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)
-- .00223679s elapsed
-- .00804055s elapsed
-- .0226273s elapsed
-- .00963621s elapsed
-- .00349231s elapsed
-- .474407s 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
-- .247702s 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);
-- .00450803s elapsed
-- .017145s elapsed
-- .132278s elapsed
-- 1.14139s elapsed
-- .517143s elapsed
-- .0710902s elapsed
-- .00652267s elapsed
-- 6.47678s 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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