Questions tagged [simplifying-expressions]

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

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5
votes
4answers
388 views

Alternative form of ArcSin[Sin[x]]

Is it possible to get the following result in Mathematica by using only built-in functions: $$\arcsin( \sin(x)) = x $$ if $x \in [-\pi /2 , \pi/2]$ $$\arcsin ( \sin(x)) = \pi - x $$ if $x \in [\pi /...
2
votes
1answer
995 views

How Simplify and Assume can be combined on matrix products?

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For ...
1
vote
1answer
50 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 ...
0
votes
0answers
28 views

Simplify without changing the denominator

I have the following expression: ...
4
votes
0answers
99 views
+50

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 ...
0
votes
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
47 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
vote
1answer
53 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 ...
0
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0answers
20 views

Posterior predictive distribution [closed]

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 ...
1
vote
0answers
35 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),...
5
votes
2answers
103 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 ...
2
votes
2answers
75 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. ...
1
vote
0answers
47 views
1
vote
1answer
96 views

Simplify rules with variable number of arguments

Problem How to simplify the following rules? The rules simplify (single, double, triple ...) summations of Kronecker delta. Replacement should occur if any summation and the Kronecker delta share an ...
1
vote
2answers
107 views
5
votes
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
397 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 ...
0
votes
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
votes
0answers
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) ...
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 ...
3
votes
3answers
84 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 ...
0
votes
1answer
77 views

WolframScript not simplifying output

I'm trying to multiply a matrix and a vector (imported from a csv) in Wolframscript to speed up a process normally done with Mathematica notebooks. This is my first time using Wolframscript, however, ...
0
votes
0answers
50 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, ...
12
votes
3answers
638 views

Remove Abs from Norms of Vectors

I have the following norm Norm[{a, b*c}] (* Sqrt[Abs[a]^2 + Abs[b c]^2] *) How do I remove the Abs from it? ...
4
votes
2answers
110 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): ...
13
votes
0answers
102 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
vote
3answers
47 views
1
vote
1answer
93 views

How to simplify an expression with no constraints?

Simplifying expressions on Mathematica is a recurrent topic. However I found myself stuck with this one: Solving an rational equation on Mathematica gives me the following expression: ...
3
votes
1answer
94 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
38 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 ...
3
votes
1answer
49 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: ...
0
votes
1answer
72 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 ...
2
votes
1answer
104 views

Simplifying integer inequalities to equality

I try (in Mathematica 10) FullSimplify[l >= l1 + l2, {l <= l1 + l2, Element[l | l1 | l2, Integers]}] But that gives back ...
4
votes
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 ...
6
votes
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: ...
7
votes
1answer
708 views

Correct way of simplifying the result of an integral

Many times Mathematica gives enormous results to simple problems. One uses the program more for trouble than for not knowing how to solve the problem. As an ejemplo I present this integral that ...
1
vote
0answers
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?
0
votes
0answers
40 views

details of the simplifying process

I have a complicated expression: ...
6
votes
1answer
50 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'...
1
vote
0answers
62 views

Find all pattern in expression

Consider this problem: I have a functional $\mathcal{F}$ acting on some function $n(t)$ such that $$ \mathcal{F}[n(t)]=0 $$ $$ \mathcal{F}[n^*(s)n(t)]=\alpha(t,s) $$ $$ \mathcal{F}[n(s)n(t)]=0 $$ ...
7
votes
1answer
277 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. ...
1
vote
2answers
54 views

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

Here is an example: $\frac{\nu y_0}{\left(x_0+\frac{1}{2}\right) \sqrt{\nu ^2+\frac{\left(4 x_0^2+4 y_0^2-1\right){}^2}{16 y_0^2}}}$ ...
2
votes
3answers
326 views

Collect distributed sums

I have another task that somehow should be trivial. Suppose I have the following expression $$ \sum_{i=1}^n \frac{2}{9} x_i + 2 \sum_{i=1}^n \frac{1}{9} x_i, $$ or in Mathematica-FullForm ...
12
votes
1answer
306 views

How to simplify -a*z+a*z to 0 where “a” is an expression

Consider the following: a = 1+(x+y+z+u)^10000 (* Out[57]= 1+(u+x+y+z)^10000 *) e = -a*z+a*z (* Out[59]= z (-1-(u+x+y+z)^10000)+z (1+(u+x+y+z)^10000) *) How can ...
26
votes
2answers
8k views

What is the proper way to verify that two expressions are equivalent?

First of all, it appears to me that $$\left|\frac{1}{x} + x^2\right| = \frac{|1 + x^3|}{|x|}$$ is true. I don't know why, but my attempt to verify it in Mathematica failed. ...
0
votes
2answers
59 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, ...
2
votes
2answers
102 views

Simplifying the expression by defining functions

I want to simplify the function below by using FullSimplify: ...
1
vote
1answer
201 views
0
votes
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 $0$: ...
2
votes
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 ...