RelationCalculator 0.0.6

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Installation Guide

Dependencies

Before installing and running the RelationCalculator package, you need to ensure the following dependencies are installed:

• Python 3.8 or higher version
• NumPy 1.18 or higher version
• Matplotlib 3.2 or higher version

Installing Dependencies

If you have not installed these dependencies yet, you can use the following pip command to install them.

If you are managing your system with pip, please use the following command:

pip install numpy matplotlib

Please note, if you have multiple versions of Python in your system, you may need to use pip3 instead of pip.

or if you are managing your system with Conda, please use the following command:

conda install numpy matplotlib

Use the following command to install RelationCalculator

If you are managing your system with pip, please use the following command:

pip install RelationCalculator

or if you are managing your system with Conda, please use the following command:

conda install -c ioea_lab relationcalculator

Relationship Counting Software Package

Module 1 : RelationsClass

Class Name ：Relation

The Relation class is used to define a relation between elements. It takes two parameters in its constructor: elements and relations.

Parameters

• elements (list, optional): A list of elements. If not provided, an empty list is created.
• relations (list of tuples, optional): A list of pairs of elements representing the relations between them. If not provided, an empty list is created.

Description

The elements parameter is converted to a list if it is present; otherwise, an empty list is created. The relations parameter is a list containing pairs of elements representing the relations between them. When traversing the relations list, if an element in a pair does not exist in the elements list, it is added to the elements list. Then, the add_relation method is called to add the relation of the pair of elements, and this pair is added to the relations_list list. Finally, the set_relation_matrix method is called to set the relation matrix.

Function Name	Functionality	Function Output
add_relation	Add an ordered pair to the current binary relation.	None
set_relation_matrix	Calculate the matrix representation of the current binary relation.	Relation matrix (np.array)
count_relations	Calculate the number of ordered pairs in the current binary relation.	Decimal number
get_all_elements	Get all elements in the current set.	list
get_all_relations	Get all ordered pairs in the current binary relation.	list
get_relation_matrix	Calculate the matrix representation of the current binary relation.	list
is_related	Determine whether two elements are related.	true/false
isReflexive	Determine whether the binary relation is reflexive.	true/false
isIrreflexive	Determine whether the binary relation is irreflexive.	true/false
isSymmetric	Determine whether the binary relation is symmetric.	true/false
isAntisymmetric	Determine whether the binary relation is antisymmetric.	true/false
isTransitive	Determine whether the binary relation is transitive.	true/false

Class Name ：RelationDefineByMatrix

Primary member variables : Matrix m

Function Name	Functionality	Function Output
matrix2num	Convert the relational boolean matrix to a binary number representation.	Binary number (output as a string)
isReflexive	Determine whether the binary relation represented by the relation matrix is reflexive.	true/false
isIrreflexitive	Determine whether the binary relation represented by the relation matrix is irreflexive.	true/false
isSymmetric	Determine whether the binary relation represented by the relation matrix is symmetric.	true/false
isAntiSymmetric	Determine whether the binary relation represented by the relation matrix is antisymmetric.	true/false
isTransitive	Determine whether the binary relation represented by the relation matrix is transitive.	true/false

Class Name ：RelationDefineByInt

Variables: Decimal number n; number of set elements size

The RelationDefineByInt class is a subclass of the Relation class, designed for handling specific situations where relations are defined through integers. It takes two parameters in its constructor: n and size.

Parameters

• n (int): An integer representing the binary representation of the relationship.
• size (int): Represents the size of the relationship matrix.

Description

In the constructor, the integer n is first converted to a binary string, which is then padded to the square of size length with '0'. This binary string is then converted into a list of integers, which is reshaped into a size by size matrix. Finally, the constructor of the superclass is called to initialize the relationship with this matrix.

For example, if we have an integer 13 (binary representation is 1101), and we want to represent this relationship in a 2x2 matrix, we can do this:

relation = RelationDefineByInt(13, 2)

This will create a relationship matrix as follows:

[[1 1]
 [0 1]]

Function Name	Functionality	Function Output
num2matrix	Convert the decimal number representation of a binary relation to a boolean matrix representation (relation matrix).	Relation matrix (np.array)
isReflexive	Determine whether the binary relation represented by this positive integer is reflexive.	true/false
isIrreflexitive	Determine whether the binary relation represented by this positive integer is irreflexive.	true/false
isSymmetric	Determine whether the binary relation represented by this positive integer is symmetric.	true/false
isAntiSymmetric	Determine whether the binary relation represented by this positive integer is antisymmetric.	true/false
isTransitive	Determine whether the binary relation represented by this positive integer is transitive.	true/false

Some special features

Function Name	Functionality	Function Output
logicMulti	Perform logical multiplication on two boolean matrices.	Relation matrix (np.array)

Usage example

from RelationCalculator import Relation,RelationDefineByInt

relation = Relation({'A','B','C'},[('C',6)])

relation.add_relation('A','B')
relation.add_relation('A','C')
relation.add_relation('B','C')

print(relation.count_relations()) #4

print(relation.is_related('A','C')) #True
print(relation.is_related('B','A'))  #False
print(relation.is_related('C',6))  #True

print(relation.get_all_elements()) #['A', 'B', 'C', 6]
print(relation.get_all_relations()) #[('C', 6), ('A', 'B'), ('A', 'C'), ('B', 'C')]

print(relation.isReflexive()) #False
print(relation.isIrreflexive()) #True
print(relation.isTransitive()) #False

print(relation.get_relation_matrix())
#[[0 1 1 0]
# [0 0 1 0]
# [0 0 0 1]
# [0 0 0 0]]

relation = RelationDefineByInt(511,3)

print(relation.get_all_elements()) #[1, 2, 3]

