feat: compute subfields via blocks

[thofma]

No description provided.

[thofma]

c?

[fieker]

cur_b - it was renamed a couple of times

[fieker]

we'll chat when in, but subfield_from_block is not called at all

[thofma]

The "linear combination" path is failing for

julia> Qx, x = QQ[:x];

julia> K, a = number_field(x^8 - x^4 + 1, :a);

julia> Hecke._subfield_primitive_element_from_basis(K, [sqrt(K(2)), sqrt(K(3))], true);
Sieving for primitive elements
Have block systems, degree of subfield is 4
Found 0 primitive elements in the basis
Finding combination of elements
ERROR: dnw

[thofma]

Error from the tests:

julia> Qx, x = QQ[:x];

julia> K, a = number_field(x^8 + 1040*x^6 + 345784*x^4 + 39199680*x^2 + 545876496, :a);

julia> b = [K(1), 1//70976*a^6 + 195//17744*a^4 + 36855//17744*a^2 + 198575//4436, 91//414570816*a^7 + 65435//414570816*a^5 + 2171611//103642704*a^3 - 14748467//11515856*a, -1175//2487424896*a^7 - 264613//621856224*a^5 - 63204521//621856224*a^3 - 81891617//17273784*a];

julia> subfield(K, b)
ERROR: probably something bad?

[codecov]

Codecov Report

❌ Patch coverage is 0% with 139 lines in your changes missing coverage. Please review.
✅ Project coverage is 5.40%. Comparing base (0861f10) to head (f5fb7fc).
⚠️ Report is 122 commits behind head on master.

Files with missing lines	Patch %	Lines
src/NumField/Subfields.jl	0.00%	126 Missing ⚠️
src/LocalField/Conjugates.jl	0.00%	13 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           master    #1829       +/-   ##
===========================================
- Coverage   76.50%    5.40%   -71.10%     
===========================================
  Files         362      365        +3     
  Lines      115035   126748    +11713     
===========================================
- Hits        88006     6853    -81153     
- Misses      27029   119895    +92866     

Files with missing lines	Coverage Δ
src/LocalField/Conjugates.jl	0.00% <0.00%> (-76.93%)	⬇️
src/NumField/Subfields.jl	0.00% <0.00%> (-69.73%)	⬇️

... and 327 files with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.