Let $\lambda$ be a partition, and let $I \subseteq R=\QQ[x,y]$ be its corresponding monomial ideal. Every standard filling of $\lambda$ provides a filtration by monomial ideals of the interval
$I \subseteq ... \subseteq R$
We compute the resulting homology spectral sequence for every standard tableau of shape $(3,2)$, where homology means Tor(coker vars R, -).
i1 : needsPackage "PushForward" o1 = PushForward o1 : Package |
i2 : needsPackage "SpechtModule" o2 = SpechtModule o2 : Package |
i3 : lambda = {3,2}
o3 = {3, 2}
o3 : List
|
i4 : R = QQ[x,y,Degrees=>{{1,0},{0,1}}]
o4 = R
o4 : PolynomialRing
|
i5 : I = ideal apply(lambda | {0}, 0..#lambda, (k,l)->y^l*x^k)
3 2 2
o5 = ideal (x , x y, y )
o5 : Ideal of R
|
i6 : boxes = flatten apply(#lambda,r->apply(lambda#r,c->(r,c)))
o6 = {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1)}
o6 : List
|
i7 : p = new Partition from lambda
o7 = Partition{3, 2}
o7 : Partition
|
i8 : tableaux = toListOfTableaux(standardTableaux p)
o8 = {| 0 1 2 |, | 0 1 3 |, | 0 1 4 |, | 0 2 3 |, | 0 2 4 |}
| 3 4 | | 2 4 | | 2 3 | | 1 4 | | 1 3 |
o8 : List
|
i9 : filts = apply(tableaux, t -> reverse apply(1 + sum lambda, k ->
module(I + ideal apply(boxes, b -> (if t_b >= k then y^(b#0)*x^(b#1) else 0_R)))))
o9 = {{image | x3 x2y y2 0 0 0 0 0 |, image | x3 x2y y2 0 0 0 0 xy |, image |
------------------------------------------------------------------------
x3 x2y y2 0 0 0 y xy |, image | x3 x2y y2 0 0 x2 y xy |, image | x3 x2y
------------------------------------------------------------------------
y2 0 x x2 y xy |, image | x3 x2y y2 1 x x2 y xy |}, {image | x3 x2y y2 0
------------------------------------------------------------------------
0 0 0 0 |, image | x3 x2y y2 0 0 0 0 xy |, image | x3 x2y y2 0 0 x2 0 xy
------------------------------------------------------------------------
|, image | x3 x2y y2 0 0 x2 y xy |, image | x3 x2y y2 0 x x2 y xy |,
------------------------------------------------------------------------
image | x3 x2y y2 1 x x2 y xy |}, {image | x3 x2y y2 0 0 0 0 0 |, image
------------------------------------------------------------------------
| x3 x2y y2 0 0 x2 0 0 |, image | x3 x2y y2 0 0 x2 0 xy |, image | x3
------------------------------------------------------------------------
x2y y2 0 0 x2 y xy |, image | x3 x2y y2 0 x x2 y xy |, image | x3 x2y y2
------------------------------------------------------------------------
1 x x2 y xy |}, {image | x3 x2y y2 0 0 0 0 0 |, image | x3 x2y y2 0 0 0
------------------------------------------------------------------------
0 xy |, image | x3 x2y y2 0 0 x2 0 xy |, image | x3 x2y y2 0 x x2 0 xy
------------------------------------------------------------------------
|, image | x3 x2y y2 0 x x2 y xy |, image | x3 x2y y2 1 x x2 y xy |},
------------------------------------------------------------------------
{image | x3 x2y y2 0 0 0 0 0 |, image | x3 x2y y2 0 0 x2 0 0 |, image |
------------------------------------------------------------------------
x3 x2y y2 0 0 x2 0 xy |, image | x3 x2y y2 0 x x2 0 xy |, image | x3 x2y
------------------------------------------------------------------------
y2 0 x x2 y xy |, image | x3 x2y y2 1 x x2 y xy |}}
o9 : List
|
i10 : disp = (deg,E) -> prune pushFwd(map(R,QQ),evaluateInDegree(deg,E)) o10 = disp o10 : FunctionClosure |
i11 : for i in 0..<#tableaux do (
print(tableaux#i);
filt = filts#i;
couple = prune TorCouple(coker vars R, filt);
plotPages((-1..3,-1..6,1..(sum lambda)), disp, couple);
)
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
warning: clearing value of symbol e to allow access to subscripted variables based on it
: debug with expression debug 3903 or with command line option --debug 3903
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
| 0 1 2 |
| 3 4 |
page 1, with differential of degree {-1, -1}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=5 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=4 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=3 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=2 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=1 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 3| 2| | |
|q=0 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 2, with differential of degree {-1, -2}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=5 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=4 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | | 1| 1| |
|q=3 ||0 |0 |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=2 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 2| 1| | |
|q=0 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 3, with differential of degree {-1, -3}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=5 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=4 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | | 1| 1| |
|q=3 ||0 |0 |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=2 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=0 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 4, with differential of degree {-1, -4}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=4 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=0 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 5, with differential of degree {-1, -5}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=4 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=0 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
