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

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9
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2answers
4k views
1
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1answer
173 views

Dealing with indicator functions

I am calculating the integral of two indicator functions with Mathematica. I'm having difficulty in imposing assumptions. What I have done so far: To define an indicator function: ...
0
votes
2answers
58 views

Unable to simplify the real part of a complex expression

Simplifying this expression shouldn't be hard. I tried adding assumptions asserting that all involved variables are real, but still the Re expression remains ...
1
vote
2answers
89 views

Expanding fractional powers

How does one expand/simplify expressions such as (2 - Sqrt[5])^(1/3)? Note that this expression equals 1/2 - 1/2 Sqrt[5]. ...
1
vote
1answer
87 views

Reduce an expression with Sqrt [closed]

r Cos[γ[t]] + 1/2 l Sqrt[1 - (r^2 Sin[γ[t]]^2)/l^2] How can I ask Mathematica to write my expression without l^2 in the ...
0
votes
1answer
52 views

Simplify an expression with ArcCos [closed]

How can simplify this expression with Mathematica ? Sin[1/2*ArcCos[x]]^2 Thank you for your help
3
votes
1answer
139 views

Factor fraction, where variable occurring in both, numerator and denominator, only appears once

I have an expression like $$\frac{1+a^2+2 a \cos\left(p\right)}{\left(1+b^2\right)z-1-a^2-2 \left(a+b z\right)\cos\left(p\right)}\text{.}\tag{1}$$ Is there a combination of Mathematica functions to ...
0
votes
1answer
62 views

Simplify expression so nothing appears in denominator

I have an expression that FullSimplify currently prefers to simplify with variables that have exponents appearing in the denominator if they have negative ...
8
votes
3answers
404 views

Getting rid of 0. in middle of expression [duplicate]

Say I have the following expression: 0.355329 + 0.355329 Cos[0.445723 u + (0. + 0.445723 I) v] How can I simplify it so that the expression is simplified to ...
3
votes
1answer
134 views

How could I expand the formula in terms of $X_{i}^{2}$ and $X_{i}X_{j}$ using Mathematica?

I have the following formula, where $X_{i}$, $i=1,2,...,n$ are variables: $F_{1}(X)$=$\frac{1}{n}\sum\limits_{k=1}^{n}\left ( ...
0
votes
0answers
35 views

Series Manipulation [duplicate]

How do I get Mathematica to realize that it should simplify the expression Sum[f[t],{t,1,Infinity}]-Sum[f[t],{t,2,Infinity}] to ...
7
votes
1answer
109 views

Rationalizing a numerator

My goal was to remove the radical from the numerator of the function: $$f(x)=\frac{\sqrt{x^2+9}-3}{x^2}$$ I first entered my function. ...
3
votes
3answers
104 views

Simplification behaviour of subscript expression: is this correct?

Why does the code (Mathematica version 10.0.2.0, Linux x86-64): Subscript[Subscript[S,i],j] Subscript[Subscript[S,i],j] // Simplify output the expression: ...
1
vote
0answers
54 views

How to make TransformationFunctions work with Simplify

Here is a transformation function that replaces f with a polynomial: ...
1
vote
0answers
31 views

Not reducing Trig Functions to zero [duplicate]

How do I tell Mathematica to reduce trig functions to zero when their arguments are integer multiples of pi or 2pi? I have this: ...
0
votes
2answers
89 views

Expression containing $\tt{I}$ is real — how can I show this is so in my notebook?

When I solve this equation (for ϕ): -16 y - (1 + 2 ϕ)^2 (-1 + 6 ϕ) == 0 Two solutions have imaginary parts in the symbolic ...
11
votes
2answers
210 views

Is mathematica's right click menu customizable to add Simplify tools?

Mathematica provide Algebraic Manipulate palette for simplifying expression. But the palette window will always stay on top, which is quite annoying. Is is ...
0
votes
0answers
113 views

Recognizing a generalized function as zero

Consider the following expression: HeavisideTheta[x]HeavisideTheta[-x] Mathematica will not simplify it further. But $\Theta(x)\Theta(-x)$ is zero if considered ...
0
votes
0answers
16 views

Ambiguous numeric factors and terms in output expressions [duplicate]

I'm pretty new to Mathematica, so I've encountered a lot of problems. Most of them I've been able to solve with Google and with the help of my friends, but there is one that I can't find the answer ...
0
votes
0answers
100 views

System of differential equations - solving for a constant

I will reformulate my question in the hopes it will be more intelligible. First, I defined the functions: ...
0
votes
0answers
71 views

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 ...
0
votes
1answer
44 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 ...
4
votes
1answer
279 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]]]]] ...
0
votes
0answers
83 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], ...
0
votes
0answers
72 views
0
votes
0answers
275 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 ...
1
vote
1answer
81 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: ...
13
votes
1answer
361 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 ...
1
vote
0answers
50 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 ...
0
votes
1answer
62 views
1
vote
2answers
66 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}} ...
11
votes
0answers
79 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: ...
1
vote
0answers
49 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 ...
0
votes
3answers
129 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: ...
6
votes
1answer
116 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 ...
0
votes
1answer
47 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 ...
3
votes
2answers
119 views
3
votes
3answers
218 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 ...
1
vote
1answer
78 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 ...
3
votes
1answer
141 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
votes
1answer
345 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 ...
1
vote
3answers
73 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 ...
3
votes
0answers
59 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: ...
0
votes
1answer
67 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
votes
2answers
468 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 ...
0
votes
1answer
132 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 ...
0
votes
1answer
49 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, ...