# Using XL Algorithm to solve overdetermined systems, simple example required

Can someone give an example of how the XL algorithm is used to solve an overdetermined system as apposed to just a general case?

I have a fairly good understanding of how steps of the algorithm work, extending the system, then linearizing the system in the hopes of obtaining a univariate polynomial which is then solved. A small example with numbers and variables over a finite field would help me to see what's going on and understand the algorithm more.

• To come up with such a system just choose $f_1,\ldots,f_m$ multivariate polynomials in $n$ variables with $n<m$, evaluate them at some point $\mathbf{a}$ to get $(c_1,\ldots,c_m)$, and then use the polynomials $(f_1-c_1,\ldots,f_m-c_m)$ – Daniel Mar 18 '18 at 1:56