| 0 1 3 |
| 2 4 |
page 1, with differential of degree {-1, -1}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=5 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=4 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=3 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=2 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=1 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 3| 2| | |
|q=0 ||0 warning: clearing value of symbol e to allow access to subscripted variables based on it
: debug with expression debug 3903 or with command line option --debug 3903
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
warning: clearing value of symbol e to allow access to subscripted variables based on it
: debug with expression debug 3903 or with command line option --debug 3903
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
|QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 2, with differential of degree {-1, -2}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=5 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
| || | | 1| 1| |
|q=4 ||0 |0 |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=3 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=2 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=1 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
| || | 2| 1| | |
|q=0 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 3, with differential of degree {-1, -3}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=4 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | | 1| | |
|q=3 ||0 |0 |QQ |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=0 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 4, with differential of degree {-1, -4}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=4 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=0 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 5, with differential of degree {-1, -5}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=4 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=0 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
| 0 1 4 |
| 2 3 |
page 1, with differential of degree {-1, -1}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=5 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=4 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=3 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=2 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=1 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 3| 2| | |
|q=0 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 2, with differential of degree {-1, -2}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=5 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
| || | | 1| 1| |
|q=4 ||0 |0 |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=3 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
| || | | 1| 1| |
|q=2 |warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
warning: clearing value of symbol e to allow access to subscripted variables based on it
: debug with expression debug 3903 or with command line option --debug 3903
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
|0 |0 |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=1 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=0 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 3, with differential of degree {-1, -3}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
| || | | 1| | |
|q=4 ||0 |0 |QQ |0 |0 |
+----++----+---+---+---+---+
| || | | 1| | |
|q=3 ||0 |0 |QQ |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=1 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=0 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 4, with differential of degree {-1, -4}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=4 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=0 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 5, with differential of degree {-1, -5}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=4 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=0 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
| 0 2 3 |
| 1 4 |
page 1, with differential of degree {-1, -1}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=5 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=4 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=3 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=2 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=1 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 3| 2| | |
|q=0 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 2, with differential of degree {-1, -2}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=5 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
| || | | 1| 1| |
|q=4 ||0 |0 |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=3 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
| || | | 1| 1| |
