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

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2
votes
1answer
86 views

Simplifying the result of DSolve

I have a system of differential equations that can be solved with DSolve. However, the coefficients are very long there are like terms which can be combined. I used //FullSimplify in my code but the ...
1
vote
2answers
98 views

Convert imaginary exponentials to goniometric expressions?

Can I force Mathematica to re-express something like $$\left\{\frac{1}{2}i\left(\frac{1}{16} e^{-2 i (\alpha (1)+4 \alpha (2))} \left(-1+e^{8 i \alpha (2)}\right) \text{d$\alpha $}(1) \left(2 \left(2 ...
4
votes
0answers
106 views

Simplest identity that cannot be proved by FullSimplify [closed]

Apparently, FullSimplify is not able to prove all true identities, but usually it does pretty well when it comes to elementary functions. I'd like to know what are ...
6
votes
2answers
212 views

ReplaceAll problem

Bug introduced in 10.1 and persisting through 10.2 or later Confirmed, as bug, by WRI: [CASE:3402234] I am trying to combine terms of the type ...
4
votes
2answers
140 views

Symmetrise a complicated expression

I am calculating the derivatives of a symmetric function $F(a_1, a_2)$ and got very complicated expressions, which I'd like to write in a symmetric form with respect to $1 \leftrightarrow 2$ (clearly ...
2
votes
1answer
118 views

Simplify trigonometric expression

Mathematica correctly simplifies the following expression: ...
0
votes
1answer
87 views

Using Simplify to perform substitutions [closed]

I have a matrix element $k_x$ and I want to substitute it as $-i\kappa$, I tried ...
0
votes
0answers
67 views

Simplifying sums of rational trigonometric functions

After simplifying the trigonometric functions as advised before (cf. Simplifying Expressions for FindMinimum), I obtained a sum of 62 similar expressions, the first three as in the below: ...
6
votes
3answers
270 views

How to simplify symbolic expressions with KroneckerProduct

Having $X,Y$ being symbols for matrices, I was wondering if there is a way to simplify expressions like KroneckerProduct[X, X] + KroneckerProduct[-X, X] to ...
1
vote
0answers
66 views

Simplify Integer powers in inequalities

I have a fairly simple expression that I am surprised Mathematica (10.1) won't simplify ...
3
votes
1answer
315 views

Separating exponential terms

Suppose I have a lot of expressions multiplied by factors such as: $$e^{-i\theta[1]-i\theta[2] - i\theta[3]-i\theta[4]-i\theta[5]}$$ I would like to separate this into a product of exponentials of ...
1
vote
2answers
153 views

Strange evaluation of an sum involving binomial coefficients

I stumbled upon this problem while playing with Mathematica 10. Can anyone help me explain the following behaviour? I define a sum ...
0
votes
2answers
90 views

Replacement rules do not apply for an expression inside a root

Say, you have an expression which looks like this: myexpr = (mess)+(some other mess)/( (mess)^3+(some other mess)^2 )^(1/3) Here the 'mess' in the name of terms ...
2
votes
1answer
218 views

Check for holomorphy of a function

Given a (rather complicated) function H(z), what is the best approach to check symbolically whether it is holomorphic? What I tried is checking explicitly the ...
3
votes
1answer
128 views

Simplify oversimplifies. What to do about it?

According to Mathematica 10: $$Simplify[\frac{\frac{1}{t^2}-1}{(t+\frac{1}{t})^2}]==\frac{1-t^2}{(1+t^2)^2}$$ However, the first equation does not tolerate $t=0$ because of a division by zero, but ...
1
vote
1answer
88 views

How to reduce trigonometric expressions under special conditions

For the following problems I used "FullSimplify" and "TrigReduce" but I manage to reduce more by hand. ...
5
votes
2answers
119 views

How to use ForAll to prove things about functions?

Suppose I first declare: $Assumptions = ForAll[{a,b}, b > a, f[b] > f[a]] I (wrongly, as it turns out) assume that that this would cause ...
2
votes
1answer
118 views

Simplifying Expressions for FindMinimum

I am currently trying to apply the FindMinimum function to find the lowest energy of an expression. My current expression as of now is relatively complicated. It is the summation of 48 similar terms, ...
3
votes
1answer
151 views

Equality of Reciprocal with Negative Exponent

I want MMA to tell me if two, rather large, expressions are equal. My minimum working example follows. I want MMA to tell me that the following is true:$$x^n = \left(\frac{1}{x}\right)^{-n}$$ I have ...
3
votes
2answers
385 views

How to enforce mathematica to analytically evaluate roots?

