Remove conflicts in packages now that "sign" is in Core

Either remove now-redundant methods or rename "sign" variables to "sgn".

M2/Macaulay2/packages/BettiCharacters.m2

@@ -1122,9 +1122,9 @@ Node
 	the sign character just constructed: the result is the
 	same as the character of the resolution.
     Example
-    	sign = character(R,15,hashTable {(0,{7}) =>
+    	sgn = character(R,15,hashTable {(0,{7}) =>
 		matrix{{1,-1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1}}})
-	dual(c,id_QQ)[-5] ** sign === c
+	dual(c,id_QQ)[-5] ** sgn === c
     Text
     	The second argument in the @TT "dual"@ command is the
 	restriction of complex conjugation to the field of
@@ -2842,8 +2842,8 @@ Node
 	    observed by tensoring with the character of the
 	    sign representation concentrated in degree 3.
     	Example
-	    sign = character(R,3, hashTable { (0,{3}) => matrix{{1,-1,1}} })
-	    dual(a,{1,2,3}) ** sign === a
+	    sgn = character(R,3, hashTable { (0,{3}) => matrix{{1,-1,1}} })
+	    dual(a,{1,2,3}) ** sgn === a
 
 ///
 
@@ -3064,10 +3064,10 @@ K = freeResolution ideal vars R
 S4 = symmetricGroupActors(R)
 A = action(K,S4)
 c = character A
-sign = character(R,5, hashTable { (-4,{-4}) => matrix{{-1,1,1,-1,1}} })
+sgn = character(R,5, hashTable { (-4,{-4}) => matrix{{-1,1,1,-1,1}} })
 -- check duality of representations in Koszul complex
 -- which is true up to a twist by a sign representation
-assert(dual(c,id_QQ) == c ** sign)
+assert(dual(c,id_QQ) == c ** sgn)
 ///
 
 end

M2/Macaulay2/packages/GradedLieAlgebras.m2

@@ -72,7 +72,6 @@ export {
     "mbRing",
     "minimalModel",
     "normalForm",
-    "sign",
     "Signs",
     "weight",    
     "VectorSpace",
@@ -2464,8 +2463,6 @@ isignlocal(BasicList,LieAlgebra):=(x,L)->
 -- the sign of an element 
 -- in the Ext-algebra
 
-
-sign=method()
 sign(LieElement) := (x)->(
     L:=class x;
    -- xx:=normalForm(x);

M2/Macaulay2/packages/Parametrization.m2

@@ -702,16 +702,6 @@ return(rslt);
 --p=rtpt(1180943,-14640196896);
 --p_(0,0)^2+1180943*p_(0,1)^2-14640196896*p_(0,2)^2
 
-sign=method()
-sign(ZZ):=(n)->(
-if n>0 then return(1);
-if n<0 then return(-1);
-0)
-sign(QQ):=(n)->(
-if n>0 then return(1);
-if n<0 then return(-1);
-0)
-
 -- Jval(ZZ,ZZ,ZZ)
 -- computes the index of the argument
 

M2/Macaulay2/packages/Permanents.m2

@@ -50,7 +50,7 @@ ryser Matrix := (M) -> (
       for i from 1 to n-1 do(del = append(del,0););--delta is of length n
 
       --take the initial product corresponding to delta all +1's
-      sign:=1;
+      sgn:=1;
       prod:=1;
       for i from 0 to n-1 do(
 	  prod=prod*s#i;
@@ -60,7 +60,7 @@ ryser Matrix := (M) -> (
       curIndex:=0;--which position in the gray code changed
       curVal:=0;--what is the new value in the changed position of the gray code
       for count from 2 to 2^n do(--start at 2 because we already took the initial product corresponding to delta consisting of all 1's
-	  sign=(-1)*sign;
+	  sgn=(-1)*sgn;
 	  --increment delta
 	  flag:=1;
 	  for k from 0 to n-1 when flag==1 do(
@@ -79,7 +79,7 @@ ryser Matrix := (M) -> (
 	  	  prod=prod*s#i;
 	      );
 
