Additional duality check, minor docs improvement

Author: grumyantsev

src/lib.rs

@@ -293,7 +293,7 @@ where
         }
     }
 
-    ///Exponent of a multivector computed using Taylor series.
+    /// Exponent of a multivector computed using Taylor series.
     pub fn exp(&self) -> Self
     where
         T: Norm + From<f64>,
@@ -376,7 +376,7 @@ where
         ret
     }
 
-    /// Hodge dual of a multivector, signature-agnostic.
+    /// Hodge dual of a multivector.
     ///
     /// For any k-blade, `b.dual() * b` is a pseudoscalar.
     pub fn dual(&self) -> Self {
@@ -394,7 +394,7 @@ where
         ret
     }
 
-    /// Hodge dual of a multivector, signature-agnostic.
+    /// Alternative Hodge dual of a multivector, such that `a.dual().undual() == a` for any `a`.
     ///
     /// For any k-blade, `b * b.undual()` is a pseudoscalar.
     pub fn undual(&self) -> Self {

tests/unit.rs

@@ -503,6 +503,22 @@ fn dual_test() {
     );
     assert_eq!((&t + &x), (&t + &x).dual().undual());
     assert_eq!((&t + &x), (&t + &x).undual().dual());
+
+    // Check consistency with Grassmann.jl (up to a sign)
+    declare_algebra!(TestA, [+,+,+,-,-,0,0]);
+    let e = TestA::basis::<f32>();
+    let [v1, v2, v3, v4, v5, v6, v7] = &e;
+    let a = -v3 * 5. + v1 * v5 * v6 - v1 * v4 * v6 * v7
+        + v2 * v3 * v6 * v7
+        + v2 * v4 * v5 * v6 * v7 * 4.
+        + v1 * v2 * v3 * v4 * v5 * v6 * 2.;
+    println!("{}", a.dual());
+    let expected = -(v7 * 2. - v1 * v3 * 4. + v1 * v4 * v5 - v2 * v3 * v5 + v2 * v3 * v4 * v7
+        - v1 * v2 * v4 * v5 * v6 * v7 * 5.);
+    println!("{}", expected);
+    assert_eq!(a.dual(), expected);
+    assert_eq!(a.undual().dual(), a);
+    assert_eq!(a, expected.undual());
 }
 
 #[test]