Non-standard reality, an arbitrage opportunity

Abstract.  In  the real world,  it is common to  encounter a
need to study real algebraic varieties computationally, when
the  real structure  is  nonstandard.   Such alternate  real
structures come  from an  antiholomorphic involution  on the
ambient  complex space.   Symbolic  methods  to handle  such
alternate  reality are  either lacking  or require  a costly
reformulation as a standard real object.

Numerical algebraic  geometry should be able  to avoid these
pitfalls, as the  real points (in any model  of reality) are
just those  fixed under  the antiholomorphic  involution.  I
will illustrate  some of  these ideas  with examples  I have
encountered in my own work.