auto_contractor.expr_arithmetic — Symbolic Expression Arithmetic

Source: qlat/auto_contractor/expr_arithmetic.py

Note: Update this document when updating the source file.

Outline

  1. Overview

  2. Core Classes

  3. Interface Functions

  4. Simplification

  5. Examples

Overview

expr_arithmetic provides a symbolic arithmetic layer for manipulating expression coefficients in the auto-contractor framework. It represents expressions as sums of Term objects, each containing a sympy coefficient and a list of Factor objects (code segments or variables). The module supports algebraic simplification, Python code compilation, and variable tracking.

Core Classes

Factor

A leaf-level code segment or variable.

Attribute

Type

Description

code

str

The string representation of the factor

variables

list[str]

Variables found in the code

otype

str

"Var" if identifier, "Expr" otherwise

 
f = Factor("a + b")       # otype = "Expr"
f = Factor("x")           # otype = "Var"

Term

A product of Factor objects multiplied by a coefficient.

Attribute

Type

Description

coef

number or sympy expr

The scalar coefficient

factors

list[Factor]

The symbolic factors

Expr

A sum of Term objects. Supports arithmetic operators (+, -, *) and simplification.

Attribute

Type

Description

terms

list[Term]

The summands

Interface Functions

Function

Description

mk_expr(x)

Convert x (int, float, str, Factor, Term, Expr) to Expr

mk_fac(x)

Alias for mk_expr; creates a factor usable in auto-contractor

mk_sym(x)

Return sympy.simplify(x)

compile_py(x, var_dict=None)

Compile expression to Python code string

is_zero(x)

Check if x is zero

Simplification

Function

Description

simplified_ea(x)

Structure-only simplification (sort, combine, drop zeros)

simplified_coef_ea(x)

Sympy coefficient simplification + structure simplification

Both return Expr or int (if the result is a pure scalar).

Examples

import qlat as q
q.begin_with_mpi([[1, 1, 1, 4]])

from qlat.auto_contractor.expr_arithmetic import mk_expr, mk_fac, simplified_ea

a = mk_expr(1)
b = mk_expr(2)
c = mk_expr(mk_fac("a + b"))
d = mk_expr(mk_fac("a + b"))
result = c * b + c + d * d
print(result)

result = simplified_ea(result)
print(result)
print(result.compile_py())

q.end_with_mpi()