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.