We compute the equation and nonminimal resolution F of the carpet of type (a,b) where $a \ge b$ over a larger finite prime field, lift the complex to the integers, which is possible since the coefficients are small. Finally we study the nonminimal strands over ZZ by computing the Smith normal form. The resulting data allow us to compute the Betti tables for arbitrary primes.
i1 : a=5,b=5
o1 = (5, 5)
o1 : Sequence
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i2 : elapsedTime T=carpetBettiTable(a,b,3)
-- 0.00131113 seconds elapsed
-- 0.00338807 seconds elapsed
-- 0.0138128 seconds elapsed
-- 0.00691297 seconds elapsed
-- 0.00238534 seconds elapsed
-- 0.158518 seconds elapsed
0 1 2 3 4 5 6 7 8 9
o2 = total: 1 36 160 315 302 302 315 160 36 1
0: 1 . . . . . . . . .
1: . 36 160 315 288 14 . . . .
2: . . . . 14 288 315 160 36 .
3: . . . . . . . . . 1
o2 : BettiTally
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i3 : J=canonicalCarpet(a+b+1,b,Characteristic=>3);
ZZ
o3 : Ideal of --[x ..x , y ..y ]
3 0 5 0 5
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i4 : elapsedTime T'=minimalBetti J
-- 0.106362 seconds elapsed
0 1 2 3 4 5 6 7 8 9
o4 = total: 1 36 160 315 302 302 315 160 36 1
0: 1 . . . . . . . . .
1: . 36 160 315 288 14 . . . .
2: . . . . 14 288 315 160 36 .
3: . . . . . . . . . 1
o4 : BettiTally
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i5 : T-T'
0 1 2 3 4 5 6 7 8 9
o5 = total: . . . . . . . . . .
1: . . . . . . . . . .
2: . . . . . . . . . .
3: . . . . . . . . . .
o5 : BettiTally
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i6 : elapsedTime h=carpetBettiTables(6,6);
-- 0.00360219 seconds elapsed
-- 0.0110208 seconds elapsed
-- 0.086427 seconds elapsed
-- 0.550996 seconds elapsed
-- 0.156313 seconds elapsed
-- 0.0297513 seconds elapsed
-- 0.00358552 seconds elapsed
-- 2.65049 seconds elapsed
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i7 : carpetBettiTable(h,7)
0 1 2 3 4 5 6 7 8 9 10 11
o7 = total: 1 55 320 891 1408 1155 1155 1408 891 320 55 1
0: 1 . . . . . . . . . . .
1: . 55 320 891 1408 1155 . . . . . .
2: . . . . . . 1155 1408 891 320 55 .
3: . . . . . . . . . . . 1
o7 : BettiTally
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i8 : carpetBettiTable(h,5)
0 1 2 3 4 5 6 7 8 9 10 11
o8 = total: 1 55 320 891 1408 1275 1275 1408 891 320 55 1
0: 1 . . . . . . . . . . .
1: . 55 320 891 1408 1155 120 . . . . .
2: . . . . . 120 1155 1408 891 320 55 .
3: . . . . . . . . . . . 1
o8 : BettiTally
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