# Source code for ufl.checks

```"""Utility functions for checking properties of expressions."""

# Copyright (C) 2013-2016 Martin Sandve Alnæs
#
# This file is part of UFL (https://www.fenicsproject.org)
#
#
# Modified by Anders Logg, 2008-2009

from ufl.core.expr import Expr
from ufl.core.terminal import FormArgument
from ufl.corealg.traversal import traverse_unique_terminals
from ufl.geometry import GeometricQuantity
from ufl.sobolevspace import H1

[docs]def is_python_scalar(expression):
"""Return True iff expression is of a Python scalar type."""
return isinstance(expression, (int, float, complex))

[docs]def is_ufl_scalar(expression):
"""Return True iff expression is scalar-valued, but possibly containing free indices."""
return isinstance(expression, Expr) and not expression.ufl_shape

[docs]def is_true_ufl_scalar(expression):
"""Return True iff expression is scalar-valued, with no free indices."""
return isinstance(expression, Expr) and not (
expression.ufl_shape or expression.ufl_free_indices
)

[docs]def is_cellwise_constant(expr):
"""Return whether expression is constant over a single cell."""
# TODO: Implement more accurately considering e.g. derivatives?
return all(e.is_cellwise_constant() for e in traverse_unique_terminals(expr))

[docs]def is_scalar_constant_expression(expr):
"""Check if an expression is a globally constant scalar expression."""
if is_python_scalar(expr):
return True
if expr.ufl_shape:
return False

# TODO: This does not consider gradients of coefficients, so false
# negatives are possible.
for e in traverse_unique_terminals(expr):
# Return False if any single terminal is not constant
if isinstance(e, FormArgument):
# Accept only globally constant Arguments and Coefficients
if e.ufl_element().embedded_superdegree > 0 or e.ufl_element() not in H1:
return False
elif isinstance(e, GeometricQuantity):
# Reject all geometric quantities, they all vary over
# cells
return False

# All terminals passed constant check
return True
```