Merge branch 'GLInvariants' of https://github.com/Macaulay2/Workshop-…

…2024-Utah into GLInvariants
Macaulay2 · Jun 2, 2024 · 9ae7643 · 9ae7643
2 parents 4b82928 + ab0d03d
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diff --git a/GLIdeals.m2 b/GLIdeals.m2
@@ -1,122 +1,134 @@
-newPackage(
-	"GLIdeals",
-    	Version => "0.1", 
-    	Date => "June 1, 2024",
-    	Authors => {
-	     {Name => "Hunter Simper", Email => "[email protected]", HomePage => "https://www.huntersimper.com"},
-	     {}
-	     },
-    	Headline => "Template for gl ideals package",
-	PackageExports => {"SchurRings","SimpleDoc"},
-    	DebuggingMode => false,
-	Reload=>true
-    	)
-
-export{"generateIlambda"}
-
-numgensILambda = method() -- TODO: Make it accept Partitions as well
-numgensILambda(Matrix, List) := (X, lam) -> (
-	myHookLength := P -> (
-		-- compute prod (P_i - P_j + j - i) / (j - i) for all i < j
-		num := 1;
-		den := 1;
-		for i in 0..#P-1 do(
-			for j in i+1..#P-1 do(
-				num = num * (P#i - P#j + j - i);
-				den = den * (j - i);
-			);
-		);
-		return num / den;
-	);
-
-	size := #lam;
-
-	r := numRows X;
-	c := numColumns X;
-	minSize := min(r, c);
-	maxSize := max(r, c);
-
-	if minSize < size then(
-		error "Partition is too large for the matrix";
-	);
-
-	P := lam | apply(minSize - size, i -> 0); -- make it size minSize
-	dimension := myHookLength(P);
-	P = P | apply(maxSize - minSize, i -> 0); -- make it size maxSize
-	return sub(dimension * myHookLength(P),ZZ);
-);
-
-
-idealILambda = method()
-idealILambda(Matrix,List) := (X,lam) -> (
-     n:=rank target X;
-     m:=rank source X;
-     kk:=baseRing ring X; 
-     if char kk !=0 then(
-		error "Base ring is not characteristic 0";
-	);
-     conjlam := toList conjugate( new Partition from lam);
-     d:=numgensILambda(X,lam);
-     lis := for i from 0 to d-1 list
-     (
-    A := random(kk^m,kk^m);
-    B := random(kk^n,kk^n);
-    N := A * X * B;
-    product for j from 0 to #conjlam-1 list det(N_{0..conjlam_j-1}^{0..conjlam_j-1}));
-    J := ideal lis;
-    minJ:=mingens J;
-
-	while rank source minJ != d do(
-		A := random(kk^m,kk^m);
-		B := random(kk^n,kk^n);
-		N := A * X * B;
-		lis = append(lis, product for j from 0 to #conjlam-1 list det(N_{0..conjlam_j-1}^{0..conjlam_j-1}));
-		J = ideal lis;
-		minJ = mingens J;
-	);
-	return ideal mingens J;
-);
-
-
-
-partitionsLeq = method();
-partitionsLeq(Partition, Partition) := (A, B) -> (
-    -- A and B are partitions
-    -- assuming weakly decreasing
-    -- return if A <= B
-    n := #B;
-    for i in 0..#A-1 do(
-        if A#i == 0 then break;
-        if i > n then return false;
-        if A#i > B#i then return false;
-    );
-    return true;
-)
-
-Partition ? Partition := (A, B) -> (
-    AleB := partitionsLeq(A, B);
-    BleA := partitionsLeq(B, A);
-    if AleB and BleA then return symbol ==;
-    if AleB then return symbol <;
-    if BleA then return symbol >;
-    return symbol incomparable;
-)
-
-Partition == Partition := (A, B) -> (
-    return (A ? B) == (symbol ==);
-)
------
-
-beginDocumentation()
-
-
-doc ///
-
-///
-
-
-end
-
-
-
-
+newPackage(
+	"GLIdeals",
+    	Version => "0.1", 
+    	Date => "June 1, 2024",
+    	Authors => {
+	     {Name => "Hunter Simper", Email => "[email protected]", HomePage => "https://www.huntersimper.com"},
