def test_different_functions_3(self):
expr = Expression('sin(2/exp(x)+7*arcsin(x))')
x = Symbol('x')
self._check__values(
Differentiation.diff(expr, x),
'cos(2/exp(x)+7*arcsin(x))*((0*(exp(x))-(2)*'
'(exp(x)))/(exp(x))^2+7*1/(1-(x)^2)^2)')
def diff(expression: Expression, symbol: Symbol, order: int = 1,
value: float = None):
"""
Calculates the symbolic derivative of a function of a certain order.
:param expression:
:type expression: Expression
:param symbol:
:type symbol: Symbol
:param order:
:type order: int
:param value:
:type value: float
:return:
:rtype: Expression
"""
for index_1 in range(order):
expression = expression.valid()
expr_tree = expression.tree(symbol)
latest_letter = sorted(list(expr_tree.keys()))[-1]
latest_expr = expr_tree[latest_letter]
expr_diff = Differentiation.__diff_main(latest_expr, expr_tree,
symbol)
index_2 = 0
while index_2 < len(expr_diff):
if type(expr_diff[index_2]) == list:
expr_diff = expr_diff[:index_2] + expr_diff[index_2] + \
expr_diff[index_2 + 1:]
index_2 += 1
result = ''.join(str(j) for j in expr_diff)
for (key, val) in expr_tree.items():
result = result.replace(key, ''.join(str(j) for j in val))
expression = Expression(result).simplify()
if value is None:
return expression
else:
exec(f'{symbol}={value}')
expression = HelpFunctions.replace_functions(str(expression))
return eval(str(expression))
def test_hyperbolic_functions_2(self):
expr = Expression('ch(x)')
x = Symbol('x')
self._check__values(Differentiation.diff(expr, x), 'sh(x)')
def test_inverse_trigonometrical_functions_4(self):
expr = Expression('arcctg(x)')
x = Symbol('x')
self._check__values(Differentiation.diff(expr, x), '-1/(1+(x)^2)')
def test_trigonometrical_functions_6(self):
expr = Expression('csc(x)')
x = Symbol('x')
self._check__values(Differentiation.diff(expr, x), '-ctg(x)*csc(x)')
def test_trigonometrical_functions_3(self):
expr = Expression('tg(x)')
x = Symbol('x')
self._check__values(Differentiation.diff(expr, x), '1/cos(x)^2')
def test_exponential_functions_2(self):
expr = Expression('ln(x)')
x = Symbol('x')
self._check__values(Differentiation.diff(expr, x), '1/(x)')
def test_symbol(self):
expr = Expression('x')
x = Symbol('x')
self._check__values(Differentiation.diff(expr, x), '1')
def test_error_2(self):
try:
expr = Expression('sin(x))').valid()
self.assertEqual(True, False)
except InvalidExpressionError:
self.assertEqual(True, True)
def test_calculations_3(self):
expr = Expression('sin(x)+cos(x)')
x = Symbol('x')
self._check__values(Differentiation.diff(expr, x, value=1),
'-0.30116867893975674')
def test_calculations_2(self):
expr = Expression('cos(x)')
x = Symbol('x')
self._check__values(Differentiation.diff(expr, x, value=1),
'-0.8414709848078965')
def test_calculations_1(self):
expr = Expression('sin(x)')
x = Symbol('x')
self._check__values(Differentiation.diff(expr, x, value=1),
'0.5403023058681398')
def test_different_functions_2(self):
expr = Expression('sin(2/exp(x))')
x = Symbol('x')
self._check__values(
Differentiation.diff(expr, x), 'cos(2/exp(x))*((0*(exp(x))-'
'(2)*(exp(x)))/(exp(x))^2)')
def test_different_functions_1(self):
expr = Expression('sin(x)^2')
x = Symbol('x')
self._check__values(Differentiation.diff(expr, x),
'exp(2*ln(sin(x)))*(2*1/(sin(x))*(cos(x)))')