From 9a33817a5f90579810ef188bd85b6fff40539b27 Mon Sep 17 00:00:00 2001
From: Federico Galetto <galetto.federico@gmail.com>
Date: Fri, 10 Jun 2022 16:10:44 -0400
Subject: [PATCH 01/11] inserted spaces around = := |

---
 Jets.m2 | 364 ++++++++++++++++++++++++++++----------------------------
 1 file changed, 182 insertions(+), 182 deletions(-)

diff --git a/Jets.m2 b/Jets.m2
index ec88175..afc7aed 100644
--- a/Jets.m2
+++ b/Jets.m2
@@ -57,7 +57,7 @@ export {
     "Saturate"
     }
 
-jetsOptions= {
+jetsOptions = {
     Projective=> false
 -- these are set up in case one needs to pass these options
 -- to jets of a RingMap
@@ -70,40 +70,40 @@ jetsOptions= {
 ---------------------------------------------------------------------------
 --create new-tier variables for jets ring
 --by appending the order n as a string to the variable names
-jetsVariables= (n,R) -> (
-    symList:= apply(gens R, baseName);
-    nString:= toString n;
+jetsVariables = (n,R) -> (
+    symList := apply(gens R, baseName);
+    nString := toString n;
     varNames:=
         for s in symList list (
 	    if instance(s,IndexedVariable) then (
-	        name:= separate("_", toString s);
-	        name#0|nString|"_"|name#1
+	        name := separate("_", toString s);
+	        name#0 | nString | "_" | name#1
             ) else (
-	        toString s|nString
+	        toString s | nString
 	    )
         );
-    varNames= apply(varNames,value)
+    varNames = apply(varNames,value)
     )
 
 --generate degree list for order n jets variables
 --this is used to create the rings of projective jets
-degGenerator= (n,R) -> (
+degGenerator = (n,R) -> (
     for d in degrees R list (
 	for l in d list n
 	)
     )
 
 --generate degrees/map for truncation ring in ideal calculation
-jetsDegrees= jetsOptions >> o -> R -> (
-    Tdegrees:= null;
-    degreeMap:= null;
+jetsDegrees = jetsOptions >> o -> R -> (
+    Tdegrees := null;
+    degreeMap := null;
     
     if o.Projective then (
-	Tdegrees= -1* {degree R_0};
-	degreeMap= d -> degree 1_R;
+	Tdegrees = -1* {degree R_0};
+	degreeMap = d -> degree 1_R;
 	) else (
-	Tdegrees= {degree 1_R};
-	degreeMap= identity;
+	Tdegrees = {degree 1_R};
+	degreeMap = identity;
 	);
     return (Tdegrees, degreeMap);
     ) 
@@ -116,118 +116,118 @@ jetsDegrees= jetsOptions >> o -> R -> (
 
 --Jets (Main Method)------------------------------------------------------
 
-jets= method(Options=>jetsOptions);
+jets = method(Options=>jetsOptions);
 
-jets(ZZ,PolynomialRing):= PolynomialRing => o -> (n,R) -> (
+jets(ZZ,PolynomialRing) := PolynomialRing => o -> (n,R) -> (
     if n<0 then error("jets order must be a non-negative integer");
     if not isCommutative R then error("jets method does not support noncommutative rings");
     
     --name to assign "storage" hashtable to be cached in the base ring
-    typeName:= if o.Projective then (projet) else (jet);
-    jetDegs:= null;--initialize degree list for jets variables
+    typeName := if o.Projective then (projet) else (jet);
+    jetDegs := null;--initialize degree list for jets variables
 
     if not R#? typeName then (
-	jetDegs= if o.Projective then degGenerator(0, R) else degrees R;
-	R#typeName= new CacheTable from {
+	jetDegs = if o.Projective then degGenerator(0, R) else degrees R;
+	R#typeName = new CacheTable from {
 	    (symbol jetsMaxOrder)=> 0,
 	    (symbol jetsRing)=> coefficientRing R[jetsVariables(0,R), 
 		                                 Join=> false,
 					 	 Degrees=> jetDegs],
 	    }
 	);
-    m:= R#typeName#jetsMaxOrder;
-    S:= R#typeName#jetsRing;
+    m := R#typeName#jetsMaxOrder;
+    S := R#typeName#jetsRing;
     
     --build jet ring tower incrementally up to order n
     if n>m then (
 	for i from m+1 to n do(
-    	    jetDegs= if o.Projective then degGenerator(i,R) else degrees R; 
-	    S= S[jetsVariables(i,R), 
+    	    jetDegs = if o.Projective then degGenerator(i,R) else degrees R; 
+	    S = S[jetsVariables(i,R), 
 		Join=> false, 
 		Degrees=> jetDegs];
             );
-     	R#typeName#jetsMaxOrder= n;
-	R#typeName#jetsRing= S;
+     	R#typeName#jetsMaxOrder = n;
+	R#typeName#jetsRing = S;
 	) else if m>n then (
 	for i from 0 to m-n-1 do (
-	    S= coefficientRing S;
+	    S = coefficientRing S;
 	    )
 	);
     
-    S#jetsInfo= new CacheTable from {
+    S#jetsInfo = new CacheTable from {
 	(symbol jetsBase)=> R,
 	(symbol Projective)=> o.Projective
 	}; 
     return S;
     )
 
-jets(ZZ,Ideal):= Ideal => o -> (n,I) -> (
+jets(ZZ,Ideal) := Ideal => o -> (n,I) -> (
     if n<0 then error("jets order must be a non-negative integer");
 
-    R:= ring I;
-    S:= null;--initializes jets ring
-    t:= local t;--initializes truncation variable
+    R := ring I;
+    S := null;--initializes jets ring
+    t := local t;--initializes truncation variable
     
-    typeName:= if o.Projective then (projet) else (jet);
+    typeName := if o.Projective then (projet) else (jet);
     
     if not I.cache#? typeName then (
-	S= jets(0,R, Projective=> o.Projective);
-	I.cache#typeName= new CacheTable from {
+	S = jets(0,R, Projective=> o.Projective);
+	I.cache#typeName = new CacheTable from {
 	    (symbol jetsMaxOrder)=> 0,
 	    (symbol jetsMatrix)=> (map(S,R,vars S)) gens I
 	    };
     	);
    
-    m:= I.cache#typeName#jetsMaxOrder;
+    m := I.cache#typeName#jetsMaxOrder;
     
     --calculate higher order entries if needed
     if n>m then (
-	S= jets(n,R, Projective=> o.Projective);
-    	(Tdegrees, degreeMap):= jetsDegrees (R, Projective=> o.Projective);
-	T:= S[t, Degrees=> Tdegrees, Join=> false]/(ideal(t^(n+1)));
+	S = jets(n,R, Projective=> o.Projective);
+    	(Tdegrees, degreeMap) := jetsDegrees (R, Projective=> o.Projective);
+	T := S[t, Degrees=> Tdegrees, Join=> false]/(ideal(t^(n+1)));
 
