Questions tagged [simplifying-expressions]

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

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19 views

Posterior predictive distribution

How can I find posterior predictive distribution and predictive intervals for 4-Component Rayleigh mixture model ? Can anybody help me in this regard? I need a program to generate lower and upper ...
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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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2answers
93 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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44 views

Simplification of expression under symmetry conditions

How to simplify the following expression: ...
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2answers
74 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
76 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
395 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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2answers
105 views
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38 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. ...
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47 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) ...
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1answer
55 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 ...
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49 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, ...
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3answers
83 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 ...
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100 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 ...
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3answers
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2answers
109 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): ...
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1answer
90 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 $...
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1answer
37 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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1answer
47 views

Is there a global parameter that limits the number of variables handled by Simplify?

It seems that Simplify is unable to handle (at least some) expressions involving 22 or more variables. Consider the code snippet below: ...
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1answer
126 views

Simplify is not simplifying a compound inequality as expected

The Simplify command is having trouble verifying a compound inequality, even while it correctly handles the two corresponding single inequalities. I'm starting ...
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1answer
71 views

What is the first slot value in this expression?

I would like to know what is the first slot value in the following expression ...
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33 views

What options should I feed to FullSimplify to make it strongly prefer elementary functions?

I want that FullSimplify strongly preferred all elementary functions as opposed to all non-elementary. Can I do it?
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2answers
357 views

An example from a Mathematica tutorial on integration returns a different answer from the tutorial

This page on "Integrals that Can and Cannot Be Done" suggests that, almost surprisingly, Mathematica can express the following integral in terms of elementary functions: ...
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40 views

details of the simplifying process

I have a complicated expression: ...
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1answer
49 views

How to Reduce conditions of Piecewise function

Edit I had problems with pasting an example to stackoverflow itself so here is the link to PasteBin containing sample code: https://pastebin.com/yi6AyrHy I have fairly big piecewise function which I'...
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62 views

Find all pattern in expression

Consider this problem: I have a functional $\mathcal{F}$ acting on some function $n(t)$ such that $$ \mathcal{F}[n(t)]=0 $$ $$ \mathcal{F}[n^*(s)n(t)]=\alpha(t,s) $$ $$ \mathcal{F}[n(s)n(t)]=0 $$ ...
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2answers
54 views

how to get rid of the denominator in the squareroot, that appears in the denominator?

Here is an example: $\frac{\nu y_0}{\left(x_0+\frac{1}{2}\right) \sqrt{\nu ^2+\frac{\left(4 x_0^2+4 y_0^2-1\right){}^2}{16 y_0^2}}}$ ...
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2answers
58 views

Simplify Integrate results

I wish to simplify the overlap of two gaussian-type orbitals, primGauOrb = ((2 α)/π)^(3/4)E^(-α (x^2 + y^2 + z^2)); And then integrate it, ...
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2answers
102 views

Simplifying the expression by defining functions

I want to simplify the function below by using FullSimplify: ...
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0answers
60 views

Why is Log[8 E^(3 Log[0.5]) != 0 [closed]

My wife and I have tried to calculate Log[8 E^(3 Log[0.5]) on a TI-Nspire and we got the result -8E-14. We have changed th settings of calculation to Exact and the result was 0 (correct) If I use ...
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1answer
56 views

A single expression that performs substitution and simplifies a trigonometric form [closed]

I'm very new to Mathematica. I searched through the online documentation, but I don't understand why it realizes that $\sin(n\pi)$ for $n\in \mathbb{Z}$ is $0$: ...
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0answers
51 views

Change a single letter changes the result

these two codes give different result. FullSimplify[a-b,Assumptions->a==1+y&&b==1+y-x] this give x ...
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2answers
102 views

Eigenvalues of a fourth-order ODE

Consider the following ODE for $y(x)$ over $x\in\left[0,\frac{1}{2}\right]$ with an eigenvalue $\lambda$ $\qquad 2x\,y''''+ 4y'''=\lambda\, y''$ The boundary conditions at $x=\frac{1}{2}$ are $y'\...
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2answers
60 views

Extract different part of a polynomial with square root $a(x)+b(x)\sqrt{c(x)}$

Say I have an expression like $a(x)+b(x)\sqrt{c(x)}+d(x)\sqrt{e(x)}+f(x)g(\sin(x))$, where a(x) to f(x) mean polynomials of $x, g(x)$ is a polynomial of $sin(x)$. I wonder how to extract the different ...
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17 views

Symbolically invert block matrix [duplicate]

In Mathematica, if I write something like: Inverse[{{a, b}, {c, d}}] I get the inverse: ...
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4answers
354 views

Remove radicals from denominator

Memo for the moderator. Sorry, I am new to "Ask a question". Is my writing correct ? Shall I receive a reply directly to my e-mail address or somewhere in the StackExchange? My question: I want ...
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2answers
39 views

How to obtain the linear terms of the expansion?

Consider the following function, which is actually linear on the going-to-expand points. I want to use Mathematica to expand the function near these points, and keep only the linear terms, i.e. the ...
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78 views

Verifying hypergeometric identity

By experiments, it's easy to convince ourselves that the following expressions are identical for positive integer $n$. ...
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46 views

Getting rid of redundant complex values with FullSimplify

Main Problem I have a function $f(x,y)$ such that $f:\mathbb{R}\to\mathbb{R}$. However its expression contains redundant imaginary values and I have not been able to simplify it with Mathematica. The ...
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1answer
27 views

Expression arrange by base

I have an expression with multiple powers, for example N^α/(B*N)^β Any simplification like FullSimplify leads to $$ N^\...
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1answer
201 views

Simplifying solution to a third-order Boundary Value problem

I have been trying to solve a physical problem during which I reach the following third-order, Linear O.D.E. The solution I get using this expression is really messy. Is there any way to simplify it ...
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5answers
117 views

How do I collect different exponents together?

Suppose I have: ...
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2answers
59 views

Simplifying polynomial in one variable by substitution

I want to simplify a polynomial in variable $x$ with integer coefficients by substitution $x\to{x}/d$ so that the coefficients become smallest possible integers. Input: ...
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2answers
58 views

Simplifying expressions with variables that can only take specific values

I am having some trouble simplifying expressions where a variable can only take a number of specific values. As an example, suppose I have the expression: $ \lambda(m) = \frac{1+m}{2} \frac{1}{(a+b)} ...
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0answers
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Simplifying the dot product [closed]

Why does the code D[x.x, x] /. {1. x -> x, x .1 -> x} gives 1.x+x.1, while ...
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0answers
37 views

Reorganize an expression such that specific expressions are evidentiated/factored

I want to rewrite an expression in a way that specific variables appear factored, like (x+y)(x-y). I know collect does something similar, but it only works if the factor you want to collect already ...
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0answers
25 views

How to simplify this hypergeometric expression?

How can I rewrite this expression in terms of a single Hypergeometric function? Is it possible? I think it is possible to convert this expression in such a way that ...
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0answers
40 views

Why does Mathematica miss some solutions for my integral?

When computing the integral of two orthogonal sine functions $\qquad \sin(n\,\pi\,x)\,\sin(m\,\pi\,x)$, where $n,\,m$ are integers > 0 Mathematica seems to miss the solution where $n=m$. I don't ...
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4answers
307 views

Simplify makes Mathematica forget that a matrix is Hermitian

Using Simplify with certain trivial assumptions makes Mathematica forget that a given matrix is Hermitian. See the minimal example below: ...