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In solving the inequality $2d^2\ge -(2(1+d)+\frac{4d^3}{1-d})(d-1)$, Mathematica returns something using Slots and Functions:

In:= Reduce[2 d^2 >= -((2*(1 + d) + ((4 d^3)/(1 - d)))*(d - 1)), d]
Out= d <= Root[1 - 2 #1^2 + 2 #1^3 &, 1]

How do I translate this output to a Latex type font, as I have written in the beginning of this question? I know I start with $d\le \sqrt[1]{1-}$, but I'm really thrown off by the # and &. Could someone put me on the right track?

Jay Schyler Raadt
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  • It's not clear what the question is. Are you asking what Root[...] means? Or are you asking how to write Root[...] in LaTeX so that it will look the same as in Mathematica? – Szabolcs Jun 13 '19 at 19:10
  • Root, # and & are foreign to me, although I am reading up on Slots and Functions. – Jay Schyler Raadt Jun 13 '19 at 19:15
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    Slots and functions are less important, please read the docs of Root. Root[1 - 2 #1^2 + 2 #1^3 &, 1] indicates the 1st root of the polynomial $1-2x^2+2x^3$. – Szabolcs Jun 13 '19 at 19:17
  • @kglr answered this in another question of yours but to add it to this thread, consider using the function ToRadicals. It gives a pretty printed version of this "d <= 1/3 (1 - 2^(2/3)/(23 - 3 Sqrt[57])^(1/3) - (23 - 3 Sqrt[57])^( 1/3)/2^(2/3))". ToRadicals is a recommended "See also" function of Root, so you could get there by reviewing that part of the documentation too. – Mark R Jun 13 '19 at 23:32

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