  Bounds for the poloidal and toroidal kinetic energies and the heat transport
are computed numerically for rotating convection at infinite Prandtl number
with both no slip and stress free boundaries. The constraints invoked in this
computation are linear or quadratic in the problem variables and lead to the
formulation of a semidefinite program. The bounds behave as a function of
Rayleigh number at fixed Taylor number qualitatively in the same way as the
quantities being bounded. The bounds are zero for Rayleigh numbers smaller than
the critical Rayleigh number for the onset of convection, they increase rapidly
with Rayleigh number for Rayleigh numbers just above onset, and increase more
slowly at large Rayleigh numbers. If the dependencies on Rayleigh number are
approximated by power laws, one obtains larger exponents from bounds on the
Nusselt number for Rayleigh numbers just above onset than from the actual
Nusselt number dependence known for large but finite Prandtl number. The
wavelength of the linearly unstable mode at the onset of convection appears as
a relevant length scale in the bounds.
