# Questions tagged [simplifying-expressions]

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

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### Efficient evaluation of real/imaginary parts of long expressions

I have the following, rather compact, but complex, expression (see below). I simply want the real part of this. Now, when I do the usual, i.e., ...
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### Another example where using FullSimplify gives different result than Simplify

I believe this question is very similar to Result of Series[expression] is different when I simplify the expression, however, due to my lack of Mathematica experience, I am reluctant to call it a bug. ...
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### Eliminating higher order trigonometric terms

I am interested in eliminating higher-order trigonometric terms from a long symbolic expression. Specifically I want to reproduce this simplification that is done (in a tutorial I am working through)...
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### Checking if two expresssions are equal in mathematica fails [closed]

I want to see if two expressions are equal. I have tried all of the methods outlined in this question but none seem to work. I have two expressions, part1 and <...
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### Finding general forms of sums in Mathematica

A general form can be obtained for some sums with binomial coefficients. Mathematica is able to find these general forms for some of the simplest sums. For others the output contains for instance ...
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### Exclude a term in an expression from any computation/simplification, e.g. being multiplied into a list or matrix

My particular problem is to find a way how to manipulate a term so that it is not multiplied into a vector (as being a list or matrix, and potentially being displayed in MatrixForm) for as long as I ...
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### Prevent simplification of trig functions

Mathematica often simplifies trigonometric expressions, for example replacing $\sin(\frac{\pi}{4})$ with $\frac{1}{\sqrt{2}}$, or replacing $\cos(\frac{3\pi}{8})$ with $\sin(\frac{\pi}{8})$. I'd like ...
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### 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 ...
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### Substitution inside an expression [duplicate]

I'm trying to get mathematica to replace an expression with a reduced form. I wanted to replace $(k/w)$ with $h$ in a particular expression, and I've tried something like: ...
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### Simultaneous equations help [closed]

I have the following: ...
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### Simplifying Algebraic Expression With Substitution

Is there a way I can make an algebraic substitution in a matrix? I tried using Simplify[P_rhs _ 51, (c44hat*rhohat)^.5 == zeta] Where P_rhs_51 is a 4x4 matrix. ...
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### Simplifying expression with square root of square roots

I have the following expression FullSimplify[ Sqrt[1 + (-1 + a) (-1 + b) + 2 Sqrt[(-1 + a) (-1 + b)]] - Sqrt[ 2 + a (-1 + b) - 2 Sqrt[(-1 + a) (-1 + b)] - b]] ...
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### Complex Infinity of Hypergeometric+Gamma function

I am solving some integral which gives an hypergeometric function+gamma function . The point is that my values of n (see the code below) are integers, so ...
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### Simplifying expressions with square roots of squares

I have a large number of expressions that are of the form, f(a,b)+Sqrt[g(a,b)^2] I understand I can use simplify and make an assumption to get either of the two ...
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### How to apply a continious substitution reduction of (-1 + 3 phi - 2 phi^3 - 6 phi^4 - 20 phi^6 + 6 phi^7 + 3 phi^8 + phi^9)//.{phi^3->1-phi^2}

I have the answer to (-1 + 3 phi - 2 phi^3 - 6 phi^4 - 20 phi^6 + 6 phi^7 + 3 phi^8 + phi^9)/.{phi^3->1- phi^2} that is not the problem. I am looking for a ...
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### Force a sum to be simplified

I want to force this sum to be simplified to 1 Sum[Cos[(Pi*l*(2*m + 1))/(n + 1)], {l, 0, n}] Only DiscretePlot3D gives the correct result showing all point to 1
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### Simplify $\tan^{-1}(\cot(a))$ to $\frac{\pi }{2}-a$ assuming $0<a<\frac{\pi }{2}$

I know Mathematica is not omnipotent, but still can't help feeling surprised when I encountered this example, and I think it's worth starting a question for it. The example is, ...
### How to calculate $(X^tX)^{-1}X^tY$? [duplicate]
This is MatrixForm[ {{1., 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1.5, 1.5, 1.5, 2, 2, 2.2, 2.4, 2.5, 2.5, 2.8, 2.8, 3, 3, 3.2, 3.3}}] $X^t$ ...