Notation, notation, notation

Upon re-reading my last post, it occurred to me that the notation chosen was likely to be confusing.

To illustrate, we will take the 4 equations previously stated, and line up all of the terms:

Constant	y =							a
Linear	y =					ax	+	b
Quadratic	y =			ax2	+	bx	+	c
Cubic	y =	ax3	+	bx2	+	cx	+	d

It will be noted that the name of equivalent coefficients changes in each equation.

If we were to use a generic form for the equation, then this name changing goes away:

y = a_nxⁿ + a_n-1x^n-1 + ... + a₃x³ + a₂x² + a₁x + a₀

Whilst this looks more complex, if we just concentrate on equations of the cubic order and lower, we get:

y = a₃x³ + a₂x² + a₁x + a₀

If a₃ is 0, then we get a quadratic equation, and so on:

y = a₂x² + a₁x + a₀

I think this is potentially less confusing than having the coefficient names change with each order of equation. It also provides for a cleaner and clearer mapping between the underlying mathematics and Java arrays, if we were to chose that mechanism to store the coefficients.