 	--a row matrix of substitution polynomials in t with coefficients
 	--in the jets ring. Calculated incrementally from variables of each
 	--level of the tower.
-	tempS:= S;
-	Tpolys:= sum join(
+	tempS := S;
+	Tpolys := sum join(
 	    (for i from 0 to n-1 list(
 		    promote(matrix t^(n-i),T) * vars tempS
 		    ) do (
-		    tempS= coefficientRing tempS)),
+		    tempS = coefficientRing tempS)),
 	    {promote (matrix t^0,T) * vars tempS}
 	    );
 	
-    	phi:= map(T,R,Tpolys,DegreeMap=> degreeMap);
+    	phi := map(T,R,Tpolys,DegreeMap=> degreeMap);
 
 	--a list of generators for I is obtained to avoid dropping/repeating
-	geners:= I_*;
+	geners := I_*;
     	--condition determining if all generators of the ideal are constants
-	constCond:= all(geners,isConstant);
+	constCond := all(geners,isConstant);
     	--add dummy generator to avoid loss of zeros
-	gensI:= if constCond then matrix{geners|{R_0}} else matrix{geners};
-    	(d,c):= coefficients(phi gensI);
+	gensI := if constCond then matrix{geners | {R_0}} else matrix{geners};
+    	(d,c) := coefficients(phi gensI);
     	--remove dummy generators if necessary
 	if constCond then (
-		L:= entries c;
-		c= matrix (for l in L list drop(l,-1));
+		L := entries c;
+		c = matrix (for l in L list drop(l,-1));
 		);
 
-	resultMatrix:= lift(c,S);
+	resultMatrix := lift(c,S);
 
 	--update value in ideal cache
-	I.cache#typeName#jetsMatrix= resultMatrix;
-	I.cache#typeName#jetsMaxOrder= n;
+	I.cache#typeName#jetsMatrix = resultMatrix;
+	I.cache#typeName#jetsMaxOrder = n;
 	m=n;
 	);
    
     --retrieve ideal of appropriate order
-    JMatrix:= I.cache#typeName#jetsMatrix; 
+    JMatrix := I.cache#typeName#jetsMatrix; 
     if zero JMatrix then return ideal(0_(jets(n,R)));
-    f:= map(jets(n,R,Projective=> o.Projective),jets(m,R, Projective=> o.Projective));
-    J:= f ideal (JMatrix^{m-n..m});
+    f := map(jets(n,R,Projective=> o.Projective),jets(m,R, Projective=> o.Projective));
+    J := f ideal (JMatrix^{m-n..m});
 
-    J.cache#jetsInfo= new CacheTable from {
+    J.cache#jetsInfo = new CacheTable from {
 	jetsBase=> I,
 	Projective=> o.Projective
 	};
@@ -235,19 +235,19 @@ jets(ZZ,Ideal):= Ideal => o -> (n,I) -> (
     return J;
     )
 
-jets(ZZ,QuotientRing):= QuotientRing => o -> (n,R) -> (
+jets(ZZ,QuotientRing) := QuotientRing => o -> (n,R) -> (
     if n<0 then error("jets order must be a non-negative integer");
-    splitQuotient:= presentation R;
-    ambientRing:= ring splitQuotient;
-    base:= null; --jets ring to be used in quotient
-    modI:= null; --jets ideal to be used in quotient
-    Q:= null; --variable to store quotient ring
+    splitQuotient := presentation R;
+    ambientRing := ring splitQuotient;
+    base := null; --jets ring to be used in quotient
+    modI := null; --jets ideal to be used in quotient
+    Q := null; --variable to store quotient ring
     
-    typeName:= if o.Projective then (projet) else (jet);
+    typeName := if o.Projective then (projet) else (jet);
     if not R#? typeName then (
-	base= jets(0, ambientRing, Projective=> o.Projective);
-	modI= jets(0, ideal(splitQuotient), Projective=> o.Projective);
-	R#typeName= new CacheTable from {
+	base = jets(0, ambientRing, Projective=> o.Projective);
+	modI = jets(0, ideal(splitQuotient), Projective=> o.Projective);
+	R#typeName = new CacheTable from {
 	    (symbol jetsRing)=> new CacheTable from {
 		0 => base/modI
 		},
@@ -258,13 +258,13 @@ jets(ZZ,QuotientRing):= QuotientRing => o -> (n,R) -> (
     --ring and a jets ideal.  Each order of the quotient is stored in a
     --cache table with the integer value of the order as the key    
     if R#typeName#jetsRing#? n then (
-	Q= R#typeName#jetsRing#n;
+	Q = R#typeName#jetsRing#n;
 	) else (
-	base= jets(n, ambientRing, Projective=> o.Projective);
-	modI= jets(n, ideal(splitQuotient), Projective=> o.Projective);
-	Q= base/modI;
-	R#typeName#jetsRing#n= Q;
-	Q#jetsInfo= new CacheTable from {
+	base = jets(n, ambientRing, Projective=> o.Projective);
+	modI = jets(n, ideal(splitQuotient), Projective=> o.Projective);
+	Q = base/modI;
+	R#typeName#jetsRing#n = Q;
+	Q#jetsInfo = new CacheTable from {
     	    jetsBase=> R,
        	    Projective=> o.Projective
 	    }
@@ -274,15 +274,15 @@ jets(ZZ,QuotientRing):= QuotientRing => o -> (n,R) -> (
     )
 
 
-jets(ZZ,RingMap):= RingMap => o -> (n,phi) -> (
+jets(ZZ,RingMap) := RingMap => o -> (n,phi) -> (
     if n<0 then error("jets order must be a non-negative integer");
-    I:= ideal(phi.matrix);
-    typeName:= if o.Projective then (projet) else (jet);
+    I := ideal(phi.matrix);
+    typeName := if o.Projective then (projet) else (jet);
     
     -- check whether jets have been calculated for this map
     if (not phi.cache#? typeName) then (
 	jets(0,I, Projective=> o.Projective);
-	phi.cache#typeName= new CacheTable from {
+	phi.cache#typeName = new CacheTable from {
 	    (symbol jetsMaxOrder)=> 0,
     	    (symbol jetsMatrix)=> (map(jets(0,phi.target, Projective=> o.Projective),
 		    	    	       jets(0,phi.source, Projective=> o.Projective),
@@ -290,31 +290,31 @@ jets(ZZ,RingMap):= RingMap => o -> (n,phi) -> (
 	    };
 	);
 
-    JR:= jets(n,phi.source, Projective=> o.Projective);
-    JS:= jets(n,phi.target, Projective=> o.Projective);
-    targets:= null;
+    JR := jets(n,phi.source, Projective=> o.Projective);
+    JS := jets(n,phi.target, Projective=> o.Projective);
+    targets := null;
     
