  We present three new eclipsing white-dwarf / M-dwarf binary systems
discovered during a search for transiting planets around M-dwarfs. Unlike most
known eclipsing systems of this type, the optical and infrared emission is
dominated by the M-dwarf components, and the systems have optical colors and
discovery light curves consistent with being Jupiter-radius transiting planets
around early M-dwarfs. We detail the PTF/M-dwarf transiting planet survey, part
of the Palomar Transient Factory (PTF). We present a Graphics Processing Unit
(GPU)-based box-least-squares search for transits that runs approximately 8X
faster than similar algorithms implemented on general purpose systems. For the
discovered systems, we decompose low-resolution spectra of the systems into
white-dwarf and M-dwarf components, and use radial velocity measurements and
cooling models to estimate masses and radii for the white dwarfs. The systems
are compact, with periods between 0.35 and 0.45 days and semimajor axes of
approximately 2 solar radii (0.01 AU). We use the Robo-AO laser guide star
adaptive optics system to tentatively identify one of the objects as a triple
system. We also use high-cadence photometry to put an upper limit on the white
dwarf radius of 0.025 solar radii (95% confidence) in one of the systems. We
estimate that 0.08% (90% confidence) of M-dwarfs are in these short-period,
post-common-envelope white-dwarf / M-dwarf binaries where the optical light is
dominated by the M-dwarf. Similar eclipsing binary systems can have arbitrarily
small eclipse depths in red bands and generate plausible small-planet-transit
light curves. As such, these systems are a source of false positives for
M-dwarf transiting planet searches. We present several ways to rapidly
distinguish these binaries from transiting planet systems.
