FIXME: re-enable PP in the Core

M2/Macaulay2/m2/varieties.m2

@@ -58,6 +58,7 @@ Proj Ring := (stashValue symbol Proj) (R ->
 	}
     )
 
+-*
 -- TODO: export and document
 -- Note: NormalToricVarieties may redefine
 PP = new ScriptedFunctor from {
@@ -82,6 +83,7 @@ PP Sequence := ProjectiveVariety => w -> Proj(ZZ[vars(0..#w-1), Degrees => toLis
 PP(Ring, ZZ)       :=
 PP(Ring, List)     := ProjectiveVariety => (K, N) -> PP^N ** K
 PP(Ring, Sequence) := ProjectiveVariety => (K, w) -> PP w ** K
+*-
 
 -- this is a kludge to make Spec ZZ/101[x,y]/(y^2-x^3) and Proj ZZ/101[x,y]/(x^2-y^2) work as expected
 -- TODO: also make Spec kk{x,y} or Spec kk<|x,y|> work when they are supported

M2/Macaulay2/packages/AssociativeAlgebras.m2

@@ -1782,8 +1782,8 @@ all(15, i -> #(flatten entries ncBasis(i, S)) == binomial(i + 3,3))
 LL = lineSchemeFourDim(S,M)
 primaryDecomposition radical LL
 netList oo
-PP = pointScheme(S,y)
-primaryDecomposition radical PP
+P = pointScheme(S,y)
+primaryDecomposition radical P
 netList oo
 
 restart
@@ -1792,12 +1792,12 @@ R = ZZ/32003 <|x_4,x_1,x_2,x_3|>
 I = ideal {x_3^2 - x_1*x_2, x_4^2 - x_2*x_1, x_1*x_3 - x_2*x_4,
            x_3*x_1 - x_2*x_3, x_1*x_4 - x_4*x_2, x_4*x_1 - x_3*x_2}
 S = R/I
-PP = pointScheme(S,y)
-netList minimalPrimes PP
+P = pointScheme(S,y)
+netList minimalPrimes P
 
-PPR = ring Mleft
-MleftSpecial = sub(Mleft, {PPR_0 => 1, PPR_1 => 2, PPR_2 => 0, PPR_3 => 0})
-MrightSpecial = sub(Mright, {PPR_0 => 1, PPR_1 => 2, PPR_2 => -1, PPR_3 => -2})
+PR = ring Mleft
+MleftSpecial = sub(Mleft, {PR_0 => 1, PR_1 => 2, PR_2 => 0, PR_3 => 0})
+MrightSpecial = sub(Mright, {PR_0 => 1, PR_1 => 2, PR_2 => -1, PR_3 => -2})
 C = first minimalPrimes minors(4,Mleft)
 Mleft % C
 ker (Mleft % C)
@@ -1824,9 +1824,9 @@ netList minimalPrimes P
 minimalPrimes ideal singularLocus P
 
 R = QQ[zz,a_1,a_2,a_3]
-PP = sub(P,R) + ideal {zz^2 + zz + 1}
-minPP = minimalPrimes PP
-minPP / degree
+P = sub(P,R) + ideal {zz^2 + zz + 1}
+minP = minimalPrimes P
+minP / degree
 
 x = baseName x
 R = ZZ/32003 <|x_4,x_1,x_2,x_3|>

M2/Macaulay2/packages/AssociativeAlgebras/doc.m2

@@ -1457,9 +1457,9 @@ doc ///
       three lines (although M2 has trouble detecting this outright):
     Example
       R = QQ[zz,X_1,X_2,X_3]
-      PP = sub(P,R) + ideal {zz^2 + zz + 1}
-      minPP = minimalPrimes PP; netList minPP
-      minPP / degree
+      P = sub(P,R) + ideal {zz^2 + zz + 1}
+      minP = minimalPrimes P; netList minP
+      minP / degree
     Text
       Indeed, this Sklyanin algebra is isomorphic to a skew polynomial algebra
       in three variables if the base field contains a cube root of unity.