     --check whether lower order jets have already been calculated
-    m:= phi.cache#typeName#jetsMaxOrder;
+    m := phi.cache#typeName#jetsMaxOrder;
     if m < n then (
 	jets(n,I, Projective=> o.Projective);
-    	targets= (I.cache#typeName#jetsMatrix);	
-	phi.cache#typeName#jetsMaxOrder= n;
-	phi.cache#typeName#jetsMatrix= targets;
+    	targets = (I.cache#typeName#jetsMatrix);	
+	phi.cache#typeName#jetsMaxOrder = n;
+	phi.cache#typeName#jetsMatrix = targets;
     	) else (
-    	targets= phi.cache#typeName#jetsMatrix^{m-n..m};
+    	targets = phi.cache#typeName#jetsMatrix^{m-n..m};
 	--need to lift 'targets' to jets of order m-n
 	targets=lift(targets,JS);
 	);
 
 --DegreeMap and DegreeLift options are set up but may not work as expected
-    psi:= map(JS,JR,
+    psi := map(JS,JR,
 	flatten transpose targets
 --	,DegreeLift=> degreeLift,
 --	DegreeMap=> degreeMap
     );
 
-    psi.cache#jetsInfo= new CacheTable from {
+    psi.cache#jetsInfo = new CacheTable from {
     	jetsBase=> phi,
     	Projective=> o.Projective
     	};	  
@@ -322,7 +322,7 @@ jets(ZZ,RingMap):= RingMap => o -> (n,phi) -> (
     return psi;
    )
 
-jets(ZZ,Graph):= Graph => o -> (n,G) -> (
+jets(ZZ,Graph) := Graph => o -> (n,G) -> (
     if n<0 then error("jets order must be a non-negative integer");
     --get the list of edges of the jets of the (hyper)graph
     --ring is flattened because graphs don't play well with towers of rings
@@ -331,7 +331,7 @@ jets(ZZ,Graph):= Graph => o -> (n,G) -> (
     graph E
     )
 
-jets(ZZ,HyperGraph):= HyperGraph => o -> (n,G) -> (
+jets(ZZ,HyperGraph) := HyperGraph => o -> (n,G) -> (
     if n<0 then error("jets order must be a non-negative integer");
     --get the list of edges of the jets of the (hyper)graph
     --ring is flattened because graphs don't play well with towers of rings
@@ -340,10 +340,10 @@ jets(ZZ,HyperGraph):= HyperGraph => o -> (n,G) -> (
     hyperGraph E
     )
 
-jets(ZZ,AffineVariety):= o -> (n,V) -> (
+jets(ZZ,AffineVariety) := o -> (n,V) -> (
     if n<0 then error("jets order must be a non-negative integer");
-    R:= ring V;
-    JR:= jets(n,R,Projective=> o.Projective);
+    R := ring V;
+    JR := jets(n,R,Projective=> o.Projective);
     if o.Projective then return Proj JR else return Spec JR;
     )
 
@@ -351,18 +351,18 @@ jets(ZZ,AffineVariety):= o -> (n,V) -> (
 
 --to potentially reduce computation time for monomial jet ideals  
 --(see documentation)
-jetsRadical= method(TypicalValue=>Ideal);
+jetsRadical = method(TypicalValue=>Ideal);
 
-jetsRadical(ZZ,Ideal):= (n,I) -> (
+jetsRadical(ZZ,Ideal) := (n,I) -> (
 
     if n<0 then error("jets order must be a non-negative integer");
     
     if isMonomialIdeal I then (
-	baseIdeal:= jets(n,I);
-	R:= ring I;
-	gensList:= flatten entries gens baseIdeal;
-	termList:= apply(gensList, t-> terms(coefficientRing R, t));
-	squarefreeGens:= apply(apply(flatten termList, support),product);
+	baseIdeal := jets(n,I);
+	R := ring I;
+	gensList := flatten entries gens baseIdeal;
+	termList := apply(gensList, t-> terms(coefficientRing R, t));
+	squarefreeGens := apply(apply(flatten termList, support),product);
 	ideal(squarefreeGens)
 	) else (
 	radical jets(n,I)
@@ -372,10 +372,10 @@ jetsRadical(ZZ,Ideal):= (n,I) -> (
 
 --to create a map sending elements of a jets ring to a jets ring of
 --higher order
-jetsProjection= method(Options=>jetsOptions,TypicalValue=>RingMap);
+jetsProjection = method(Options=>jetsOptions,TypicalValue=>RingMap);
 
-jetsProjection(ZZ,ZZ,PolynomialRing):=
-jetsProjection(ZZ,ZZ,QuotientRing):= o -> (t,s,R) -> (
+jetsProjection(ZZ,ZZ,PolynomialRing) :=
+jetsProjection(ZZ,ZZ,QuotientRing) := o -> (t,s,R) -> (
 
     if t < s then error("first argument must be less than or equal to the second");    
     if t<0 or s<0 then error("jets orders must be non-negative integers");
@@ -432,7 +432,7 @@ beginDocumentation()
 -- TESTS
 ----------------------------------------------------------------------
 TEST ///
-    R= QQ[x,y,z];
+    R = QQ[x,y,z];
     assert(degrees jets(2,R)==={{1}, {1}, {1}})
     assert(degrees jets(2,R,Projective=> true) === {{2}, {2}, {2}})
     I=ideal(y-x^2,z-x^3);
@@ -442,17 +442,17 @@ TEST ///
 
 --for non uniform degrees
 TEST ///
-    R= QQ[x,y,z, Degrees=> {2,3,1}];
+    R = QQ[x,y,z, Degrees=> {2,3,1}];
     assert(degrees jets(2,R)==={{2}, {3}, {1}})
     assert(degrees jets(2,R,Projective=> true) === {{2}, {2}, {2}})
-    I= ideal(x*y, x*z^2);
-    J= ideal(x^3-y*z^3, y+x*z);
+    I = ideal(x*y, x*z^2);
+    J = ideal(x^3-y*z^3, y+x*z);
     assert(isHomogeneous jets(2,I))
     assert(isHomogeneous jets(2,I,Projective=>true))
     assert(isHomogeneous jets(2,J))
     assert(isHomogeneous jets(2,J,Projective=>true))
-    X= radical jets(2,I);
-    Y= jetsRadical(2,I);
+    X = radical jets(2,I);
+    Y = jetsRadical(2,I);
     assert(X == Y)
     assert(mingens X === mingens Y);
 ///
@@ -460,10 +460,10 @@ TEST ///
 TEST ///
     R=QQ[x,y, Degrees=> {2,3}];
     S=QQ[a,b,c, Degrees=> {1,1,2}]
-    phi= map(S,R, {a^2 + c, b*c});
-    f= jets(2,phi);
-    testx= c2+2*a0*a2+a1^2;
-    testy= b0*c2+c0*b2+b1*c1;
+    phi = map(S,R, {a^2 + c, b*c});
+    f = jets(2,phi);
+    testx = c2+2*a0*a2+a1^2;
+    testy = b0*c2+c0*b2+b1*c1;
     assert(f x2===testx)
     assert(f y2===testy)
     assert(isHomogeneous jets(3,phi))
@@ -473,17 +473,17 @@ TEST ///
 --for ideals with constant generators
 TEST ///
     R=QQ[x]
-    I0= ideal(2_R)
+    I0 = ideal(2_R)
     Ftest0=jets(2,I0)
     assert(Ftest0==jets(2,R))
-    I1= ideal(2_R,x)
+    I1 = ideal(2_R,x)
     Ftest1=jets(2,I1)
-    assert(Ftest1== jets(2,R))
+    assert(Ftest1 == jets(2,R))
     S=ZZ[x]
-    J0= ideal(2_S)
-    Ztest0= jets(2,J0)
+    J0 = ideal(2_S)
+    Ztest0 = jets(2,J0)
     assert(Ztest0!=jets(2,S))
-    J1= ideal(2_S,x) 
+    J1 = ideal(2_S,x) 
     Ztest1=jets(2,J1)
     assert(Ztest1!=jets(2,S))
 ///
@@ -501,36 +501,36 @@ TEST ///
 --for quotients and varieties
 TEST ///
     R=QQ[x,y]
-    I= ideal(y^2,x^3)
+    I = ideal(y^2,x^3)
     Q=R/I
-    JR= jets(2,R)
-    JI= jets(2,I)
-    JQ= jets(2,Q)
+    JR = jets(2,R)
+    JI = jets(2,I)
+    JQ = jets(2,Q)
     assert(JR===ambient JQ)
     assert(JI===ideal JQ)
     assert(presentation (JR/JI)===presentation JQ)
-    V= Spec Q
-    JV= jets(2,V)
+    V = Spec Q
+    JV = jets(2,V)
     assert(ring JV===JQ)   
 ///
 
