Expression Classes

The most important feature of PyQBPP is its ability to create expressions for solving combinatorial optimization problems. The following three classes are used for this purpose:

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

Var class

An instance of this class represents a variable symbolically. Each Var instance consists of a unique ID and a string used for display.

from pyqbpp import var

x = var("x")
print(x)

This simply prints x.

Term class

An instance of this class represents a product term involving an integer coefficient and zero or more Var objects.

from pyqbpp import var

x = var("x")
y = var("y")
t = 2 * x * y
print(t)

This program prints 2*x*y.

Expr class

An instance of this class represents an expression involving an integer constant term and zero or more Term objects.

from pyqbpp import var

x = var("x")
y = var("y")
f = 3 + 2 * x * y + 3 * x
print(f)

This program prints 3 +2*x*y +3*x.

Expressions can be written using basic operators such as +, -, and *, as well as parentheses. Expressions are automatically expanded and stored as an Expr object:

from pyqbpp import var

x = var("x")
y = 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

Using toExpr() for explicit construction

To explicitly create an Expr from an integer, a Var, or a Term, the toExpr() function is available. This is useful when building up an expression incrementally:

from pyqbpp import var, toExpr

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

This program prints:

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