Questions tagged [simplifying-expressions]

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

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2
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3answers
104 views

Simplifying square roots of squared reals

I am using Mathematica to check some long, tedious calculations and I am stumped by some mysterious behavior. If I simplify a long expression that clearly has square real factors under a radical, for ...
1
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0answers
30 views

How can I enforce the recurrence relations of SphericalHarmonics?

Spherical harmonics satisfy a number of recurrence relations as reported here. How can I enforce them in order to simplify a complicated relation like this one: ...
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0answers
32 views

High Memory Usage in Parallel but No CPU Usage

I am simplifying an expression in Mathematica in parallel. The memory usage is exploding. It seems that Mathematica is creating many Kernels which have no CPU usage, but considerable RAM usage (see ...
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0answers
44 views

How to reduce the probability density function of binary normal distribution to the form of textbook

The probability density function of binary normal distribution in textbooks is in the following form: ...
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0answers
113 views
+100

FullSimplify of expressions with Mathematical Constants

Writing: ...
5
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1answer
38 views

Is it better to use a single binary operator in each Assumption entry?

I am trying to understand why FullSimplify[x^a < 1, {0 < x^a < 1}] does not simplify but ...
3
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1answer
62 views

How to Refine HeavisideTheta or UnitStep?

Look at the following chunk of code: Assuming[x > 0, Refine@HeavisideTheta[x]] It yields 1. However the same method does ...
2
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1answer
59 views

Computing the entropic risk measure symbolically in MMA

Using the link Definition, it is possible to compute the entropic risk measure as follows: $$ EVaR=\text{inf}_{z>0}\{z^{-1}\ln\left(\frac{M_X(z)}{\alpha}\right)\}, $$ wherein $X$ is a random ...
0
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0answers
40 views

Wigner 3j-symbol in mathematica

I am looking for a nice and workable formulation of the 3j-symbol in terms of hypergeometric functions. On the wolfram webpage I found: http://functions.wolfram.com/HypergeometricFunctions/...
2
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2answers
72 views

How to simplify this sums of exponentials?

I got expressions that look like $$ \frac{1}{2} \mathrm e^{-\mathrm i r x} \left[\mathrm e^{2\mathrm i r x} \left(1 + \mathrm e^{-2\mathrm i x}\right)^r + \left(1 + \mathrm e^{2\mathrm i x}\right)^r\...
4
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2answers
267 views

Definition of a general rule

By defining: rule = Sqrt[expr_^2] :> expr; and writing: Sqrt[x^2] /. rule I get: x which is what is desired (...
1
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1answer
63 views

Problem with simplification [closed]

I have an expression that I think should be simplified to zero but Mathematica gives me a weird result. I have Simplify[-2*Sqrt[2*a] + Sqrt[(2^3)*a]] The result ...
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0answers
18 views

Comparing fractions by using partial fractions or a specific factorisation?

Trying to reproduce the results of a paper I had to solve a difficult integral. I obtain: \begin{equation} A=-N\left ( \epsilon r+\log(1+r) +\frac{rx^2(1-r\tau + \tau r^2 (\tau +1))}{1+r}+\frac{ry^2(-...
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0answers
22 views

Simplify each coefficient of coefficientlist individually and automatically substitute any repeats

I have a 13x13 polynomial coefficient list that I create with: CoefficientList[Expand[myequation] /. Equal -> Subtract,{x,z}] I would now like to simplify ...
2
votes
1answer
47 views

How to use `TransformationFunctions` to simplify this expression

I see this interesting question here. But I want to simplify it with the help of Simplify function (Maybe the ...
1
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1answer
96 views

How can I always get the simplest solution from Integrate? [closed]

When I evaluate this. Integrate[1/(x (1 + x^4)^(1/4)), x] // FullSimplify In 11.3 I get ...
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0answers
36 views

Canceling factors from numerator and denominator with complex number

I have the following expression: $\text{expr} = i \frac{\sqrt{a-b}}{\sqrt{b-a}}x$. Clearly simplifying expression gives $\text{expr}=x$ by cancelling the numerator and denominator. However, I am not ...
2
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1answer
90 views

`Series` gives wrong result

The following code shows that Series gives different results depending on whether one simplifies the expression in the first place. Let's assume all variables real. ...
1
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2answers
38 views

Simplify expression with non-commutative products

I am using NCAlgebra but I am open to any solution. I would like to simplify some expressions with many terms (a few dozens) using: the fact that each term is a ...
0
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0answers
33 views

Cancelling power terms in numerator and denominator

.Dear Community. I have the following expression in Mathematica: (1 + x) (x + (w/(A (1 - y)))^(1/y)) (A (1 - y))^(1/y) I would like to simplify it so that terms ...
0
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1answer
48 views
1
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1answer
31 views

Factorizing non commutative terms

Is it possible to factor a ** b ** c - a ** b ** d as a ** b ** (c - d) ? I am using ...
4
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1answer
247 views

How to use Mathematica to simplify this kind of trig sum?

$$ S=\sum_{k=0}^{10}\sin\left(\frac{(2+4k)\pi}{23}\right) =\sum_{k=0}^{10}e^\left(i\frac{(2+4k)\pi}{23}\right) =e^{i\frac{2\pi}{23}}\sum_{k=0}^{10}e^{i\frac{4k\pi}{23}} =e^{iu}\sum_{k=0}^{10}\left(e^{...
0
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0answers
59 views

Simplify expression to Floor

I would like to simplify the expression below to Floor[L/2], for L \[Element] Integers: ...
4
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3answers
216 views

How to simplify this formula?

$$ \int \frac{1}{\sqrt{1-2 x^3}} \, dx $$ Integrate[1/Sqrt[1 - 2 x^3], x]// FullSimplify The result is very complex. Then I want to differentiate it with the ...
0
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0answers
34 views

Imposing symmetry conditions

I have functions with some symmetry properties, how I have to impose the corresponding conditions within Mathematica, in order to perform all simplifications automatically? ...
2
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0answers
44 views

Determine if a mathematical statement always holds

I know that $\exists a,a\in\mathbb{Z}\land a+1>a$ is always true, and $\forall a,a\in\mathbb{Z}\Rightarrow a+1>a$ is also always true; I try to use function ...
1
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1answer
55 views

How can I show that the equation holds?

