1 USING: koszul tools.test kernel sequences assocs namespaces
6 { V{ { } } V{ { 1 } } V{ { 2 3 } { 7 8 } } V{ { 4 5 6 } } }
8 { { 1 } { 2 3 } { 4 5 6 } { 7 8 } { } } graded
11 SYMBOLS: x1 x2 x3 x4 x5 x6 z1 z2 ;
13 [ H{ { { x1 } 3 } } ] [ x1 3 wedge ] unit-test
15 [ H{ { { x1 } 3 } { { x2 } 4 } } ]
16 [ x1 3 wedge x2 4 wedge alt+ ] unit-test
21 [ H{ { { x1 x2 z2 } 1 } { { x3 x4 z1 } -1 } } ]
22 [ z1 z2 wedge d ] unit-test
25 boundaries get clear-assoc
33 [ { 1 0 0 1 } ] [ { x y z } graded-betti ] unit-test
36 boundaries get clear-assoc
40 [ { 1 1 0 } ] [ { x y } graded-betti ] unit-test
43 boundaries get clear-assoc
45 x1 x2 wedge x3 x4 wedge alt+ z d=
48 [ { x1 x2 x3 x4 z } graded-betti ] unit-test
50 [ { { 1 4 5 0 0 } { 0 0 5 4 1 } } ]
51 [ { x1 x2 x3 x4 } { z } bigraded-betti ] unit-test
53 ! Free 2-step on 4 generators
54 boundaries get clear-assoc
56 SYMBOLS: e12 e13 e14 e23 e24 e34 ;
65 [ { 1 4 20 56 84 90 84 56 20 4 1 } ]
66 [ { x1 x2 x3 x4 e12 e13 e14 e23 e24 e34 } graded-betti ]
69 ! Make sure this works
70 [ ] [ e12 d alt. ] unit-test
73 { x1 x2 x3 x4 x5 x6 } { w z }
74 bigraded-laplacian-kernel bigraded-basis.