I am interested in simplifying expressions involving HeavisideTheta. A simple example could be: HeavisideTheta[1 + x - x^2 + x^3] The best I can achieve is with ...
1
vote
1answer
90 views

Pulling out a prefactor from a dot product

I have three complicated vectors u, v and w as well as three simple prefactors ...
2
votes
2answers
78 views

Trouble simplifying using Replace

I have the following expression: w.a.b.r+w.c.d.r I want to get: w.(a.b+c.d).r So far I used ReplaceRepeated: ...
1
vote
1answer
61 views

How to apply Simplify only to elements of list that cause specific Warning

I have a set of replacement rules I use to analytically compute nested integrals of very long symbolic expressions since Integrate literally takes forever. To do ...
0
votes
1answer
375 views

Simplifying symbolic expressions involving dot products

I have a function that outputs a large expression containing dot products of vectors. None of the vector components are known, so all dot products are symbolic. For instance, part of the output may ...
4
votes
1answer
141 views

Dealing with 6 VERY large equations. Am I doing this correctly, and can I expect a solution?

I'm new to Mathematica, but so far, everything seems straight forward and intuitive, which is really nice. However, I've come to use this software since I have to show a rather nasty 3x3 matrix is ...
14
votes
1answer
462 views

How to enlarge Mathematica's knowledge about certain functions?

I'm often troubled with the following task. I need to carry out symbolical computations involving certain special functions. Let me take as an example Barnes gamma-function. It is included in ...
5
votes
3answers
1k views

How to simplify 1 - Cos[2x] to 2 Sin[x]^2?

I want to reduce all Cos[2 x] to 1 - 2Sin[x]^2, it seems Mathematica will always simplify ...
0
votes
1answer
54 views

Expanding a function with trigonometric expressions in a controlled manner by excluding addition identities

I want to simplify a nonlinear equation with trigonometric terms. After I've expanded I don't want to loose open terms to Trigonometric Addition Formulas (http://mathworld.wolfram.com/...
7
votes
2answers
123 views

Simplify expression to Integer

I have the following function: f[n_]:=(n-1) E Gamma[n,1]; I know that this expression always evaluates to an Integer, but Mathematica doesn't always output the ...
9
votes
1answer
119 views

FullSimplify Produces Result that Includes Hold

Bug fixed in 10.2.0 In the course of developing a solution to Question 79183, I solved the equation ...
10
votes
3answers
1k views

Simplifying trig expressions containing Sqrt or Abs

The following Maple code can simplify abs(sin(x)) into -sin(x) given the condition ...
3
votes
1answer
112 views

Simplify a huge expression with limited memory

I would like to perform some analytical sums such as the following ...
0
votes
1answer
65 views

How to simplify a quotient with exponents (using power rules)

I'm trying to simplify the following expression (b (1 - x)^n (-1 + x)^-n (-1 + x - w x)^n)/(n (-1 + w) (1 - x + w x)). All parameters and the variable x should ...
-2
votes
1answer
43 views

How can I simplify this simple formula? [closed]

:) If we have x+(x*l), is it possible to simplify this, on having only one single x?
2
votes
3answers
161 views

Question on alternate forms of polynomial output

EDIT: Would it be possible to do something like let $y=ax+b$ then use Collect[] or Apart[] on the new expression? How would I go about this. I've tried using Collect[%,ax+b], Collect[%,{ax+b}], and ...
0
votes
0answers
41 views

How to print intermediate steps of simplifying a power formula? [duplicate]

To answer the question of proving Fibonacci sequence is periodic mod 5 without using induction., I came across Mathematica to prove $$F_{n}\equiv F_{n+20}\pmod 5$$ for all $n \geq 2$ I defined: $F[n]...
6
votes
1answer
89 views

How to simplify expressions by closing open inequalities?

Recently I have often acquired results which consist of combinations of 0, 1 and 2-dimensional (in)equalities. For instance, consider a very simple case with ineq1 ...
14
votes
1answer
309 views

What's wrong with Simplify and FullSimplify?

I have a quite complex list of equations and inequalities I combine to a boundary condition for my cost function. After investigation of two days I found the bug (I really name it a bug!). One of my ...
4
votes
1answer
93 views

What options need to be set for Simplify to perform a certain manipulations similar to FullSimplify?

Simplify performs algebraic transformations and is fast, while FullSimplify tries a wide range of transformations involving ...
9
votes
2answers
928 views
0
votes
1answer
234 views

Simplifying square root expressions

I have read lots of questions on square root simplification on MMA, but I haven't really seen my problem posted (or understood a clear way to deal with this issue). I am simplifying some expressions "...
0
votes
1answer
64 views

How can I manipulate a long expression to order it by factors/derivatives of a particular function?

I have a Mathematica notebook that generates a linear expression involving derivatives of a given variable. Expanded (and simplified for our purposes), it looks something like this: \begin{equation} ...
1
vote
0answers
78 views

Inverse Laplace computation Mathematica [closed]

I have a transfer function such as following, which I would like to find its inverse: F=(a*s^2)/(b*s^3+c*s^2+d*s+e) I have a numeric value for a b c d and e but ...
2
votes
1answer
192 views

Simplification of exponential

I would like to understand why FullSimplify doesn't entirely simplify this expression ...
1
vote
0answers
113 views

Summing the probability distribution to 1 to convince myself

I have worked out a probability distribution and want to check its sum which is necessarily 1. First we write $$ r \triangleq \frac{(2 \lambda + \mu)^2}{2(\mu + \lambda)^2}, \quad s \triangleq \...
6
votes
4answers
215 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 ...