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Given that our problem seems quite difficult, let
us focus on a simpler problem.
Consider the equation
with the restriction that c(x,y) is an expression of fixed value.
The graph of the equation would either be empty,
if , or the entire plane, if c(x,y) = 0.
After a suitable formalization, this problem may be proven
to be non-computable, unless a very restricted set of operators
is allowed in the construction of c:
for any fixed computer program, there will
be equations which it cannot graph correctly.
Next: 1.6 Perseverance
Up: 1 Motivation
Previous: 1.4 Numerical Round-Off