Prints the Betti table of the canonical carpet and a list of pairs, with first element a quadric and second element the sequence of ranks of the homotopies for that quadric on Fi, for i = 1..g-2.
i1 : homotopyRanks(7,3)
0 1 2 3 4 5
total: 1 10 16 16 10 1
0: 1 . . . . .
1: . 10 16 . . .
2: . . . 16 10 .
3: . . . . . 1
+-------------------------+---------------+
o1 = || x_1^2-x_0x_2 | |{1, 0, 8, 0, 1}|
+-------------------------+---------------+
|| x_1x_2-x_0x_3 | |{1, 0, 8, 0, 1}|
+-------------------------+---------------+
|| x_2^2-x_1x_3 | |{1, 0, 8, 0, 1}|
+-------------------------+---------------+
|| x_2y_0-2x_1y_1+x_0y_2 ||{1, 0, 8, 0, 1}|
+-------------------------+---------------+
|| x_3y_0-2x_2y_1+x_1y_2 ||{1, 0, 8, 0, 1}|
+-------------------------+---------------+
|| x_2y_1-2x_1y_2+x_0y_3 ||{1, 0, 8, 0, 1}|
+-------------------------+---------------+
|| x_3y_1-2x_2y_2+x_1y_3 ||{1, 0, 8, 0, 1}|
+-------------------------+---------------+
|| y_1^2-y_0y_2 | |{1, 0, 8, 0, 1}|
+-------------------------+---------------+
|| y_1y_2-y_0y_3 | |{1, 0, 8, 0, 1}|
+-------------------------+---------------+
|| y_2^2-y_1y_3 | |{1, 0, 8, 0, 1}|
+-------------------------+---------------+
|
i2 : homotopyRanks(7,3, Characteristic => 2)
0 1 2 3 4 5
total: 1 10 19 19 10 1
0: 1 . . . . .
1: . 10 16 3 . .
2: . . 3 16 10 .
3: . . . . . 1
+-----------------+---------------+
o2 = || x_1^2+x_0x_2 | |{1, 0, 0, 2, 1}|
+-----------------+---------------+
|| x_1x_2+x_0x_3 ||{1, 0, 0, 0, 1}|
+-----------------+---------------+
|| x_2^2+x_1x_3 | |{1, 0, 0, 2, 1}|
+-----------------+---------------+
|| x_2y_0+x_0y_2 ||{1, 0, 0, 0, 1}|
+-----------------+---------------+
|| x_3y_0+x_1y_2 ||{1, 0, 0, 0, 1}|
+-----------------+---------------+
|| x_2y_1+x_0y_3 ||{1, 0, 0, 0, 1}|
+-----------------+---------------+
|| x_3y_1+x_1y_3 ||{1, 0, 0, 0, 1}|
+-----------------+---------------+
|| y_1^2+y_0y_2 | |{1, 0, 0, 2, 1}|
+-----------------+---------------+
|| y_1y_2+y_0y_3 ||{1, 0, 0, 0, 1}|
+-----------------+---------------+
|| y_2^2+y_1y_3 | |{1, 0, 0, 2, 1}|
+-----------------+---------------+
|