Why does reduce return the root of a pure function?

Asked Sep 29 '18 at 21:01

Active Sep 29 '18 at 21:01

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I want to find the zeros of some nonlinear function in a certain range, say $f(x)=x^4+\frac{x}{1-x}-c$. If I enter

f[x_] := x^4 + x/(1 - x) - c
Reduce[f[x] == 0 && 0 < x < 1, x, Reals]

I get the result

c > 0 && x == Root[c + (-1 - c) #1 - #1^4 + #1^5 &, 2]

My familiarity with Mathematica is very limited, and I don't really know how to interpret the output. I think the Root[$\cdot$,2] notation is telling me that I need to use the second root of the $\cdot$ expression, which is a pure function here, but what does that mean? What would be the argument passed to the pure function?

asked Sep 29 '18 at 21:01

Chris_77

Have you read the documentation? – AccidentalFourierTransform Sep 29 '18 at 21:04
Yes, there wasn't really an explanation of what the # sign means there either. I was hoping to find some symbolic representation that I could port back to Matlab, where I do most of my calculations – Chris_77 Sep 29 '18 at 21:10
"some symbolic representation" - it's the root of a fifth-order polynomial, that result's as good as it gets. – J. M.'s missing motivation Sep 29 '18 at 21:17

Why does reduce return the root of a pure function?

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