define blade addition, subtraction, scalar multiplication

Change-Id: I126530ee703ba00933222e9eaef3cb21f6aa7bd3

rigid_geometric_algebra/blade.hpp

@@ -70,6 +70,29 @@ struct blade
     return {-std::forward<Self>(self).coefficient};
   }
 
+  /// addition
+  ///
+  friend constexpr auto operator+(const blade& lhs, const blade& rhs) -> blade
+  {
+    return {lhs.coefficient + rhs.coefficient};
+  }
+
+  /// subtraction
+  ///
+  friend constexpr auto operator-(const blade& lhs, const blade& rhs) -> blade
+  {
+    return {lhs.coefficient - rhs.coefficient};
+  }
+
+  /// scalar multiplication
+  ///
+  template <class T>
+    requires std::is_invocable_r_v<value_type, std::multiplies<>, T, value_type>
+  friend constexpr auto operator*(const T& lhs, const blade& rhs) -> blade
+  {
+    return {lhs * rhs.coefficient};
+  }
+
   /// obtain the blade with indices in canonical form
   ///
   /// Returns same blade expressed in canonical form - i.e. with indices in

test/blade_test.cpp

@@ -67,4 +67,32 @@ auto main() -> int
         eq(rga::blade<0, 1, 2>{1}, -rga::blade<0, 2, 1>{1}) and
         eq(rga::blade<0, 1, 2>{1}, -rga::blade<2, 1, 0>{1}));
   };
+
+  "addition"_test = [] {
+    const auto b0 = rga::blade<>{};
+    const auto b1 = rga::blade<>{1};
+    const auto b2 = rga::blade<>{2};
+
+    return expect(
+        eq(b0, b0 + b0) and eq(b1, b0 + b1) and eq(b2, b0 + b2) and
+        eq(b1, b1 + b0) and eq(b2, b2 + b0) and eq(b2, b1 + b1) and
+        eq(b2, b2 + b0 + b0));
+  };
+
+  "subtraction"_test = [] {
+    const auto b0 = rga::blade<>{};
+    const auto b1 = rga::blade<>{1};
+    const auto b2 = rga::blade<>{2};
+
+    return expect(
+        eq(b0, b0 - b0) and eq(-b1, b0 - b1) and eq(-b2, b0 - b2) and
+        eq(b1, b1 - b0) and eq(b2, b2 - b0) and eq(b0, b1 - b1) and
+        eq(b2, b2 - b0 - b0));
+  };
+
+  "scalar multiplication"_test = [] {
+    return expect(
+        eq(rga::blade<>{2}, 2 * rga::blade<>{1}) and
+        eq(rga::blade<>{2}, 2.0 * rga::blade<>{1}));
+  };
 }