Editorial

Welcome to the first issue of Parabola Incorporating Function for 2011. The first article in, by John Perram, describes different meanings of equality. For example, we might write $y=x^2+x+1$ to define $y$ or to represent an equation. In the former meaning we regard $y$ as a symbol to represent $x^2+x+1$. In the latter meaning we think that for a given value of $y$ there will be values of $x$ for which both $y$ and $x^2+x+1$ have the same value. We usually know which meaning of equality to adopt based on different context. But context is a very human thing. Computer algebra systems (CAS) need to know the difference too and this can be achieved through different syntax.One possibility, is the use of $:=$ for an assignment operator and $=$ for equals in an equation. The meaning of $y:=x^2+x+1$ is that $y$ has been assigned as a name for $x^2+x+1$ whereas $y=x^2+x+1$ represents an equation without any assignment of the name $y$ to $x^2+x+1$. We could write $E :=y=x^2+x+1$ to assign the name $E$ to the equation $y=x^2+x+1$. Part of the power of CAS has come from precision in dealing with equality through syntax.