Warning! This function is very rough currently. It workes if one uses it in the intended manner, as in the example below. But it should be much more general, handling other rings with grace, and also it should handle arbitrary (graded) chain complexes.
i1 : R = QQ[a..d] o1 = R o1 : PolynomialRing |
i2 : I = ideal(a^3, b^3, c^3, d^3, (a+3*b+7*c-4*d)^3)
3 3 3 3 3 2 2 3 2
o2 = ideal (a , b , c , d , a + 9a b + 27a*b + 27b + 21a c + 126a*b*c +
------------------------------------------------------------------------
2 2 2 3 2 2
189b c + 147a*c + 441b*c + 343c - 12a d - 72a*b*d - 108b d - 168a*c*d
------------------------------------------------------------------------
2 2 2 2 3
- 504b*c*d - 588c d + 48a*d + 144b*d + 336c*d - 64d )
o2 : Ideal of R
|
i3 : C = res(ideal gens gb I, Strategy=>4.1)
1 9 25 31 18 4
o3 = R <-- R <-- R <-- R <-- R <-- R
0 1 2 3 4 5
o3 : ChainComplex
|
i4 : betti C
0 1 2 3 4 5
o4 = total: 1 9 25 31 18 4
0: 1 . . . . .
1: . . . . . .
2: . 5 1 . . .
3: . 1 3 1 . .
4: . 3 17 13 4 .
5: . . 4 13 10 3
6: . . . 4 3 1
7: . . . . 1 .
o4 : BettiTally
|
i5 : Cs = constantStrands(C, RR_53)
1
o5 = HashTable{0 => RR <-- 0 <-- 0 <-- 0 <-- 0 <-- 0 }
53
1 2 3 4 5
0
5
3 => 0 <-- RR <-- 0 <-- 0 <-- 0 <-- 0
53
0 2 3 4 5
1
1 1
4 => 0 <-- RR <-- RR <-- 0 <-- 0 <-- 0
53 53
0 3 4 5
1 2
3 3
5 => 0 <-- RR <-- RR <-- 0 <-- 0 <-- 0
53 53
0 3 4 5
1 2
17 1
6 => 0 <-- 0 <-- RR <-- RR <-- 0 <-- 0
53 53
0 1 4 5
2 3
4 13
7 => 0 <-- 0 <-- RR <-- RR <-- 0 <-- 0
53 53
0 1 4 5
2 3
13 4
8 => 0 <-- 0 <-- 0 <-- RR <-- RR <-- 0
53 53
0 1 2 5
3 4
4 10
9 => 0 <-- 0 <-- 0 <-- RR <-- RR <-- 0
53 53
0 1 2 5
3 4
3 3
10 => 0 <-- 0 <-- 0 <-- 0 <-- RR <-- RR
53 53
0 1 2 3
4 5
1 1
11 => 0 <-- 0 <-- 0 <-- 0 <-- RR <-- RR
53 53
0 1 2 3
4 5
o5 : HashTable
|
i6 : CR=Cs#8
13 4
o6 = 0 <-- 0 <-- 0 <-- RR <-- RR <-- 0
53 53
0 1 2 5
3 4
o6 : ChainComplex
|
i7 : SVDBetti C, betti C
0 1 2 3 4 5 0 1 2 3 4 5
o7 = (total: 1 5 17 20 7 ., total: 1 9 25 31 18 4)
0: 1 . . . . . 0: 1 . . . . .
1: . . . . . . 1: . . . . . .
2: . 5 . . . . 2: . 5 1 . . .
3: . . . . . . 3: . 1 3 1 . .
4: . . 16 10 1 . 4: . 3 17 13 4 .
5: . . 1 10 6 . 5: . . 4 13 10 3
6: . . . . . . 6: . . . 4 3 1
7: . . . . . . 7: . . . . 1 .
o7 : Sequence
|
This function should be defined for any graded chain complex, not just ones created using res(I, Strategy=>4.1). Currently, it is used to extract information from the not yet implemented ring QQhybrid, whose elements, coming from QQ, are stored as real number approximations (as doubles, and as 1000 bit floating numbers), together with its remainders under a couple of primes, together with information about how many multiplications were performed to obtain this number.