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/* PIA - Lenguajes Modernos de Programación
* FACULTAD DE CIENCIAS FÍSICO MATEMÁTICAS
* Luis Sebastián Martínez Vega - LCC */
#include "include/differentiator.hpp"
#include "include/expressions.hpp"
Differentiator::Differentiator() {
differential = NULL;
ptr = NULL;
}
// Regla del constante. f(x)=c, f'(x)=0.
Expression *Differentiator::visit(Literal *expr) const {
return new Literal(0);
}
// Regla de la variable. f(x)=x, f'(x)=1
Expression *Differentiator::visit(Variable *expr) const {
return new Literal(1);
}
// Reglas de funciones trigonométricas.
Expression *Differentiator::visit(Function *expr) const {
Expression *diff;
switch (expr->getFunctionName()) {
case i_sin:
diff = new MultiplicationExpression(new Function(expr->getArg()->copy(), i_cos), expr->getArg()->diff(this));
return diff;
case i_cos:
diff = new MultiplicationExpression(new NegationExpression(new Function(expr->getArg()->copy(), i_sin)), expr->getArg()->diff(this));
return diff;
case i_tan:
diff = new MultiplicationExpression(new PowerExpression(new Function(expr->getArg()->copy(), i_sec), new Literal(2)),
expr->getArg()->diff(this));
return diff;
case i_csc:
diff = new MultiplicationExpression(new MultiplicationExpression(new NegationExpression(new Function(expr->getArg()->copy(), i_csc)),
new Function(expr->getArg()->copy(), i_ctg)), expr->getArg()->diff(this));
return diff;
case i_sec:
diff = new MultiplicationExpression(new MultiplicationExpression(new Function(expr->getArg()->copy(), i_sec),
new Function(expr->getArg()->copy(), i_tan)), expr->getArg()->diff(this));
return diff;
case i_ctg:
diff = new MultiplicationExpression(new NegationExpression(new PowerExpression(new Function(expr->getArg()->copy(), i_csc),
new Literal(2))), expr->getArg()->copy());
return diff;
}
}
// Regla de la negación. (La derivada del lado derecho.)
Expression *Differentiator::visit(NegationExpression *expr) const {
return new NegationExpression(expr->getRight()->diff(this));
}
// Regla de la suma (las derivadas del lado izquierdo y derecho).
Expression *Differentiator::visit(AddExpression *expr) const {
return new AddExpression(expr->getLeft()->diff(this), expr->getRight()->diff(this));
}
/* Regla de la resta. Igual que la de la suma, pero restando los derivandos
en vez de sumarlos. */
Expression *Differentiator::visit(SubExpression *expr) const {
return new SubExpression(expr->getLeft()->diff(this), expr->getRight()->diff(this));
}
// Regla de la potencia. f(x)=x^c, f'(x)=c*x^(c-1)}*f'(x).
Expression *Differentiator::visit(PowerExpression *expr) const {
Literal *c = dynamic_cast<Literal *>(expr->getRight());
Expression *left = expr->getLeft();
return new MultiplicationExpression(new MultiplicationExpression
(new Literal(c->getValue()), new PowerExpression(left->copy(), new Literal(c->getValue() - 1))),
left->diff(this));
}
// Regla del producto.
Expression *Differentiator::visit(MultiplicationExpression *expr) const {
Expression *u = expr->getLeft();
Expression *v = expr->getRight();
return new AddExpression(new MultiplicationExpression(u->copy(), v->diff(this)), new MultiplicationExpression(v->copy(), u->diff(this)));
}
// Regla de la división.
Expression *Differentiator::visit(DivisionExpression *expr) const {
Expression *u = expr->getLeft();
Expression *v = expr->getRight();
return new DivisionExpression(new SubExpression(new MultiplicationExpression(v->copy(), u->diff(this)),
new MultiplicationExpression(u->copy(), v->diff(this))), new PowerExpression(v->copy(), new Literal(2)));
}
// Función wrapper.
Expression *deriv(Expression *to_deriv) {
Differentiator d;
return to_deriv->diff(&d);
}
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