Add tests for generic coeffss, fix a regression

The commit adds basic tests for generic
coefficients for some Nemo fields.

It also fixes a regression in multi-modular
when randomized linear algebra was not
used for guessing a prime.

src/groebner/parameters.jl

@@ -243,6 +243,11 @@ function AlgorithmParameters(ring::PolyRing, kwargs::KeywordArguments; hint=:non
         end
     end
 
+    # Over Z_p, linalg = :randomized signals randomized linear algebra.
+    # Over Q, linalg = :randomized has almost no effect since multi-modular
+    # tracing is used by default. Still, we say "almost" since some routines in
+    # multi-modular tracing may compute Groebner bases in Zp for
+    # checking/verification, and they benefit from linalg = :randomized.
     linalg = kwargs.linalg
     if ring.ground === :zp && (linalg === :randomized || linalg === :auto)
         # Do not use randomized linear algebra if the field characteristic is
@@ -257,7 +262,8 @@ function AlgorithmParameters(ring::PolyRing, kwargs::KeywordArguments; hint=:non
             end
             linalg = :deterministic
         end
-    else
+    end
+    if ring.ground == :generic
         linalg = :deterministic
     end
     if linalg === :auto

src/input_output/AbstractAlgebra.jl

@@ -59,7 +59,9 @@ function io_extract_ring(polynomials)
     else
         # Detect that K is either AbstractAlgebra.QQ or Nemo.QQ
         base = AbstractAlgebra.base_ring(K)
-        if !(AbstractAlgebra.base_ring(base) == Union{})
+        if !(hasmethod(AbstractAlgebra.base_ring, typeof(base)))
+            ground = :generic
+        elseif !(AbstractAlgebra.base_ring(base) == Union{})
             ground = :generic
         end
     end

test/groebner.jl

@@ -159,14 +159,18 @@ end
     # - Zp
     # - Zp for large p
     # - QQ
+    n = 5
     syss = [
-        Groebner.Examples.cyclicn(5, k=GF(2^40 + 15)),
-        Groebner.Examples.cyclicn(5, k=GF(2)),
-        Groebner.Examples.cyclicn(5, k=GF(nextprime(big(2)^1000))),
-        Groebner.Examples.cyclicn(5, k=QQ)
+        Groebner.Examples.cyclicn(n, k=GF(2^40 + 15)),
+        Groebner.Examples.cyclicn(n, k=GF(2^40 + 15), internal_ordering=:lex),
+        Groebner.Examples.cyclicn(n, k=GF(2)),
+        Groebner.Examples.cyclicn(n, k=GF(nextprime(big(2)^1000))),
+        Groebner.Examples.cyclicn(n, k=GF(nextprime(big(2)^1000)), internal_ordering=:lex),
+        Groebner.Examples.cyclicn(n, k=QQ)
     ]
     for sys in syss
-        ring = Groebner.PolyRing(5, Groebner.DegRevLex(), 0, :generic)
+        ord = internal_ordering(parent(sys[1])) == :lex ? Groebner.Lex() : Groebner.DegRevLex()
+        ring = Groebner.PolyRing(n, ord, 0, :generic)
         exps, cfs = get_data(sys, Groebner.CoeffGeneric)
         gbexps, gbcfs = groebner(ring, exps, cfs)
         gb = groebner(sys)

test/input_output/Nemo.jl

@@ -26,6 +26,8 @@ import Nemo, Primes
 end
 
 @testset "Nemo.jl, generic" begin
+    # Test generic coefficients with some interesting fields from Nemo.jl.
+
     # Single extension
     K, a = Nemo.finite_field(3, 2, "a")
     R, (X, Y) = K["X", "Y"]
@@ -39,6 +41,19 @@ end
     # sys = [a * b * X - Y, X * Y - 1]
     # res = [Y^2 + b^5 + b^4 + 2*b^2 + 2*b + 2, X + (b^3 + 2*b^2 + b)*Y]
     # @test groebner(sys) == res
+
+    # Q bar
+    Q_bar = Nemo.algebraic_closure(Nemo.QQ)
+    R, (X, Y) = Q_bar["X", "Y"]
+    e2 = Nemo.root_of_unity(Q_bar, 5, 2)
+    e3 = Nemo.root_of_unity(Q_bar, 5, 3)
+    e4 = Nemo.root_of_unity(Q_bar, 5, 4)
+    @test groebner([e3*X - e2*Y]) == [X - e4*Y]
+
+    # Cyclic extension
+    K, a = Nemo.cyclotomic_field(5)
+    R, (X, Y) = K["X", "Y"]
+    @test groebner([a*X + 1]) == [X - a^3 - a^2 - a - 1]
 end
 
 @testset "Nemo.jl, input-output" begin