def _print_Derivative(self, e):
mrow = self.dom.createElement('mrow')
x = self.dom.createElement('mo')
if requires_partial(e):
x.appendChild(self.dom.createTextNode('∂'))
y = self.dom.createElement('mo')
y.appendChild(self.dom.createTextNode('∂'))
else:
x.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
y = self.dom.createElement('mo')
y.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
brac = self.dom.createElement('mfenced')
brac.appendChild(self._print(e.expr))
mrow = self.dom.createElement('mrow')
mrow.appendChild(x)
mrow.appendChild(brac)
for sym in e.variables:
frac = self.dom.createElement('mfrac')
m = self.dom.createElement('mrow')
x = self.dom.createElement('mo')
if requires_partial(e):
x.appendChild(self.dom.createTextNode('∂'))
else:
x.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
y = self._print(sym)
m.appendChild(x)
m.appendChild(y)
frac.appendChild(mrow)
frac.appendChild(m)
mrow = frac
return frac
def _print_Derivative(self, e):
mrow = self.dom.createElement('mrow')
x = self.dom.createElement('mo')
if requires_partial(e):
x.appendChild(self.dom.createTextNode('∂'))
y = self.dom.createElement('mo')
y.appendChild(self.dom.createTextNode('∂'))
else:
x.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
y = self.dom.createElement('mo')
y.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
brac = self.dom.createElement('mfenced')
brac.appendChild(self._print(e.expr))
mrow = self.dom.createElement('mrow')
mrow.appendChild(x)
mrow.appendChild(brac)
for sym in e.variables:
frac = self.dom.createElement('mfrac')
m = self.dom.createElement('mrow')
x = self.dom.createElement('mo')
if requires_partial(e):
x.appendChild(self.dom.createTextNode('∂'))
else:
x.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
y = self._print(sym)
m.appendChild(x)
m.appendChild(y)
frac.appendChild(mrow)
frac.appendChild(m)
mrow = frac
return frac
def _print_Derivative(self, expr):
if requires_partial(expr.expr):
diff_symbol = r'\partial'
else:
diff_symbol = r'd'
tex = []
dim = 0
for x, num in expr.variable_count:
dim += num
if num == 1:
tex.append(r"%s" % self._print(x))
else:
tex.append(r"%s^{%s}" % (self.parenthesize_super(
self._print(x)), self._print(num)))
if (isinstance(expr.expr, AppliedUndef)
and self._settings["applied_no_args"]
and self._settings["der_as_subscript"]):
tex = ",".join(tex)
return self._print_Function(expr.expr) + r"_{%s}" % tex
tex = diff_symbol + " " + (diff_symbol + " ").join(reversed(tex))
if (isinstance(expr.expr, AppliedUndef)
and self._settings["applied_no_args"]):
if dim == 1:
return r"\frac{%s %s}{%s}" % (
diff_symbol, self._print_Function(expr.expr), tex)
else:
return r"\frac{%s^{%s} %s}{%s}" % (diff_symbol, self._print(
dim), self._print_Function(expr.expr), tex)
return super()._print_Derivative(expr)
def _print_Derivative(self, expr):
if requires_partial(expr.expr):
diff_symbol = r"\partial"
else:
diff_symbol = r"d"
tex = r"%s_{" % (diff_symbol)
for x, num in reversed(expr.variable_count):
if num == 1:
tex += r"%s " % (self._print(x))
else:
for i in range(num):
tex += r"%s " % (self._print(x))
tex += r"}"
# if dim == 1:
# tex = r"\frac{%s}{%s}" % (diff_symbol, tex)
# else:
# tex = r"\frac{%s^{%s}}{%s}" % (diff_symbol, self._print(dim), tex)
if any(_coeff_isneg(i) for i in expr.args):
return r"%s %s" % (
tex,
self.parenthesize(
expr.expr, PRECEDENCE["Mul"], is_neg=True, strict=True),
)
return r"%s %s" % (
tex,
self.parenthesize(
expr.expr, PRECEDENCE["Mul"], is_neg=False, strict=True),
)
def _print_Derivative(self, e):
x = self.dom.createElement('apply')
diff_symbol = self.mathml_tag(e)
if requires_partial(e):
diff_symbol = 'partialdiff'
x.appendChild(self.dom.createElement(diff_symbol))
x_1 = self.dom.createElement('bvar')
