// Functions used in paper 9:
// _When is projectivity detected on subalgebras?_ by Jon F. Carlson

// Section 2: Criterion for projectivity

IsProjective := function(M, L, n)
  V := VectorSpace(BaseRing(L[1]), Dimension(M));
  S := &+[ sub< V | RowSpace(x) > : x in L ];
  if (Dimension(M) - Dimension(S))*n eq Dimension(M) then
    return true;
  end if;
  return false;
end function;