Add mstd, divrem back

[fingolfin]

Adds back the changes from PR #625

[hannes14]

The problem is the handling of a special case in depth: depth(I, F) is infinity (reported as -1) if F in I*F is.
This is tested in src/Modules/homological-algebra.jl:456: if is_zero(F) || is_equal((I*F)[1], F) return -1 end
but also in Singular (Singular/LIB/homolog.lib(1784)): if (size(reduce(M,std(I*M),5))==0) {return (-1); }
https://github.com/oscar-system/Oscar.jl/blob/master/src/Modules/homological-algebra.jl#L458
continues:

 MX = singular_module(F)
 SG = Singular.Module(base_ring(MX), MX(zero(F)))
 singular_assure(I)
 return Singular.LibHomolog.depth(SG, I.gens.S)

which results in a zero-module passed to Singular, which triggers the test above.
Possible solutions:

• remove the special case test from homolog.lib and build a new Singular_jll or
• change the Oscar part above to:

   MX = singular_module(F)
   SG = Singular.Module(base_ring(MX), MX(F))
   singular_assure(I)
   return Singular.LibHomolog.depth(SG, I.gens.S)

@wdecker

[fingolfin]

@hannes14 @wdecker so what's the status of this? IIRC the plan was to adjust Singular again, then update Singular_jll, then we can merge this PR? Or what else do we do?

[hannes14]

see JuliaPackaging/Yggdrasil#6577
this is Singular 4.3.2 with changes to function "depth"

[fingolfin]

I've tested this locally and there it seems to be fine now:

julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);

julia> F = free_module(R, 1);

julia> I = ideal(R, [x*z-z, x*y-y, x])
ideal(x*z - z, x*y - y, x)

julia> depth(I, F)
3

Let's wait and see what the OscarCI tests say.

[hannes14]

works with Singular_jll "403.201.000" and "403.201.001", but if we want to avoid the problems with "depth",
we need "403.201.001". libsingular_julia_jll should be "0.30.0", but this refers to Singular_jll "403.201.000"

• do we need a new libsingular_julia_jll with only this dependency changed?

[fingolfin]

I don't think we need an libsingular_julia_jll update