# Questions tagged [simplifying-expressions]

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

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### Why is Log[8 E^(3 Log[0.5]) != 0 [closed]

My wife and I have tried to calculate Log[8 E^(3 Log[0.5]) on a TI-Nspire and we got the result -8E-14. We have changed th settings of calculation to Exact and the result was 0 (correct) If I use ...
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### A single expression that performs substitution and simplifies a trigonometric form

I'm very new to Mathematica. I searched through the online documentation, but I don't understand why it realizes that $\sin(n\pi)$ for $n\in \mathbb{Z}$ is $0$: ...
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### solve equation (or simplify) in real field still gives complex solutions (Solved)

Original post: I try to solve for this equations for $\sin\theta_1$ and $\cos\theta_1$, which should be a straightforward thing because it's nothing but a linear system ...
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### Change a single letter changes the result

these two codes give different result. FullSimplify[a-b,Assumptions->a==1+y&&b==1+y-x] this give x ...
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### 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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### 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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### Reduce system of nonlinear equations to one nonlinear equation

I have a system of nonlinear equations: ...
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### 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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### How to split the expressions into four parts include the coefficients of Sin[x], Cos[x], and Exp[x], respectively?

Given three expressiones as ...
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### 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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### Simplify a series expansion including trigonometric expressions

I have the expression ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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. ...