SymPy | Python中的 Permutation.length()

Introduction

Permutation is a mathematical concept that represents a bijective map from a set to itself. In SymPy, Permutation is implemented as a class, and it provides a number of methods to work with permutations. The length() method is one such method, and it is used to calculate the length of a permutation, which is the number of cycles in its cycle decomposition.

Syntax

The syntax of the length() method is as follows:

permutation.length()

Parameters

The length() method does not take any parameters.

Returns

The length() method returns the number of cycles in the cycle decomposition of the permutation.

Examples

Let's say we have a permutation of size 4:

from sympy.combinatorics import Permutation

p = Permutation([3, 1, 2, 0])

The cycle decomposition of this permutation is:

[(0, 3), (1,), (2,)]

The first cycle has length 2, the second cycle has length 1, and the third cycle has length 2. Therefore, the length of this permutation is 3.

We can use the length() method to confirm this:

length = p.length()
print(length)

Output:

3

Conclusion

The length() method in SymPy's Permutation class is a convenient way to calculate the length of a permutation, which is the number of cycles in its cycle decomposition. This method can be used to perform various operations involving permutations, such as calculating the order of a group of permutations.