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

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2answers
118 views

How to get the $0$ result for this limit?

Consider the following series: $$\sigma (\text{x$\_$})\text{:=}\sqrt{\sum _{k=0}^{x-1} \frac{(x! x!) (-1)^{x-k}}{(x-k) (k! (2 x-k)!)}+\frac{\pi ^2}{12}}$$ From the following codes, it seems that the ...
1
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1answer
134 views

NIntegrate (Helium Singlet and Triplet) [closed]

I have two integrals that I am calculating using nested NIntegrate. One is for the singlet helium atom and another for triplet. (here, I am calculating variationally the approximate energies and ...
0
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0answers
25 views

Simplifying self-reciprocal rational function [duplicate]

I have trouble transforming self-reciprocal rational functions in one variable like ...
0
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0answers
29 views

Quickly Solving a High-Order Root System of Equations of Arbitrary Form

I have the following system of equations that involve some rather complicated exponents: $$ \left\{\frac{\mathit{a} \sigma ^{41/34}}{\mathit{m}^{8/119} \mathcal{M}^{28/17}}=1,\frac{\mathit{b}\mathit{...
1
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1answer
79 views

Simplifying Radicals in Numerator and Denominator

I am new to Mathematica. So I am sorry if the question seems elementary. I wanted to simplify an expression but it seems that some radicals ($\sqrt{u}$ and $\sqrt{u-1}$) in numerator or denominator ...
1
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1answer
49 views

Approximating exponentials in a nice to read format

I need to make some approximations, basically I have something like $$ e^{i*a} = -0.735145 + 0.67791*I $$ and I want to approximate this to something that is easily readable, like $$ e^{\frac{3*\...
1
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2answers
93 views

Simplify complex square roots

I want to simplify the following expression as follows: $$\sqrt{\left(\gamma -\kappa _2\right){}^2-16 G_2^2}=i\sqrt{-\left(\gamma -\kappa _2\right){}^2+16 G_2^2}$$ I am trying ...
0
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1answer
62 views

Make Mathematica not simplify an expression [closed]

I've run into this problem countless times, and it is making Mathematica extremely unusable for me. I input an expression into Mathematica, and it tries to simplify the expression. However, in doing ...
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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
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2answers
102 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
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1answer
88 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
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1answer
56 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
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1answer
63 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 exponents,...
-2
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1answer
83 views

Simplify a expression with cos 2x

I would like to simplify the following expression : r Cos[γ[t]] + Sqrt[l^2 - r^2/2 + 1/2 r^2 Cos[2 γ[t]]] by using the mathematical expression : ...
8
votes
3answers
409 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 <...
0
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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 ...
3
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1answer
56 views

Why doesn't a real variable's conjugate evaluate to itself?

I have this code (it's just a snippet to exemplify my issue): Assuming[Element[a, Reals],Conjugate[a]] Which results in the output: ...
3
votes
1answer
135 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 ( a_{0}X_{k}+a_{1}X_{k}(\frac{k}{n})+a_{1}\sum\limits_{i=k}^{n}X_{i}\frac{1}...
1
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0answers
57 views

How to make TransformationFunctions work with Simplify

Here is a transformation function that replaces f with a polynomial: ...
7
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1answer
110 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. ...
4
votes
1answer
43 views

Simplify With Assumptions Not Using Distributive Property Of Dot Product

Given the following expression Assuming[(n | d | t) ∈ Vectors[3, Reals] && n.t == 0, FullSimplify[(n + d).t]] Why does mathematica give me the below ...
0
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2answers
91 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 ...
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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
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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 to....
0
votes
1answer
45 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 ...
11
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2answers
217 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 ...
2
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1answer
81 views

Simplify fractions and square roots

I would like to 'Simplify' Sqrt[5/6]/2 to Sqrt[5/24] I've tried to penalize Times and Rational using ComplexityFunction, ...
3
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3answers
109 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: $(...
0
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0answers
84 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], ...
1
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0answers
51 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 ...
1
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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}} ...
1
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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
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1answer
96 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: ...
0
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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: <...
0
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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 ...
6
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1answer
122 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 (...
3
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2answers
128 views

Show Factorial instead of Gamma in the result of RSolve

Now I wanted to solve for a recurring function with RSolve. Here's how I tried: ...
2
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1answer
81 views

How to make Simplify (and FullSimplify) give a default output if $Assumptions are contradictory

I have a function (deep inside my package) that looks like ...
3
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3answers
230 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 ...
3
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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 ...
1
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3answers
77 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 ...
0
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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: ...
0
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1answer
63 views

I have a term 'Keff' in terms of 'W'. I need to write 'W' in terms of 'Keff'. Does Mathematica provide an option for that

I have read similar answers on this topic. I am still not able to execute my code.The code is as follows. ...
0
votes
1answer
139 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
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1answer
51 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, ...
1
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1answer
61 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.
1
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0answers
36 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 ...
1
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1answer
108 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 ...
1
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1answer
80 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 ...