Module 2 : CaculatorClass

Class Name ：Calculator

Variables: number of set elements

Function Name	Functionality	Function Output
count_all_relations	Calculate the total number of relations on a set with size elements.	Decimal number
generate_all_relations	Calculate the binary representation of all relations on a set with size elements.	Binary number (output as a string) list
generate_all_relations_as_matrices	Calculate the boolean matrix representation of all relations on a set with size elements.	Relation matrix list
count_reflexive_relations	Calculate the total number of reflexive relations on a set with size elements.	Decimal number
generate_reflexive_relations	Calculate the binary representation of reflexive relations on a set with size elements.	Binary number (output as a string) list
generate_reflexive_relations_as_matrices	Calculate the boolean matrix representation of reflexive relations on a set with size elements.	Relation matrix list
count_irreflexive_relations	Calculate the total number of irreflexive relations on a set with size elements.	Decimal number
generate_all_irreflexive_relations	Calculate the binary representation of irreflexive relations on a set with size elements.	Binary number (output as a string) list
generate_irreflexive_relations_as_matrices	Calculate the boolean matrix representation of irreflexive relations on a set with size elements.	Relation matrix list
count_symmetric_relations	Calculate the total number of symmetric relations on a set with size elements.	Decimal number
generate_all_symmetric_relations	Calculate the binary representation of symmetric relations on a set with size elements.	Binary number (output as a string) list
generate_symmetric_relations_as_matrices	Calculate the boolean matrix representation of symmetric relations on a set with size elements.	Relation matrix list
count_antisymmetric_relations	Calculate the total number of antisymmetric relations on a set with size elements.	Decimal number
generate_all_antisymmetric_relations	Calculate the binary representation of antisymmetric relations on a set with size elements.	Binary number (output as a string) list
generate_antisymmetric_relations_as_matrices	Calculate the boolean matrix representation of antisymmetric relations on a set with size elements.	Relation matrix list
count_reflexive_symmetric_relations	Calculate the total number of relations that are both reflexive and symmetric on a set with size elements.	Decimal number
generate_all_reflexive_symmetric_relations	Calculate the binary representation of relations that are both reflexive and symmetric on a set with size elements.	Binary number (output as a string) list
generate_reflexive_symmetric_relations_as_matrices	Calculate the boolean matrix representation of relations that are both reflexive and symmetric on a set with size elements.	Relation matrix list
count_irreflexive_symmetric_relations	Calculate the total number of relations that are both irreflexive and symmetric on a set with size elements.	Decimal number
generate_all_irreflexive_symmetric_relations	Calculate the binary representation of relations that are both irreflexive and symmetric on a set with size elements.	Binary number (output as a string) list
generate_irreflexive_symmetric_relations_as_matrices	Calculate the boolean matrix representation of relations that are both irreflexive and symmetric on a set with size elements.	Relation matrix list
count_nonreflexive_nonirreflexive_relations	Calculate the total number of relations that are neither reflexive nor irreflexive on a set with size elements.	Decimal number
generate_all_nonreflexive_nonirreflexive_relations	Calculate the binary representation of relations that are neither reflexive nor irreflexive on a set with size elements.	Binary number (output as a string) list
generate_nonreflexive_nonirreflexive_relations_as_matrices	Calculate the boolean matrix representation of relations that are neither reflexive nor irreflexive on a set with size elements.	Relation matrix list
count_nonreflexive_nonirreflexive_symmetric_relations	Calculate the total number of symmetric relations that are neither reflexive nor irreflexive on a set with size elements.	Decimal number
generate_all_nonreflexive_nonirreflexive_symmetric_relations	Calculate the binary representation of symmetric relations that are neither reflexive nor irreflexive on a set with size elements.	Binary number (output as a string) list
generate_nonreflexive_nonirreflexive_symmetric_relations_as_matrices	Calculate the boolean matrix representation of symmetric relations that are neither reflexive nor irreflexive on a set with size elements.	Relation matrix list
count_transitive_relations	Calculate the total number of transitive relations on a set with size elements.	Decimal number
generate_all_transitive_relations	Calculate the binary representation of transitive relations on a set with size elements.	Binary number (output as a string) list
generate_transitive_relations_as_matrices	Calculate the boolean matrix representation of transitive relations on a set with size elements.	Relation matrix list
count_partialOrder_relations	Calculate the total number of partial order relations on a set with size elements.	Decimal number
generate_all_partialOrder_relations	Calculate the binary representation of partial order relations on a set with size elements.	Binary number (output as a string) list
generate_partialOrder_relations_as_matrices	Calculate the boolean matrix representation of partial order relations on a set with size elements.	Relation matrix list
count_quasiOrder_relations	Calculate the total number of quasi-order relations on a set with size elements.	Decimal number
generate_all_quasiOder_relations	Calculate the binary representation of quasi-order relations on a set with size elements.	Binary number (output as a string) list
generate_quasiOder_relations_as_matrices	Calculate the boolean matrix representation of quasi-order relations on a set with size elements.	Relation matrix list

Some special features

Function Name	Functionality	Function Output
plot_matrices	Convert the boolean matrix to a grayscale image for representation.	Image

Usage example

from RelationCalculator import Calculator,plot_matrices

c = Calculator(3)

print(c.count_all_relations()) #512

print(c.count_transitive_relations()) #171

plot_matrices(c.generate_transitive_relations_as_matrices(),9,19,"output.png")