 --for graphs
 TEST ///
     R=QQ[x,y,z]
-    G= graph(R,{{x,y},{y,z},{x,z}})
-    JG= jets(1,G)
-    JR= jets(1,R)
+    G = graph(R,{{x,y},{y,z},{x,z}})
+    JG = jets(1,G)
+    JR = jets(1,R)
     use ring JG
-    test= {{x0,y0},{x0,z0},{y0,z0},{x1,y0},{x1,z0},{y1,x0},{y1,z0},{z1,x0},{z1,y0}}
+    test = {{x0,y0},{x0,z0},{y0,z0},{x1,y0},{x1,z0},{y1,x0},{y1,z0},{z1,x0},{z1,y0}}
     assert((set edges JG) === (set test))
 ///
 
 --for projections
 TEST ///
     R=QQ[x,y,z]
-    I= ideal(y-x^2,z-x^3)
-    JI= jets(1,I)
-    p= jetsProjection(3,1,R)
+    I = ideal(y-x^2,z-x^3)
+    JI = jets(1,I)
+    p = jetsProjection(3,1,R)
     assert(ring p JI === jets(3,R))
 ///
 ----------------------------------------------------------------------
@@ -612,7 +612,7 @@ Node
 	    
 	    For polynomial rings, data is stored under @TT "*.jet"@.
     	Example
-	    R= QQ[x,y]
+	    R = QQ[x,y]
 	    R.?jet
 	    jets(3,R)
 	    R.?jet
@@ -628,7 +628,7 @@ Node
 	    Generators for lower orders are recovered from this matrix
 	    without additional computations.
     	Example
-	    I= ideal (x^2 - y)
+	    I = ideal (x^2 - y)
 	    I.cache.?jet
 	    elapsedTime jets(3,I)
 	    I.cache.?jet
@@ -641,7 +641,7 @@ Node
 	    that is stored separately under @TT "*.jet.jetsRing"@
 	    (order zero jets are always included by default).
     	Example
-	    Q= R/I
+	    Q = R/I
 	    Q.?jet
 	    jets(3,Q)
 	    Q.?jet
@@ -655,8 +655,8 @@ Node
 	    Lower orders map are recovered from this matrix
 	    without additional computations.
     	Example
-	    S= QQ[t]
-	    f= map(S,Q,{t,t^2})
+	    S = QQ[t]
+	    f = map(S,Q,{t,t^2})
 	    isWellDefined f
 	    f.cache.?jet
 	    elapsedTime jets(3,f)
@@ -704,8 +704,8 @@ Node
 	    in all lower orders.  The grading or multigrading of the jets ring 
 	    follows from that of the base ring.
     	Example	    
-	    R= QQ[x,y,z,Degrees=>{2,1,3}]
-	    JR= jets(2,R)
+	    R = QQ[x,y,z,Degrees=>{2,1,3}]
+	    JR = jets(2,R)
 	    describe JR
     	    degrees (flattenRing JR)_0	    
     	Text
@@ -715,7 +715,7 @@ Node
 	    	Jets via Hasse-Schmidt Derivations")@.
     	Example
 	    R=QQ[x,y,z,Degrees=>{2,1,3}]
-	    JR= jets(2,R,Projective=>true)
+	    JR = jets(2,R,Projective=>true)
 	    degrees (flattenRing JR)_0
     	Text
 	    The convention for labeling variables in the jets of polynomial ring
@@ -723,7 +723,7 @@ Node
 	    base ring. Existing subscripts are preserved.
     	Example
 	    A=QQ[a_1..a_3]
-	    JA= jets(1,A)
+	    JA = jets(1,A)
 	    describe JA
     	Text
 	    Note that the coefficient ring of the polynomial ring does not need
@@ -732,7 +732,7 @@ Node
     	Example
 	    Zi=ZZ[i]/ideal(i^2+1)
 	    B=Zi[b_1..b_3]
-	    JB= jets(1,B)
+	    JB = jets(1,B)
 	    describe JB
     Caveat
     	With @TT "Projective=>true"@ the jet variables of order zero have degree 0,
@@ -758,9 +758,9 @@ Node
 	    This function is provided by the package
 	    @TO Jets@.
     	Example	    
-	    R= QQ[x,y]
-	    I= ideal (x^3 + y^3 - 3*x*y)
-    	    J= jets(3,I);
+	    R = QQ[x,y]
+	    I = ideal (x^3 + y^3 - 3*x*y)
+    	    J = jets(3,I);
 	    netList J_*
 	Text
 	    When the @TO [jets,Projective]@ option is set to true, the degree
@@ -770,11 +770,11 @@ Node
 	    As a result, the jets of any ideal will be homogeneous regardless
 	    of the homogeneity of the base ideal, or that of its affine jets.
 	Example
-	    R= QQ[x,y,z]
-	    I= ideal (y-x^2, z-x^3)
-	    JI= jets(2,I)
+	    R = QQ[x,y,z]
+	    I = ideal (y-x^2, z-x^3)
+	    JI = jets(2,I)
 	    isHomogeneous JI
-	    JIproj= jets(2,I,Projective=>true)
+	    JIproj = jets(2,I,Projective=>true)
 	    isHomogeneous JIproj
     Caveat
     	With @TT "Projective=>true"@ the jet variables of order zero have degree 0,
@@ -800,10 +800,10 @@ Node
 	    @TO (jets,ZZ,PolynomialRing)@ of the ambient ring of @TT "Q"@ with 
 	    @TO (jets,ZZ,Ideal)@ of the ideal defining @TT "Q"@
     	Example	    
-	    R= QQ[x,y];
-	    I= ideal(y^2-x^3);
-    	    Q= R/I;
-	    JQ= jets(2,Q);
+	    R = QQ[x,y];
+	    I = ideal(y^2-x^3);
+    	    Q = R/I;
+	    JQ = jets(2,Q);
 	    describe JQ
     Caveat
     	Forming quotients triggers a Groebner basis computation, which may be time consuming.
@@ -826,20 +826,20 @@ Node
 	    This function is provided by the package
 	    @TO Jets@.
     	Example	    
-	    R= QQ[x,y,z]
-	    S= QQ[t]
-	    f= map(S,R,{t,t^2,t^3})
-	    Jf= jets(2,f);
+	    R = QQ[x,y,z]
+	    S = QQ[t]
+	    f = map(S,R,{t,t^2,t^3})
+	    Jf = jets(2,f);
 	    matrix Jf
     	Text
 	    This function can also be applied when the source and/or the target
 	    of the ring homomorphism are quotients of a polynomial ring
     	Example
-	    I= ideal(y-x^2,z-x^3)
-	    Q= R/I
-	    g= map(S,Q,{t,t^2,t^3})
+	    I = ideal(y-x^2,z-x^3)
+	    Q = R/I
+	    g = map(S,Q,{t,t^2,t^3})
 	    isWellDefined g
-	    Jg= jets(2,g);
+	    Jg = jets(2,g);
 	    isWellDefined Jg
 