-	  permanent = permanent+sign*prod;
+	  permanent = permanent+sgn*prod;
 	  );
 
       permanent
@@ -117,7 +117,7 @@ glynn Matrix := (M) -> (
       for i from 1 to n-2 do(del = append(del,0););--delta is of length n-1 because first position is always positive, so we don't consider it in the gray code
 
       --take the initial product corresponding to delta all +1's
-      sign:=1;
+      sgn:=1;
       prod:=1;
       for i from 0 to n-1 do(
 	  prod=prod*s#i;
@@ -127,7 +127,7 @@ glynn Matrix := (M) -> (
       curIndex:=0;--which position in the gray code changed
       curVal:=0;--what is the new value in the changed position of the gray code
       for count from 2 to 2^(n-1) do(--start at 2 because we already took the initial product corresponding to delta consisting of all 1's
-	  sign=(-1)*sign;
+	  sgn=(-1)*sgn;
 	  --increment delta
 	  flag:=1;
 	  for k from 0 to n-2 when flag==1 do(
@@ -146,7 +146,7 @@ glynn Matrix := (M) -> (
 	  	  prod=prod*s#i;
 	      );
 
-	  perm = perm+sign*prod;
+	  perm = perm+sgn*prod;
 	  );
 
       --need to divide in Glynn's formula

M2/Macaulay2/packages/Permutations.m2

@@ -33,7 +33,6 @@ export {
     "isCDG",
     "foataBijection",
     "ord",
-    "sign",
     "isEven",
     "isOdd",
     "isDerangement",
@@ -327,7 +326,6 @@ ord Permutation := ZZ => w -> (
 
 -- see https://en.wikipedia.org/wiki/Parity_of_a_permutation for different ways
 -- to compute the sign or parity of a permutation
-sign = method()
 sign Permutation := ZZ => w -> (
     if even(#w - #(cycleDecomposition w)) then 1 else -1
 )
@@ -377,4 +375,4 @@ installPackage "Permutations"
 restart
 needsPackage "Permutations"
 elapsedTime check "Permutations"
-viewHelp "Permutations"
+viewHelp "Permutations"

M2/Macaulay2/packages/RealRoots.m2

@@ -81,17 +81,6 @@ isArtinian (Ring) := Boolean => R->(
     dim R === 0
     )
 
-
---Computes the sign of a real number
-sign = method()
-for A in {ZZ,QQ,RR} do
-sign (A) := ZZ => n->(
-     if n < 0 then -1 
-     else if n == 0 then 0
-     else if n > 0 then 1
-     )
-
-
 --Computes the sign of a real univariate polynomial at a given real number
 signAt = method()
 for A in {ZZ,QQ,RR} do

M2/Macaulay2/packages/Resultants.m2

@@ -384,14 +384,14 @@ detectGrassmannian (QuotientRing) := (G) -> (
 
 duality = method(TypicalValue => RingMap); -- p. 94 [Gelfand, Kapranov, Zelevinsky - Discriminants, resultants, and multidimensional determinants, 1994]
 
-sign = (permutation) -> sub(product(subsets(0..#permutation-1,2),I->(permutation_(I_1)-permutation_(I_0))/(I_1-I_0)),ZZ); -- thanks to Nivaldo Medeiros 
+sgn = (permutation) -> sub(product(subsets(0..#permutation-1,2),I->(permutation_(I_1)-permutation_(I_0))/(I_1-I_0)),ZZ); -- thanks to Nivaldo Medeiros 
 tosequence = (L) -> if #L != 1 then toSequence L else L_0;
 
 duality(PolynomialRing) := (R) -> (  -- returns the map R:=G(k,P^n) ---> G(n-k-1,P^n*)
    (k,n,KK,p) := detectGrassmannian R; 
    G := ambient Grass(k,n,KK,Variable=>p);
    G' := ambient Grass(n-k-1,n,KK,Variable=>p);  
-   L := for U in subsets(set(0..n),n-k) list sign( (sort toList(set(0..n)-U)) | sort toList U)  *  (p_(tosequence sort toList(set(0..n)-U)))_G;
+   L := for U in subsets(set(0..n),n-k) list sgn( (sort toList(set(0..n)-U)) | sort toList U)  *  (p_(tosequence sort toList(set(0..n)-U)))_G;
    return(map(R,G,vars R) * map(G,G',L));
 );
 