Suppose we have the following data: $ r=\frac{vk}{h^2}$ $u[i,j]$ is a function of two variables with $i,j$ integers. $\frac{u[i,j+1]-u[i,j]}{k}=v\frac{u[i+1,j]-2u[i,j]+u[i-1,j]}{h^2}$ Then I would ...
1
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1answer
44 views

Simplify without changing the denominator

I have the following expression: ...
0
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1answer
33 views

Hiding trivial conditions when using Reduce

I use Reduce to find conditions on some parameters such that certain inequalities are fulfilled. An additional condition is that all parameters are positive. The first problem is that I have to ...
2
votes
1answer
53 views

Simplifying an expression with many Kronecker deltas

I have an expression with lots of Kronecker deltas, with terms like: $\delta_{1,a}v_1+\delta_{2,a}v_2+\delta_{3,a}v_3+\delta_{4,a}v_4$ where $v$ is some four-component vector and the indices $a,b$, ...
1
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1answer
54 views

Refine Max[#] with assumptions breaks with more elements

Can someone please explain the following phenomenon to me? I am using Refine to evaluate a symbolic Max expression with a ...
1
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0answers
37 views

How to use Collect function to reverse the transformation

I want to use the collect function to combine (x^3+3 x^2 y+x^2+3 x y^2+2 x y+x+y^3+y^2+1) into ((x + y)^3 + (x + y)^2 + x + 1),...
4
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0answers
104 views

Simplify, ComplexityFunction, and expression rearrangement

Context: Mathematica is being used to simplify expressions. These expressions are then exported to be used in a C-family language. Naturally enough, desiderata include execution speed, and avoidance ...
5
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2answers
105 views

How to simplify Sum's and Product's of arbitrary length?

I would expect Sum[Subscript[x,i], {i, 1, n}] + Sum[-Subscript[x,i], {i, 1, n}] and ...
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0answers
50 views

Simplification of expression under symmetry conditions

How to simplify the following expression: ...
2
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2answers
76 views

How to reduce this equation to the form of y == k*x + b

I want to reduce this equation to the form of y == kx + b, but I cann't do that using MMA. ...
5
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1answer
77 views

Does Mathematica know about identity involving ArcSin(Cos(x))? [duplicate]

Given that $0 < x < \pi/2$, it can be shown that $$\arcsin(\cos(x)) = \pi/2-x,$$ however, I was unable to make Mathematica to simplify the LHS into the RHS. I was guessing that, ...
7
votes
2answers
404 views

Using Reduce over integers produces weird result

Using Reduce to solve $x^2(1+x)=y(3y-1)$, over integers should yield $$(x, y) = (-1,0),(0,0),(1,1),(4,-5),(6,-9)$$ However, when I enter ...
1
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2answers
110 views
0
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0answers
40 views

Simpler closed form for spherical coordinates of points on great circle?

Short version: how to simplify this expression given these conditions? Note that expr[[3]] is equal to 1, although Mathematica won't simplify it as such. ...
0
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0answers
50 views

How to simplify an expression with implicit vector functions and cross product operation?

1.The pattern is set in order to calculate the integral of a derivate of a function (to return original function, first fundamental theorem of calculus) ...
4
votes
1answer
56 views

Simplify root inside of root

xxx=(2 Sqrt[1 - 2/(1 + Sqrt[G1])] G1 + 2 Sqrt[((-1 + Sqrt[G1]) G1)/(1 + Sqrt[G1])])/(-1 + 2 G1) I have quite complicated expression. I want to simplify little ...
0
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2answers
97 views

Simplifying polynomial fractions with same `DiracDelta` function in both denominator and numerator

I am trying to simplify an expression with multiple Diracdelta functions in both numerator and denominator. For example, ...
3
votes
3answers
90 views

isolating a specific variable to one side in an equation

I am trying to do a simple operation of manipulating an equation of multiple variables (say, $x,y,z$), so that I can get one of the these variables on the LHS and everything else on the RHS. It should ...
13
votes
0answers
104 views

Reduce[Sin[x]==0,x] splitting odd and even multiples of Pi

as from Title, I'm wondering why Mathematica does not automatically give a single, simple solution for the problem Reduce[Sin[x] == 0, x] for which I obtain the ...
1
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3answers
49 views
4
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2answers
112 views

Analytical full-width half-maximum of hyperbolic functions composition

I'm trying to find the analytical FWHM of the following function (that I know has a Bell-type envelope): ...
3
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1answer
99 views

Taking Real, Im, and Abs of polynomial fractions

I want to find out real imaginary and Abs of polynomial fractions composed of real-valued variables. For example, consider we have a polynomial fraction $f=\dfrac{a_1 +b_1 i }{a_2 +b_2 i }$ where $...
0
votes
1answer
41 views

Simplifying terms by substitution and/or elimination [closed]

I would like to simplify the output of a calculation. For example, in the output image below, y^3 and y^(5/2) can be simplified ...

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