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Next: 1.6 Perseverance Up: 1 Motivation Previous: 1.4 Numerical Round-Off

1.5 Computability

Given that our problem seems quite difficult, let us focus on a simpler problem. Consider the equation

figure5390

with the restriction that c(x,y) is an expression of fixed value. The graph of the equation would either be empty, if tex2html_wrap_inline32007 , 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 up previous notation contents
Next: 1.6 Perseverance Up: 1 Motivation Previous: 1.4 Numerical Round-Off
Jeff TupperMarch 1996