 Node
@@ -869,15 +869,15 @@ Node
 	    the @TO EdgeIdeals@ package, which is automatically exported
 	    when loading @TO Jets@.
     	Example	    
-	    R= QQ[x,y,z]
-	    G= graph(R,{{x,y},{y,z}})
-	    JG= jets(2,G)
+	    R = QQ[x,y,z]
+	    G = graph(R,{{x,y},{y,z}})
+	    JG = jets(2,G)
 	    vertexCovers JG
 	Text
 	    We can also calculate the jets of a  @TO "EdgeIdeals::HyperGraph"@.
 	Example
-	    R= QQ[u,v,w,x,y,z]
-	    H= hyperGraph(R,{{u},{v,w},{x,y,z}})
+	    R = QQ[u,v,w,x,y,z]
+	    H = hyperGraph(R,{{u},{v,w},{x,y,z}})
     	    jets(1,H)
     Caveat
         Rings of jets are usually constructed as towers of rings with
@@ -905,8 +905,8 @@ Node
 	    Returns the jets of an @TO AffineVariety@ as an @TO AffineVariety@. 
 	Example
 	    R=QQ[x,y]
-	    I= ideal(y^2-x^2*(x+1))
-	    A= Spec(R/I)
+	    I = ideal(y^2-x^2*(x+1))
+	    A = Spec(R/I)
 	    jets(2,A)
     	Text
 	    If @TO [jets,Projective]@ is set to true, then jets are computed
@@ -1100,20 +1100,20 @@ Node
 	    
 	    An ideal generated by squarefree monomials:
 	Example
-	    R= QQ[x,y,z]
-	    I= ideal (x*z, y*z)
-	    J= jets(1,I); 
-	    MP= radical J;
-	    GS= jetsRadical(1,I);
+	    R = QQ[x,y,z]
+	    I = ideal (x*z, y*z)
+	    J = jets(1,I); 
+	    MP = radical J;
+	    GS = jetsRadical(1,I);
 	    netList sort MP_* | netList sort GS_*
     	Text
 	    An ideal with genereators which are not squarefree:
 	Example
-	    R= QQ[x,y,z]
-	    I= ideal(x*y^2, z*x, x^3)
-	    J= jets(1,I); 
-	    MP= radical J;
-	    GS= jetsRadical(1,I);
+	    R = QQ[x,y,z]
+	    I = ideal(x*y^2, z*x, x^3)
+	    J = jets(1,I); 
+	    MP = radical J;
+	    GS = jetsRadical(1,I);
 	    netList sort MP_* | netList sort GS_*
 	    MP == GS
 
@@ -1144,9 +1144,9 @@ Node
 	    
     	Example
 	    R=QQ[x,y]
-	    f= jetsProjection(5,2,R)
+	    f = jetsProjection(5,2,R)
 	    use jets(2,R)
-	    p= (x2 + 2*x1*y1 + x0*y2^2)
+	    p = (x2 + 2*x1*y1 + x0*y2^2)
 	    f p
 
 Node
@@ -1244,8 +1244,8 @@ Node
     	Text
 	    Shorthand for @TO jets@
 	Example
-	    R= QQ[x,y]
-	    I= ideal(y^2-x^3)
+	    R = QQ[x,y]
+	    I = ideal(y^2-x^3)
 	    JJ_2 R
 	    JJ_2 I
 

From 0cd6e37e1c01002d9624cb7f1ba1eeac86cede94 Mon Sep 17 00:00:00 2001
From: Federico Galetto <galetto.federico@gmail.com>
Date: Fri, 10 Jun 2022 16:26:16 -0400
Subject: [PATCH 02/11] removed return at the end of functions

---
 Jets.m2 | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Jets.m2 b/Jets.m2
index afc7aed..0c07531 100644
--- a/Jets.m2
+++ b/Jets.m2
@@ -105,7 +105,7 @@ jetsDegrees = jetsOptions >> o -> R -> (
 	Tdegrees = {degree 1_R};
 	degreeMap = identity;
 	);
-    return (Tdegrees, degreeMap);
+    (Tdegrees, degreeMap)
     ) 
 
 
@@ -158,7 +158,7 @@ jets(ZZ,PolynomialRing) := PolynomialRing => o -> (n,R) -> (
 	(symbol jetsBase)=> R,
 	(symbol Projective)=> o.Projective
 	}; 
-    return S;
+    S
     )
 
 jets(ZZ,Ideal) := Ideal => o -> (n,I) -> (
@@ -232,7 +232,7 @@ jets(ZZ,Ideal) := Ideal => o -> (n,I) -> (
 	Projective=> o.Projective
 	};
     
-    return J;
+    J
     )
 
 jets(ZZ,QuotientRing) := QuotientRing => o -> (n,R) -> (
@@ -270,7 +270,7 @@ jets(ZZ,QuotientRing) := QuotientRing => o -> (n,R) -> (
 	    }
 	);
     
-    return Q;
+    Q
     )
 
 
@@ -319,7 +319,7 @@ jets(ZZ,RingMap) := RingMap => o -> (n,phi) -> (
     	Projective=> o.Projective
     	};	  
     
-    return psi;
+   psi
    )
 
 jets(ZZ,Graph) := Graph => o -> (n,G) -> (

From c255165e0a51389b4f10da736d76a76b28e6acf3 Mon Sep 17 00:00:00 2001
From: Federico Galetto <galetto.federico@gmail.com>
Date: Fri, 10 Jun 2022 16:33:37 -0400
Subject: [PATCH 03/11] substituted referee's jetsVariable function