for sym in e.variables:
x_1.appendChild(self._print(sym))
x.appendChild(x_1)
x.appendChild(self._print(e.expr))
return x
def _print_Derivative(self, e):
x = self.dom.createElement('apply')
diff_symbol = self.mathml_tag(e)
if requires_partial(e):
diff_symbol = 'partialdiff'
x.appendChild(self.dom.createElement(diff_symbol))
x_1 = self.dom.createElement('bvar')
for sym in e.variables:
x_1.appendChild(self._print(sym))
x.appendChild(x_1)
x.appendChild(self._print(e.expr))
return x
def _print_Derivative(self, e):
if requires_partial(e):
d = '∂'
else:
d = self.mathml_tag(e)
# Determine denominator
m = self.dom.createElement('mrow')
dim = 0 # Total diff dimension, for numerator
for sym, num in reversed(e.variable_count):
dim += num
if num >= 2:
x = self.dom.createElement('msup')
xx = self.dom.createElement('mo')
xx.appendChild(self.dom.createTextNode(d))
x.appendChild(xx)
x.appendChild(self._print(num))
else:
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode(d))
m.appendChild(x)
y = self._print(sym)
m.appendChild(y)
mnum = self.dom.createElement('mrow')
if dim >= 2:
x = self.dom.createElement('msup')
xx = self.dom.createElement('mo')
xx.appendChild(self.dom.createTextNode(d))
x.appendChild(xx)
x.appendChild(self._print(dim))
else:
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode(d))
mnum.appendChild(x)
mrow = self.dom.createElement('mrow')
frac = self.dom.createElement('mfrac')
frac.appendChild(mnum)
frac.appendChild(m)
mrow.appendChild(frac)
# Print function
mrow.appendChild(self._print(e.expr))
return mrow
def _print_Derivative(self, e):
if requires_partial(e):
d = '∂'
else:
d = self.mathml_tag(e)
# Determine denominator
m = self.dom.createElement('mrow')
dim = 0 # Total diff dimension, for numerator
for sym, num in reversed(e.variable_count):
dim += num
if num >= 2:
x = self.dom.createElement('msup')
xx = self.dom.createElement('mo')
xx.appendChild(self.dom.createTextNode(d))
x.appendChild(xx)
x.appendChild(self._print(num))
else:
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode(d))
m.appendChild(x)
y = self._print(sym)
m.appendChild(y)
mnum = self.dom.createElement('mrow')
if dim >= 2:
x = self.dom.createElement('msup')
xx = self.dom.createElement('mo')
xx.appendChild(self.dom.createTextNode(d))
x.appendChild(xx)
x.appendChild(self._print(dim))
else:
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode(d))
mnum.appendChild(x)
mrow = self.dom.createElement('mrow')
frac = self.dom.createElement('mfrac')
frac.appendChild(mnum)
frac.appendChild(m)
mrow.appendChild(frac)
# Print function
mrow.appendChild(self._print(e.expr))
return mrow
def _print_Derivative(self, e):
x = self.dom.createElement('apply')
diff_symbol = self.mathml_tag(e)
if requires_partial(e):
diff_symbol = 'partialdiff'
x.appendChild(self.dom.createElement(diff_symbol))
x_1 = self.dom.createElement('bvar')
for sym, times in reversed(e.variable_count):
x_1.appendChild(self._print(sym))
if times > 1:
degree = self.dom.createElement('degree')
degree.appendChild(self._print(sympify(times)))
x_1.appendChild(degree)
x.appendChild(x_1)
x.appendChild(self._print(e.expr))
return x
def _print_Derivative(self, e):
x = self.dom.createElement('apply')
diff_symbol = self.mathml_tag(e)
if requires_partial(e):
diff_symbol = 'partialdiff'
x.appendChild(self.dom.createElement(diff_symbol))
x_1 = self.dom.createElement('bvar')
for sym, times in reversed(e.variable_count):
x_1.appendChild(self._print(sym))
if times > 1:
degree = self.dom.createElement('degree')
degree.appendChild(self._print(sympify(times)))
x_1.appendChild(degree)
x.appendChild(x_1)
x.appendChild(self._print(e.expr))
return x
def test_requires_partial():
x, y, z, t, nu = symbols('x y z t nu')
n = symbols('n', integer=True)
f = x * y