|q=2 ||0 |0 |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=1 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
| || | 2| 1| | |
|q=0 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 3, with differential of degree {-1, -3}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+--warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
warning: clearing value of symbol e to allow access to subscripted variables based on it
: debug with expression debug 3903 or with command line option --debug 3903
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
--++----+---+---+---+---+
| || | | 1| 1| |
|q=4 ||0 |0 |QQ |QQ |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | | 1| | |
|q=1 ||0 |0 |QQ |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=0 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 4, with differential of degree {-1, -4}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
| || | | 1| | |
|q=4 ||0 |0 |QQ |0 |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=0 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 5, with differential of degree {-1, -5}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=4 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=0 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
| 0 2 4 |
| 1 3 |
page 1, with differential of degree {-1, -1}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=5 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=4 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=3 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=2 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 2| 1| |
|q=1 ||0 |QQ |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 3| 2| | |
|q=0 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 2, with differential of degree {-1, -2}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=5 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
| || | | 1| 1| |
|q=4 ||0 |0 |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=3 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
| || | | 1| 1| |
|q=2 ||0 |0 |QQ |QQ |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=1 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| 1| | |
|q=0 ||0 |QQ |QQ |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 3, with differential of degree {-1, -3}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
| || | | 1| | |
|q=4 ||0 |0 |QQ |0 |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=0 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 4, with differential of degree {-1, -4}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
| || | | 1| | |
|q=4 ||0 |0 |QQ |0 |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=0 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
page 5, with differential of degree {-1, -5}:
+----++----+---+---+---+---+
|q=6 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| || | 1| | | |
|q=5 ||0 |QQ |0 |0 |0 |
+----++----+---+---+---+---+
|q=4 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=3 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=2 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=1 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=0 ||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
|q=-1||0 |0 |0 |0 |0 |
+----++----+---+---+---+---+
| ||p=-1|p=0|p=1|p=2|p=3|
+----++----+---+---+---+---+
|
By changing the display function, we can view degree information
i12 : disp = (deg,E) -> degrees minimalPresentation evaluateInDegree(deg,E); |
i13 : for i in 0..<#tableaux do (
print(tableaux#i);
filt = filts#i;
couple = prune TorCouple(coker vars R, filt);
plotPages((-1..3,-1..6,1..(sum lambda)), disp, couple);
)
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
warning: clearing value of symbol e to allow access to subscripted variables based on it
: debug with expression debug 3903 or with command line option --debug 3903
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
| 0 1 2 |
| 3 4 |
page 1, with differential of degree {-1, -1}:
+----++----+------------------------+----------------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+------------------------+----------------+--------+---+
|q=5 ||{} |{{0, 0}} |{{0, 1}, {1, 0}}|{{1, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=4 ||{} |{{1, 0}} |{{1, 1}, {2, 0}}|{{2, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=3 ||{} |{{2, 0}} |{{2, 1}, {3, 0}}|{{3, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=2 ||{} |{{0, 1}} |{{0, 2}, {1, 1}}|{{1, 2}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=1 ||{} |{{1, 1}} |{{1, 2}, {2, 1}}|{{2, 2}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=0 ||{} |{{2, 1}, {0, 2}, {3, 0}}|{{2, 2}, {3, 1}}|{} |{} |
+----++----+------------------------+----------------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+------------------------+----------------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+------------------------+----------------+--------+---+
page 2, with differential of degree {-1, -2}:
+----++----+----------------+--------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+----------------+--------+--------+---+
|q=5 ||{} |{{0, 0}} |{{0, 1}}|{} |{} |
+----++----+----------------+--------+--------+---+
