Read a compiled power's constant exponent for its value

BREAKING-CHANGES.md

@@ -746,11 +746,13 @@ remainder over `Complex` already did.
 numerator, as evaluation has it, where both compilers took the principal power, and `Compile<double, double>` gave
 `NaN`.** `(-8)^(1/3)` evaluates to `-2`, `(-8)^(2/3)` to `4`. Newton's method, which `Solve` falls back to, runs on the
 compiled function, so a root needing the real root was not found either. A base off the real line, a positive one, an
-even denominator or one of ten or more is the principal power, as before.
+even denominator or one of ten or more is the principal power, as before. An exponent with no variable is read for its
+value, as evaluation reads it, so `x^(1/(1 + 2))` and `x^((1/3) provided 2 > 1)` are the real root as well.
 
 | Input | Was (2.6.0) | Now |
 |---|---|---|
 | `"x^(1/3)".ToEntity().Compile("x").Call(-8)` | `<1.0000000000000002; 1.7320508075688772>` | `<-2; 0>` |
+| `"x^(1/(1 + 2))".ToEntity().Compile("x").Call(-8)` | `<1.0000000000000002; 1.7320508075688772>` | `<-2; 0>` |
 | `"x^(1/3)".ToEntity().Compile<double, double>("x")(-8)` | `NaN` | `-2` |
 | `"(3 - 4x)^(1/3) + sqrt(4 + 4x) = 3".ToEntity().Solve("x")` | `{ (-2.466…) / 4, 2.952… / 4 }` | `{ (-2.466…) / 4, 2.952… / 4, 33.514… / 4 }` |
 

Sources/AngouriMath/Functions/Compilation/IntoFE/Compiler.cs

@@ -173,7 +173,7 @@ private protected override void CompileNode(Compiler compiler)
                 Exponent.InnerCompile(compiler);
                 Base.InnerCompile(compiler);
                 compiler.Instructions.Add(
-                    Exponent is Rational { ERational: var ratio } && Core.Compilation.RealProducts.TakesTheRealRootOfANegative(ratio)
+                    Core.Compilation.RealProducts.RealRootExponent(Exponent) is { } ratio
                         ? new(InstructionType.CALL_REAL_ROOT_POW, ratio.Numerator.IsEven ? 0 : 1)
                         : new(InstructionType.CALL_POW));
             }

Sources/AngouriMath/Functions/Compilation/IntoLinq/CompilationProtocol.cs

@@ -281,7 +281,7 @@ Divf when ShouldBeAtLeastDouble(left) is var newLeft && ShouldBeAtLeastDouble(ri
                                  right),
                 // A rational exponent with an odd denominator below ten takes the real root of a negative
                 // real, as evaluation does: (-8)^(1/3) is -2, which was 1 + 1.73i, and NaN over double.
-                Powf { Exponent: Rational { ERational: var ratio } } when Core.Compilation.RealProducts.TakesTheRealRootOfANegative(ratio)
+                Powf { Exponent: var exponent } when Core.Compilation.RealProducts.RealRootExponent(exponent) is { } ratio
                     && ShouldBeAtLeastDouble(left) is var newLeft
                     && ShouldBeAtLeastDouble(right) is var newRight
                     && (newLeft.Type == typeof(System.Numerics.Complex) || newLeft.Type == typeof(double))

Sources/AngouriMath/Functions/Compilation/RealProducts.cs

@@ -106,6 +106,17 @@ internal static bool TakesTheRealRootOfANegative(PeterO.Numbers.ERational expone
             => !exponent.Denominator.Equals(PeterO.Numbers.EInteger.One) && !exponent.Denominator.IsEven
                 && exponent.Denominator.CompareTo(PeterO.Numbers.EInteger.FromInt32(10)) < 0;
 
+        /// <summary>
+        /// The rational <paramref name="exponent"/> is, where it is one that
+        /// <see cref="TakesTheRealRootOfANegative"/>, or null. One with no variable is read for its value,
+        /// as evaluation reads it: written otherwise than as a rational, <c>x^(1/(1 + 2))</c> and
+        /// <c>x^((1/3) provided 2 &gt; 1)</c> compiled to the principal power, <c>1 + 1.73i</c> at -8,
+        /// where evaluation takes the exponent <c>1/3</c> and is -2.
+        /// </summary>
+        internal static PeterO.Numbers.ERational? RealRootExponent(Entity exponent)
+            => (exponent is Entity.Number.Rational || exponent.Vars.Count > 0 ? exponent : exponent.InnerSimplified)
+                is Entity.Number.Rational { ERational: var ratio } && TakesTheRealRootOfANegative(ratio) ? ratio : null;
+
         /// <summary>
         /// A whole power of a number that is not real, as a product of its factors, which is how evaluation takes it.
         /// <see cref="System.Numerics.Complex.Pow(System.Numerics.Complex, System.Numerics.Complex)"/> takes <c>e^(n ln z)</c>,

Sources/Tests/UnitTests/Common/CompiledOddRootTest.cs

@@ -31,6 +31,12 @@ public sealed class CompiledOddRootTest
         [InlineData("x^(4/3)", -8)]
         [InlineData("x^(3/5)", -32)]
         [InlineData("(1 + x)^(1/3) + 2", -9)]
+        // An exponent with no variable is read for its value, as evaluation reads it: written
+        // otherwise than as a rational, it took the principal power, 1 + 1.73i.
+        [InlineData("x^(1/(1 + 2))", -8)]
+        [InlineData("x^(3^(-1))", -8)]
+        [InlineData("x^(1/(3 provided 3 > 1))", -8)]
+        [InlineData("x^((2/3) provided 2 > 1)", -8)]
         public void TheCompiledFormsTakeTheRealRoot(string expression, double at)
         {
             var entity = expression.ToEntity();