Dik T. Winter wrote: > In article <firstname.lastname@example.org> email@example.com writes: > > Tony wrote: > ... > > > I was wondering what the reason is for having multiple levels of operator > > > precedence? > ... > > As far as addition/subtraction vs multiplication/division is concerned, > > one reason is to ensure that the distributive property of > > multiplication works sensibly. For example, we want 3*(4 + 6) = 3*4 + > > 3*6 = 3*(6 + 4) = 3*6 + 3*4. > > > > And for exponentiation we want, for example, 3*3^2 = 3^3, not (3*3)^2 > > That is not the reason. You could just as well have left to right > operation when you use sufficiently many parenthesis in the euqations. > E.g. 3*(4 + 6) = (3*4) + (3*6).
Well, obviously any precedence can be enforced with parentheses. I meant make it work *without* the need for parentheses, just as in your example below.
> > But try to write the polynomial x^7 + 2x^6 - 3x^5 + 2x^4 +7x^3 - 3x^2 - 5x + 8 > without assuming precedence. It is to avoid large numbers of parenthesis.