---
 Jets.m2 | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/Jets.m2 b/Jets.m2
index 0c07531..d06c889 100644
--- a/Jets.m2
+++ b/Jets.m2
@@ -70,6 +70,7 @@ jetsOptions = {
 ---------------------------------------------------------------------------
 --create new-tier variables for jets ring
 --by appending the order n as a string to the variable names
+-*
 jetsVariables = (n,R) -> (
     symList := apply(gens R, baseName);
     nString := toString n;
@@ -84,6 +85,19 @@ jetsVariables = (n,R) -> (
         );
     varNames = apply(varNames,value)
     )
+*-
+jetsVariables= (n,R) -> (
+    symList := apply(gens R, baseName);
+    nString := toString n;
+    for s in symList list (
+        if instance(s,IndexedVariable) then (
+	    name := (toString s#0) | nString;
+	    (getSymbol name)_(s#1)
+            ) else (
+	    getSymbol (toString s | nString)
+	    )
+    	)
+    )
 
 --generate degree list for order n jets variables
 --this is used to create the rings of projective jets

From 98d7e0057b63bb2a2a686d4eec04ad32ea5309f4 Mon Sep 17 00:00:00 2001
From: Federico Galetto <galetto.federico@gmail.com>
Date: Fri, 10 Jun 2022 16:39:33 -0400
Subject: [PATCH 04/11] more spaces around == and === (in tests and docs)

---
 Jets.m2 | 88 ++++++++++++++++++++++++++++-----------------------------
 1 file changed, 44 insertions(+), 44 deletions(-)

diff --git a/Jets.m2 b/Jets.m2
index d06c889..af0fa33 100644
--- a/Jets.m2
+++ b/Jets.m2
@@ -447,7 +447,7 @@ beginDocumentation()
 ----------------------------------------------------------------------
 TEST ///
     R = QQ[x,y,z];
-    assert(degrees jets(2,R)==={{1}, {1}, {1}})
+    assert(degrees jets(2,R) === {{1}, {1}, {1}})
     assert(degrees jets(2,R,Projective=> true) === {{2}, {2}, {2}})
     I=ideal(y-x^2,z-x^3);
     assert(not(isHomogeneous jets(2,I)))
@@ -457,7 +457,7 @@ TEST ///
 --for non uniform degrees
 TEST ///
     R = QQ[x,y,z, Degrees=> {2,3,1}];
-    assert(degrees jets(2,R)==={{2}, {3}, {1}})
+    assert(degrees jets(2,R) === {{2}, {3}, {1}})
     assert(degrees jets(2,R,Projective=> true) === {{2}, {2}, {2}})
     I = ideal(x*y, x*z^2);
     J = ideal(x^3-y*z^3, y+x*z);
@@ -478,8 +478,8 @@ TEST ///
     f = jets(2,phi);
     testx = c2+2*a0*a2+a1^2;
     testy = b0*c2+c0*b2+b1*c1;
-    assert(f x2===testx)
-    assert(f y2===testy)
+    assert(f x2 === testx)
+    assert(f y2 === testy)
     assert(isHomogeneous jets(3,phi))
     assert(isHomogeneous jets(3,phi,Projective=>true))
 ///
@@ -489,7 +489,7 @@ TEST ///
     R=QQ[x]
     I0 = ideal(2_R)
     Ftest0=jets(2,I0)
-    assert(Ftest0==jets(2,R))
+    assert(Ftest0 == jets(2,R))
     I1 = ideal(2_R,x)
     Ftest1=jets(2,I1)
     assert(Ftest1 == jets(2,R))
@@ -508,8 +508,8 @@ TEST ///
     I=ideal(y^2-x^3)
     PC=principalComponent(2,I)
     P=primaryDecomposition jets(2,I)
-    C=first select(P,c -> degree c==6)
-    assert(PC==C)
+    C=first select(P,c -> degree c == 6)
+    assert(PC == C)
 ///
 
 --for quotients and varieties
@@ -520,12 +520,12 @@ TEST ///
     JR = jets(2,R)
     JI = jets(2,I)
     JQ = jets(2,Q)
-    assert(JR===ambient JQ)
-    assert(JI===ideal JQ)
-    assert(presentation (JR/JI)===presentation JQ)
+    assert(JR == =ambient JQ)
+    assert(JI == =ideal JQ)
+    assert(presentation (JR/JI) == =presentation JQ)
     V = Spec Q
     JV = jets(2,V)
-    assert(ring JV===JQ)   
+    assert(ring JV === JQ)   
 ///
 
 --for graphs
@@ -728,7 +728,7 @@ Node
 	    Proposition 6.6 (c) of @arXiv("math/0407113","P. Vojta,
 	    	Jets via Hasse-Schmidt Derivations")@.
     	Example
-	    R=QQ[x,y,z,Degrees=>{2,1,3}]
+	    R = QQ[x,y,z,Degrees=>{2,1,3}]
 	    JR = jets(2,R,Projective=>true)
 	    degrees (flattenRing JR)_0
     	Text
@@ -736,7 +736,7 @@ Node
 	    is to append the order of the jets to name of the variables in the
 	    base ring. Existing subscripts are preserved.
     	Example
-	    A=QQ[a_1..a_3]
+	    A = QQ[a_1..a_3]
 	    JA = jets(1,A)
 	    describe JA
     	Text
@@ -744,8 +744,8 @@ Node
 	    to be a field. The jets of the input polynomial ring will be a
 	    polynomial ring with the same coefficient ring as the input.
     	Example
-	    Zi=ZZ[i]/ideal(i^2+1)
-	    B=Zi[b_1..b_3]
+	    Zi = ZZ[i]/ideal(i^2+1)
+	    B = Zi[b_1..b_3]
 	    JB = jets(1,B)
 	    describe JB
     Caveat
@@ -918,7 +918,7 @@ Node
     	Text
 	    Returns the jets of an @TO AffineVariety@ as an @TO AffineVariety@. 
 	Example
-	    R=QQ[x,y]
+	    R = QQ[x,y]
 	    I = ideal(y^2-x^2*(x+1))
 	    A = Spec(R/I)
 	    jets(2,A)
@@ -1157,7 +1157,7 @@ Node
 	    Throws an error if @TT "t<s"@.
 	    
