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

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0answers
36 views

How to simplify a ratio [closed]

I have a ration of the form $\frac{p^2}{(p^2+1)^2}$. I can simplify it using $p^2=p^2+1-1$, and to get $\frac{p^2}{(p^2+1)^2}=\frac{1}{p^2+1}-\frac{1}{(p^2+1)^2}$. How can I create the rule to do it ...
4
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1answer
42 views

What do I need to know about simplifying expressions involving Symbolic Tensors?

I want to use Mathematica to show that the inner product of a vector with itself is equal to the square of its norm. This is what I tried: ...
0
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1answer
52 views

Different Results from Simplify, dependent on explicit vs computed rules

Can anybody explain why these two pieces of code are giving me different results? Heres the inputs: ...
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2answers
114 views

Imaginary part of complex number, nothing works?

I want to find the imaginary part of the complex number (a+i*b). say I have a function in the following form: ...
4
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1answer
84 views

Simplify Class invariant $G(25)$

How to simplify $$\frac{\sqrt[3]{\vartheta _3\left(0,e^{-5 \pi }\right)}}{\sqrt[12]{2} \sqrt[6]{\vartheta _2\left(0,e^{-5 \pi }\right) \vartheta _4\left(0,e^{-5 \pi }\right)}}$$ This is a ...
0
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1answer
45 views

Simplify doesn't simplify multiple conditions from Reduce

Consider the following simple example where I try to solve an equation and then apply a bounded interval to find the right result out of an infinite amount of solutions: ...
0
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3answers
75 views

How to select coefficient of an exponential function

Suppose I have these set of equations: sol = DSolve[{ x'[t] == -RandomReal[]*x[t] + y[t], y'[t] == x[t] - *y[t] , x[0] == 1, y[0] == 0}, {x[t], y[t]}, t] The ...
1
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2answers
79 views

How can I eliminate a parameter by substitution and simplification?

I have this equation k = (a b c t)/(Sqrt[(f + t)^2]) and I want to set p = t/(t + f) In which way I can eliminate ...
4
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4answers
228 views

Another confusion with simplify

After reading some of the questions concerning Simplify, I still didn't find a solution to my confusion. I want Mathematica to simplify ...
1
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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 ...
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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 ...
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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
84 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
51 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
96 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 ...
0
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2answers
59 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
108 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
89 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
58 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
0
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1answer
64 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
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3answers
412 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
58 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
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1answer
136 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
58 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
112 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
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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 ...
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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
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1answer
48 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
votes
2answers
221 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
votes
1answer
86 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
86 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
52 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
51 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
100 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
votes
3answers
131 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
49 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
votes
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
133 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
91 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
233 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
144 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 ...