diff --git a/.github/workflows/Runtests.yml b/.github/workflows/Runtests.yml
index 861eb583..a8cc1175 100644
--- a/.github/workflows/Runtests.yml
+++ b/.github/workflows/Runtests.yml
@@ -9,12 +9,14 @@ jobs:
         julia-arch: [x64]
         os: [ubuntu-latest, windows-latest]
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@latest
         with:
           version: ${{ matrix.julia-version }}
       - uses: julia-actions/julia-buildpkg@latest
       - uses: julia-actions/julia-runtest@latest
+        with:
+          depwarn: error
       - uses: julia-actions/julia-processcoverage@v1
       - uses: codecov/codecov-action@v3
         with:
diff --git a/benchmark/CI-scripts/run_benchmarks.jl b/benchmark/CI-scripts/run_benchmarks.jl
index bfd7dd16..807faa54 100644
--- a/benchmark/CI-scripts/run_benchmarks.jl
+++ b/benchmark/CI-scripts/run_benchmarks.jl
@@ -8,11 +8,11 @@ import Nemo
 
 suite = []
 
-function compute_gb(system, trials=7)
+function compute_gb(system, trials=7; kws...)
     times = []
     for _ in 1:trials
         GC.gc()
-        time = @elapsed groebner(system)
+        time = @elapsed groebner(system; kws...)
         push!(times, time)
     end
     minimum(times)
@@ -91,6 +91,17 @@ push!(
         )
     )
 )
+push!(
+    suite,
+    (
+        problem_name="groebner, threaded, AA, GF(2^31-1), cyclic 8",
+        result=compute_gb(
+            Groebner.cyclicn(8, ordering=:degrevlex, ground=GF(2^31 - 1)),
+            5,
+            threaded=:yes
+        )
+    )
+)
 
 function learn_and_apply(system)
     times = []
diff --git a/benchmark/CI-scripts/runtests.jl b/benchmark/CI-scripts/runtests.jl
index 1a6bedd6..b815f88f 100644
--- a/benchmark/CI-scripts/runtests.jl
+++ b/benchmark/CI-scripts/runtests.jl
@@ -14,12 +14,18 @@ const IGNORE_SMALL_ABSOLUTE_DEVIATION = 1e-3
 # Run benchmarks on the latest stable version of Groebner.jl
 dir_stable = (@__DIR__) * "/run-on-stable"
 @info "Benchmarking Groebner.jl, stable" dir_stable
-@time run(`julia --project=$dir_stable $dir_stable/run_benchmarks.jl`, wait=true)
+@time run(
+    `julia --threads=$(nthreads()) --project=$dir_stable $dir_stable/run_benchmarks.jl`,
+    wait=true
+)
 
 # Run benchmarks on the nightly version of Groebner.jl
 dir_nightly = (@__DIR__) * "/run-on-nightly"
 @info "Benchmarking Groebner.jl, nightly" dir_nightly
-@time run(`julia --project=$dir_nightly $dir_nightly/run_benchmarks.jl`, wait=true)
+@time run(
+    `julia --threads=$(nthreads()) --project=$dir_nightly $dir_nightly/run_benchmarks.jl`,
+    wait=true
+)
 
 # Compare results
 function compare()
diff --git a/experimental/constprop.jl b/experimental/constprop.jl
index 04b6ef6a..0e57d6e0 100644
--- a/experimental/constprop.jl
+++ b/experimental/constprop.jl
@@ -1,22 +1,15 @@
 module Foo
 
-vanish_enabled() = true
-
-macro vanish(expr)
-    m = __module__
-    quote
-        if !$m.vanish_enabled()
-            $(esc(expr))
-        else
-            nothing
-        end
-    end
+macro unreachable()
+    :(@assert false)
 end
 
-function critical_loop(x)
-    for i in eachindex(x)
-        @vanish println(x[i])
-        x[i] = x[i]^2
+function do_stuff(x)
+    if x > 0
+        x^2
+    else
+        @unreachable
+        x
     end
 end
 
diff --git a/experimental/examples/threaded-apply.jl b/experimental/examples/threaded-apply.jl
index 33151024..9d563864 100644
--- a/experimental/examples/threaded-apply.jl
+++ b/experimental/examples/threaded-apply.jl
@@ -1,9 +1,12 @@
 using AbstractAlgebra, Primes, Base.Threads
 using BenchmarkTools
-# using Groebner
+using Groebner
+
+@info "Using $(nthreads()) Julia threads"
 
 # Computes the bases of the given system modulo different primes
 function compute_bases(system, batch_size::Int)
+    @assert iszero(batch_size % 4)
     prime = 2^30 + 3
     Zp = GF(prime)
 