     	Example
-	    R=QQ[x,y]
+	    R = QQ[x,y]
 	    f = jetsProjection(5,2,R)
 	    use jets(2,R)
 	    p = (x2 + 2*x1*y1 + x0*y2^2)
@@ -1214,18 +1214,18 @@ Node
 	    in the affine plane. We compute the principal component of the
 	    jets of order two.
     	Example
-	    R=QQ[x,y]
-	    I=ideal(x*y*(x+y-1))
-	    PC=principalComponent(2,I)
+	    R = QQ[x,y]
+	    I = ideal(x*y*(x+y-1))
+	    PC = principalComponent(2,I)
     	Text
 	    Despite the name, the principal component need not be a component
 	    of the jet scheme (i.e., it need not be irreducible). In this example,
 	    the principal component has degree 3 and is the union of three components
 	    of degree 1.
     	Example
-	    P=primaryDecomposition jets(2,I)
-	    any(P,c -> c==PC)
-	    PC==intersect(select(P,c -> degree c==1))
+	    P = primaryDecomposition jets(2,I)
+	    any(P,c -> c == PC)
+	    PC == intersect(select(P,c -> degree c == 1))
     Caveat
     	This function requires computation of a singular locus,
 	a saturation (or quotient), and jets, with each step being
@@ -1274,9 +1274,9 @@ Node
 	    "R.A. Goward and K.E. Smith, The jet scheme of a monomial scheme")@ [GS06],
 	    the ideal of jets of a monomial ideal is typically not a monomial ideal.
 	Example
-	    R=QQ[x,y,z]
-	    I=ideal(x*y*z)
-	    J2I=jets(2,I)
+	    R = QQ[x,y,z]
+	    I = ideal(x*y*z)
+	    J2I = jets(2,I)
 	Text
 	    However, by [GS06, Theorem 3.1], the radical is always a (squarefree) monomial ideal. In
 	    fact, the proof of [GS06, Theorem 3.2] shows that the radical is generated by the terms of the
@@ -1296,11 +1296,11 @@ Node
 	    the second jet scheme of the example above. Note that we need to flatten the polynomial ring
 	    of jets because the @TT "LocalRings"@ package does not allow towers of rings.
 	Example
-	    P=minimalPrimes J2I
-	    (A,f)=flattenRing ring J2I
+	    P = minimalPrimes J2I
+	    (A,f) = flattenRing ring J2I
 	    needsPackage "LocalRings"
-	    M=cokernel gens f J2I
-	    mult=for p in P list (
+	    M = cokernel gens f J2I
+	    mult = for p in P list (
 		Rp := localRing(A,f p);
 		length(M ** Rp)
 		);
@@ -1332,13 +1332,13 @@ Node
       	    IMG ("src" => replace("PKG", "Jets", currentLayout#"package") | "graph.png",
 		"alt" => "a graph on 5 vertices", "height" => "300")
 	Example
-	    R=QQ[a..e]
-	    G=graph({{a,c},{a,d},{a,e},{b,c},{b,d},{b,e},{c,e}})
+	    R = QQ[a..e]
+	    G = graph({{a,c},{a,d},{a,e},{b,c},{b,d},{b,e},{c,e}})
 	Text
 	    We compute the first and second order jets, and list their edges.
     	Example
-	    J1G=jets(1,G); netList pack(7,edges J1G)
-	    J2G=jets(2,G); netList pack(7,edges J2G)
+	    J1G = jets(1,G); netList pack(7,edges J1G)
+	    J2G = jets(2,G); netList pack(7,edges J2G)
 	Text
 	    As predicted in [GHW21, Theorem 3.1], all jets have the same
 	    chromatic number.
@@ -1375,14 +1375,14 @@ Node
 	    vanishing of minors of size $r+1$.  We illustrate computationally some
 	    of the known results about jets.
 	Example
-	    R=QQ[x_(1,1)..x_(3,3)]
-	    G=genericMatrix(R,3,3)
+	    R = QQ[x_(1,1)..x_(3,3)]
+	    G = genericMatrix(R,3,3)
 	Text
 	    Since $X_0$ is a single point, its first jet scheme consists of a
 	    single (smooth) point.
     	Example
-	    I1=minors(1,G)
-	    JI1=jets(1,I1)
+	    I1 = minors(1,G)
+	    JI1 = jets(1,I1)
 	    dim JI1, isPrime JI1
 	Text
 	    The jets of $X_2$ (the variety of maximal minors) are known to be
@@ -1391,8 +1391,8 @@ Node
 		or Corollary 4.13 in @HREF("https://doi.org/10.1090/S0002-9947-2012-05564-4",
 		    "R. Docampo, Arcs on determinantal varieties")@ [Doc13]).
 	Example
-	    I3=minors(3,G)
-	    JI3=jets(1,I3)
+	    I3 = minors(3,G)
+	    JI3 = jets(1,I3)
 	    isPrime JI3
     	Text
     	    As for the case of $2\times 2$ minors, Theorem 5.1 in [KS05], Theorem 5.1 in
@@ -1402,9 +1402,9 @@ Node
 	    the components further. As expected, the first jet scheme of $X_1$ has
 	    two components, one of them an affine space.
     	Example
-	    I2=minors(2,G)
-	    JI2=jets(1,I2)
-	    P=primaryDecomposition JI2; #P
+	    I2 = minors(2,G)
+	    JI2 = jets(1,I2)
+	    P = primaryDecomposition JI2; #P
 	    P_1
     	Text
 	    The other component is the so-called principal component of the jet
@@ -1414,7 +1414,7 @@ Node
 	    @TO principalComponent@ method with the option
 	    @TO [principalComponent,Saturate]@ set to @TT "false"@ to speed up computations.
     	Example
-	    radical JI2==JI2
+	    radical JI2 == JI2
 	    P_0 == principalComponent(1,I2,Saturate=>false)
 	    P_0
     	Text

From 89f979d41705ee072745fbe4a5480bc36f085290 Mon Sep 17 00:00:00 2001
From: Federico Galetto <galetto.federico@gmail.com>
Date: Fri, 10 Jun 2022 16:58:53 -0400
Subject: [PATCH 05/11] updated doc examples to match paper

---
 Jets.m2 | 12 +++++++++---
 1 file changed, 9 insertions(+), 3 deletions(-)

diff --git a/Jets.m2 b/Jets.m2
index af0fa33..57be5f3 100644
--- a/Jets.m2
+++ b/Jets.m2
@@ -1279,8 +1279,8 @@ Node
 	    J2I = jets(2,I)
 	Text
 	    However, by [GS06, Theorem 3.1], the radical is always a (squarefree) monomial ideal. In
-	    fact, the proof of [GS06, Theorem 3.2] shows that the radical is generated by the terms of the
-	    jet equations constructed as in the introduction. This observation provides an alternative
+	    fact, the proof of [GS06, Theorem 3.2] shows that the radical is generated by the individual
+	    terms in the generators of the ideal of jets. This observation provides an alternative
 	    algorithm for computing radicals of jets of monomial ideals, which can be faster than the
 	    default radical computation in Macaulay2.
     	Example
@@ -1385,11 +1385,17 @@ Node
 	    JI1 = jets(1,I1)
 	    dim JI1, isPrime JI1
 	Text
-	    The jets of $X_2$ (the variety of maximal minors) are known to be
+	    The jets of $X_2$ (the determinantal hypersurface) are known to be
 	    irreducible (see Theorem 3.1 in @HREF("https://doi.org/10.1016/j.jpaa.2004.06.001",
 		    "T. Košir, B.A. Sethuraman, Determinantal varieties over truncated polynomial rings")@ [KS05],
 		or Corollary 4.13 in @HREF("https://doi.org/10.1090/S0002-9947-2012-05564-4",
 		    "R. Docampo, Arcs on determinantal varieties")@ [Doc13]).
+	    Since $X_2$ is a complete intersection and has rational singularities
+	    (see Corollary 6.1.5(b) in @HREF("https://doi.org/10.1017/CBO9780511546556",
+		    "J. Weyman, Cohomology of vector bundles and syzygies")@),
+	    this also follows from a more general result of M. Mustaţă
+	    (Theorem 3.3 in @HREF("https://doi.org/10.1007/s002220100152",
+		    "Jet schemes of locally complete intersection canonical singularities")@).
 	Example
 	    I3 = minors(3,G)
 	    JI3 = jets(1,I3)

