# Tagged Questions

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

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### 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 ...
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### 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: ...
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### 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: ...
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: ...
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 ...
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### 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: ...
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### 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 ...
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### 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 ...
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 ...
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 ...
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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### Simplifying self-reciprocal rational function [duplicate]

I have trouble transforming self-reciprocal rational functions in one variable like ...
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### 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 ...
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### 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 ...
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 ...
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]. ...
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 ...
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
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,...
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 : ...
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 <...
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 ...
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: ...
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### 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], ...
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 ...
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}} ...
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 ...
100 views

I've got an $Assumptions variable that I'd like to apply to my whole notebook, looking like so at the moment: ... 3answers 131 views ### Manipulation linear systems of equations I have the following system of equations: i1 = ix - β*ib; i2 = (β + 1)*ib; i3 = ix + ib; vx = i1*Rc + i3*Rb; v1 = i2*Rϵ + i3*Rb; v1 = -ib*rπ; I tried using: <... 1answer 49 views ### inverting PowerExpand Since I couldn't respond to the question "Can you give a situation in which you would want to do this?", I will post this situation as a new question. I am plotting a complicated expression with a ... 1answer 122 views ### What is the reason that$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 (... 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: ... 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 ...