Questions tagged [simplifying-expressions]
Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
1,618
questions
2
votes
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
vote
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:
...
0
votes
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 ...
1
vote
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:
...
3
votes
0answers
113 views
5
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
vote
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 ...
0
votes
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(-...
1
vote
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
vote
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
...
1
vote
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
votes
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
vote
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
votes
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
votes
1answer
48 views
Why is my answer not fully being simplified with the Simplify[] and FullSimplify[] functions?
The code for my program is as follows:
...
1
vote
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
votes
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
votes
0answers
59 views
Simplify expression to Floor
I would like to simplify the expression below to Floor[L/2], for L \[Element] Integers:
...
4
votes
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
votes
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
votes
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
vote
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
vote
1answer
44 views
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
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
vote
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
vote
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
votes
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
votes
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
...
1
vote
0answers
50 views
Simplification of expression under symmetry conditions
How to simplify the following expression:
...
2
votes
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
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
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
vote
2answers
110 views
Q: Problem - FullSimplify returns 0, FindRoot returns value & FindInstance requires system abend
The function at issue:
...
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
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
votes
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
vote
3answers
49 views
4
votes
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
votes
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 ...
