The MAPLE Objects

MAPLE classifies the basic expressions, involving only rational constants, names of variables and the operators +, -, *, / and ^, according to three types: the type +, the type * and the type ^. Expressions like x+y and x+y+z are of type +, as are x-y+z, which MAPLE stores as x+(-l)*y+z, and (x*y)+(z*t), which is the sum of the two terms x*y and z*t. For MAPLE, the operator + isn’t a binary operator that is generalized by recurrence but an n-ary operator whose operands all play a symmetric role.Expressions like x*y and x*y*z are of type *, as are x*y/z, which MAPLE stores as x*y*z^(- l), and (x+y)*(z+t) which, written like this, is the product of the two terms (x+y) and (z+t). Like the operator +, the operator * is an n-ary operator.Expressions like x^y, 1/x, (x+y) ^(-3) as well as x^ (1/2) or (x-y+z) ^ (1/3) are of type ^. For MAPLE, the operator ^ is a binary operator and MAPLE doesn’t accept x^y^z, one must thus specify x^(y^z) or (x^y)^z.