jbmkahdeksan/pvn_algebra

Python implementation of Pura Vida Neutrosophic Algebra

Pura Vida Neutrosophic Algebra is a initiative lead byRanulfo Paiva Barbosa and Florentin Smarandache. This project aims to implement these ideas into a Python module which can be utilized for other several applications.

Content

A simple neutrosophic number is a number of the form "X = a + bI". Where "a" is a real or complex coefficient and "b" is a real or complex number binded to indeterminacy (I).

Having two simple neutrosophic numbers X = a + bI and Y = c + dI. Operations for Simple Neutrosophic Number stated in Pura Vida Neutrosophic Algebra are:

• Addition using Max-Plus algebra.
  • add_max(X, Y) = max(a, c) + max(b, d)I
• Addition using Min-Plus (Tropical) algebra. Having two simple neutrosophic numbers X = a + bI and Y = c + dI.
  • add_min(X, Y) = min(a, c) + min(b, d)I
• Multiplication. Having two simple neutrosophic numbers X = a + bI and Y = c + dI.
  • multiply(X, Y) = (a + c) + (b + d)I

Limitations

Current features missing:

• Support for complex numbers as coefficients

How to use

Adding this project to PyPI is intended for a better adoption Right now you can copy and paste the code to your project.

Here is a simple example of the current features:

Install

pip install pvn_algebra

Import

import pvn_algebra as pvna

Create a number

X = pvna.NeutrosophicNumber("-3.4 + 3I") or Y = pvna.NeutrosophicNumber(3, -3.4)

Operations

pvna.number.add_min(X, Y)

pvna.number.add_max(X, Y)

pvna.number.multipy(X, Y)

Matrices

A = np.matrix([
    [NeutrosophicNumber(-8, 1), NeutrosophicNumber(5, -1)],
    [NeutrosophicNumber(3, 8), NeutrosophicNumber(23, -2)]
])

B = np.matrix([
    [NeutrosophicNumber(3, 2), NeutrosophicNumber(13, 3)],
    [NeutrosophicNumber(7, 9), NeutrosophicNumber(3, 5)]
])

C = pvna.matrix.add_min(A, B)

D = pvna.matrix.add_max(A, B)

A = np.matrix([
    [NeutrosophicNumber(-1,0), NeutrosophicNumber(2,0), NeutrosophicNumber(0,-1)],
    [NeutrosophicNumber(3,0), NeutrosophicNumber(0, 1), NeutrosophicNumber(0,0)]
])

B = np.matrix([
    [NeutrosophicNumber(0,1), NeutrosophicNumber(1,0), NeutrosophicNumber(2,0), NeutrosophicNumber(4,0)],
    [NeutrosophicNumber(1,0), NeutrosophicNumber(0,1), NeutrosophicNumber(0,0), NeutrosophicNumber(2,0)],
    [NeutrosophicNumber(5,0), NeutrosophicNumber(-2,0), NeutrosophicNumber(0,3), NeutrosophicNumber(0,-1)]
])

E = matrix.multiply(A, B)