def diff(expression, variable):
vals = WildResults()
f,a,b = wilds('f a b')
expression = expression.simplify()
if variable not in expression:
return symbolic(0)
elif expression.match(variable):
return symbolic(1)
elif expression.match(f(a,b), vals) and vals.f in _known_functions:
return _diff_known_function(expression, variable)
elif expression.match(f(a), vals) and vals.f in _known_functions:
return _diff_known_function(vals.f(vals.a), vals.a) * diff(vals.a, variable)
raise DifferentiationError("d/d%s %s" % (variable,expression))
def diff(expression, variable):
vals = WildResults()
f,a,b = wilds('f a b')
expression = expression.simplify()
if variable not in expression:
return symbolic(0)
elif expression.match(variable):
return symbolic(1)
elif expression.match(f(a,b), vals) and vals.f in _known_functions:
return _diff_known_function(expression, variable)
elif expression.match(f(a), vals) and vals.f in _known_functions:
return _diff_known_function(vals.f(vals.a), vals.a) * diff(vals.a, variable)
raise DifferentiationError("d/d%s %s" % (variable,expression))
def _simplify_known_values(exp):
a,b,c = core.wilds('a b c')
vals = {}
if exp.match(a(b,c), vals) \
and 'numeric' in vals['a'].kargs \
and isinstance(vals['b'], core._KnownValue) \
and isinstance(vals['c'], core._KnownValue):
cast = vals['a'].kargs['cast'] if 'cast' in vals['a'].kargs else (lambda x: x)
nfn = getattr(operator, vals['a'].kargs['numeric'])
return core.symbolic(nfn(cast(vals['b'].value()), cast(vals['c'].value())))
else:
return exp
def _simplify_bitops(exp):
a,b = core.wilds('a b')
vals = core.WildResults()
if exp.match(a ^ a):
return core.symbolic(0)
elif exp.match(a | a, vals):
return vals.a
elif exp.match(a & a, vals):
return vals.a
elif exp.match((a << b) >> b, vals) or exp.match((a >> b) << b, vals):
return vals.a
else:
return exp
def _simplify_bitops(exp):
a, b = core.wilds('a b')
vals = core.WildResults()
if exp.match(a ^ a):
return core.symbolic(0)
elif exp.match(a | a, vals):
return vals.a
elif exp.match(a & a, vals):
return vals.a
elif exp.match((a << b) >> b, vals) or exp.match((a >> b) << b, vals):
return vals.a
else:
return exp
def _simplify_known_values(exp):
a, b, c = core.wilds('a b c')
vals = {}
if exp.match(a(b,c), vals) \
and 'numeric' in vals['a'].kargs \
and isinstance(vals['b'], core._KnownValue) \
and isinstance(vals['c'], core._KnownValue):
cast = vals['a'].kargs['cast'] if 'cast' in vals['a'].kargs else (
lambda x: x)
nfn = getattr(operator, vals['a'].kargs['numeric'])
return core.symbolic(
nfn(cast(vals['b'].value()), cast(vals['c'].value())))
else:
return exp