Questions tagged [simplifying-expressions]

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

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Simplifying square root where all parameters are reals

How can I simplify the following expression, with considering that all parameters are reals? you can find the code here: ...
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1answer
78 views

Help with simplification

Could anyone please help me simply the following expression ...
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44 views

How can i simplify an expression using the Real-Valued Root?

My expression is $$ f(x)= x\gamma\,(-1+\sqrt[3]{-1} \,-\sqrt[3]{-1^2}) $$ Simplifying using FullSimplify[f(x)] FullSimplify[Re[f(x)]] returns a value of $0$ ...
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Testing expressions with === (SameQ) between original expression and after Factor[], Expand[] and FullSimplify[] [closed]

a=16x^4 y^5 (81-z^4)-54xy^2 (81-z^4) Out[30]= -54 xy^2 (81-z^4)+16 x^4 y^5 (81-z^4) b=Factor[a] Out[31]= 2 (27 xy^2-8 x^...
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Does Assumptions not work on Root objects?

Typically, one can restrict symbolic quantities using Assumptions. Suppose, for instance, that I want to solve $a=x^2$ for $x$, with $a>0$, restricting my answer to the positive root. ...
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How to reform a expression to improve numerical stability?

In engineering, we usually have to solve a function numerically, which has no symbolic computation ability and may using a low percision data type like fp32 or even ...
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20 views

How to get Trig Form from Root

Simplify`TrigToRoot[Cos[Pi/9]] gives out Root[-1 - 6 #1 + 8 #1^3 &, 3] But when I want to do the inverse operation: <...
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1answer
34 views

Select forms of indexed variables from an expression

I want to select some certain terms from a long expression. The expression contains parts like k[1,2](k[3,4]+k[5,6])/k[2,3] I hope to get all terms with the form ...
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2answers
122 views

Organizing Algebraic Expressions (for $ \mathrm\LaTeX $ conversion)

I would ideally like to not have to spend a lot of time writing LaTeX for complicated algebraic expressions that I've worked out in Mathematica. I know that I can "copy-as-LaTeX", but my current issue ...
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1answer
57 views

How to impose rules of indexed variables?

I'm trying to use the following rule: x[b,c,d]+x[a,c,d]+x[a,b,d]+x[a,b,c]->0 for all distinct integers a,b,c,d to simplify a messy expression with terms like ...
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1answer
84 views

How to get rid of Conjugate in the result of Simplify? [closed]

FullSimplify[B^4 + A^3 E^(-I α) Conjugate[ AE^(-I α)], α ∈ Reals && A ∈ Reals && B ∈ Reals] I recently have the problem of simplifying a complex-...
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1answer
68 views

Inverse Laplace Transform how to find the exact solution

So I want to obtain a inverse Laplace transform from mathematica but I get this: How can I get the solution?
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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 ...
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35 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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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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53 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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1answer
42 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 ...
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1answer
68 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 ...
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1answer
68 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 ...
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1answer
100 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/...
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2answers
82 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\...
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2answers
283 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 (...
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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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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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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 ...
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1answer
52 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 ...
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1answer
97 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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38 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 ...
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2answers
166 views

`Series` gives wrong result

Bug introduced in 10.0 or earlier and persisting through 12.0. The following code shows that Series gives different results depending on whether one simplifies the ...
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2answers
60 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 ...
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40 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 ...
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1answer
72 views
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1answer
41 views

Factorizing non commutative terms

Is it possible to factor a ** b ** c - a ** b ** d as a ** b ** (c - d) ? I am using ...
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1answer
259 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^{...
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65 views

Simplify expression to Floor

I would like to simplify the expression below to Floor[L/2], for L \[Element] Integers: ...
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3answers
237 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 ...
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0answers
37 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? ...
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0answers
51 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 ...
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1answer
65 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 ...
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1answer
48 views

Simplify without changing the denominator

I have the following expression: ...
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1answer
34 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 ...
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1answer
61 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 $a,b$, ...
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1answer
58 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 ...
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0answers
39 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),...
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117 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 ...
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2answers
124 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
51 views

Simplification of expression under symmetry conditions

How to simplify the following expression: ...
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2answers
85 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. ...
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1answer
88 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, ...
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2answers
417 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 ...

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