USING: koszul test kernel sequences hashtables namespaces ;
IN: temporary

[
    { V{ { } } V{ { 1 } } V{ { 2 3 } { 7 8 } } V{ { 4 5 6 } } }
] [
    { { 1 } { 2 3 } { 4 5 6 } { 7 8 } { } } graded
] unit-test

SYMBOLS: x1 x2 x3 x4 z1 z2 ;

[ H{ { { x1 } 3 } } ] [ x1 3 wedge ] unit-test

[ H{ { { x1 } 3 } { { x2 } 4 } } ]
[ x1 3 wedge x2 4 wedge alt+ ] unit-test

x1 x2 wedge z1 d=
x3 x4 wedge z2 d=

[ H{ { { x1 x2 z2 } 1 } { { x3 x4 z1 } -1 } } ]
[ z1 z2 wedge d ] unit-test

! Unimodular example
boundaries get clear-hash

SYMBOLS: x y z ;

x y wedge z d=
y z wedge x d=
z x wedge y d=

[ { 1 0 0 1 } ] [ { x y z } graded-betti ] unit-test

! Solvable example
boundaries get clear-hash

x y wedge y d=

[ { 1 1 0 } ] [ { x y } graded-betti ] unit-test

! Nilpotent example
boundaries get clear-hash

x1 x2 wedge x3 x4 wedge alt+ z d=

[ { 1 4 5 5 4 1 } ]
[ { x1 x2 x3 x4 z } graded-betti ] unit-test

[ { { 1 4 5 0 0 } { 0 0 5 4 1 } } ]
[ { x1 x2 x3 x4 } { z } bigraded-betti ] unit-test

! Free 2-step on 4 generators
boundaries get clear-hash

SYMBOLS: e12 e13 e14 e23 e24 e34 ;

x1 x2 wedge e12 d=
x1 x3 wedge e13 d=
x1 x4 wedge e14 d=
x2 x3 wedge e23 d=
x2 x4 wedge e24 d=
x3 x4 wedge e34 d=

[ { 1 4 20 56 84 90 84 56 20 4 1 } ]
[ { x1 x2 x3 x4 e12 e13 e14 e23 e24 e34 } graded-betti ]
unit-test