From 3ababa8b699f302339597157677ae1d19b3db0e8 Mon Sep 17 00:00:00 2001
From: Federico Galetto <galetto.federico@gmail.com>
Date: Fri, 10 Jun 2022 23:08:05 -0400
Subject: [PATCH 06/11] shorter degree generator function

---
 Jets.m2 | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/Jets.m2 b/Jets.m2
index 57be5f3..2137a52 100644
--- a/Jets.m2
+++ b/Jets.m2
@@ -101,11 +101,7 @@ jetsVariables= (n,R) -> (
 
 --generate degree list for order n jets variables
 --this is used to create the rings of projective jets
-degGenerator = (n,R) -> (
-    for d in degrees R list (
-	for l in d list n
-	)
-    )
+degGenerator = (n,R) -> apply(degrees R, d -> toList((#d):n))
 
 --generate degrees/map for truncation ring in ideal calculation
 jetsDegrees = jetsOptions >> o -> R -> (

From 9e0d19fce87b179413b4748ef442bc2718d1df5c Mon Sep 17 00:00:00 2001
From: Federico Galetto <galetto.federico@gmail.com>
Date: Fri, 10 Jun 2022 23:13:31 -0400
Subject: [PATCH 07/11] not storing monomials when calling on coefficients

---
 Jets.m2 | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Jets.m2 b/Jets.m2
index 2137a52..a95bd48 100644
--- a/Jets.m2
+++ b/Jets.m2
@@ -216,7 +216,7 @@ jets(ZZ,Ideal) := Ideal => o -> (n,I) -> (
 	constCond := all(geners,isConstant);
     	--add dummy generator to avoid loss of zeros
 	gensI := if constCond then matrix{geners | {R_0}} else matrix{geners};
-    	(d,c) := coefficients(phi gensI);
+    	c := last coefficients(phi gensI);
     	--remove dummy generators if necessary
 	if constCond then (
 		L := entries c;

From 2002ebe62135d6e1a0b44312e366b4783b9327ca Mon Sep 17 00:00:00 2001
From: Federico Galetto <galetto.federico@gmail.com>
Date: Fri, 10 Jun 2022 23:15:48 -0400
Subject: [PATCH 08/11] fixed test 5

---
 Jets.m2 | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Jets.m2 b/Jets.m2
index a95bd48..b6bd1d1 100644
--- a/Jets.m2
+++ b/Jets.m2
@@ -510,15 +510,15 @@ TEST ///
 
 --for quotients and varieties
 TEST ///
-    R=QQ[x,y]
+    R = QQ[x,y]
     I = ideal(y^2,x^3)
-    Q=R/I
+    Q = R/I
     JR = jets(2,R)
     JI = jets(2,I)
     JQ = jets(2,Q)
-    assert(JR == =ambient JQ)
-    assert(JI == =ideal JQ)
-    assert(presentation (JR/JI) == =presentation JQ)
+    assert(JR === ambient JQ)
+    assert(JI === ideal JQ)
+    assert(presentation (JR/JI) === presentation JQ)
     V = Spec Q
     JV = jets(2,V)
     assert(ring JV === JQ)   

From f8524b705f547395c851fdc21f2453e0ee2303b3 Mon Sep 17 00:00:00 2001
From: Federico Galetto <galetto.federico@gmail.com>
Date: Fri, 10 Jun 2022 23:45:20 -0400
Subject: [PATCH 09/11] improved last column removal, removed DegreeLift/Map
 options

---
 Jets.m2 | 15 ++-------------
 1 file changed, 2 insertions(+), 13 deletions(-)

diff --git a/Jets.m2 b/Jets.m2
index b6bd1d1..ce4893f 100644
--- a/Jets.m2
+++ b/Jets.m2
@@ -218,13 +218,8 @@ jets(ZZ,Ideal) := Ideal => o -> (n,I) -> (
 	gensI := if constCond then matrix{geners | {R_0}} else matrix{geners};
     	c := last coefficients(phi gensI);
     	--remove dummy generators if necessary
-	if constCond then (
-		L := entries c;
-		c = matrix (for l in L list drop(l,-1));
-		);
-
+	if constCond then c = c_{0..(numColumns c - 2)};
 	resultMatrix := lift(c,S);
-
 	--update value in ideal cache
 	I.cache#typeName#jetsMatrix = resultMatrix;
 	I.cache#typeName#jetsMaxOrder = n;
@@ -317,13 +312,7 @@ jets(ZZ,RingMap) := RingMap => o -> (n,phi) -> (
 	targets=lift(targets,JS);
 	);
 
---DegreeMap and DegreeLift options are set up but may not work as expected
-    psi := map(JS,JR,
-	flatten transpose targets
---	,DegreeLift=> degreeLift,
---	DegreeMap=> degreeMap
-    );
-
+    psi := map(JS,JR,flatten transpose targets);
     psi.cache#jetsInfo = new CacheTable from {
     	jetsBase=> phi,
     	Projective=> o.Projective

From 68a9002f0ecd15791c51b2eecec17d7a4e24cad2 Mon Sep 17 00:00:00 2001
From: Federico Galetto <galetto.federico@gmail.com>
Date: Fri, 10 Jun 2022 23:46:58 -0400
Subject: [PATCH 10/11] debugging to false

---
 Jets.m2 | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Jets.m2 b/Jets.m2
index ce4893f..4bd7cd7 100644
--- a/Jets.m2
+++ b/Jets.m2
@@ -34,7 +34,7 @@ newPackage(
      Headline => "compute jets of various algebraic, geometric and combinatorial objects",
      PackageImports => {"SimpleDoc","EdgeIdeals"},
      PackageExports => {"EdgeIdeals"},
-     DebuggingMode => true
+     DebuggingMode => false
      )
 
 

From 608c11da14b4bf693af84b84b3d65366faa0860a Mon Sep 17 00:00:00 2001
From: Federico Galetto <galetto.federico@gmail.com>
Date: Fri, 10 Jun 2022 23:47:29 -0400
Subject: [PATCH 11/11] bumped version to 1.1

---
 Jets.m2 | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Jets.m2 b/Jets.m2
index 4bd7cd7..240f9fc 100644
--- a/Jets.m2
+++ b/Jets.m2
@@ -17,8 +17,8 @@
 
 newPackage(
      "Jets",
-     Version => "1.0",
-     Date => "June 29, 2021",
+     Version => "1.1",
+     Date => "June 10, 2022",
      AuxiliaryFiles => true,
      Authors => {
 	 {