Integers unit test

Integers unit test is a set of test cases, as part of a software testing process or quality assurance, designed to verify and validate that the implementation of integers, their properties, and their associated operations within a programming language or software system works properly, accurately, and as expected.

A comprehensive integers unit test might include test cases for evaluating the following aspects:

1. Instantiation:
- Test if integers can be correctly instantiated with their respective values
- Test if system can correctly recognize and store negative integers

2. Integer properties:
- Test if integers are immutable
- Test if a set of integers is countable and has order
- Test if integers are closed under addition, subtraction, and multiplication

3. Basic operations:
- Test if addition, subtraction, multiplication, and division all work correctly
- Test if subtraction operation reverses the sign of the integers
- Test if multiplication and division operations maintain or flip the sign of the integers as expected
- Test if the priority of operators is respected (i.e., multiplication and division take precedence over addition and subtraction)

4. Edge cases:
- Test for extreme values like the minimum and maximum integer representable in the system
- Test for zero related cases like multiplication and division by zero
- Test how the system handles integer overflow and underflow

5. Conversion and representation:
- Test if integers can be correctly converted to/from other data types (e.g., float, string)
- Test if integers can be represented correctly in different numeral systems (e.g., binary, hexadecimal)

An example of integer unit test in Python:

```python
import unittest

class TestIntegers(unittest.TestCase):

def test_instantiation(self):
a = 42
b = -7
self.assertEqual(a, 42)
self.assertEqual(b, -7)

def test_operations(self):
a = 10
b = 5
self.assertEqual(a + b, 15)
self.assertEqual(a - b, 5)
self.assertEqual(a * b, 50)
self.assertEqual(a / b, 2)

def test_zero_cases(self):
a = 42
b = 0
self.assertEqual(a * b, 0)
with self.assertRaises(ZeroDivisionError):
a / b

def test_conversion(self):
a = 42
self.assertEqual(float(a), 42.0)
self.assertEqual(str(a), "42")
self.assertEqual(bin(a), "0b101010")
self.assertEqual(hex(a), "0x2a")

if __name__ == '__main__':
unittest.main()
```

This example checks for correct instantiation, basic integer operations, zero-related cases, and integer conversion. Other cases, like edge values or integer properties, can be added to create a more comprehensive test suite.