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

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Handling Accuracy and Simplifying

I have the following problem. I have a system of non-linear equations that I log-linearize around a certain point, let's call it point A, using a function that I ...
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1answer
37 views

Solving a trigonometric equation for all $x$ using constant coefficients

I want to find the coefficients $a$, $b$, $c$, etc. that make an equation like $a+bx=x$ true for all $x$, but for trigonometric functions of $x$. For example ...
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1answer
249 views

Infinite expression encountered when simplifying ArcTan sums although the result is finite

If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ...
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0answers
78 views

How to simplify a messy integrand by integrating by parts

I have a function x[t] and a messy integral over t, containing x[t], ...
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0answers
72 views
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243 views

Simplifying terms in a Sum expression

I have a sum in the form of pure function s = Sum[f[k], {k, 0, # - 1}] & of perhaps complicated terms f[k]. The terms ...
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1answer
66 views

Subtracting Series

When I input the following $$\sum_{n=0}^{m+1}x[n]-\sum_{n=0}^{m}x[n]$$ which in InputForm is: ...
12
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1answer
334 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 ...
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1answer
67 views

How to impose Assumptions for a list of variables?

I've got an $Assumptions variable that I'd like to apply to my whole notebook, looking like so at the moment: ...
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0answers
43 views

Eliminate a variable from a differential equation and an algebra equation then collect the remaining variables

Recently, I am attempting to eliminate a variable from a differential equation (DE) and an algebra equation (AE), then collect the remaining variables as a new (grand) parameter. Actually, I have ...
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1answer
61 views
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2answers
65 views

Translating syntax of a pure function

I have a matrix in complex exponential form. I want to factor out the complex exponential form and then express the inside in the a+i*b form. For example: \begin{bmatrix} e^{i \frac{\pi}{4}} ...
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0answers
77 views

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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0answers
37 views

Write trigs in terms of Cosine only

I have a long expression having terms that go in squares like Sin[x]^2 and Sin[x/2]^2 and so on... I would like to rewrite my ...
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3answers
122 views

Manipulation linear systems of equations

I have the following system of equations: i1 = ix - β*ib; i2 = (β + 1)*ib; i3 = ix + ib; vx = i1*Rc + i3*Rb; v1 = i2*Rϵ + i3*Rb; v1 = -ib*rπ; I tried using: ...
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1answer
113 views

What is the reason that $zz^*$ is not written as $ |z|^2$ sometimes?

For a general (complex) number $z$ I sometimes get terms that explicitly writes (for instance) $$2zz^*+|z|^2. $$ I should add that these expressions come from long calculations involving packages ...
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1answer
44 views

inverting PowerExpand

Since I couldn't respond to the question "Can you give a situation in which you would want to do this?", I will post this situation as a new question. I am plotting a complicated expression with a ...
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2answers
83 views
3
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3answers
175 views

How can I make Mathematica trigger the simplification of ArcCos[a]+ArcCos[b]?

According to this Wikipedia subsection my guess is that I should be able to convince Mathematica to return zero when doing ...
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1answer
64 views

Extract coefficients from trigonometric polynomial [closed]

Suppose I have: f[r_, ϕ_] = C1 Cos[ϕ]r + C3 Sin[3 ϕ] r + C4 Sin[4 ϕ] r^4; How do I extract the coefficient of a chosen trigonometric term, let's say ...
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1answer
133 views

FullSimplify does not distribute Abs over multiplication

FullSimplify[Abs[x]^2, x \[Element] Reals] reasonably returns x^2, but the barely-more-complicated expression ...
6
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1answer
304 views

Using FunctionExpand to evaluate symbolic derivatives

Some symbolic derivatives of certain special functions are not expanded automatically, but FunctionExpand often helps to get a derivative-free closed form ...
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3answers
58 views

Simplfying with Log and Exp functions

Short question, I have: $ \log \left(0.617424 e^{-1.19761 (W-0.427026)^2}\right)-\log \left(0.617424 e^{-1.19761 (0.116019\, -W)^2}\right) $ W is real and ...
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0answers
58 views

Derive logistic choice probabilities symbolically

More generally, I am interested in learning what the current limitations of Mathematica are when using it for doing pure mathematics. A recent blog post by Stephen Wolfram (see: ...
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1answer
66 views

Difficulties in algebraic simplifications

I am a new user, and I am a bit puzzled while experimenting with Mathematica functions, their derivatives and derivatives of functions. I have an expression such as: ...
8
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2answers
451 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 ...
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1answer
94 views

Getting mathematica to factor out constants and apply euler's identity to a table

I'm doing some quantum mechanics homework that I'm going to eventually generalize to higher spin states, so the solutions are going to need to be decently independent of the dimensions of the table ...
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1answer
48 views

How can I prevent exponents from appearing in an expression?

