RealRange(a,b)

ComplexRange(,)

RealRange is a Maple program -- it analyzes the input parameters; ComplexRange is not a program.

In this example, the two endpoints are equal and it simplifies to zero.

Here there is no automatic simplification:

The automatic simplification is triggered after the conversion happens:

A ComplexRange is an object more general than a RealRange in that it contains it as a particular case. When working with a ComplexRange or its RealRange representation, three typical constructions are used. Note the corresponding notation in the following examples. The conversion (when possible) always returns a sequence of two elements.

Case 1: a ComplexRange is itself an object

Case 2: a construction indicating that z has values in some ComplexRange, expressed using the :: operator

Case 3: a construction indicating that z has values in some ComplexRange, expressed using the in operator

Note that, unlike ComplexRange, RealRange requires numerical arguments, so when the former has not this kind of argument the conversion is not possible.

Without numerical arguments, this cannot be converted:

Expressing complex and real ranges as relations

ComplexRanges are used for example to express the branch cuts of mathematical functions

When you input  or , it is implicitly assumed that . This is used to simplify the notation in the output of some conversions. For example,

assume[parametric], assuming, convert[RealRange], convert[relation], FunctionAdvisor