PyNormaliz-inequalities 0.1.1

A Python package for interacting with PyNormaliz using inequalities.

PyNormaliz_inequalities

Python utility package for interacting with PyNormaliz

Installation

To install the package, use pip:

pip install PyNormaliz_inequalities

Usage

This package provides a convenient interface to PyNormaliz, allowing users to specify inequalities in a natural format. Below are some usage examples:

Example 1: Basic Usage

from PyNormaliz_inequalities import Variable, InequalitySystem, evaluate_quasipolynomial

a = Variable()
b = Variable()

inequalities = InequalitySystem()
inequalities.add_inequality(a >= 0)
inequalities.add_inequality(b >= 0)
inequalities.add_inequality(a + b >= 1)

quasipolynomial = inequalities.construct_homogeneous_cone().HilbertQuasiPolynomial()
print([evaluate_quasipolynomial(quasipolynomial, n) for n in range(10)])

Example 2: Complex Inequalities

from PyNormaliz_inequalities import Variable, InequalitySystem, evaluate_quasipolynomial

a = Variable()
b = Variable()
c = Variable()

inequalities = InequalitySystem()
inequalities.add_inequality(a >= 0)
inequalities.add_inequality(b >= 0)
inequalities.add_inequality(c >= 0)
inequalities.add_inequality(a > 2*b)
inequalities.add_inequality(b > c)

quasipolynomial = inequalities.construct_homogeneous_cone().HilbertQuasiPolynomial()
print([evaluate_quasipolynomial(quasipolynomial, n) for n in range(10)])

Example 3: Using Inequality System

from PyNormaliz_inequalities import Variable, InequalitySystem, evaluate_quasipolynomial

x = Variable()
y = Variable()

inequalities = InequalitySystem()
inequalities.add_inequality(x >= 2)
inequalities.add_inequality(y >= x)

quasipolynomial = inequalities.construct_homogeneous_cone().HilbertQuasiPolynomial()
print([evaluate_quasipolynomial(quasipolynomial, n) for n in range(10)])

Explanation

The PyNormaliz_inequalities package provides a convenient interface to PyNormaliz, allowing users to specify inequalities in a natural format. It supports creating variables, expressions, and inequalities, and converting them to vector representations suitable for PyNormaliz. The package also includes functionality to construct homogeneous cones and compute Hilbert quasi-polynomials.

The main components of the package are:

• Variable: Represents a variable in an inequality.
• Expression: Represents a linear expression involving variables.
• Inequality: Represents an inequality involving expressions.
• InequalitySystem: Manages a system of inequalities and provides methods to interact with PyNormaliz.

The package also includes utility functions for converting inequalities to vector representations and evaluating quasi-polynomials.