The tanz surface is the quartic surface
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named by Hauser. Its German name means "dance." Its singular points form the z-axis and the y-axis.
Over the real numbers, the equation can be written 
. Since the right side
is nonnegative, every solution with 
has 
and 
. Consequently, in this region the real zero
set consists only of the two crossing lines, with no
nearby two-dimensional sheet. This illustrates why a rendering of an algebraic
surface can miss lower-dimensional parts of its real zero
set.
