75 lines
1.4 KiB
Factor
75 lines
1.4 KiB
Factor
USING: koszul tools.test kernel sequences assocs namespaces ;
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IN: koszul.tests
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{
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{ V{ { } } V{ { 1 } } V{ { 2 3 } { 7 8 } } V{ { 4 5 6 } } }
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} [
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{ { 1 } { 2 3 } { 4 5 6 } { 7 8 } { } } graded
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] unit-test
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SYMBOLS: x1 x2 x3 x4 x5 x6 z1 z2 ;
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{ H{ { { x1 } 3 } } } [ x1 3 wedge ] unit-test
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{ H{ { { x1 } 3 } { { x2 } 4 } } }
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[ x1 3 wedge x2 4 wedge alt+ ] unit-test
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x1 x2 wedge z1 d=
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x3 x4 wedge z2 d=
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{ H{ { { x1 x2 z2 } 1 } { { x3 x4 z1 } -1 } } }
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[ z1 z2 wedge d ] unit-test
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! Unimodular example
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boundaries get clear-assoc
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SYMBOLS: x y w z ;
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x y wedge z d=
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y z wedge x d=
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z x wedge y d=
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{ { 1 0 0 1 } } [ { x y z } graded-betti ] unit-test
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! Solvable example
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boundaries get clear-assoc
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x y wedge y d=
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{ { 1 1 0 } } [ { x y } graded-betti ] unit-test
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! Nilpotent example
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boundaries get clear-assoc
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x1 x2 wedge x3 x4 wedge alt+ z d=
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{ { 1 4 5 5 4 1 } }
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[ { x1 x2 x3 x4 z } graded-betti ] unit-test
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{ { { 1 4 5 0 0 } { 0 0 5 4 1 } } }
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[ { x1 x2 x3 x4 } { z } bigraded-betti ] unit-test
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! Free 2-step on 4 generators
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boundaries get clear-assoc
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SYMBOLS: e12 e13 e14 e23 e24 e34 ;
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x1 x2 wedge e12 d=
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x1 x3 wedge e13 d=
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x1 x4 wedge e14 d=
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x2 x3 wedge e23 d=
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x2 x4 wedge e24 d=
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x3 x4 wedge e34 d=
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{ { 1 4 20 56 84 90 84 56 20 4 1 } }
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[ { x1 x2 x3 x4 e12 e13 e14 e23 e24 e34 } graded-betti ]
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unit-test
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! Make sure this works
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{ } [ e12 d alt. ] unit-test
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{ } [
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{ x1 x2 x3 x4 x5 x6 } { w z }
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bigraded-laplacian-kernel bigraded-basis.
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] unit-test
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