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Questions tagged [simplifying-expressions]

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

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0
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1answer
29 views

TensorReduce causes “inhomogeneous dimensions” error

I want to use TensorReduce to realize the following property of wedge: ...
0
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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 ...
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1answer
34 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 ...
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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
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0answers
41 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)\...
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2answers
116 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 ...
12
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1answer
469 views

Rearrange an algebraic expression so that each variable appears only once

Mathematica gave me a solution to an equation in this form: ans1 = (b c)/(a - a c + b c) $\text{ans1} = \frac{b c}{a - a c + b c}$ From solving the same equation ...
8
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1answer
187 views

Function to convert TensorContract[_TensorProduct, indices] into equivalent Dot + Tr version

Mathematica can use either Dot + Tr to represent some tensors, or TensorContract + ...
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1answer
78 views

Simplify function with a derivative

This may be a very simple question: how can I substitute out a term involving a derivative in Mathematica? I have the following derivative: ...
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0answers
55 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)...
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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: ...
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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. ...
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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
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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 ...
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0answers
25 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 ...
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0answers
28 views
3
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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 ...
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1answer
79 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
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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 $c$. ...
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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] ...
2
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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...
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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, ...
1
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0answers
53 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
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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
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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: ...
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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
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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
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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 ...
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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 ...
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2answers
86 views

Simplify part of an expression produced by solve

Mathematica outputs an answer using Solve[] but it is not as simplified as it can be. By manually arranging this expression I know that the parts I've highlighted in yellow can actually be simplified ...
2
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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
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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 ...
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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 ...
6
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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: ...
3
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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 - ...
2
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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 ...
11
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1answer
419 views

x DiracDelta[x] simplifies to 0, desired or a bug?

Bug introduced in 5.0 or earlier, persisting through 12.0. I encountered this when trying to answer this question: x DiracDelta[x] // Simplify (* 0 *) Is this a ...
4
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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
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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 <...
15
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2answers
429 views

Factor a polynomial Root into Roots of smallest possible degree

Suppose I have a polynomial Root representing an algebraic number. I want to represent it as a product of several polynomial Root...
3
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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 ...
1
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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 ...
3
votes
1answer
251 views

Find RSolve solution reflecting special structure of DifferenceRoot[Function[{\[FormalY], \[FormalN]}

RSolve yields a large (multi-page) solution (LeafCount=25891) containing a number of 7F6 (and higher) hypergeometric functions when applied to ...
0
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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 ...
0
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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 ...
3
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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 ...
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. ...