³The 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: \(\mathrm {solve}(\{x=a,x=b,y=c,y=d\},\{x,y\})\) 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 \(\{a-b\}\).