+	     {}
+	     },
+    	Headline => "Template for gl ideals package",
+	PackageExports => {"SchurRings","SimpleDoc"},
+    	DebuggingMode => false,
+	Reload=>true
+    	)
+
+export{"idealILambda"}
+
+numgensILambda = method() -- TODO: Make it accept Partitions as well
+numgensILambda(Matrix, List) := (X, lam) -> (
+	myHookLength := P -> (
+		-- compute prod (P_i - P_j + j - i) / (j - i) for all i < j
+		num := 1;
+		den := 1;
+		for i in 0..#P-1 do(
+			for j in i+1..#P-1 do(
+				num = num * (P#i - P#j + j - i);
+				den = den * (j - i);
+			);
+		);
+		return num / den;
+	);
+
+	size := #lam;
+
+	r := numRows X;
+	c := numColumns X;
+	minSize := min(r, c);
+	maxSize := max(r, c);
+
+	if minSize < size then(
+		error "Partition is too large for the matrix";
+	);
+
+	P := lam | apply(minSize - size, i -> 0); -- make it size minSize
+	dimension := myHookLength(P);
+	P = P | apply(maxSize - minSize, i -> 0); -- make it size maxSize
+	return sub(dimension * myHookLength(P),ZZ);
+);
+
+
+detLam = method()
+detLam = (X,lam) -> (
+    (m,n) := (numColumns(X), numRows(X));
+    base := ring X;
+    C := 1;
+    for i in lam do(
+	C = C*determinant(submatrix(X,{0..i},{0..i}));
+    );
+    return C 
+    )
+
+
+
+idealILambda = method()
+idealILambda(Matrix,List) := (X,lam) -> (
+     n:=rank target X;
+     m:=rank source X;
+     kk:=baseRing ring X; 
+     if char kk !=0 then(
+		error "Base ring is not characteristic 0";
+	);
+     conjlam := toList conjugate( new Partition from lam);
+     d:=numgensILambda(X,lam);
+     lis := for i from 0 to d-1 list
+     (
+    A := random(kk^m,kk^m);
+    B := random(kk^n,kk^n);
+    N := A * X * B;
+    product for j from 0 to #conjlam-1 list det(N_{0..conjlam_j-1}^{0..conjlam_j-1}));
+    J := ideal lis;
+    minJ:=mingens J;
+
+	while rank source minJ != d do(
+		A := random(kk^m,kk^m);
+		B := random(kk^n,kk^n);
+		N := A * X * B;
+		lis = append(lis, product for j from 0 to #conjlam-1 list det(N_{0..conjlam_j-1}^{0..conjlam_j-1}));
+		J = ideal lis;
+		minJ = mingens J;
+	);
+	return ideal minJ;
+);
+
+
+
+partitionsLeq = method();
+partitionsLeq(Partition, Partition) := (A, B) -> (
+    -- A and B are partitions
+    -- assuming weakly decreasing
+    -- return if A <= B
+    n := #B;
+    for i in 0..#A-1 do(
+        if A#i == 0 then break;
+        if i > n then return false;
+        if A#i > B#i then return false;
+    );
+    return true;
+)
+
+Partition ? Partition := (A, B) -> (
+    AleB := partitionsLeq(A, B);
+    BleA := partitionsLeq(B, A);
+    if AleB and BleA then return symbol ==;
+    if AleB then return symbol <;
+    if BleA then return symbol >;
+    return symbol incomparable;
+)
+
+Partition == Partition := (A, B) -> (
+    return (A ? B) == (symbol ==);
+)
+-----
+
+beginDocumentation()
+
+
+doc ///
+
+///
+
+
+end
+
+
+
diff --git a/randomLam.m2 b/randomLam.m2
@@ -0,0 +1,14 @@
+randomLam = method();
+randomLam(ZZ, ZZ) := (n,k) -> (
+    L=new MutableList from {};
+    sumsofar = 0;
+    for i from 0 to (n-2) do(
+        x = random(0, k-sumsofar);
+        L#i=x;
+        sumsofar = sumsofar + x;
+        );
+    L#(n-1) = k - sumsofar;
+    L=toList L;
+    L=rsort L;
+    return delete(0,L)
+    )