
Section 9.1 Basic properties of interval mathematics 319
only the expression or algorithm for the function is required. No explicit formulas for
the derivative or slope are needed. The computer interprets the arithmetic operations
in the expression by differentiation or slope arithmetic. The arithmetic is hidden in the
runtime system of the compiler. It is activated by type specification of the operands.
For details see [37, 39, 215, 216, 365, 546, 548], and Section 9.2 on differentiation
arithmetic. Thus the computer is able to produce and enclose the centered form via the
derivative or slope automatically.
Without going into further details, we menti ...