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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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### 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 ...
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 ...
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 ...
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: ...
35 views

### making replacements when patterns don't match exactly

I want to simplified some mathematical expressions, and they are similar to ...
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 ...
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 <...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
42 views

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### Reduce system of nonlinear equations to one nonlinear equation

I have a system of nonlinear equations: ...
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 ...
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 ...
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 ...
28 views

### Simplify a series expansion including trigonometric expressions

I have the expression ...
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 ...
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...
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 $c$. ...
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] ...
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: ...
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: ...
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. ...
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 ...
41 views

### how to force TransformationFunctions

I have this function: F[z_, y_, θ_] = Sqrt/(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 ...
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: ...
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 ...
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 ...
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 ...
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] ...
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 - ...
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: ...
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 ...
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 ...
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 <...
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, ...
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 ...
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: ...
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 ...
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 ...
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 ...