precise central point for power mean

[araujoms]

It turns out the same technique applies to the power mean cone, allowing a rather simple solution.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.76%. Comparing base (a6c2fc2) to head (3402d4e).
⚠️ Report is 2 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #860      +/-   ##
==========================================
+ Coverage   96.72%   96.76%   +0.03%     
==========================================
  Files          56       56              
  Lines        9102     9106       +4     
==========================================
+ Hits         8804     8811       +7     
+ Misses        298      295       -3     

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[lkapelevich]

Any idea why https://app.codecov.io/gh/jump-dev/Hypatia.jl/pull/860?dropdown=coverage&src=pr&el=h1&utm_medium=referral&utm_source=github&utm_content=checks&utm_campaign=pr+comments&utm_term=jump-dev#9df442195d09281f8e579aef25862544-R278
is not covered by https://github.com/jump-dev/Hypatia.jl/blob/master/test/cone.jl#L603?

[araujoms]

Because it gets caught by

Hypatia.jl/src/Cones/hypopowermean.jl

Line 70 in 01488be

if all(isequal(inv(T(d))), cone.α)

and thus uses the code from hypogeomean. I've removed the unused branch.