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Dividing by a reciprocal gives a value where the quotient has none: 1/(1/x) is x

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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 with O4 in SimplificationContract.md and reproduce the listed expressions using work/soundcheck. Trace the named rules in Common, CollapseMultipleFractions, Power, CommonDenominator, and Trigonometric, then compare with the rational canonical form issue #1618. Done means simplification preserves the original definedness conditions and regression checks cover the reported cases.

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

Descripción

What you ran:

"1/(1/x)".Simplify();
"(x^(-1))^(-1)".Simplify();
"a / csc(x)".Simplify();
"1 / sec(x)".Simplify();
"1 / cotan(x)".Simplify();
"a / (b / x)".Simplify();
"a / x^(-1)".Simplify();
"(y + 2) / y^(-1)".Simplify();

What it did: each answer has a value where the expression has none. Measured on master at dcf5ba7c:

expression Simplify at expression there answer there
1/(1/x) x x = 0 NaN 0
(x^(-1))^(-1) x x = 0 NaN 0
a / csc(x) sin(x) * a x = 0 NaN 0
1 / sec(x) cos(x) x = pi/2 NaN 0
1 / cotan(x) tan(x) x = 0 NaN 0
a / (b / x) a * x / b provided not b = 0 x = 0 NaN 0
a / x^(-1) a * x x = 0 NaN 0
(y + 2) / y^(-1) (2 + y) * y y = 0 NaN 0

The last one keeps b's condition and drops x's.

What it should have done: keep the condition the expression was defined under, as cancelling already does: (1/x)/(1/x) is 1 provided not x = 0. O4 of SimplificationContract.md forbids turning undefined into a value.

The rules that do it, found by applying each rule on its own and comparing both sides at sample points (work/soundcheck, for #1252): dividing-by-a-quotient-multiplies-by-its-reciprocal (Common), quotient-whose-denominator-is-a-quotient and quotient-of-two-quotients (CollapseMultipleFractions), a-power-of-a-power-multiplies-the-exponents (Power), a-quotient-of-symbolic-parts-is-grouped-pairwise (CommonDenominator, at all three levels), and a-quotient-by-a-cosecant-is-a-sine (Trigonometric). a-power-times-a-product-containing-its-own-base-raises-the-exponent widens too (y^0 * y → y^1), but Simplify keeps that condition by another route. #1618 is the same defect in the rational canonical form.

Lenguaje dominante
C#
Estrellas
831
Forks
79
Merge medio
2 h 22 min
PR fusionados (30 d)
507

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