Substituting for a derivative's variable is dropped: derivative(x^3, x) at x = 1 evaluates to 3 x^2
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還沒有人認領這個 Issue。
評估
研究方向
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.
由索引模型根據 Issue 內容生成。
描述
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.
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