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)
-- 0.00322327 seconds elapsed
-- 0.00987092 seconds elapsed
-- 0.0421723 seconds elapsed
-- 0.0176776 seconds elapsed
-- 0.0053522 seconds elapsed
-- 0.342698 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
-- 0.307713 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);
-- 0.00689261 seconds elapsed
-- 0.0314451 seconds elapsed
-- 0.215236 seconds elapsed
-- 1.91813 seconds elapsed
-- 0.66435 seconds elapsed
-- 0.0716822 seconds elapsed
-- 0.01099 seconds elapsed
-- 7.10465 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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