M2/Macaulay2/packages/Cremona.m2

@@ -315,11 +315,11 @@ toMap (Ideal,ZZ,ZZ) := o -> (I,v,jj) -> (
    K := coefficientRing ring I; 
    d := numgens ring I -1;
    x := local x;
-   PP := K[x_0..x_d];
-   C := homComp(v-jj+1,sub(I,vars PP));
+   PPd := K[x_0..x_d];
+   C := homComp(v-jj+1,sub(I,vars PPd));
    n := numgens C -1;
    if n == -1 then return toMap(sub(matrix{{}},ring I),Dominant=>o.Dominant);
-   bs := gens homComp(v,sub(I,vars PP));
+   bs := gens homComp(v,sub(I,vars PPd));
    N := numgens source bs -1;
    if N == -1 then return toMap(sub(matrix{{}},ring I),Dominant=>o.Dominant);
    a := local a; b := local b;
@@ -331,8 +331,8 @@ toMap (Ideal,ZZ,ZZ) := o -> (I,v,jj) -> (
    sols := sub(ideal selectInSubring(1,gens gb sys),K[a_0..a_N]);
    f := map parametrize sols;
    if dim target f <= 0 then return toMap(sub(matrix{{}},ring I),Dominant=>o.Dominant);
-   PP' := PP[gens target f];
-   linSys := transpose sub(sub((coefficients (sub(matrix f,PP') * transpose sub(bs,PP'))_(0,0))_1,PP),vars ring I);
+   PPd' := PPd[gens target f];
+   linSys := transpose sub(sub((coefficients (sub(matrix f,PPd') * transpose sub(bs,PPd'))_(0,0))_1,PPd),vars ring I);
    toMap(linSys,Dominant=>o.Dominant)
 );
 
@@ -1946,8 +1946,8 @@ rationalMap (AbstractRationalMap) := o -> (Phi) -> (
    a := local a;
    R := K[flatten for i to m list toList(a_(i,0)..a_(i,binomial(n+d,d)-1))];
    x := local x;
-   PP := R[x_0..x_n];
-   F := matrix{for i to m list (matrix{toList(a_(i,0)..a_(i,binomial(n+d,d)-1))} * transpose gens (ideal vars PP)^d)_(0,0)};
+   PPn := R[x_0..x_n];
+   F := matrix{for i to m list (matrix{toList(a_(i,0)..a_(i,binomial(n+d,d)-1))} * transpose gens (ideal vars PPn)^d)_(0,0)};
    M := apply(N,i -> sub(F,apply(n+1,j -> x_j => B_(i,j))) || submatrix(V,{i},));
    eqs := sum(M,m -> trim minors(2,m));
    if Phi#"verbose" then <<"-- obtained "<<numgens eqs<<" linear equations with "<<toString((m+1) * binomial(n+d,d))<<" unknowns over "<<toString(K)<<endl;
@@ -1960,8 +1960,8 @@ rationalMap (AbstractRationalMap) := o -> (Phi) -> (
    if #S == 0 then error "something went wrong while calculating forms";
    S0 := first S;
    g := gens R;
-   PP = K[x_0..x_n];
-   G := sub(sub(sub(F,apply(#g,i -> g_i => S0_i)),PP),vars Pn);
+   PPn = K[x_0..x_n];
+   G := sub(sub(sub(F,apply(#g,i -> g_i => S0_i)),PPn),vars Pn);
    phi := rationalMap(Pn,Pm,G);
    if #S > 1 then maps phi;
    Phi#"degForms" = max flatten degrees ideal compress matrix phi;

M2/Macaulay2/packages/IntegralClosure.m2

@@ -2446,10 +2446,10 @@ TEST ///
   debug IntegralClosure
   kk=ZZ/2
   S=kk[a,b,c,d]
-  PP = monomialCurveIdeal(S,{1,3,4})
-  betti res PP
-  for count from 1 to 10 list parametersInIdeal PP
-  for count from 1 to 10 list canonicalIdeal (S/PP)
+  P = monomialCurveIdeal(S,{1,3,4})
+  betti res P
+  for count from 1 to 10 list parametersInIdeal P
+  for count from 1 to 10 list canonicalIdeal (S/P)
 ///     
 
 -- MES TODO: test canonicalIdeal1 here?
@@ -2482,10 +2482,10 @@ TEST ///
   kk=ZZ/101
   S=kk[a,b,c,d]
   canonicalIdeal S
-  PP = monomialCurveIdeal(S,{1,3,4})
-  betti res PP
-  R = S/PP
-  w=canonicalIdeal R
+  P = monomialCurveIdeal(S,{1,3,4})
+  betti res P
+  R = S/P
+  w = canonicalIdeal R
   w1 = canonicalIdeal1 R -- a different, somewhat less pleasing answer...
   -- check that these two different canonical ideals are isomorphic.
   F = homomorphism (Hom(w,w1))_{0}

M2/Macaulay2/packages/K3Carpets.m2

@@ -591,8 +591,8 @@ schemeInProduct(Ideal, List, Symbol) := (I,Maps,X) ->(
     S := ring I;
     kkk := coefficientRing S;
     dims := apply(Maps, f -> numcols f-1);
-    PP := productOfProjectiveSpaces (dims, symbol X, kkk);
-    schemeInProduct(I,Maps,PP)
+    P := productOfProjectiveSpaces (dims, symbol X, kkk);
+    schemeInProduct(I,Maps,P)
 )
  ///
  restart

