add Number * VirtualTally, VirtualTally == VirtualTally, expressions …

…fixes

M2/Macaulay2/m2/expressions.m2

@@ -446,6 +446,8 @@ scan(assocList, opClass -> (
 	if opClass#?unit then (
 	    installMethod(opClass#operator,Expression,opClass#unit,(x,y) -> x);
 	    installMethod(opClass#operator,opClass#unit,Expression,(x,y) -> y);
+	    installMethod(opClass#operator,opClass,opClass#unit,(x,y) -> x);
+	    installMethod(opClass#operator,opClass#unit,opClass,(x,y) -> y);
 	    )
 ))
        - ZeroExpression     := identity
@@ -552,6 +554,7 @@ matrixOpts := m -> ( -- helper function
     )
 expressionValue MatrixExpression := x -> (
     (opts,m) := matrixOpts x;
+    if #m === 0 then return map(ZZ^0,ZZ^0,0); -- not great but best one can do
     m = (if opts.MutableMatrix then mutableMatrix else matrix) applyTable(m,expressionValue);
     -- TODO: keep track of blocks too
     if opts.Degrees === null then m else (
@@ -566,7 +569,7 @@ toString'(Function, MatrixExpression) := (fmt,x) -> concatenate(
 -----------------------------------------------------------------------------
 VectorExpression = new HeaderType of Expression
 VectorExpression.synonym = "vector expression"
-expressionValue VectorExpression := x -> vector apply(toList x,expressionValue)
+expressionValue VectorExpression := x -> if #x===0 then vector(map(ZZ^0,ZZ^1,0)) else vector apply(toList x,expressionValue)
 toString'(Function,VectorExpression) := (fmt,v) -> concatenate(
      "vector {",
      between(", ",apply(toList v,fmt)),
@@ -612,10 +615,10 @@ keywordTexMath = new HashTable from { -- both unary and binary keywords
     symbol #? => "\\#?",
     symbol % => "\\%",
     symbol & => "\\&",
-    symbol ^ => "\\wedge",
-    symbol ^^ => "\\wedge\\wedge",
-    symbol <| => "\\langle",
-    symbol |> => "\\rangle",
+    symbol ^ => "\\wedge ",
+    symbol ^^ => "\\wedge\\wedge ",
+    symbol <| => "\\langle ",
+    symbol |> => "\\rangle ",
     symbol _* => "{}_*", -- temporary solution to KaTeX issue https://github.com/KaTeX/KaTeX/issues/3576
     symbol ^* => "{}^*" -- temporary solution to KaTeX issue https://github.com/KaTeX/KaTeX/issues/3576
     }

M2/Macaulay2/m2/set.m2

@@ -38,25 +38,31 @@ Tally + Tally := Tally => (x,y) -> merge(x,y,plus) -- no need to check for zero
 Tally - Tally := Tally => (x,y) -> select(merge(x,applyValues(y,minus),plus),i -> i > 0) -- sadly, can't use continueIfNonPositive
 
 VirtualTally ? VirtualTally := (x,y) -> (
-     w := values ((new VirtualTally from x) - (new VirtualTally from y));
-     if #w === 0 then symbol ==
-     else if all(w,i -> i>0) then symbol >
-     else if all(w,i -> i<0) then symbol <
-     else incomparable)
+    flag:=symbol ==;
+    for k in keys x|keys y do
+    if ((cmp := x_k?y_k) =!= symbol ==) and (cmp === incomparable or (flag =!= cmp and first(flag =!= symbol ==,flag = cmp))) then return incomparable;
+    flag
+    )
 
 zeroVirtualTally := new VirtualTally from {}
 toVirtualTally := i -> if i === 0 then zeroVirtualTally else error "comparison of a virtual tally with a nonzero integer"
-VirtualTally == ZZ := (x,i) -> x === toVirtualTally i
-ZZ == VirtualTally := (i,x) -> toVirtualTally i === x
+VirtualTally == ZZ := (x,i) -> x == toVirtualTally i
+ZZ == VirtualTally := (i,x) -> toVirtualTally i == x
 VirtualTally ? ZZ := (x,i) -> x ? toVirtualTally i
 ZZ ? VirtualTally := (i,x) -> toVirtualTally i ? x
+VirtualTally == VirtualTally := (x,y) -> (x ? y) === symbol ==
 
+-*
 zeroTally := new Tally from {}
 toTally := i -> if i === 0 then zeroTally else error "comparison of a tally with a nonzero integer"
-Tally == ZZ := (x,i) -> x === toTally i
-ZZ == Tally := (i,x) -> toTally i === x
+Tally == ZZ := (x,i) -> x == toTally i
+ZZ == Tally := (i,x) -> toTally i == x
 Tally ? ZZ := (x,i) -> x ? toTally i
 ZZ ? Tally := (i,x) -> toTally i ? x
+*-
+
+RingElement * VirtualTally := Number * VirtualTally := (i,v) -> if i==0 then new class v from {} else applyValues(v,y->y*i)
+Number * Tally := (i,v) -> if i<=0 then new class v from {} else applyValues(v,y->y*i)
 
 sum VirtualTally := (w) -> sum(pairs w, (k,v) -> v * k)
 product VirtualTally := (w) -> product(pairs w, (k,v) -> k^v)