M2/Macaulay2/packages/SchurComplexes.m2

@@ -251,7 +251,7 @@ homologicalDegree(HashTable,List,List) := (T,evengen,oddgen) -> sum for b in key
 ------Straightening algorithm
 
 --Inputs: U= List, V= permutation represented as a list. Outputs: sign of the induced permutation on the unmarked elements of U.
-sign = (U,V)-> (
+sgn = (U,V)-> (
     n:=#U;
     answer:=1;
     for i from 0 to n-2 do (
@@ -288,7 +288,7 @@ shuffle = (T, vio, downCol2, lambdaprime) -> (
     indicesofL:=toList (0..(#L-1));
     subsetsofLofsizetruncatedcol1:=subsets(indicesofL,#truncatedcol1);
     pairs1:=apply(subsetsofLofsizetruncatedcol1, x-> (x, indicesofL-(set x)));
-    signs:=apply(pairs1, x-> sign(L,join(x)));
+    signs:=apply(pairs1, x-> sgn(L,join(x)));
     outputlist:={}; 
     dividedContributions := for i from 0 to (#pairs1-1) list (
 	dividedContribution := 1; --contribution from divided power multiplication

M2/Macaulay2/packages/SpechtModule.m2

@@ -912,8 +912,8 @@ garnirElement(YoungTableau,ZZ,ZZ,ZZ):= (tableau,coef,a,b)-> (
 	    for j from a+1 to conju#b do (  
 	    	newTableau_(j-1,b) = AB#(comb#j);
 		);
-	    sign:=sortColumnsTableau(newTableau);
-	    spechtModuleElement (newTableau, (coef) *sign*permutationSign(conjugacyClass(comb)))
+	    sgn:=sortColumnsTableau(newTableau);
+	    spechtModuleElement (newTableau, (coef) *sgn*permutationSign(conjugacyClass(comb)))
       	    ));
 
 	);
@@ -941,9 +941,9 @@ sortColumnsTableau SpechtModuleElement := element ->
 	    y := youngTableau(element#partition,t);
 	    coef := element#values#t;
 	    remove(element#values,t);
-	    sign:= sortColumnsTableau(y);
-	    if(element#values#?(entries y)) then element#values#(entries y) = element#values#(entries y)+sign*coef
-	    else element#values#(entries y) = coef*sign;
+	    sgn:= sortColumnsTableau(y);
+	    if(element#values#?(entries y)) then element#values#(entries y) = element#values#(entries y)+sgn*coef
+	    else element#values#(entries y) = coef*sgn;
 	     )   
 	);
     )
@@ -1193,14 +1193,14 @@ higherSpechtPolynomial(YoungTableau, YoungTableau, PolynomialRing) := o-> (S,T,R
 	rowPermutations := rowPermutationTableaux indexTableau S;
 	ans = spechtPolynomial(T,R,AsExpression =>o.AsExpression)*sum(rowPermutations, tab -> product apply (numcols S, i->
 		(
-		    (sortedList,sign) := sortList(tab_i);
+		    (sortedList,sgn) := sortList(tab_i);
 		    sortedList = sortedList  -  toList (0..(#(tab_i)-1));
 		    sortedList = reverse sortedList;
 		    firstZero := position(sortedList,i->i==0);
 		    lastNonZero:= 0;
 	 	    if (firstZero === null) then lastNonZero = #sortedList-1 else lastNonZero = firstZero -1;
 		    partition:= new Partition from sortedList_{0..lastNonZero};
-		    sign*schurPolynomial(T_i,partition,R,AsExpression => o.AsExpression)
+		    sgn*schurPolynomial(T_i,partition,R,AsExpression => o.AsExpression)
 		    )))
 	);
     ans