i1 : R = ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4}
o1 = R
o1 : QuotientRing
|
i2 : A = koszulComplexDGA(R)
o2 = {Ring => R }
Underlying algebra => R[T , T , T , T ]
1 2 3 4
Differential => {a, b, c, d}
isHomogeneous => true
o2 : DGAlgebra
|
i3 : apply(maxDegree A + 1, i -> numgens prune homology(i,A))
o3 = {1, 4, 6, 4, 1}
o3 : List
|
i4 : HA = homologyAlgebra(A) Computing generators in degree 1 : -- used 0.00131094 seconds Computing generators in degree 2 : -- used 0.0103525 seconds Computing generators in degree 3 : -- used 0.0285308 seconds Computing generators in degree 4 : -- used 0.00888357 seconds Finding easy relations : -- used 0.0175367 seconds Computing relations in degree 1 : -- used 0.00216142 seconds Computing relations in degree 2 : -- used 0.00212823 seconds Computing relations in degree 3 : -- used 0.00216066 seconds Computing relations in degree 4 : -- used 0.00219671 seconds Computing relations in degree 5 : -- used 0.00215117 seconds o4 = HA o4 : PolynomialRing |
i5 : R = ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4,a^3*b^3*c^3*d^3}
o5 = R
o5 : QuotientRing
|
i6 : A = koszulComplexDGA(R)
o6 = {Ring => R }
Underlying algebra => R[T , T , T , T ]
1 2 3 4
Differential => {a, b, c, d}
isHomogeneous => true
o6 : DGAlgebra
|
i7 : apply(maxDegree A + 1, i -> numgens prune homology(i,A))
o7 = {1, 5, 10, 10, 4}
o7 : List
|
i8 : HA = homologyAlgebra(A) Computing generators in degree 1 : -- used 0.0014415 seconds Computing generators in degree 2 : -- used 0.0119702 seconds Computing generators in degree 3 : -- used 0.012816 seconds Computing generators in degree 4 : -- used 0.0129821 seconds Finding easy relations : -- used 0.135782 seconds Computing relations in degree 1 : -- used 0.0113212 seconds Computing relations in degree 2 : -- used 0.0114469 seconds Computing relations in degree 3 : -- used 0.0115773 seconds Computing relations in degree 4 : -- used 0.0116556 seconds Computing relations in degree 5 : -- used 0.031256 seconds o8 = HA o8 : QuotientRing |
i9 : numgens HA o9 = 19 |
i10 : HA.cache.cycles
3 3 3 3 2 3 3 3 2 3 3 3 3 2 3 3
o10 = {a T , b T , c T , d T , a b c d T , a b c d T T , a b c d T T ,
1 2 3 4 1 1 2 1 2
-----------------------------------------------------------------------
2 3 3 3 2 3 3 3 2 3 3 3 3 2 3 3
a b c d T T , a b c d T T , a b c d T T T , a b c d T T T ,
1 3 1 4 1 2 3 1 2 3
-----------------------------------------------------------------------
3 3 2 3 2 3 3 3 3 2 3 3 2 3 3 3
a b c d T T T , a b c d T T T , a b c d T T T , a b c d T T T ,
1 2 3 1 2 4 1 2 4 1 3 4
-----------------------------------------------------------------------
2 3 3 3 3 2 3 3 3 3 2 3 3 3 3 2
a b c d T T T T , a b c d T T T T , a b c d T T T T , a b c d T T T T }
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
o10 : List
|
i11 : Q = ZZ/101[x,y,z] o11 = Q o11 : PolynomialRing |
i12 : I = ideal{y^3,z*x^2,y*(z^2+y*x),z^3+2*x*y*z,x*(z^2+y*x),z*y^2,x^3,z*(z^2+2*x*y)}
3 2 2 2 3 2 2 2 3
o12 = ideal (y , x z, x*y + y*z , 2x*y*z + z , x y + x*z , y z, x , 2x*y*z +
-----------------------------------------------------------------------
3
z )
o12 : Ideal of Q
|
i13 : R = Q/I o13 = R o13 : QuotientRing |
i14 : A = koszulComplexDGA(R)
o14 = {Ring => R }
Underlying algebra => R[T , T , T ]
1 2 3
Differential => {x, y, z}
isHomogeneous => true
o14 : DGAlgebra
|
i15 : apply(maxDegree A + 1, i -> numgens prune homology(i,A))
o15 = {1, 7, 7, 1}
o15 : List
|
i16 : HA = homologyAlgebra(A) Computing generators in degree 1 : -- used 0.00133876 seconds Computing generators in degree 2 : -- used 0.0108292 seconds Computing generators in degree 3 : -- used 0.0114204 seconds Finding easy relations : -- used 0.0770863 seconds Computing relations in degree 1 : -- used 0.00687932 seconds Computing relations in degree 2 : -- used 0.0216455 seconds Computing relations in degree 3 : -- used 0.00734491 seconds Computing relations in degree 4 : -- used 0.00846812 seconds o16 = HA o16 : QuotientRing |
i17 : R = ZZ/101[a,b,c,d] o17 = R o17 : PolynomialRing |
i18 : S = R/ideal{a^4,b^4,c^4,d^4}
o18 = S
o18 : QuotientRing
|
i19 : A = acyclicClosure(R,EndDegree=>3)
o19 = {Ring => R }
Underlying algebra => R[T , T , T , T ]
1 2 3 4
Differential => {a, b, c, d}
isHomogeneous => true
o19 : DGAlgebra
|
i20 : B = A ** S
o20 = {Ring => S }
Underlying algebra => S[T , T , T , T ]
1 2 3 4
Differential => {a, b, c, d}
isHomogeneous => true
o20 : DGAlgebra
|
i21 : HB = homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14) Computing generators in degree 1 : -- used 0.007675 seconds Computing generators in degree 2 : -- used 0.0163928 seconds Computing generators in degree 3 : -- used 0.0180379 seconds Computing generators in degree 4 : -- used 0.00963096 seconds Computing generators in degree 5 : -- used 0.0016167 seconds Computing generators in degree 6 : -- used 0.00145442 seconds Computing generators in degree 7 : -- used 0.00146968 seconds Finding easy relations : -- used 0.0190368 seconds Computing relations in degree 1 : -- used 0.00192028 seconds Computing relations in degree 2 : -- used 0.00201017 seconds Computing relations in degree 3 : -- used 0.00209589 seconds Computing relations in degree 4 : -- used 0.00184473 seconds Computing relations in degree 5 : -- used 0.0019355 seconds Computing relations in degree 6 : -- used 0.00188499 seconds Computing relations in degree 7 : -- used 0.0256656 seconds Computing relations in degree 8 : -- used 0.00172447 seconds Computing relations in degree 9 : -- used 0.00209834 seconds Computing relations in degree 10 : -- used 0.00177493 seconds Computing relations in degree 11 : -- used 0.00166838 seconds Computing relations in degree 12 : -- used 0.00177765 seconds Computing relations in degree 13 : -- used 0.00214693 seconds Computing relations in degree 14 : -- used 0.00169082 seconds o21 = HB o21 : PolynomialRing |