A quotient of logarithms tends to the logarithms of its arguments' limits

BREAKING-CHANGES.md

@@ -88,6 +88,19 @@ definite integral, a sum, a product and a limit bind their variable, and are unc
 | `"derivative(a x^2, x)".ToEntity().Substitute("a", "x").Evaled` | `2 * x_1 * x` | `2 * x * x` |
 | `"derivative(x^3, x)".ToEntity().Substitute("x", 1)` | `derivative(x ^ 3, x)` | `apply(lambda(x, derivative(x ^ 3, x)), 1)` |
 
+### A quotient of logarithms tends to the logarithms of its arguments' limits
+
+**Silent: a limit of a quotient of logarithms whose arguments tend to symbolic values answered the quotient of those
+values.** The logarithm is continuous, so the quotient tends to the quotient of the values' logarithms. With numbers it
+did, and `ln(x + 2) / ln(x + 3)` at 0 was `ln(2) / ln(3)`. With symbols it was not:
+`ln(y + x) / ln(z + x)` at 0 was `y / z` ([#2271](https://github.com/asc-community/AngouriMath/issues/2271)).
+
+| Input | Was (2.6.0) | Now |
+|---|---|---|
+| `"limit(ln(y + x) / ln(z + x), x, 0)".ToEntity().Simplify()` | `y / z` | `ln(y) / ln(z)` |
+| `"limit(ln(a + 1/x) / ln(b + 1/x), x, +oo)".ToEntity().Simplify()` | `a / b` | `ln(a) / ln(b)` |
+| `"limit(ln(1 + x) / ln(y + x), x, 0)".ToEntity().Simplify()` | `1 / y` | `0 provided not ln(y) = 0` |
+
 ### A quadratic whose discriminant is a square is answered without the root
 
 **Silent: the same roots, written as what they are.** The quadratic formula wrote `sqrt(b^2 - 4ac)` whatever the

Sources/.editorconfig

@@ -75,6 +75,9 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
 [Tests/UnitTests/Calculus/ModulusPhaseTest.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 
+[Tests/UnitTests/Calculus/LogarithmsOfSymbolicLimitsTest.cs]
+file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
+
 [Tests/UnitTests/Calculus/LimitAtAJumpTest.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 

Sources/AngouriMath/Functions/Continuous/Limits/Solvers/Limit.Solvers.cs

@@ -314,7 +314,10 @@ private static bool IsRealValued(Entity expr, Variable x)
                         { Evaled.IsNaN: true } => null,
                         { } res when res.ContainsNode("+oo") || res.ContainsNode("-oo") => div.InnerSimplified,
                         { Evaled: Complex } limit => limit,
-                        _ => upperLogLimit / lowerLogLimit,
+                        // The logarithm is continuous, so the quotient tends to the quotient of the
+                        // limits' logarithms, not of the limits: ln(y + x) / ln(z + x) at 0 answered
+                        // y / z -- https://github.com/asc-community/AngouriMath/issues/2271.
+                        _ => div.InnerSimplified,
                     };
                 }
             }

Sources/Tests/UnitTests/Calculus/LogarithmsOfSymbolicLimitsTest.cs

@@ -0,0 +1,33 @@
+//
+// Copyright (c) 2019-2026 Angouri.
+// AngouriMath is licensed under MIT.
+// Details: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.
+// Website: https://am.angouri.org.
+//
+
+using AngouriMath.Extensions;
+using Xunit;
+
+namespace AngouriMath.Tests.Calculus
+{
+    /// <summary>
+    /// A quotient of logarithms whose arguments tend to symbolic values tends to the quotient of those values' logarithms,
+    /// the logarithm being continuous. It answered the quotient of the values themselves: ln(y + x) / ln(z + x) at 0 was
+    /// y / z, while the same limit with numbers, ln(x + 2) / ln(x + 3), was ln(2) / ln(3).
+    /// <a href="https://github.com/asc-community/AngouriMath/issues/2271">#2271</a>
+    /// </summary>
+    [Trait("Area", "Calculus")]
+    public sealed class LogarithmsOfSymbolicLimitsTest
+    {
+        [Theory]
+        [InlineData("limit(ln(y + x) / ln(z + x), x, 0)", "ln(y) / ln(z)")]
+        [InlineData("limitright(ln(a + x) / ln(b + x), x, 0)", "ln(a) / ln(b)")]
+        [InlineData("limit(ln(a + 1/x) / ln(b + 1/x), x, +oo)", "ln(a) / ln(b)")]
+        [InlineData("limit(ln(a + e^(-x)) / ln(b + e^(-x)), x, +oo)", "ln(a) / ln(b)")]
+        [InlineData("limit(log(b + 1/x, a + 1/x), x, +oo)", "ln(a) / ln(b)")]
+        [InlineData("limit(ln(1 + x) / ln(y + x), x, 0)", "0 provided not ln(y) = 0")]
+        [InlineData("limit(ln(x + 2) / ln(x + 3), x, 0)", "ln(2) / ln(3)")]
+        public void ItIsTheQuotientOfTheLogarithms(string limit, string value)
+            => Assert.Equal(value.ToEntity(), limit.ToEntity().Simplify());
+    }
+}