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

My expression is $$f(x)= x\gamma\,(-1+\sqrt{-1} \,-\sqrt{-1^2})$$ 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= -54 xy^2 (81-z^4)+16 x^4 y^5 (81-z^4) b=Factor[a] Out= 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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### How to get Trig Form from Root

SimplifyTrigToRoot[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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Simplify expression to Floor

I would like to simplify the expression below to Floor[L/2], for L \[Element] Integers: ...
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### 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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### 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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### 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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### 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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### Simplify without changing the denominator

I have the following expression: ...
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### 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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### 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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### 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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### 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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### 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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### 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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### Simplification of expression under symmetry conditions

How to simplify the following expression: ...
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### 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. ...
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, ...
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 ...