Questions tagged [simplifying-expressions]

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

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Eigenvalues of a fourth-order ODE

Consider the following ODE for $y(x)$ over $x\in\left[0,\frac{1}{2}\right]$ with an eigenvalue $\lambda$ $\qquad 2x\,y''''+ 4y'''=\lambda\, y''$ The boundary conditions at $x=\frac{1}{2}$ are $y'\...
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2answers
42 views

Extract different part of a polynomial with square root $a(x)+b(x)\sqrt{c(x)}$

Say I have an expression like $a(x)+b(x)\sqrt{c(x)}+d(x)\sqrt{e(x)}+f(x)g(\sin(x))$, where a(x) to f(x) mean polynomials of $x, g(x)$ is a polynomial of $sin(x)$. I wonder how to extract the different ...
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0answers
15 views

Symbolically invert block matrix [duplicate]

In Mathematica, if I write something like: Inverse[{{a, b}, {c, d}}] I get the inverse: ...
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4answers
309 views

Remove radicals from denominator

Memo for the moderator. Sorry, I am new to "Ask a question". Is my writing correct ? Shall I receive a reply directly to my e-mail address or somewhere in the StackExchange? My question: I want ...
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2answers
37 views

How to obtain the linear terms of the expansion?

Consider the following function, which is actually linear on the going-to-expand points. I want to use Mathematica to expand the function near these points, and keep only the linear terms, i.e. the ...
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63 views

Verifying hypergeometric identity

By experiments, it's easy to convince ourselves that the following expressions are identical for positive integer $n$. ...
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0answers
45 views

Getting rid of redundant complex values with FullSimplify

Main Problem I have a function $f(x,y)$ such that $f:\mathbb{R}\to\mathbb{R}$. However its expression contains redundant imaginary values and I have not been able to simplify it with Mathematica. The ...
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1answer
27 views

Expression arrange by base

I have an expression with multiple powers, for example N^α/(B*N)^β Any simplification like FullSimplify leads to $$ N^\...
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1answer
200 views

Simplifying solution to a third-order Boundary Value problem

I have been trying to solve a physical problem during which I reach the following third-order, Linear O.D.E. The solution I get using this expression is really messy. Is there any way to simplify it ...
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5answers
112 views

How do I collect different exponents together?

Suppose I have: ...
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2answers
59 views

Simplifying polynomial in one variable by substitution

I want to simplify a polynomial in variable $x$ with integer coefficients by substitution $x\to{x}/d$ so that the coefficients become smallest possible integers. Input: ...
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2answers
57 views

Simplifying expressions with variables that can only take specific values

I am having some trouble simplifying expressions where a variable can only take a number of specific values. As an example, suppose I have the expression: $ \lambda(m) = \frac{1+m}{2} \frac{1}{(a+b)} ...
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0answers
35 views

Simplifying the dot product [closed]

Why does the code D[x.x, x] /. {1. x -> x, x .1 -> x} gives 1.x+x.1, while ...
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0answers
30 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 ...
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0answers
23 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 ...
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0answers
39 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 ...
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4answers
297 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: ...
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0answers
35 views

making replacements when patterns don't match exactly

I want to simplified some mathematical expressions, and they are similar to ...
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1answer
93 views

Simplify seems to give wrong result [closed]

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 ...
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0answers
49 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 <...
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2answers
79 views

Abs[]^2 , Conjugate[], ComplexExpand[], and Simplify

I think this is a numeric problem but would like to see where it occurs. I create a complex rational polynomial as follows and make it a function of f ...
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3answers
59 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 ...
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0answers
67 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
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1answer
117 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 ...
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1answer
31 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
50 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
51 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 ...
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0answers
45 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
122 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 ...
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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)...
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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. ...
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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) \...
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0answers
31 views

Reduce system of nonlinear equations to one nonlinear equation

I have a system of nonlinear equations: ...
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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 ...
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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 ...
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0answers
28 views
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1answer
101 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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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
86 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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0answers
55 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] ...
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2answers
178 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: ...
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0answers
37 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: ...
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1answer
104 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. ...
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1answer
653 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
42 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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1answer
44 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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1answer
39 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
67 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 ...
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0answers
43 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 ...