M2/Macaulay2/packages/Macaulay2Doc/changes.m2

@@ -737,8 +737,8 @@ document {
 			 to the value of the ", TO [newPackage, PackageImports], " or ", TO [newPackage, PackageExports], " option, to ensure that needed definitions are visible." },
                     LI { "the Schubert2 functions ", TT "projectiveSpace", " and ", TT "projectiveSpace'", "have been renamed ", TO "Schubert2::abstractProjectiveSpace", "  and ",
                      	 TO "Schubert2::abstractProjectiveSpace'", ".  The reason is that there were name conflicts with the ", TO "NormalToricVarieties::NormalToricVarieties", " package.  
-			 Since ", TT "PP", " is no longer protected, you may put ", TT "PP = abstractProjectiveSpace", 
-                     	 " in your init file and then use something like ", TT "X = PP 4", ", although ", TT "PP^4", " will no longer work." },
+			 Since ", TT "PP", " is now a method, you may put ", TT "PP ZZ := abstractProjectiveSpace", 
+                     	 " in your init file and then use something like ", TT "X = PP 4", "." },
 		    LI { "The deprecated old-style block comment syntax has been disabled.  Now one types ", TT "-* COMMENT *-", " instead of ", TT "{* COMMENT *}", "." } } },
      	  LI { "new packages:",
      	       UL {

M2/Macaulay2/packages/MultiprojectiveVarieties.m2

@@ -203,6 +203,7 @@ setParametrizationOfWeightedProjectiveSpace = P -> (
     P.cache#"rationalParametrization" = g;
     P
 );
+-- TODO: conflicts with PP from Core
 PP = new ScriptedFunctor from {
     symbol ring => null,
     argument => (

M2/Macaulay2/packages/NoetherianOperators.m2

@@ -3760,8 +3760,8 @@ viewHelp "NoetherianOperators"
 -- We compute the ideal as explained in the introduction.
 U= QQ[x_1,x_2,x_3,x_4,u_1,u_2,u_3,u_4,y_1,y_2];
 A = matrix {{u_3,u_1,u_2},{u_1,u_2,u_4}};
-PP = minors(2,A);
-JJ=ideal{PP,x_1-u_1-y_1,x_2-u_2-y_2,x_3-u_3,x_4-u_4,y_1^3,y_2+x_2*y_1^2};
+P = minors(2,A);
+JJ=ideal{P,x_1-u_1-y_1,x_2-u_2-y_2,x_3-u_3,x_4-u_4,y_1^3,y_2+x_2*y_1^2};
 J=ideal{eliminate(JJ,{u_1,u_2,u_3,u_4,y_1,y_2})};
 R=QQ[x_1,x_2,x_3,x_4];
 F=map(R,U);

M2/Macaulay2/packages/NormalToricVarieties/ToricVarietiesDocumentation.m2

@@ -633,7 +633,7 @@ doc ///
 	    projectiveSpace = n -> Proj (QQ[x_0..x_n]);
 	    projectiveSpace 2
 	Example	    
-	    PP = toricProjectiveSpace;	    
+	    PP ZZ := toricProjectiveSpace;
 	    PP 2
     SeeAlso
         "making normal toric varieties"

M2/Macaulay2/packages/Polymake.m2

@@ -62,8 +62,8 @@ getPropertyNames(List) := (F) -> (
       -- F is a list of lines, as from a polymake file
       -- returns a list of strings, names of known properties
       FF := removeComments(F);
-      PP := select(FF, s-> match("^[[:space:]]*[[:alpha:]]", s));
-      apply(PP, s -> toString s)
+      names := select(FF, s -> match("^[[:space:]]*[[:alpha:]]", s));
+      apply(names, toString)
       )     
 
 getProperty = method()

M2/Macaulay2/packages/QuaternaryQuartics/Section8Doc.m2

@@ -122,10 +122,10 @@ doc ///
     Example
       JJ = randomElementsFromIdeal({3},SS);
       IDD=X+JJ;
-      PP=IDD:SS;
-      BB= randomElementsFromIdeal({5},PP);
+      UU=IDD:SS;
+      BB= randomElementsFromIdeal({5},UU);
       BU=BB+X;
-      BT=BU:PP;
+      BT=BU:UU;
       degree BT
     Text 
       We look for singularities of $BT$. Since the computation of singular locus is too long, we just check the rank of the jacobian matrix in one of the components of $SingSS$ and get that $BT$ is singular in that locus.

