FieldElement Class

FieldElement Class 00401

I would like to start the topic of Cryptocurrency with such concepts as “FINAL FIELDS”. This code defines a Python class called FieldElement that is designed for finite field arithmetic. A finite field, also known as a Galois field, is a mathematical structure where arithmetic operations such as addition and multiplication are performed modulo a prime number. The FieldElement class is initialized with a value and a prime number, ensuring that the value remains within the field's range.

Characteristics:

[Category] <-------------------------------------------> [Blockchain Creatione]
[Creator] <-----------------------------------------------------> [InNotSystem13]
[Project] <---------------------------------------------------> [FieldElement Class]
[Identifier] <--------------------------------------------------------> [00401]
[Contract] <------------> [0x86E926fEB6e2Fe2562fe9C558347a4b785f60c8C]
[Chain] <---------------------------------------------------------> [BSC Chain]
[Type] <----------------------------------------------------> [Application]

Binance Smart Chain (BSC)

Price: 1 USDT

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    class FieldElement:
        def __init__(self, value, prime):
            if value >= prime or value < 0:
                error_msg = "Value {} not in the field range 0 to {}".format(value, prime - 1)
                raise ValueError(error_msg)
            self.value = value
            self.prime = prime

        # Method for inequality check
        def __ne__(self, other):
            if isinstance(other, FieldElement):
                return self.value != other.value and self.prime == other.prime
            return NotImplemented

    # Example of usage
    a = FieldElement(3, 13)
    b = FieldElement(7, 13)
    c = FieldElement(3, 13)

    print(a != b)  # Returns True, as 3 is not equal to 7
    print(a != c)  # Returns False, as 3 is equal to 3

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Smart-Contract #000-00000000000011 0x86E926fEB6e2Fe2562fe9C558347a4b785f60c8C

successfully created

Author's message: The provided example demonstrates the usage of this class. It creates three FieldElement instances, a, b, and c, and checks for inequality between them. The output shows that a != b returns True because 3 is not equal to 7, while a != c returns False because 3 is equal to 3.