# [Maxima] Newbie question - Can Maxima be used to

Richard Owlett rowlett at atlascomm.net
Sun Apr 27 08:18:54 CDT 2008

```Barton Willis wrote:

> -----maxima-bounces at math.utexas.edu wrote: -----
>
>
>>I then have a system of 3 quadratic equations in 3 unknowns.
>>I wish to solve it by a method whose name I can't recall.
>>[subtracting multiple of one equation from another such that matrix
>>representation has only 0's below the diagonal]
>
>
> Maybe you are thinking of Gauss elimination?

That rings a bell, faintly.

> Gauss elimination solves linear, not quadratic equations.

That may be a problem for me. But the set of equations I have may be a
"special" and/or "degenerate" case. Although the natural way to set up
the problem yields equations where the independent variables appear in
1st and 2nd order terms, I suspect the 2nd order terms cancel.

> To solve linear or nonlinear polynomial
> equations,
> use the Maxima function 'algsys.' Here is an example:
>
> (%i3) algsys([x^2 + y^2 + z^2 = 1, x^2 + 3 * z^2 = 2, x*z = -1],[x,y,z]);
> (%o3)
> [[x=sqrt(1-sqrt(2)*%i),y=sqrt(2*sqrt(2)*%i-1)/sqrt(3),z=-1/sqrt(1-sqrt(2)*%i)],
>  ....
>
> In Maxima, %i is the imaginary unit--that is, %i = sqrt(-1).
>
>
>>In a way I wish to use it as an intelligent algebraicly aware notepad.exe.
>
>
> I think you can use / think of Maxima in this way.
>
> Welcome to Maxima. Let us know if you have questions.
>
> Barton
>

Let's rephrase the question.

Define
a=f1(x,y,z,a,b)
b=f2(x,y,z,c,d)
x,y,z are independent variables
a-d   are symbolic constants

I would like to symbolically evaluate (a+b) or (a-b)

I hope I'm clearer this time. Thanks.

```