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

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4
votes
1answer
77 views

Simplify $\tan(\arctan(a) - \arctan(b))$

I want to simplify the expression $\tan(\arctan(a) - \arctan(b))$ to $\tfrac{a-b}{1+a\cdot b}$ (if $b \neq - \tfrac{1}{a}$). Right now, the output of ...
1
vote
2answers
250 views

Force Mathematica to simplify an ArcTan[]?

I understand that there are many solutions that will produce the same arctangent, nevertheless I really need a simplification: ...
5
votes
2answers
91 views

Rewriting expression in terms of factor

I have two expressions: expr = (a - R)^2 (a + 2 R)/(2 R^3); factor = 1 - a^2/R^2; I would like to write expr in terms of ...
1
vote
2answers
88 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 ...
10
votes
1answer
123 views

Use of some functions of the Developer Utility Package, such as BesselSimplify

The Developer Utilities Package contains several functions that look interesting: BesselSimplify GammaSimplify ...
-2
votes
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 : ...
4
votes
1answer
37 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 ...
2
votes
1answer
62 views
0
votes
1answer
47 views

Quick simplification of a fraction of 2 trigonometric equations

I would like to simplify a fraction of 2 trigonometric functions ...
4
votes
1answer
81 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
votes
1answer
86 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: ...
3
votes
1answer
31 views
3
votes
1answer
55 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: ...
13
votes
3answers
2k views

Combining Cos[ ] terms

A function that is the sum of two Cosine terms of the same frequency x[t_] := a1 Cos[w0 t + b1] + a2 Cos[w0 t + b2]; can be simplified to a single ...
3
votes
1answer
65 views

How to prevent extraction of constants from radical sign?

To me, the expression Sqrt[2]Sqrt[x] is more complex than Sqrt[2x]. But even if I merely input the latter, I get the former as ...
0
votes
0answers
38 views

Unexpected behavior of SameQ [duplicate]

I am new to Mathematica and I wanted to test the equality between 2 expressions using SameQ. I obtained the following result (note that I defined $r = \{x,y,z\}$, which is not shown below): It ...
2
votes
1answer
90 views

What function can transform A*Cos[x]+B*Sin[x] to Q*Sin[x+R] form? [duplicate]

I've tried several functions related to trigonometric transformations, namely TrigFactor, TrigExpand, ...
0
votes
0answers
59 views

Is this problem parametrically solvable or it can just be solved for specific $\sigma$ and $\theta$?

In order to solve This problem: What is the maximum value of coefficient fv with the constraint that the matrix is positive semi-definite?, I have used the following code (Determinant is computed by ...
1
vote
1answer
160 views

Why does Mathematica not restrict the domains of Rational Expressions?

As taught in High School Mathematics: $$\begin{array}{ccl} \left\{ {(x-3)(x+3)\over 5(x+3)} : \ x\ne -3 \right\} & \ne & \left\{ {x-3\over 5} : \ x\in\mathbb{R} \right\} \\ \left\{ ...
1
vote
2answers
113 views

Update: Calculate Tensor products and traces with Mathematica

My goal is to algebraically simplify expressions involving tensor products and taking the trace. That is, I would like to compute $\operatorname{Tr}\left( \prod_i(id+a_i \otimes b_i) \right)$, using ...
1
vote
1answer
78 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, ...
1
vote
0answers
34 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
votes
1answer
37 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
votes
1answer
51 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: ...
1
vote
2answers
85 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: ...
1
vote
2answers
116 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 ...
0
votes
3answers
67 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 ...
0
votes
1answer
39 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: ...
1
vote
2answers
73 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
votes
4answers
221 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
vote
1answer
128 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
votes
0answers
25 views

Simplifying self-reciprocal rational function [duplicate]

I have trouble transforming self-reciprocal rational functions in one variable like ...
1
vote
1answer
388 views

Factor vector out of a matrix

I am wondering how to factor a[1],a[2],...,a[4] out of sim so that I can write sim as the ...
0
votes
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} ...
1
vote
1answer
70 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
vote
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 $$ ...
0
votes
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 ...
9
votes
2answers
4k views
1
vote
1answer
170 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
57 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
85 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
137 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
399 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
107 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. ...