assert requires_partial(Derivative(f, x)) is True
assert requires_partial(Derivative(f, y)) is True
## integrating out one of the variables
assert requires_partial(
Derivative(Integral(exp(-x * y),
(x, 0, oo)), y, evaluate=False)) is False
## bessel function with smooth parameter
f = besselj(nu, x)
assert requires_partial(Derivative(f, x)) is True
assert requires_partial(Derivative(f, nu)) is True
## bessel function with integer parameter
f = besselj(n, x)
assert requires_partial(Derivative(f, x)) is False
# this is not really valid (differentiating with respect to an integer)
# but there's no reason to use the partial derivative symbol there. make
# sure we don't throw an exception here, though
assert requires_partial(Derivative(f, n)) is False
## bell polynomial
f = bell(n, x)
assert requires_partial(Derivative(f, x)) is False
# again, invalid
assert requires_partial(Derivative(f, n)) is False
## legendre polynomial
f = legendre(0, x)
assert requires_partial(Derivative(f, x)) is False
f = legendre(n, x)
assert requires_partial(Derivative(f, x)) is False
# again, invalid
assert requires_partial(Derivative(f, n)) is False
f = x**n
assert requires_partial(Derivative(f, x)) is False
assert requires_partial(
Derivative(
Integral((x * y)**n * exp(-x * y),
(x, 0, oo)), y, evaluate=False)) is False
# parametric equation
f = (exp(t), cos(t))
g = sum(f)
assert requires_partial(Derivative(g, t)) is False
# function of unspecified variables
f = symbols('f', cls=Function)
assert requires_partial(Derivative(f, x)) is False
assert requires_partial(Derivative(f, x, y)) is True
def test_requires_partial_unspecified_variables():
x, y = symbols('x y')
# function of unspecified variables
f = symbols('f', cls=Function)
assert requires_partial(Derivative(f, x)) is False
assert requires_partial(Derivative(f, x, y)) is True
def test_requires_partial():
x, y, z, t, nu = symbols('x y z t nu')
n = symbols('n', integer=True)
f = x * y
assert requires_partial(Derivative(f, x)) is True
assert requires_partial(Derivative(f, y)) is True
## integrating out one of the variables
assert requires_partial(Derivative(Integral(exp(-x * y), (x, 0, oo)), y, evaluate=False)) is False
## bessel function with smooth parameter
f = besselj(nu, x)
assert requires_partial(Derivative(f, x)) is True
assert requires_partial(Derivative(f, nu)) is True
## bessel function with integer parameter
f = besselj(n, x)
assert requires_partial(Derivative(f, x)) is False
# this is not really valid (differentiating with respect to an integer)
# but there's no reason to use the partial derivative symbol there. make
# sure we don't throw an exception here, though
assert requires_partial(Derivative(f, n)) is False
## bell polynomial
f = bell(n, x)
assert requires_partial(Derivative(f, x)) is False
# again, invalid
assert requires_partial(Derivative(f, n)) is False
## legendre polynomial
f = legendre(0, x)
assert requires_partial(Derivative(f, x)) is False
f = legendre(n, x)
assert requires_partial(Derivative(f, x)) is False
# again, invalid
assert requires_partial(Derivative(f, n)) is False
f = x ** n
assert requires_partial(Derivative(f, x)) is False
assert requires_partial(Derivative(Integral((x*y) ** n * exp(-x * y), (x, 0, oo)), y, evaluate=False)) is False
# parametric equation
f = (exp(t), cos(t))
g = sum(f)
assert requires_partial(Derivative(g, t)) is False
f = symbols('f', cls=Function)
assert requires_partial(Derivative(f(x), x)) is False
assert requires_partial(Derivative(f(x), y)) is False
assert requires_partial(Derivative(f(x, y), x)) is True
assert requires_partial(Derivative(f(x, y), y)) is True
assert requires_partial(Derivative(f(x, y), z)) is True
assert requires_partial(Derivative(f(x, y), x, y)) is True