|q=4 ||{} |{} |{} |{} |{} |
+----++----+----------------+--------+--------+---+
|q=3 ||{} |{} |{{3, 0}}|{{3, 1}}|{} |
+----++----+----------------+--------+--------+---+
|q=2 ||{} |{{0, 1}} |{{0, 2}}|{} |{} |
+----++----+----------------+--------+--------+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+----------------+--------+--------+---+
|q=0 ||{} |{{0, 2}, {3, 0}}|{{3, 1}}|{} |{} |
+----++----+----------------+--------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+----------------+--------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+----------------+--------+--------+---+
page 3, with differential of degree {-1, -3}:
+----++----+--------+--------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=5 ||{} |{{0, 0}}|{{0, 1}}|{} |{} |
+----++----+--------+--------+--------+---+
|q=4 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=3 ||{} |{} |{{3, 0}}|{{3, 1}}|{} |
+----++----+--------+--------+--------+---+
|q=2 ||{} |{{0, 1}}|{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=0 ||{} |{{3, 0}}|{{3, 1}}|{} |{} |
+----++----+--------+--------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+--------+--------+--------+---+
page 4, with differential of degree {-1, -4}:
+----++----+--------+---+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+---+---+---+
|q=4 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=0 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
| ||p=-1|p=0 |p=1|p=2|p=3|
+----++----+--------+---+---+---+
page 5, with differential of degree {-1, -5}:
+----++----+--------+---+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
warning: clearing value of symbol e to allow access to subscripted variables based on it
: debug with expression debug 3903 or with command line option --debug 3903
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
------+---+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+---+---+---+
|q=4 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=0 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
| ||p=-1|p=0 |p=1|p=2|p=3|
+----++----+--------+---+---+---+
| 0 1 3 |
| 2 4 |
page 1, with differential of degree {-1, -1}:
+----++----+------------------------+----------------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+------------------------+----------------+--------+---+
|q=5 ||{} |{{0, 0}} |{{0, 1}, {1, 0}}|{{1, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=4 ||{} |{{1, 0}} |{{1, 1}, {2, 0}}|{{2, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=3 ||{} |{{0, 1}} |{{0, 2}, {1, 1}}|{{1, 2}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=2 ||{} |{{2, 0}} |{{2, 1}, {3, 0}}|{{3, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=1 ||{} |{{1, 1}} |{{1, 2}, {2, 1}}|{{2, 2}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=0 ||{} |{{2, 1}, {0, 2}, {3, 0}}|{{2, 2}, {3, 1}}|{} |{} |
+----++----+------------------------+----------------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+------------------------+----------------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+------------------------+----------------+--------+---+
page 2, with differential of degree {-1, -2}:
+----++----+----------------+----------------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+----------------+----------------+--------+---+
|q=5 ||{} |{{0, 0}} |{{0, 1}} |{} |{} |
+----++----+----------------+----------------+--------+---+
|q=4 ||{} |{} |{{2, 0}} |{{2, 1}}|{} |
+----++----+----------------+----------------+--------+---+
|q=3 ||{} |{{0, 1}} |{{0, 2}, {1, 1}}|{{1, 2}}|{} |
+----++----+----------------+----------------+--------+---+
|q=2 ||{} |{{2, 0}} |{{2, 1}, {3, 0}}|{{3, 1}}|{} |
+----++----+----------------+----------------+--------+---+
|q=1 ||{} |{{1, 1}} |{{1, 2}} |{} |{} |
+----++----+----------------+----------------+--------+---+
|q=0 ||{} |{{3, 0}, {0, 2}}|{{3, 1}} |{} |{} |
+----++----+----------------+----------------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+----------------+----------------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+----------------+----------------+--------+---+
page 3, with differential of degree {-1, -3}:
+----++----+--------+--------+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+--------+---+---+
|q=4 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=3 ||{} |{} |{{0, 2}}|{} |{} |
+----++----+--------+--------+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=0 ||{} |{{0, 2}}|{} |{} |{} |
+----++----+--------+--------+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
| ||p=-1|p=0 |p=1 |p=2|p=3|
+----++----+--------+--------+---+---+
page 4, with differential of degree {-1, -4}:
+----++----+--------+---+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+-----warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
warning: clearing value of symbol e to allow access to subscripted variables based on it
: debug with expression debug 3903 or with command line option --debug 3903
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
---+---+---+---+
|q=4 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=0 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
