Expression Classes

PyQBPP uses three internal classes to represent expressions:

Class	Contains	Details
Var	A variable	a 32-bit ID and a string to display
Term	A product term	Zero or more variables and an integer coefficient
Expr	An expression	Zero or more terms and an integer constant term

Unlike C++ QUBO++, you do not need to be aware of these class distinctions in PyQBPP. Python’s dynamic typing automatically converts between types as needed. For example, 2 * x * y creates a Term internally, but you can use += or other operators on it and it will be converted to an Expr automatically.

The following program demonstrates how expressions are built and simplified:

import pyqbpp as qbpp

x = qbpp.var("x")
y = qbpp.var("y")
f = (x + y - 2) * (x - 2 * y + 3)
print("f =", f)
f.simplify()
print("simplified f =", f)

This program prints:

f = -6 +x*x +y*x -2*x*y -2*y*y +3*x +3*y -2*x +4*y
simplified f = -6 +x +7*y +x*x -x*y -2*y*y

Expressions can also be built incrementally starting from a plain integer:

import pyqbpp as qbpp

x = qbpp.var("x", 4)
f = -1
for i in range(len(x)):
    f += x[i]
print(f)

This program prints:

-1 +x[0] +x[1] +x[2] +x[3]