i1 : R = ZZ/101[a,b,c,d,e];
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i2 : I = intersect(ideal(a,b),ideal(c,d,e))
o2 = ideal (b*e, a*e, b*d, a*d, b*c, a*c)
o2 : Ideal of R
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i3 : C = freeResolution I
1 6 9 5 1
o3 = R <-- R <-- R <-- R <-- R
0 1 2 3 4
o3 : Complex
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i4 : naiveTruncation(C, 1, 2)
6 9
o4 = R <-- R
1 2
o4 : Complex
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i5 : C16 = naiveTruncation(C, 1, 6)
6 9 5 1
o5 = R <-- R <-- R <-- R
1 2 3 4
o5 : Complex
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i6 : isWellDefined C16
o6 = true
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i7 : naiveTruncation(C, 1, infinity)
6 9 5 1
o7 = R <-- R <-- R <-- R
1 2 3 4
o7 : Complex
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i8 : naiveTruncation(C, -13, 2)
1 6 9
o8 = R <-- R <-- R
0 1 2
o8 : Complex
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i9 : naiveTruncation(C, -infinity, 2)
1 6 9
o9 = R <-- R <-- R
0 1 2
o9 : Complex
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i10 : naiveTruncation(C, , 2)
1 6 9
o10 = R <-- R <-- R
0 1 2
o10 : Complex
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i11 : C' = naiveTruncation(C,, 1)
1 6
o11 = R <-- R
0 1
o11 : Complex
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i12 : C'' = naiveTruncation(C, 2, infinity)
9 5 1
o12 = R <-- R <-- R
2 3 4
o12 : Complex
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i13 : f = inducedMap(C, C')
1 1
o13 = 0 : R <--------- R : 0
| 1 |
6 6
1 : R <----------------------- R : 1
{2} | 1 0 0 0 0 0 |
{2} | 0 1 0 0 0 0 |
{2} | 0 0 1 0 0 0 |
{2} | 0 0 0 1 0 0 |
{2} | 0 0 0 0 1 0 |
{2} | 0 0 0 0 0 1 |
o13 : ComplexMap
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i14 : g = inducedMap(C'', C)
9 9
o14 = 2 : R <----------------------------- R : 2
{3} | 1 0 0 0 0 0 0 0 0 |
{3} | 0 1 0 0 0 0 0 0 0 |
{3} | 0 0 1 0 0 0 0 0 0 |
{3} | 0 0 0 1 0 0 0 0 0 |
{3} | 0 0 0 0 1 0 0 0 0 |
{3} | 0 0 0 0 0 1 0 0 0 |
{3} | 0 0 0 0 0 0 1 0 0 |
{3} | 0 0 0 0 0 0 0 1 0 |
{3} | 0 0 0 0 0 0 0 0 1 |
5 5
3 : R <--------------------- R : 3
{4} | 1 0 0 0 0 |
{4} | 0 1 0 0 0 |
{4} | 0 0 1 0 0 |
{4} | 0 0 0 1 0 |
{4} | 0 0 0 0 1 |
1 1
4 : R <------------- R : 4
{5} | 1 |
o14 : ComplexMap
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i15 : assert isShortExactSequence(g,f)
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