CoCoA » CoCoALib

Anna told me she has an impl (of exactly what I don't recall).
Let's make it available -- I'd like it to be available in C5 too.

For what it's worth, here's my impl in C5 language

Define ElimOrdMat(N, ElimIndets)
  // Check entries of ElimIndets are (distinct) ints in range 1..N
  TopLevel ZZ;
  M := NewMat(N,N,0);
  Foreach i In ElimIndets Do
    M[1,i] := 1;
  EndForeach;
  E := len(ElimIndets);
  For i := 2 To E Do
    M[i, ElimIndets[E+2-i]] := -1;
  EndFor;

  KeepIndets := [k | k In 1..N And Not(k IsIn ElimIndets)];
  Foreach j In KeepIndets Do
    M[E+1,j] := 1;
  EndForeach;
  K := len(KeepIndets);
  For i := 2 To len(KeepIndets) Do
    M[E+i, KeepIndets[K+2-i]] := -1;
  EndFor;
  Return M;
EndDefine; -- ElimOrdMat

Probably the functions ElimMat-like are good enough for this.
At least we should write some explicit example here (for CoCoA-5 #78, and for CoCoALib)