expressions involving powers of $\mathbf{i}$, such as $\mathbf{i}^x$ where $x$ is unknown. For ...
7
votes
2answers
3k views

How do I simplify a vector expression?

I am doing vector analysis. I have figured out that the following expression won't be simplified in Mathematica: Simplify[Dot[x, y] - Dot[y, x]] I think the ...
7
votes
2answers
621 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 ...
7
votes
2answers
196 views

Why isn't Simplify doing more simplification of this expression?

When I try this Simplify[(1-a)*(1/(1+x*m))^(1-a)(1+m)^(1-a) + (1-a)*(x*m)^a*((x*m)/(1+x*m))^(1-a)*(1+m)^(1-a)] the output is $$\frac{(1-a) (1+m)^{1-a} ...
7
votes
2answers
296 views

FullSimplify giving unexpected result

When I perform a FullSimplify on the list $$ \left\{-\sqrt{5-2 \sqrt{6}},\sqrt{5-2 \sqrt{6}},-\sqrt{5+2 \sqrt{6}},\sqrt{5+2 \sqrt{6}}\right\} $$ I get $$ ...
7
votes
2answers
206 views

Is there a way to show the details of a numerical computation?

I have recently started using Mathematica as a calculator while teaching (definitely overkill, but I try to use as few tools as possible). I would like my students to be able to trace simple numerical ...
7
votes
2answers
163 views

How do I invoke the default complexity function?

Documentation on ComplexityFunction says: With the default setting ComplexityFunction->Automatic, forms are ranked ...
7
votes
4answers
445 views

Attaching persistent assumptions to symbol definition

Is it possible to attach assumptions to a symbol? This relates to this question. Most of my work involves physical equations, i.e. there are basic assumptions on variables that will always hold true ...
7
votes
2answers
476 views

How to automatically get rid of trig functions in an expression?

I have a large expression containing many terms like this: Sin[1/2 ArcTan[(2 Log[5])/(Log[5]^2 - 2)]] where a trig function is invoked on a rational multiple ...
7
votes
3answers
291 views

Simplify with Assumptions Sqrt[(expr)^2]

While trying to simplify expressions in the form Sqrt[(expr)^2] when expr>0 I noticed a peculiar behavior that was not ...
7
votes
1answer
887 views

Simplify an expression containing NonCommutativeMultiply

How does mathematica evaluate the following expression to zero: ...
7
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1answer
397 views

Why does Simplify with TimeConstraint return Removed[$$Failure]?

Bug introduced in 7.0 or earlier and fixed in 10.0.0 I have a rather ugly Mathematica expression (edit: shown below) that I would like to simplify with a time constraint; simplifying without a time ...
7
votes
1answer
179 views

Why does Mathematica not simplify the Gudermannian function?

The Gudermannian function is built into Mathematica, but does not reduce to simpler terms in some simple cases. In particular, the Gudermannian is an odd function of real arguments but Mathematica ...
7
votes
1answer
375 views

RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
7
votes
1answer
254 views

Limit for Matrix expression

Let's assume that $Q_0$ is $3\times 3$ matrix with $\det Q_0\neq0 $ and $$ Q_{i+1} = \frac{1}{2}\left[ Q_i+(Q_i^{-1})^T \right] $$ I need to find next limit: $\lim _{i \to +\infty}$$Q_i$. In other ...
7
votes
1answer
225 views

Why does simplification in Mathematica depend on variable names

Mathematica fails to put the following into an obvious simplest form: ...
6
votes
4answers
151 views

Minimizing a function with a constant $l > 0$

I'm VERY new to Mathematica and would like some help with minimizing a function. $$f(x) = \frac{1}{2} \sqrt{\frac{\left(l^4+x^4\right)^2}{l^4 x^2}}$$ I want to find which $x-value$ (probably ...
6
votes
2answers
405 views

Simplify Binomial Function

The following input ...
6
votes
2answers
140 views

Partial result of aborted evaluation of FullSimplify

When FullSimplify invoked on a large expression, it can run for hours. If I do not have time to wait, and abort the evaluation, I get no result, although, ...
6
votes
3answers
137 views

How to simplify my expression to the style of “a+b*I”?

How to simplify my expression to the style of "a+b*I"? Expand[(E^(I θ) (-1 + E^(I n θ)))/(-1 + E^(I θ))] ...
6
votes
2answers
200 views

How to simplify Boolean expression

I would like to simplify $$((p\oplus q)=True)\wedge(p=True)$$ to $$q=False$$ I was hoping BooleanMinimize[((p ⊻ q) == 1) ∧ (p == True)] would do the trick, but ...
6
votes
2answers
264 views

A short notation to fix the assumption that all involved parameters are, say, positive

Often I make simplifications or other operations with assumptions. Sometimes the assumptions simply state that all parameters involved are positive. I wonder, if there is a short notation for such a ...
6
votes
1answer
1k views

Simplify $\cos(n \pi)$ and $\sin(n \pi)$ when n is an integer

I was trying to calculate this integral in Mathematica 9: 2/π Integrate[ Cosh[a x] Cos[n x], {x, 0, π}, Assumptions -> n ∈ Integers] I got as a result : ...
6
votes
1answer
686 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
176 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 ...
6
votes
1answer
1k 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
144 views

Is there a version of Together that doesn't cancel common factors?

I'm running code that produces a long combination of rational functions with free constants that need to be tuned such that the combination vanishes. My current method is to put the combination over ...
6
votes
1answer
402 views

Simplifying a trigonometric sum

I want to caculate Cos[θ] + Cos[2 θ]+ ... + Cos[n θ] Sum[Cos[k θ], {k, 1, n}] ...
6
votes
1answer
300 views

Forcing Mathematica to use certain simplification rule

I'm trying to force Mathematica to use following transformation function ...
6
votes
1answer
777 views

Why does this sum not simplify properly?

I was trying to get Mathematica to simplify some moderately ugly sums and I ran into some pretty weird behaviour, which I tracked down to the following example. I'm working with ...
6
votes
1answer
92 views

Strange behavior when setting NumericQ of a symbol

It happens both in v9&v10. If you try this a^0 a^0 (1/a)^(3/2) a^0 (1/a)^(5/2) Mathematica returns 1 (1/a)^(3/2) (1/a)^(5/2) It's trivial. ...
6
votes
2answers
213 views

Simplify 2D polyhedral Regions like Interval

I don't think there's a built in "RegionSimplify" for polyhedral Regions and derived akin to how Interval automatically simplifies its argument expression: ...
6
votes
1answer
142 views

Moles/Liters doesn't get simplified to Molar even though Molar*Liters gets simplified to Moles

Why can't Mathematica 9 simplify mol/L to M, when it can simplify M*L to mol? ...
6
votes
0answers
206 views

Using FunctionExpand to evaluate symbolic derivatives

Some symbolic derivatives of certain special function are not expanded automatically, but FunctionExpand often helps to get a derivative-free closed form ...
5
votes
2answers
387 views

Simplify — is this simplest result Mathematica can provide?

I have a question about Simplify: When I do a simplification the returned result is not as simple as I want. When I ask for the Norm of an complex expression, ...
5
votes
3answers
617 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. ...