triggered by https://discourse.julialang.org/t/from-toy-to-production-code-with-sparse-matrix-and-sparse-direct-factorizations/89105/13

Code somehow runs but is not clean

* how to handle pivoting is clear, LinearAlgebra of 1.9 provides RowNonZero() pivoting and lupivottype(T)
strategy, this needs to be used on 1.9, we need to define our own for <1.9

* As in the test example for LinearAlgebra, we need to define
  lupivottype, abs and isless for finite fields. See
  https://github.com/JuliaLang/julia/blob/1471cd9782aad18f54d8cb04316193ada15e37bd/stdlib/LinearAlgebra/test/generic.jl#L470
  Otherwise the code does not compile. May be one can avoid this by modularizing LU.

* The BIGGY problem is more serious: it occurs that BIGGY is used as an undefined marker of unititialized matrix entries.
  It is not to be expected that finite fields will have some "unitialized" value.
  Getting rid of this would need a rewrite of the input methods. This IMHO would improve the API - push! is very efficient,
  so we can rely on this, no need to estimate nnz  before.