def eval(cls, i, j):
"""
Evaluates the discrete delta function.
Examples
========
>>> from sympy.functions.special.tensor_functions import KroneckerDelta
>>> from sympy.abc import i, j, k
>>> KroneckerDelta(i, j)
KroneckerDelta(i, j)
>>> KroneckerDelta(i, i)
1
>>> KroneckerDelta(i, i + 1)
0
>>> KroneckerDelta(i, i + 1 + k)
KroneckerDelta(i, i + k + 1)
# indirect doctest
"""
if (i > j) is True:
return cls(j, i)
diff = C.Abs(i - j)
if diff == 0:
return S.One
elif diff.is_number:
return S.Zero
elif i != 0 and diff.is_nonzero:
return cls(0, diff.args[0])
if i.assumptions0.get("below_fermi") and \
j.assumptions0.get("above_fermi"):
return S.Zero
if j.assumptions0.get("below_fermi") and \
i.assumptions0.get("above_fermi"):
return S.Zero
# to make KroneckerDelta canonical
# following lines will check if inputs are in order
# if not, will return KroneckerDelta with correct order
if i is not min(i, j, key=default_sort_key):
return cls(j, i)
def eval(cls, i, j):
"""
Evaluates the discrete delta function.
Examples
========
>>> from sympy.functions.special.tensor_functions import KroneckerDelta
>>> from sympy.abc import i, j, k
>>> KroneckerDelta(i, j)
KroneckerDelta(i, j)
>>> KroneckerDelta(i, i)
1
>>> KroneckerDelta(i, i + 1)
0
>>> KroneckerDelta(i, i + 1 + k)
KroneckerDelta(i, i + k + 1)
# indirect doctest
"""
if (i > j) is True:
return cls(j, i)
diff = C.Abs(i - j)
if diff == 0:
return S.One
elif diff.is_number:
return S.Zero
elif i != 0 and diff.is_nonzero:
return KroneckerDelta(0, diff.args[0])
if i.assumptions0.get("below_fermi") and \
j.assumptions0.get("above_fermi"):
return S.Zero
if j.assumptions0.get("below_fermi") and \
i.assumptions0.get("above_fermi"):
return S.Zero