- solving linear systems is easy as only the inversion of a matrix
is required
- system of polynomial equations

- Grobner basis according to lexicographic ordering of variables
(very high time complexity)
- the system of polynomial equations and its Grobner basis have
the same solution
- example

- Grobner basis of these polynomials with variables ordering

- this is in "triangular" form
- can be determined by solving the 3rd equation;
after substituting into the 2nd equation, we
can determine , etc.
- one approximate solution is
- solving (even numerically) of a polynomial equation in one variable
is much simpler than solving a system of polynomial equations
- solving a polynomial system is transformed into the successive
solution of equations in one variable; see the example
Grobner bases

Richard Liska