Add dot product method

Author: d-torrance

M2/Macaulay2/m2/modules.m2

@@ -138,6 +138,7 @@ Vector / Number := Vector / RingElement := Vector => (v,r) -> vector(v#0 / r)
 Vector + Vector := Vector => (v,w) -> vector(v#0+w#0)
 Vector - Vector := Vector => (v,w) -> vector(v#0-w#0)
 Vector ** Vector := Vector => (v,w) -> vector(v#0**w#0)
+Vector · Vector := (v,w) -> (transpose matrix v * matrix w)_(0,0)
 
 Vector == Vector := (v,w) -> v === w
 

M2/Macaulay2/packages/Macaulay2Doc/doc_module.m2

@@ -192,6 +192,7 @@ document {
 	TO (entries, Vector),
 	TO (symbol **, Vector, Vector),
 	TO (symbol ||, Vector, Vector),
+	TO (symbol ·, Vector, Vector),
     },
 }
 

M2/Macaulay2/packages/Macaulay2Doc/operators/times.m2

@@ -214,3 +214,26 @@ doc ///
       toggle the input method using @KBD "C-\\"@  or
       @KBD "M-x toggle-input-method"@.
 ///
+
+doc ///
+  Key
+    (symbol ·, Vector, Vector)
+  Headline
+    dot product
+  Usage
+    v · w
+  Inputs
+    v:Vector
+    w:Vector
+  Outputs
+    :{Number, RingElement}
+  Description
+    Text
+      This function computes the dot product of two elements of a free module.
+      In particular, if $v,w\in R^n$ are represented as $n\times 1$ matrices,
+      then $v\cdot w$ is the sole entry of the $1\times 1$ matrix $v^Tw$.
+    Example
+      v = vector {1, 2, 3}
+      w = vector {4, 5, 6}
+      v · w
+///

M2/Macaulay2/tests/normal/vector.m2

@@ -33,3 +33,6 @@ assert Equation(v / 2, vector(N, {1/2, 1, 3/2}))
 v = vector {x, y, z}
 kk = frac R
 assert Equation(v / x, vector map(kk^3, kk^{-1}, {{1}, {y/x}, {z/x}}))
+
+w = vector {y, z, x}
+assert Equation(v · w, x*y + x*z + y*z)