Systems of algebraic equations like the following two equations in unknowns {x,y}:

Eq1: m3*x^3+m1*x+n2*y^2+n1*y =r1;

Eq2: a3*x^3 +a2*x^2+b2*y^2+b1*y=r2;

Can also be handled by Riccati equations as its sole developments.

Normally we will parameterize it and handle its systems of differential equations via Riccati.

Certainly, one can extend the system both by many variables, like, x,y,z,u, as well as number of equations.

If you can solve the above system by Maple, the result would be a polynomial of degree 6 as RootOf.

Thus since I have an independent solution of my system of algebraic equations, certainly I will also have a key to Maple polynomial solution.

You see we indeed can base our studies completely on Riccati.

According to my last 10 years of extensive focus on Riccati, there is no other way we can initiate a solid studies as classes.

This means you are able to find a solution of a problem by a special trick, but it cannot be extended to others as a class, unless it is based on Riccati as a sequence of developments.

How I can convince MIT, Harvard, Princeton and Cambridge, that the way of the future is Riccati, the other subjects are long depreciated and not appropriate?

They are in their own games and also silent!(as well as blind)

You can view and criticize all of my claims in my first 10 lecture notes (200 pages each with software).

This is NEW EXACT MATH world.

cliclic...@freenet.de wrote a nonsense .My answer:

http://mathforum.org/kb/message.jspa?messageID=6220345&tstart=0

I have already provided an example of solving a non-linear system of ODE via Riccati (in this NG). Generally the procedures for algebraic systems are the same.

Generally more complex and parametric polynomials can be handled in this domain.

As I recall from my experience of problem solving with Maple, it is difficult to handle parametric ones (particularly more than degree 5).

And those quintic (s) solvable by Maple, generally have simple differential equations.

Normally algebraic methods are not fit to solve complex parametric polynomials (specially for degrees greater than 5).

I have no doubt, because of this unfit structure of methods such as Galois; the entire existence of the field is questionable.