output of prune_with_map_projection

[RafaelDavidMohr]

I don't understand the output of prune_with_map_projection. To port it over to Oscar, I need this function to tell me which of the generators of the corresponding factor module are non-minimal. I.e. if I take

julia> R, (x, y) = Singular.polynomial_ring(Singular.QQ, ["x", "y"])
(Singular polynomial ring (QQ),(x,y),(dp(2),C), spoly{n_Q}[x, y])

julia> v = vector(R, x, R(-1))
x*gen(1)-gen(2)

julia> M = Singular.Module(R, v)
Singular Module over Singular polynomial ring (QQ),(x,y),(dp(2),C), with Generators:
x*gen(1)-gen(2)

then prune_with_map_projection returns

julia> Singular.prune_with_map_projection(M)
(Singular Module over Singular polynomial ring (QQ),(x,y),(dp(2),C), with Generators:
0, [0], Int32[1, 2])

and as far as I understood the last entry of this should instead be Int32[1] since we kept around gen(1) and scratched gen(2).
Similarly

julia> v = vector(R, R(-1), x)
x*gen(2)-gen(1)

julia> M = Singular.Module(R, v)
Singular Module over Singular polynomial ring (QQ),(x,y),(dp(2),C), with Generators:
x*gen(2)-gen(1)

julia> Singular.prune_with_map_projection(M)
(Singular Module over Singular polynomial ring (QQ),(x,y),(dp(2),C), with Generators:
0, [0], Int32[1, 1])

Here the last entry should instead be Int32[2] since we kept around gen(2) and scratched gen(1).

Maybe I just don't understand the output? @ederc @hannes14

[hannes14]

julia> M = Singular.Module(R, v) Singular Module over Singular polynomial ring (QQ),(x,y),(dp(2),C), with Generators: x*gen(1)-gen(2) ``` then `prune_with_map_projection` returns ``` julia> Singular.prune_with_map_projection(M) (Singular Module over Singular polynomial ring (QQ),(x,y),(dp(2),C), with Generators: 0, [0], Int32[1, 2]) ``` and as far as I understood the last entry of this should instead be `Int32[1]` since we kept around `gen(1)` and scratched `gen(2)`.

The size of the Int32 vector is always rank(parent(M)) [1,2] maps gen(1) to gen(1), gen(20 to gen(2), but result has only rank 1 -> scratched `gen(2)`

Similarly ``` julia> v = vector(R, R(-1), x) x*gen(2)-gen(1) julia> M = Singular.Module(R, v) Singular Module over Singular polynomial ring (QQ),(x,y),(dp(2),C), with Generators: x*gen(2)-gen(1) julia> Singular.prune_with_map_projection(M) (Singular Module over Singular polynomial ring (QQ),(x,y),(dp(2),C), with Generators: 0, [0], Int32[1, 1]) ``` Here the last entry should instead be `Int32[2]` since we kept around `gen(2)` and scratched `gen(1)`.

here map gen(1) to gen(1) and gen(2) to gen(1), they cannot go to the same: -> scratched `gen(1)` If there are equel entries, the last wins, the other are scratched. If there are entries large than the resulting rank, these components are scratched.

[RafaelDavidMohr]

I think I understand, thank you for the explanation!