M2/Macaulay2/packages/RandomCurvesOverVerySmallFiniteFields.m2

@@ -80,13 +80,13 @@ isSmoothCurve (Ideal) := C -> (
 	dim(projectionCenter+C) != 0 or dim(projectionCenter+C) != 0) do();
         x := getSymbol"x";
 	y := getSymbol"y";	  
-	PP := kk[x_0..x_3,y_0..y_(n-5)];
-	f := map(S,PP, gens(projectionCenter) | random(S^1,S^{n-4:-1}) ); 
+	P := kk[x_0..x_3,y_0..y_(n-5)];
+	f := map(S, P, gens(projectionCenter) | random(S^1,S^{n-4:-1}) ); 
 	C' := preimage_f(C);
 	--C1'=eliminate(C' + ideal(x_0..x_3), toList(x_0..x_3));
         --if not dim(projectionCenter+C) == 0 then (use S; <<"bad projection center" <<endl; return false);
 --	use S; 
-	C1 := eliminate(C',toList(apply(n-4,i->PP_(i+4))));
+	C1 := eliminate(C',toList(apply(n-4,i->P_(i+4))));
 	 not (degree C1 == degree C)) do();
 	S1 := kk[x_0..x_3]; 
 	C2 := substitute(C1,S1);

M2/Macaulay2/packages/RationalPoints2.m2

@@ -771,8 +771,8 @@ rationalPoints(Ideal) := opts -> I -> (
                         -- shuffle and homogenize so that the first non-zero coordinate is 1
                         result = flatten table(pow_unused ELS, result, homogCoord @@ shuffle_ind);
                         -- extra points lying in a projective subspace
-                        PP := findProjPoints(ideal 0_unusedR);
-                        result = result | PP / (x->homogCoord shuffle(ind, x, ((n-unused):0_k)));
+                        PPts := findProjPoints(ideal 0_unusedR);
+                        result = result | PPts / (x->homogCoord shuffle(ind, x, ((n-unused):0_k)));
                     );
                 );
             ) else ( -- affine case
@@ -1211,7 +1211,7 @@ Description
   numbers the result will be given as a precise value.
  Example
   globalHeight {1/1,2/3,5/8}
-  PP = Proj(QQ[x,y,z]); pt = PP(1/1,2/3,5/8);
+  P2 = Proj(QQ[x,y,z]); pt = P2(1/1,2/3,5/8);
   globalHeight pt
   F = toField(QQ[u]/(u^3-5));
   globalHeight {u,u^2/5,1_F}

M2/Macaulay2/packages/ReesAlgebra.m2

@@ -449,11 +449,11 @@ intersectInP(Ideal,Ideal) := o->(I,J) ->(
          error" ring should be a polynomial ring over a field";
     X:=symbol X;
     Y:=symbol Y;
-    PP := kk[X_0..X_(n-1),Y_0..Y_(n-1)];
+    P' := kk[X_0..X_(n-1),Y_0..Y_(n-1)];
     diag := ideal apply(n, i-> X_i-Y_i);
-    toP := map(P,PP/diag,vars P | vars P);
-    inX := map(PP,P,apply(n,i->X_i));
-    inY := map(PP,P,apply(n,i->Y_i));
+    toP := map(P,P'/diag,vars P | vars P);
+    inX := map(P',P,apply(n,i->X_i));
+    inY := map(P',P,apply(n,i->Y_i));
     II := inX I + inY J;
     L := distinguished(diag,II);
     apply(L, l-> {l_0, trim toP l_1})

M2/Macaulay2/packages/ResLengthThree.m2

@@ -100,9 +100,9 @@ resLengthThreeTorAlg(ChainComplex,List) := (F,sym) -> (
    P := ambient A;
    Q := ring F;
    kk := coefficientRing first flattenRing Q;
-   PP := kk monoid P;
-   I := ideal mingens sub(ideal A, PP);
-   B := PP/I;
+   S := kk monoid P;
+   I := ideal mingens sub(ideal A, S);
+   B := S/I;
    B.cache#"l" = A.cache#"l";
    B.cache#"m" = A.cache#"m";
    B.cache#"n" = A.cache#"n";

M2/Macaulay2/packages/Schubert2/doc.m2

@@ -464,9 +464,9 @@ Node
      todd P
      chi OO_P(3)
    Text
-     The name is quite long.  Here is one way to make it shorter
+     The name is quite long.  Here is one way to make it shorter, by overwriting the @TO PP@ method:
    Example
-     PP = abstractProjectiveSpace
+     PP ZZ := abstractProjectiveSpace
      X = PP 4
    Text
      To compute the Hilbert polynomial of a sheaf on projective space, we work