Document unicode math operators

M2/Macaulay2/d/lex.d

@@ -318,6 +318,8 @@ gettoken1(file:PosFile,sawNewline:bool):Token := (
 	  else if ismathoperator(peek2(file)) then (
 	       for i from 1 to utf8charlength(char(ch))
 	       do tokenbuf << char(getc(file));
+	       if peek(file) == int('=') -- augmented assignment operator
+	       then tokenbuf << char(getc(file));
 	       return Token(makeUniqueWord(takestring(tokenbuf), parseWORD),
 		   newPosition(file, line, column), globalDictionary, dummySymbol, sawNewline))
 	  else if isalpha(ch) then ( -- valid symbols are an alpha (letters, any unicode) followed by any number of alphanum (alpha, digit, dollar, prime)

M2/Macaulay2/m2/help.m2

@@ -300,6 +300,15 @@ getSource(Symbol, Package) := (S, pkg) -> (
     )
 
 -- Handling operators
+
+-- for each unicode operator, we give a pair:
+-- * unicode name
+-- * TeX name (for emacs TeX input mode -- null if not available)
+unicodeOperators := hashTable {
+    symbol · => ("middle dot", "\\cdot"),
+    symbol ⊠ => ("squared times", "\\boxtimes"),
+    symbol ⧢ => ("shuffle product",)}
+
 -- e.g. symbol +
 getOperator := key -> if operator#?key then (
     op := toString key;
@@ -328,7 +337,15 @@ getOperator := key -> if operator#?key then (
 	    PARA {"This operator may be used as a binary operator in an expression like ", TT ("x" | op | "y"), ". ",
 		"The user may ", TO2{ "Macaulay2Doc :: :=", "install a method" }, " for handling such expressions with code such as"},
 	    PRE ("         X "|op|" (x,y) -> ..."),
-	    PARA {"where ", TT "X", " is the class of ", TT "x", "."}}
+	    PARA {"where ", TT "X", " is the class of ", TT "x", "."}},
+	if unicodeOperators#?key then {
+	    PARA {"To insert this character in Emacs, you may press ", KBD "C-x 8 RET", " or ", KBD "M-x insert-char",
+		" and then enter ", format unicodeOperators#key#0, " in the minibuffer."},
+	    if (texcmd := unicodeOperators#key#1) =!= null
+	    then PARA {"Alternatively, you may press ", KBD "C-x RET C-\\", "  or ", KBD "M-x set-input-method",
+		" and then enter \"TeX\" in the minibuffer.  Afterwards, typing \"", texcmd,
+		"\" will input the character.  You may then toggle the input method using ", KBD "C-\\", " or ",
+		KBD "M-x toggle-input-method"}},
 	))
 
 -- TODO: expand this

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

@@ -34,3 +34,13 @@ Node
     Example
       {1, 2} ** {10, 20, 30}
 ///
+
+document {
+    Key => symbol ⊠,
+    Headline => "a binary operator, usually used for exterior product",
+}
+
+document {
+    Key => symbol ⧢,
+    Headline => "a binary operator, usually used for shuffle product",
+}

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

@@ -196,3 +196,8 @@ document {
 	  },
      SeeAlso => {(degree,Matrix),degrees}
      }
+
+document {
+    Key => symbol ·,
+    Headline => "a binary operator, usually used for dot product",
+}

M2/Macaulay2/packages/Macaulay2Doc/ov_language.m2

@@ -1070,6 +1070,7 @@ document {
 	  TO symbol + ,
 	  TO symbol - ,
 	  TO symbol * ,
+	  TO symbol · ,
 	  TO symbol / ,
 	  TO symbol // ,
 	  TO symbol % ,
@@ -1078,6 +1079,8 @@ document {
 	  TO symbol ++ ,
 	  TO symbol ** ,
           TO symbol ^** ,
+	  TO symbol ⊠ ,
+	  TO symbol ⧢ ,
           TO symbol ~ ,
 	  TO symbol (*) ,
           TO symbol : ,

M2/Macaulay2/tests/normal/augmented-assignment.m2

@@ -74,6 +74,15 @@ assert Equation(x#0, 28)
 Foo @ Foo := (x, y) -> Foo(4*x#0 - 5*y#0)
 x @= Foo 7
 assert Equation(x#0, 77)
+Foo · Foo := (x,y) -> Foo(6*x#0 * 7*y#0)
+x ·= Foo 8
+assert Equation(x#0, 25872)
+Foo ⊠ Foo := (x,y) -> Foo((8*x#0) // (9*y#0))
+x ⊠= Foo 9
+assert Equation(x#0, 2555)
+Foo ⧢ Foo := (x,y) -> Foo(10*x#0 + 11*y#0)
+x ⧢= Foo 10
+assert Equation(x#0, 25660)
 
 -- local variable
 x := 2