[NBLUG/talk] Graphing implicit equations

Mitch Patenaude mrp at sonic.net
Fri Mar 5 13:38:00 PST 2004


On Friday, Mar 5, 2004, at 13:15 US/Pacific, Augie Schwer wrote:
> I have never heard of the term "implicit equation", but a quick google
> gave me the examples x + y = 1 and xy = 16. If these are indeed 
> "implicit
> equations" then you could very easily rewrite them as y = 1 - x and
> y = 16 / x respectively.
>
> In which case you could use gnuplot to plot the graph:
>
> gnuplot> plot 16 / x

Yeah.. but the point of implicit equations is often that they can't
(easily) be solved for y.  There are simple examples like
     x^2 + y^2 = 1 (a circle)
which aren't too tough, but what if the implicit equation is:
     y^2 = x^3 + 5x^2 + 10

Then that's a lot more complicated... your best hope is to parameterize 
it, and then use gnuplot to plot the result.  That's an elliptic curve, 
like the ones used for cryptography.  In real life the coefficients are 
larger and the math is done modulo some large prime.

   -- Mitch




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