# [SciPy-user] (numerical) "solving" 2-dimensional equations ?

Bill Baxter wbaxter@gmail....
Sun Apr 8 17:36:04 CDT 2007

```This isn't really an answer but I think the keyword for googling would
be "algebraic equations" with words like "plotting" or "graphing".

For the simple case you gave you can solve by making it a function of
one var or the other:
y = +/- sqrt( 4 - x^2 )

But note the +/- there because there are two solutions to anything of
the form x^2 = c

If you're looking to handle arbitrary algebraic curves of arbitrary
degree, it's not so simple.

One simple way to get an approximation is to evaluate it implicitly on
a pixel grid.
For each pixel you look at the value of  abs( x^2 + y^2 - 4 ).  If
it's less than some small number then paint the pixel black.  This
isn't a very robust way to draw it though, just simple.  :-)

On 4/9/07, Stef Mientki <s.mientki@ru.nl> wrote:
>
>
> Alan G Isaac wrote:
> > On Sun, 08 Apr 2007, Stef Mientki apparently wrote:
> >
> >>         sqr (x) + sqr (y) = 4
> >>
> >
> > Draw it parametrically.
> >
> Sorry, what do you mean by that, (how do it, where do I find more
> information)?
>
> cheers,
> Stef
> > Cheers,
> > Alan Isaac
```