def derivative_of_a_multiplication():
return Theorem(
"derivada del producto",
"\\frac{d(f(x) * g(x))}{dx}",
"\\frac{d(f(x))}{dx} * g(x) + \\frac{d(g(x))}{dx} * f(x)",
{},
)
def solution_tree(self, expression: Expression) -> SolutionTreeNode:
logger.info("get solution tree for: " + expression.to_string())
theorems = []
if expression.contains_derivative():
theorems += DerivativeTheorems.get_all()
if expression.contains_integral():
theorems += IntegrateTheorems.get_all()
return self.solution_tree_for(expression, theorems,
Theorem('none', None, None, {}))
def theorem(theo: dict) -> Theorem:
if theo.get("name") == IntegrateByPartsTheorem().name:
return IntegrateByPartsTheorem()
elif theo.get("name") == IntegrateByPartsApplyTheorem().name:
return IntegrateByPartsApplyTheorem()
elif theo.get("name") == IntegrateByPartsReplaceUVTheorem().name:
return IntegrateByPartsReplaceUVTheorem()
return Theorem(theo.get("name"),
theo.get("left") if 'left' in theo else None,
theo.get("right") if 'right' in theo else None,
theo.get("conditions") if 'conditions' in theo else {})
def setUp(self):
self.derivative_sum_theorem = Theorem("Derivada de la suma",
"\\frac{d(f(x) + g(x))}{dx}",
"\\frac{d(f(x))}{dx} + \\frac{d(g(x))}{dx}",
[])
def integrate_of_a_sum():
return Theorem("Integral de la suma", "\\int (f(x) + g(x)) dx",
"(\\int (f(x)) dx) + (\\int (g(x)) dx)", {})
def integrate_multiply_for_constant():
return Theorem("Integral por una constante", "\\int ( a * f(x)) dx",
"a * \\int (f(x)) dx",
{"a": ["IS_REAL", "IS_CONSTANT"]})
def theorem_to_json(theorem: Theorem):
return theorem.to_json()
def derivative_of_a_sum():
return Theorem("Derivada de la suma", "\\frac{d(f(x) + g(x))}{dx}",
"\\frac{d(f(x))}{dx} + \\frac{d(g(x))}{dx}", {})
def derivative_multiply_for_constant():
return Theorem("Derivada por un numero real",
"\\frac{d( a * f(x))}{dx}", "a * \\frac{d(f(x))}{dx}",
{"a": ["IS_REAL", "IS_CONSTANT"]})
def derivative_of_a_division():
return Theorem(
"derivada de la division", "\\frac{d(\\frac{f(x)}{g(x)})}{dx}",
"\\frac{ \\frac{ d(f(x))}{dx} * g(x) - \\frac{d(g(x))}{dx} * f(x) }{g(x)^ 2}",
{})