Date: 2020-10-07 18:10:00

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## 7 Built-in Preﬁx Operators

In the following subsections are descriptions of the most useful preﬁx operators built into REDUCE that are not deﬁned in other sections (such as substitution operators). Some are fully deﬁned internally as procedures; others are more nearly abstract operators, with only some of their properties known to the system.

In many cases, an operator is described by a prototypical header line as follows. Each formal parameter is given a name and followed by its allowed type. The names of classes referred to in the deﬁnition are printed in lower case, and parameter names in upper case. If a parameter type is not commonly used, it may be a speciﬁc set enclosed in brackets { … }. Operators that accept formal parameter lists of arbitrary length have the parameter and type class enclosed in square brackets indicating that zero or more occurrences of that argument are permitted. Optional parameters and their type classes are enclosed in angle brackets.

7.1 Numerical Operators
7.2 Mathematical Functions
7.3 Bernoulli Numbers and Euler Numbers
7.4 Fibonacci Numbers and Fibonacci Polynomials
7.5 Motzkin numbers
7.6 CHANGEVAR operator
7.7 CONTINUED_FRACTION Operator
7.8 DF Operator
7.9 INT Operator
7.10 LENGTH Operator
7.11 MAP Operator
7.12 MKID Operator
7.13 The Pochhammer Notation
7.14 PF Operator
7.15 SELECT Operator
7.16 SOLVE Operator
7.17 Even and Odd Operators
7.18 Linear Operators
7.19 Non-Commuting Operators
7.20 Symmetric and Antisymmetric Operators
7.21 Declaring New Preﬁx Operators
7.22 Declaring New Inﬁx Operators
7.23 Creating/Removing Variable Dependency

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