| ||p=-1|p=0 |p=1|p=2|p=3|
+----++----+--------+---+---+---+
page 5, with differential of degree {-1, -5}:
+----++----+--------+---+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+---+---+---+
|q=4 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=0 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
| ||p=-1|p=0 |p=1|p=2|p=3|
+----++----+--------+---+---+---+
| 0 1 4 |
| 2 3 |
page 1, with differential of degree {-1, -1}:
+----++----+------------------------+----------------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+------------------------+----------------+--------+---+
|q=5 ||{} |{{0, 0}} |{{0, 1}, {1, 0}}|{{1, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=4 ||{} |{{1, 0}} |{{1, 1}, {2, 0}}|{{2, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=3 ||{} |{{0, 1}} |{{0, 2}, {1, 1}}|{{1, 2}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=2 ||{} |{{1, 1}} |{{1, 2}, {2, 1}}|{{2, 2}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=1 ||{} |{{2, 0}} |{{3, 0}, {2, 1}}|{{3, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=0 ||{} |{{3, 0}, {2, 1}, {0, 2}}|{{3, 1}, {2, 2}}|{} |{} |
+----++----+------------------------+----------------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+------------------------+----------------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+------------------------+----------------+--------+---+
page 2, with differential of degree {-1, -2}:
+----++----+--------+--------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=5 ||{} |{{0, 0}}|{{0, 1}}|{} |{} |
+----++----+--------+--------+--------+---+
|q=4 ||{} |{} |{{2, 0}}|{{2, 1}}|{} |
+----++----+--------+--------+--------+---+
|q=3 ||{} |{{0, 1}}|{{0, 2}}|{} |{} |
+----++----+--------+--------+--------+---+
|q=2 ||{} |{} |{{2, 1}}|{{2, 2}}|{} |
+----++----+--------+--------+--------+---+
|q=1 ||{} |{{2, 0}}|{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=0 ||{} |{{0, 2}}|{{2, 2}}|{} |{} |
+----++----+--------+--------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+--------+--------+--------+---+
page 3, with differential of degree {-1, -3}:
+----++----+--------+--------+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+--------+---+---+
|q=4 ||{} |{} |{{2, 0}}|{} |{} |
+----++----+--------+--------+---+---+
|q=3 ||{} |{} |{{0, 2}}|{} |{} |
+----++----+--------+--------+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=1 ||{} |{{2, 0}}|{} |{} |{} |
+----++----+--------+--------+---+---+
|q=0 ||{} |{{0, 2}}|{} |{} |{} |
+----++----+--------+--------+---+---+
|q=-1||{} |{} |{} |{} |{} |warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
warning: clearing value of symbol e to allow access to subscripted variables based on it
: debug with expression debug 3903 or with command line option --debug 3903
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
+----++----+--------+--------+---+---+
| ||p=-1|p=0 |p=1 |p=2|p=3|
+----++----+--------+--------+---+---+
page 4, with differential of degree {-1, -4}:
+----++----+--------+---+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+---+---+---+
|q=4 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=0 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
| ||p=-1|p=0 |p=1|p=2|p=3|
+----++----+--------+---+---+---+
page 5, with differential of degree {-1, -5}:
+----++----+--------+---+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+---+---+---+
|q=4 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=0 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
| ||p=-1|p=0 |p=1|p=2|p=3|
+----++----+--------+---+---+---+
| 0 2 3 |
| 1 4 |
page 1, with differential of degree {-1, -1}:
+----++----+------------------------+----------------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+------------------------+----------------+--------+---+
|q=5 ||{} |{{0, 0}} |{{1, 0}, {0, 1}}|{{1, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=4 ||{} |{{0, 1}} |{{1, 1}, {0, 2}}|{{1, 2}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=3 ||{} |{{1, 0}} |{{1, 1}, {2, 0}}|{{2, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=2 ||{} |{{2, 0}} |{{2, 1}, {3, 0}}|{{3, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=1 ||{} |{{1, 1}} |{{1, 2}, {2, 1}}|{{2, 2}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=0 ||{} |{{2, 1}, {0, 2}, {3, 0}}|{{2, 2}, {3, 1}}|{} |{} |
+----++----+------------------------+----------------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+------------------------+----------------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+------------------------+----------------+--------+---+
page 2, with differential of degree {-1, -2}:
+----++----+----------------+--------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+----------------+--------+--------+---+
|q=5 ||{} |{{0, 0}} |{{1, 0}}|{} |{} |
+----++----+----------------+--------+--------+---+
|q=4 ||{} |{} |{{0, 2}}|{{1, 2}}|{} |
+----++----+----------------+--------+--------+---+
|q=3 ||{} |{{1, 0}} |{{1, 1}}|{} |{} |
+----++----+----------------+--------+--------+---+
|q=2 ||{} |{} |{{3, 0}}|{{3, 1}}|{} |
+----++----+----------------+--------+--------+---+
|q=1 ||{} |{{1, 1}} |{{1, 2}}|{} |{} |
