Questions tagged [simplifying-expressions]
Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
1,531
questions
0
votes
1answer
30 views
Expression with Boole
Let us have an expression for example, this:
2 (-1 + p) (3 - 4 p + 2 p^2) Boole[\[FormalX] == 1] - 9 (1 - 2 p + p^2) Boole[\[FormalX] == 2] ...
For the whole ...
0
votes
1answer
36 views
How to force Mathematica to give answer in certain functional form?
I want Mathematica to evaluate $$0=\psi (x) \left(\frac{k x^2}{2}-\text{En}\right)-\frac{\hbar ^2 \psi ''(x)}{2 m}$$ and give me answer in terms of the Hermite polynomials but it gives me result in ...
1
vote
1answer
45 views
Simplify product of cosh and sech expressions
I would like to simplify a product of hyperbolic cosine and hyperbolic secant functions, with the key simplifying assumption being that the two are inverses of each other. This sounds like a silly ...
1
vote
0answers
42 views
Efficient application of the fundamental theorem of calculus
How can the following definite integral be computed with Mathematica?
$$
-\frac14\int_1^{\infty}\!\!\frac{\sqrt{-4 x^4-4 x^2 z-(y^2+z)^2}}{x (x^2+z)}\theta\!\left(-4 x^4-4 x^2 z-(y^2+z)^2\right)\...
3
votes
2answers
117 views
Simplification of logarithms
From the Wolfram functions web site it is known that
$$\log(z_1)+\log(z_2)=\log(z_1z_2),\text{ for $z_1+z_2>0$}$$
In an answer to this question Alexei Boulbitch wrote a useful function ...
0
votes
0answers
56 views
Simplifying a differential equation acting on a product of functions
I have a function $f(x_1, \ldots , x_n)$ in $n$-variables that satisfies a fourth order linear differential equation (say $Df=0$). The function $f(x_1, \ldots, x_n)$ is of the form $f(x_1, \ldots, x_n)...
0
votes
0answers
36 views
FullSimplify output depends on symbol name
Using g rather than b as variable name changes output. As far as I know neither b nor g are restricted symbols. Can this be reproduced on other builds? Using Mathematica 12.0.0.0 on a Mac.
...
0
votes
0answers
44 views
Using FullSimplify to simply expressions involving differential operators
I am trying to simplify some long formulas involving differential operators in $n$ variables. For example, I want to simplify
$$\left(\frac{\partial}{\partial x}-\frac{\partial}{\partial y}\right) \...
0
votes
0answers
26 views
Reduce system of nonlinear equations to one nonlinear equation
I have a system of nonlinear equations:
...
0
votes
1answer
66 views
Substituting and exponential term by another expression
I would like to do, in every calculation that I perform, the following substitution:
$e^x -> (1+x)$.
That is, every term with an exponential should become the Taylor series to the first-order ...
2
votes
2answers
55 views
How to split the expressions into four parts include the coefficients of Sin[x], Cos[x], and Exp[x], respectively?
Given three expressiones as
...
0
votes
0answers
26 views
Vanishing with the derivative terms in perturbation theory
Following the question in here, now I would like to make the terms with derivatives to vanish. To shortly explain, given a variable decomposed as follows:
$a(t,r) = a(r) + \delta a(t,r)$
in my long ...
0
votes
0answers
28 views
3
votes
1answer
98 views
Strange behavior of `Apart`
Here is a piece of sad comedy based on some Apart behavior. Is there a way to make Apart do the expected step?
Consider a very ...
2
votes
2answers
87 views
Exponentiation with parentheses
Why doesn't the following always simplify to 0?
Simplify[a^(b c) - (a^b)^c]
If we Assume a...
1
vote
1answer
80 views
Assuming that only the 2nd order terms are zero
I am dealing with first-order perturbative theory, that is, any variable may be decomposed as
$a = a + \delta a$
and the same would occur with several different variables, let's say, $b$ and $c$. ...
1
vote
0answers
54 views
Assumptions with conditions
How does one specify the assumption that a function is real for real arguments?
Compare
Simplify[Re[I f[x]], Assumptions -> f[x_] ∈ Reals]
...
2
votes
2answers
158 views
Simplify appears to give different results
I have an issue with Simplify (and FullSimplify) giving a different numerical expression to the pre-Simplified expression. The function is an alternating sum of trigonometric quantities:
...
0
votes
0answers
33 views
Output of Reduce + Simplify
I'm using Reduce to solve some equations and then simplify to eliminate some undesired results. The problem is that, when I apply Simplify, it messes with my output from reduce.
As an example:
...
4
votes
1answer
100 views
Mathematica not simplifying rational powers in complex expressions
I have the following expressions and I would like to obtain a final result purely in the real domain.
...
8
votes
1answer
613 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 ...
0
votes
0answers
41 views
how to force TransformationFunctions
I have this function:
F[z_, y_, θ_] = Sqrt[3]/(2*π)*w^2/z^2 *
Exp[-w^2*(θ^2/z - 3*y*θ/z^2 + 3*y^2/z^3)]
I want to calculate
...
0
votes
1answer
40 views
Simplifying sums and showing equality - limitations?
Is it possible to verify the following lhs,rhs involving the sums
are equal, with Mathematica?
I can verify it for individual values of $d$ variable:
...
0
votes
1answer
36 views
Distribute dot and multiplication on a sum
I have a simple problem, I would like to get the following:
In= Distribute[a.(b+c)*d]
Out= a.b*d+a.c*d
Meaning that I would like the dot product and the ...
2
votes
0answers
50 views
How to remove the Riemann tensor derivatives using Bianchi identity?
