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Substituting for a derivative's variable is dropped: derivative(x^3, x) at x = 1 evaluates to 3 x^2

Cerrado
  • ¿Algo no está bien?
#2,189 0 comentarios 0 reacciones 0 asignados Ver en GitHub

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Evaluación

Dificultad
4/5
Tiempo estimado
3-5 días
Aptitud para principiantes
48/100
Tipo de issue
Error
Claridad
Bastante claro
Estado de actividad
Activo
Stack tecnológico
csharp
Área
backend

Línea de trabajo

Start by reading the existing tests and implementation for Substitute on derivative and indefinite integral nodes, then compare them with the FreeVariables behavior and the test pinned by #1045. Add coverage for the derivative and integral examples in the issue, including evaluation after substitution. Done means substitution yields the expected values, with behavior for unevaluated derivatives such as derivative(f(x), x) at a point decided and covered.

Escrito por el modelo de indexación a partir del texto del issue.

Descripción

Substitute leaves the variable of a derivative alone, and so does the variable of an indefinite integral. The answer evaluated afterwards is wrong:

master 5e7731fe2 and 2.6.0 should be
"derivative(x^3, x)".ToEntity().Substitute("x", 1).Evaled 3 * x ^ 2 3
"derivative(x^3, x, 2)".ToEntity().Substitute("x", 2).Evaled 2 * x * 3 12
"integral(x^2, x)".ToEntity().Substitute("x", 1).Evaled x ^ 3 / 3 + C 1/3 + C

Substituting and evaluating do not commute: derivative(x^3, x).Evaled is 3 * x ^ 2, in which x is free.

FreeVariables already reports that x as free. #1045 left both nodes out of its binders because "d/dt denotes a function of t", and pinned that with a test. Substitute still treats the variable as bound. That reading dates from 2020 (x = 0 -> derive(temp_1 ^ 2 + a, temp_1) -> derive(temp_1 ^ 2 + a, temp_1)), and #1811 kept it.

What is open is how to write a derivative that cannot be computed, evaluated at a point: derivative(f(x), x) with x := 1. SymPy writes Subs(Derivative(f(x), x), x, 1). Two candidates here:

  • apply(lambda(x, derivative(f(x), x)), 1);
  • a node for evaluation at a point.
Lenguaje dominante
C#
Estrellas
831
Forks
79
Merge medio
1 h 16 min
PR fusionados (30 d)
521

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  4. Abre un pull request que haga referencia al número del issue.

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