I've found posts dealing with showing/hiding exponents for numbers, like in scientific notation. But what if I have a general expression? I have an expression like this, ...
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1answer
54 views

Simplify the following transformed equation [closed]

y=7f(-1/6(x-1))+1 The base function is f(x)=x^2. I just don't understand where the ^2 went and how to simplify this. Any help is much appreciated, thanks.
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0answers
33 views

Factoring rationals from equation based on digit complexity?

Consider an equation of the following type: ( poly = (3 x)/35 + (6 y)/7 ) == 0 If we apply the command Factor to this ...
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1answer
71 views

Simplify not working for a real part of a complex expression [closed]

When I try to get the real part of a term, for example: $\qquad \Re\left(\frac{e^{-i k} \left(2 k^2+\pi ^2 \left(-1+e^{i k}\right)\right)}{\pi ^2-k^2}\right)$ Mathematica will output the same thing ...
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1answer
2k views

A one line proof that one is zero using Mathematica 10

a = (Sqrt[2] + 1) (Sqrt[2] - 1) - 1; {a/a, Simplify[a]/a, b/b == Simplify[b]/b} {1, 0, True} This one line "proof" that ...
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1answer
43 views

Reliable testing of identities (example: modular functions)

Take, for illustration, the following function (bonus points for anyone who identifies where it comes from!), defined on the upper half plane: ...
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0answers
42 views

How to combine similar terms in a density matrix expression? [Ref: Quantum Computing]

I tried the following : Simplify, FullSimplify, and Expand. Due to this problem, I am not ...
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0answers
47 views

Running out of memory when doing non-commutative arithmetic

I need to calculate particular coefficients of the composition of two power series in non-commutative variables. The code below which works fine truncates power series in degree $n=5$. For $n=6$ (the ...
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1answer
80 views

Problem with simplification KroneckerDelta

Bug introduced in 8.0 or earlier and fixed in 9.0 I have: ...
3
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3answers
414 views

Fullsimplify does not simplify Abs'[1.-a]

I have to simplyfy an expression involving Abs' This works: FullSimplify[Abs'[1 - a], a ∈ Reals] Sign[1 - a] but this ...
12
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1answer
207 views

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, ...
20
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3answers
296 views

FullSimplify wrongly reduces expression to zero

Bug introduced in 9.0 and persisting through 10.3 I get the following output with a fresh Mathematica (ver 10.0.2.0 on Mac) session ...
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0answers
58 views

DiracDelta of a function

If I have, for instance, FunctionExpand[DiracDelta[x^2+x-3]] it evaluates to ...
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3answers
68 views

Series: two varibles, how to eliminate the (product) higher order

I have a function of $f(x,y)$, where $x,y$ are very small numbers. I want to series expand it to the $3$rd power. However I don't want the terms such that $x^2y^2$, $xy^3$ etc. because I would reckon ...
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1answer
190 views

Expansion of functions in the real domain

When I try FullSimplify[FunctionExpand[x^(1/12)(1/12) LerchPhi[x,1,1/12]]] I have a nice answer with many complex numbers. Is there any way to have the ...
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0answers
38 views

Reduce excess Log[] [closed]

I am trying to solve a differential equation using DSolve: DSolve[y'[t] == t^10 eps^-y[t], y[t], t] And get the following output: ...
7
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1answer
138 views

Why don't 1. (0. + a) or (0. + 1. a) simplify?

I'm handling some mixed-numeric-analytic expressions, and I feel I'm missing some subtleties of how Mathematica handles simplification of such expressions. In particular, I was initially puzzled by ...
3
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1answer
126 views

Separate variables in equation

I need to know is there a way to separate the desired variables in the equation at one side of the equality. For instance, the following equation ...
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1answer
48 views

Need help simplifying final expression [closed]

I was carrying out a function and ended up with the desired answer, but for some reason, Mathematica keeps giving me the answer in a strange numerical form. ...
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1answer
89 views

FactorialPower and Factorial

After some computation, I have obtained a function FactorialPower[1, n, -1]. Clearly, FactorialPower[1, n, -1] equals ...
2
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1answer
75 views