For the third-order Lovelock gravity, after varying the Lagrangian versus the metric, I found some derivatives of the Riemann tensor which should not be appeared. How can I remove them? Maybe using ...
0
votes
0answers
41 views
How to get rid of these matrices?
I have divided a complicated Lagrangian to some separated terms to be able to Simplify it. The thing is, in the general case (non-divided Lagrangian) the problem is ...
0
votes
3answers
70 views
expression containing radicals of imaginary numbers
I can't bear an expression containing radicals of imaginary numbers,
in case it can be expressed as in terms of radicals of real numbers only.
For example, I can't bear the expression
Sqrt[2 + i]
...
3
votes
1answer
53 views
Simplifying symbolic expression with Heaviside step function
When inputing
Integrate[HeavisideTheta[s - t], {s, 0, 1}, Assumptions -> {t > 0}]
Mathematica correctly simplifies if to
-(-1 + t) HeavisideTheta[1 - ...
6
votes
3answers
505 views
Factoring the square of this polynomial?
I have a polynomial $$\frac{b^4}{a^4}-\frac{2 b^2}{a^2}+1$$ and I want to complete the square to get this kind of expression: $$\left(1-\frac{b^2}{a^2}\right)^2.$$
I had try:
...
4
votes
1answer
171 views
How can I change Simplify
I have an application where I strongly prefer $1+\frac{3}{2+3x}$ over $\frac{5+3x}{2+3x}$, and $\sin(2x)$ over $2\sin(x)\cos(x)$. In general, I prefer to minimize the number of occurrences of the ...
2
votes
1answer
68 views
Solving 2D convection-conduction equation via using Fourier integral transform: the disappearance of the convection term?(with code)
I am currently solving a 2D convection-conduction equation. The convection is only working on the x direction. The governing equation and its associated conditions are given as
where T is the ...
2
votes
0answers
75 views
Expression manipulation
How can one write $\frac{ad+bc}{bd}$ in $\frac{a}{b}+\frac{c}{d}$ form? In other words, is there something opposite of Together[]?
Edit
My intend was to write
<...
0
votes
1answer
61 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, ...
3
votes
3answers
75 views
Identify complex expression and replace
I'm having trouble finding a way (if there is) to analyse an expression, identify a complex pattern in it and then replace it with another thing. I think it will be easier to explain my problem with ...
0
votes
1answer
62 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:
...
1
vote
1answer
39 views
Implementing global Assumptions [closed]
Why do the following commands
$Assumptions = {Element[x, Reals], x > 0};
Solve[{x^2 == 1}, {x}]
Solve[{x^2 == -1}, {x}]
give
...
0
votes
0answers
34 views
Completely expand and simplify logical expressions?
Consider a logical expression such as
expr = (a == b + q - w || c == d) && (q + c - d == w || e == r);
I wonder if there is a function that would ...
3
votes
0answers
34 views
How to speed up xTensor simplification?
I need to compute a variation of the 4th rang symmetric tensor. I've written a code that successfully computes it, but when I use the resulting tensor to compute the second variation the ...
0
votes
2answers
43 views
FullSimplify not finding trig substitution with other terms present
Consider the following:
FullSimplify[Cos[x - y - z] + Cos[x + y + z] + 1]
Mathematica simply returns the exact expression with no simplification. However, if I ...
7
votes
2answers
91 views
Fullsimplify output depends on variable order
Bug introduced in 5.2 or earlier and persisting through 12.0 or later
Mathematica 11.3.0.0 (used on a Mac) seems to give different results when using FullSimplify. ...
5
votes
1answer
79 views
Make assumption for function with variable argument
I would like to assume that a>t[b_] for any b, such that e.g. Simplify[a>t[c]]==True. ...
0
votes
2answers
44 views
0
votes
0answers
47 views
Convert Part of an Expression Using ExpToTrig
I'm wondering if there's a nice way to convert only parts of an expression, say exponential functions of varible $\theta$ to trig. The motivation is best descripbed by the following example.
...
0
votes
0answers
70 views
Time spent on a transformation exceeded 300 when solving the optimization problem
I have the code which shows below to solve an optimization problem, but it will show that it's over the time constraint of 300 seconds. Is there anyone who could help me solve it. Thanks.
...
0
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0answers
57 views
0
votes
3answers
82 views
How to simplify a three variables expression with Simplify?
I want to calculate the value of $\nabla\cdot\frac{1}{(x^2+y^2+z^2)^{1.5}}(x\hat{x}+y\hat{y}+z\hat{z})$. I used the following syntax:
...
2
votes
1answer
72 views
How do I force this simplification?
I am trying to calculate:$$\epsilon_{ijk}n^iM1^j\epsilon^{lmk}n_lM2_m$$
Defining the vectors as:
M1={M1x,M1y,M1z}
M2={M2x,M2y,M2z}
n={nx,ny,nz}
and using
...
0
votes
0answers
23 views
Optimizing and Parallel Computing for Large Dyadic Intervals
I need help with the efficiency of my code i.e. less time so I can compute for large range of values.
My function n[x] takes in a number x and outputs the ...
8
votes
4answers
374 views
How can I automate this tensor computation?
I am doing this work by hand, but it takes a lot of time and I make several calculation errors, so I was thinking to make Mathematica to calculate this for me, but I am stuck at the very beginning.
I ...
3
votes
2answers
59 views
Simplify the cubic root of cube assuming real and positive variable
I know this is very simple but I couldn't find a reasonable solution for it in the archive. It seems that my Mathematica does not take into account the assumptions when it wants to simplify the ...
