Questions tagged [simplifying-expressions]
Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
1,542
questions
0
votes
0answers
9 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 ...
0
votes
0answers
15 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 ...
1
vote
0answers
32 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 ...
8
votes
4answers
286 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:
...
0
votes
0answers
35 views
making replacements when patterns don't match exactly
I want to simplified some mathematical expressions, and they are similar to
...
1
vote
1answer
91 views
Simplify seems to give wrong result [on hold]
I have an very long expression named "Bug", which is made by different precision numbers. When I directly apply Simplify, it seems to give me a wrong result. However when I apply SetPrecision to set ...
0
votes
0answers
48 views
Dealing with positive power variables in Taylor expansion and assumptions
I would like to compute the Taylor expansion of monomials whose powers are nonnegative rational variables.
First, here is a function which encodes the multivariate Taylor expansion at the points <...
2
votes
3answers
58 views
Replace function and its derivatives by zero
If I try to replace the function u0 and its derivatives by zero in the following examplary expression
...
0
votes
0answers
66 views
How do I solve a cubic equation for values of x?
I have partially differentiated an equation w.r.t. x, see picture below, and want to isolate x in the equation to solve for a local maximum.
Can I use Mathematica to get it on a cubic form? and how ...
2
votes
1answer
112 views
Forcing the simplification of ratios of radicals
Mathematica seems to have trouble with expressions like
$$\sqrt{\frac{1}{x}} \sqrt{x}$$
Oddly, it doesn't have trouble with
$$\frac{\sqrt{x}}{\sqrt{x}}$$
which will happily simplify to $1$ even ...
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
44 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
49 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?
$$
-\frac14\int_1^{\infty}\!\!\frac{\sqrt{-4 x^4-4 x^2 z-(y^2+z)^2}}{x (x^2+z)}\theta\!\left(-4 x^4-4 x^2 z-(y^2+z)^2\right)\...
3
votes
2answers
119 views
Simplification of logarithms
From the Wolfram functions web site it is known that
$$\log(z_1)+\log(z_2)=\log(z_1z_2),\text{ for $z_1+z_2>0$}$$
In an answer to this question Alexei Boulbitch wrote a useful function ...
0
votes
0answers
58 views
Simplifying a differential equation acting on a product of functions
I have a function $f(x_1, \ldots , x_n)$ in $n$-variables that satisfies a fourth order linear differential equation (say $Df=0$). The function $f(x_1, \ldots, x_n)$ is of the form $f(x_1, \ldots, x_n)...
0
votes
0answers
37 views
FullSimplify output depends on symbol name
Using g rather than b as variable name changes output. As far as I know neither b nor g are restricted symbols. Can this be reproduced on other builds? Using Mathematica 12.0.0.0 on a Mac.
...
0
votes
0answers
45 views
Using FullSimplify to simply expressions involving differential operators
I am trying to simplify some long formulas involving differential operators in $n$ variables. For example, I want to simplify
$$\left(\frac{\partial}{\partial x}-\frac{\partial}{\partial y}\right) \...
0
votes
0answers
31 views
Reduce system of nonlinear equations to one nonlinear equation
I have a system of nonlinear equations:
...
0
votes
1answer
72 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
28 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
100 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
83 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
166 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
35 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
103 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
632 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
43 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
38 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
61 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
42 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
71 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
514 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
172 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
70 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
64 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
76 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
63 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
40 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
39 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
38 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. ...
