^{1}The difference between linear and non–linear inconsistent systems is based on the algorithms
which produce this information as a side effect when attempting to find a formal solution;
example: solve({x = a,x = b,y = c,y = d},{x,y}gives a set {a -b,c -d}while
solve({x^{2} = a,x^{2} = b,y^{2} = c,y^{2} = d},{x,y}leads to {a -b}.