A lambda is applied to its argument before its body is simplified

BREAKING-CHANGES.md

@@ -77,6 +77,18 @@ its rows in the order it finds them, which can differ from the eliminator's
 | `MathS.Equations("x*y", "x + y^2 - 1").Solve("x", "y")` | `[[1, 0]]` | `[[1, 0], [0, 1], [0, -1]]` |
 | `MathS.Equations("x*y + 3*x - 5*y - 15", "x^2 - 3*x - 4*y - 10").Solve("x", "y")` | `[[1, -3], [2, -3]]` | `[[5, 0], [1, -3], [2, -3]]` |
 
+### A lambda applied to a vector multiplies by it as a vector
+
+**Silent: a matrix of vectors becomes the product.** Applying a lambda simplified its body first, and a simplified
+body treats its parameter as a number: `[[0, -1], [1, 0]] * u` became `[[0, -u], [u, 0]]`, and the vector then put in
+for `u` made a matrix of vectors. A lambda written in place is now applied before its body is simplified
+([#2132](https://github.com/asc-community/AngouriMath/issues/2132)). `Evaled` and `Simplify()` agree.
+
+| Input | Was (2.6.0) | Now |
+|---|---|---|
+| `apply(lambda(u, [[0, -1], [1, 0]] * u), [p, q])` | `[[0, [-p, -q]], [[p, q], 0]]` | `[-q, p]` |
+| `apply(lambda(u, [1, 1]T * u), [p, q])` | `[[[p, q], [p, q]]]` | `p + q` |
+
 ### A square system is not answered with rows that are no solution
 
 **Silent: a row that is no solution is gone, and a system with a row that fails for some values is `null`.**

Sources/AngouriMath/Functions/Evaluation/Evaluation.Omni/Evaluation.Omni.Classes.cs

@@ -547,6 +547,16 @@ private static Entity ApplyOthersIfNeeded(Entity outer, LList<Entity> arguments)
 
             /// <inheritdoc/>
             protected override Entity InnerSimplify(bool isExact)
+                // A lambda written in place is applied to its argument before its body is
+                // simplified. Simplified first, the body treats its parameter as a number:
+                // [[0, -1], [1, 0]] * u becomes [[0, -u], [u, 0]], and the vector [p, q] put in
+                // for u afterwards made a matrix of vectors where the product is [-q, p].
+                // https://github.com/asc-community/AngouriMath/issues/2132
+                => Expression is Lambda(var parameter, var body) && Arguments is (var first, var rest)
+                    ? ApplyOthersIfNeeded(body.Substitute(parameter, first.InnerSimplified(isExact)), rest).InnerSimplified(isExact)
+                    : ApplyingTheSimplified(isExact);
+
+            private Entity ApplyingTheSimplified(bool isExact)
                 => ((Expression.InnerSimplified(isExact), Arguments.Map(arg => arg.InnerSimplified(isExact))) switch
                 {
                     (var identifier, LEmpty<Entity>) => identifier,

Sources/Tests/UnitTests/Common/LambdaCalculusTest.cs

@@ -223,5 +223,19 @@ [Fact] public void EtaReduction8()
                     )
                 )".Simplify()
             );
+
+        // A lambda is applied to its argument before its body is simplified: simplified first,
+        // the body treats its parameter as a number, so [[0, -1], [1, 0]] * u became
+        // [[0, -u], [u, 0]] and the vector put in for u made a matrix of vectors.
+        // https://github.com/asc-community/AngouriMath/issues/2132
+        [Theory]
+        [InlineData("apply(lambda(u, [[0, -1], [1, 0]] * u), [p, q])", "[-q, p]")]
+        [InlineData("apply(lambda(u, [1, 1]T * u), [p, q])", "p + q")]
+        [InlineData("apply(lambda(u, v, [u, v]T * [1, 2]), 3, 4)", "11")]
+        public void ALambdaIsAppliedToAVectorAsAVector(string application, string expected)
+        {
+            Assert.Equal(expected.ToEntity(), application.ToEntity().InnerSimplified);
+            Assert.Equal(expected.ToEntity(), application.ToEntity().Simplify());
+        }
     }
 }