+----++----+----------------+--------+--------+---+
|q=0 ||{} |{{3, 0}, {0, 2}}|{{3, 1}}|{} |{} |
+----++----+----------------+--------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+----------------+--------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+----------------+--------+--------+---+
page 3, with differential of degree {-1, -3}:
+----++----+--------+--------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=5 ||{} |{{0, 0}}|warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
warning: clearing value of symbol e to allow access to subscripted variables based on it
: debug with expression debug 3903 or with command line option --debug 3903
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=4 ||{} |{} |{{0, 2}}|{{1, 2}}|{} |
+----++----+--------+--------+--------+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=1 ||{} |{} |{{1, 2}}|{} |{} |
+----++----+--------+--------+--------+---+
|q=0 ||{} |{{0, 2}}|{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+--------+--------+--------+---+
page 4, with differential of degree {-1, -4}:
+----++----+--------+--------+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+--------+---+---+
|q=4 ||{} |{} |{{0, 2}}|{} |{} |
+----++----+--------+--------+---+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=0 ||{} |{{0, 2}}|{} |{} |{} |
+----++----+--------+--------+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
| ||p=-1|p=0 |p=1 |p=2|p=3|
+----++----+--------+--------+---+---+
page 5, with differential of degree {-1, -5}:
+----++----+--------+---+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+---+---+---+
|q=4 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=0 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
| ||p=-1|p=0 |p=1|p=2|p=3|
+----++----+--------+---+---+---+
| 0 2 4 |
| 1 3 |
page 1, with differential of degree {-1, -1}:
+----++----+------------------------+----------------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+------------------------+----------------+--------+---+
|q=5 ||{} |{{0, 0}} |{{1, 0}, {0, 1}}|{{1, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=4 ||{} |{{0, 1}} |{{1, 1}, {0, 2}}|{{1, 2}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=3 ||{} |{{1, 0}} |{{2, 0}, {1, 1}}|{{2, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=2 ||{} |{{1, 1}} |{{2, 1}, {1, 2}}|{{2, 2}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=1 ||{} |{{2, 0}} |{{3, 0}, {2, 1}}|{{3, 1}}|{} |
+----++----+------------------------+----------------+--------+---+
|q=0 ||{} |{{3, 0}, {2, 1}, {0, 2}}|{{3, 1}, {2, 2}}|{} |{} |
+----++----+------------------------+----------------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+------------------------+----------------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+------------------------+----------------+--------+---+
page 2, with differential of degree {-1, -2}:
+----++----+--------+--------+--------+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=5 ||{} |{{0, 0}}|{{1, 0}}|{} |{} |
+----++----+--------+--------+--------+---+
|q=4 ||{} |{} |{{0, 2}}|{{1, 2}}|{} |
+----++----+--------+--------+--------+---+
|q=3 ||{} |{{1, 0}}|{{2, 0}}|{} |{} |
+----++----+--------+--------+--------+---+
|q=2 ||{} |{} |{{1, 2}}|{{2, 2}}|{} |
+----++----+--------+--------+--------+---+
|q=1 ||{} |{{2, 0}}|{} |{} |{} |
+----++----+--------+--------+--------+---+
|q=0 ||{} |{{0, 2}}|{{2, 2}}|{} |{} |
+----++----+--------+--------+--------+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+--------+--------+---+
| ||p=-1|p=0 |p=1 |p=2 |p=3|
+----++----+--------+--------+--------+---+
page 3, with differential of degree {-1, -3}:
+----++----+--------+--------+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+--------+---+---+
|q=4 ||{} |{} |{{0, 2}}|{} |{} |
+----++----+--------+--------+---+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=0 ||{} |{{0, 2}}|{} |{} |{} |
+----++----+--------+--------+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
| ||p=-1|p=0 |p=1 |p=2|p=3|
+----++----+--------+--------+---+---+
page 4, with differential of degree {-1, -4}:
+----++----+--------+--------+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+--------+---+---+
|q=4 ||{} |{} |{{0, 2}}|{} |{} |
+----++----+--------+--------+---+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
|q=0 ||{} |{{0, 2}}|{} |{} |{} |
+----++----+--------+--------+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+--------+---+---+
| ||p=-1|p=0 |p=1 |p=2|p=3|
+----++----+--------+--------+---+---+
page 5, with differential of degree {-1, -5}:
+----++----+--------+---+---+---+
|q=6 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=5 ||{} |{{0, 0}}|{} |{} |{} |
+----++----+--------+---+---+---+
|q=4 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=3 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=2 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=1 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=0 ||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
|q=-1||{} |{} |{} |{} |{} |
+----++----+--------+---+---+---+
| ||p=-1|p=0 |p=1|p=2|p=3|
+----++----+--------+---+---+---+
|