It is made slightly worse by the fact that its counterpart "negative fractional part" is never explicitly defined on the website -- at least, I cannot seem to find it. But I'm assuming that if it does exist, it would have a definition something like the one I gave in post #10.
]]>If you recall characteristic and mantissa of log to the base 10 in logarithm tables, the concept becomes clear.
I do not agree. Eric's page is ambiguous to me in this case.
I agree with Knuth:
For instance Knuth adopts the third representation 0.12345 × 10+3 in the example above, and calls 0.12345 the fraction part of the number; he adds:[7] "[...] it is an abuse of terminology to call the fraction part a mantissa, since this concept has quite a different meaning in connection with logarithms [...]".
But as this is the interpretation that the OP wanted I can only blame myself for not asking him to clear up the confusion in how I see that page.
]]>Nope, I am not sure. I will agree then that - phi is not a solution.
]]>The page he gave http://mathworld.wolfram.com/Mantissa.html describes it like that.
]]>From the link you gave, mant is the positive fractional part .
So:
f[x_] := Abs[FractionalPart[x]];
n = -(8/5);
FindRoot[f[1/x] == f[x] && f[1/y] == f[y^2] && f[z] == f[z^2], {{x, n}, {y, n}, {z, n}}, WorkingPrecision -> 50]
yields a root at
{x -> -1.6180339887498948482045868343656381177203091798058,
y -> -1.6180339887498948482045868343656381177203091798058,
z -> -1.6180339887498948482045868343656381177203091798058}
which is
When you have time would you post the execution?
My solution is a numerical one and I will post it when I can.
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