Affine Transform Explanation and Python Code for clarification

Here is a simple example of how you could implement affine arithmetic in Python using a class to represent affine forms:

class AffineForm:
    def __init__(self, value, error):
        self.value = value
        self.error = error
    
    def __add__(self, other):
        # Add two affine forms by adding the values and summing the errors
        return AffineForm(self.value + other.value, self.error + other.error)
    
    def __sub__(self, other):
        # Subtract two affine forms by subtracting the values and summing the errors
        return AffineForm(self.value - other.value, self.error + other.error)
    
    def __mul__(self, other):
        # Multiply two affine forms by multiplying the values and adding the errors
        return AffineForm(self.value * other.value, self.value * other.error + self.error * other.value)
    
    def __truediv__(self, other):
        # Divide two affine forms by dividing the values and adding the errors
        return AffineForm(self.value / other.value, (self.error * other.value + self.value * other.error) / other.value ** 2)
    
    def __str__(self):
        # Override the string representation to show the value and error
        return f"{self.value} ± {self.error}"

# Example usage
a = AffineForm(3, 0.1)
b = AffineForm(4, 0.2)

print(a + b)  # prints "7 ± 0.3"
print(a - b)  # prints "-1 ± 0.3"
print(a * b)  # prints "12 ± 0.8"
print(a / b)  # prints "0.75 ± 0.1"
}
  

This implementation defines the basic arithmetic operations (addition, subtraction, multiplication, and division) for affine forms, and overrides the string representation to show the value and error in a more readable format. You can then create affine forms using the AffineForm constructor, and perform arithmetic operations on them using the usual operator syntax. Here's an example of how you could use the Affine class:

a = Affine(10, 0.1)
b = Affine(20, 0.2)
c = a + b
print(c.value)  # prints 30
print(c.error)  # prints 0.3