@@ -27,11 +30,12 @@ end
 
 # Same as the above, but uses multi-threading
 function compute_bases_threaded(system, batch_size::Int)
+    @assert iszero(batch_size % 4)
     prime = 2^30 + 3
     Zp = GF(prime)
 
     system_zp = map(f -> map_coefficients(c -> Zp(c), f), system)
-    trace, _ = Groebner.groebner_learn(system_zp)
+    trace, _ = Groebner.groebner_learn(system_zp, threaded=:yes)
 
     bases = Vector{typeof(system_zp)}(undef, batch_size)
     buffer_traces = map(_ -> deepcopy(trace), 1:nthreads())
@@ -40,8 +44,7 @@ function compute_bases_threaded(system, batch_size::Int)
     buffer_systems_zp =
         map(zp -> map(f -> map_coefficients(c -> zp(c), f), system), buffer_zp)
 
-    # :static guarantees that threadid() is constant within one iteraton
-    Base.Threads.@threads :static for j in 1:batch_size
+    Base.Threads.@threads for j in 1:batch_size
         t_id = threadid()
 
         system_zp = buffer_systems_zp[j]
@@ -58,11 +61,12 @@ end
 
 # Same as the above, but also uses batch size 4
 function compute_bases_threaded_batched(system, batch_size::Int)
+    @assert iszero(batch_size % 4)
     prime = 2^30 + 3
     Zp = GF(prime)
 
     system_zp = map(f -> map_coefficients(c -> Zp(c), f), system)
-    trace, _ = Groebner.groebner_learn(system_zp)
+    trace, _ = Groebner.groebner_learn(system_zp, threaded=:yes)
 
     bases = Vector{typeof(system_zp)}(undef, batch_size)
     buffer_traces = map(_ -> deepcopy(trace), 1:nthreads())
@@ -71,8 +75,7 @@ function compute_bases_threaded_batched(system, batch_size::Int)
     buffer_systems_zp =
         map(zp -> map(f -> map_coefficients(c -> zp(c), f), system), buffer_zp)
 
-    # :static guarantees that threadid() is constant within one iteraton
-    Base.Threads.@threads :static for j in 1:4:batch_size
+    Base.Threads.@threads for j in 1:4:batch_size
         t_id = threadid()
 
         system_zp = (
@@ -94,19 +97,11 @@ function compute_bases_threaded_batched(system, batch_size::Int)
     return bases
 end
 
-system = Groebner.katsuran(10, ground=ZZ, ordering=:degrevlex)
+system = Groebner.noonn(7, ground=ZZ, ordering=:degrevlex)
 begin
-    GC.gc()
-    @time bases_1 = compute_bases(system, 2^5)
-    GC.gc()
-    @time bases_2 = compute_bases_threaded(system, 2^5)
-    GC.gc()
-    @time bases_3 = compute_bases_threaded_batched(system, 2^5)
+    n = 2^8
+    @time bases_1 = compute_bases(system, n)
+    @time bases_2 = compute_bases_threaded(system, n)
+    @time bases_3 = compute_bases_threaded_batched(system, n)
     @assert all(bases_1 .== bases_2) && all(bases_2 .== bases_3)
 end;
-
-GC.gc()
-@profview compute_bases_threaded_batched(system, 2^8);
-
-# @btime compute_bases($system, 5, 8);
-# @btime compute_bases_threaded($system, 5, 8);
diff --git a/src/Groebner.jl b/src/Groebner.jl
index c207f05b..b76f629b 100644
--- a/src/Groebner.jl
+++ b/src/Groebner.jl
@@ -101,10 +101,14 @@ import TimerOutputs
 const _threaded = Ref(true)
 
 function __init__()
+    _threaded[] = !(get(ENV, "GROEBNER_NO_THREADED", "") == "1")
+
     # Setup the global logger
-    update_logger(loglevel=Logging.Info)
+    _groebner_log_lock[] = ReentrantLock()
+    logger_update(loglevel=Logging.Info)
 
-    _threaded[] = !(get(ENV, "GROEBNER_NO_THREADED", "") == "1")
+    # Setup performance counters
+    _groebner_timer_lock[] = ReentrantLock()
 
     nothing
 end
@@ -121,7 +125,7 @@ include("utils/timeit.jl")
 # Provides the macro `@stat` for collecting statistics
 include("utils/statistics.jl")
 
-# include("utils/versioninfo.jl")
+include("utils/versioninfo.jl")
 
 # Minimalistic plotting with Unicode
 include("utils/plots.jl")
diff --git a/src/arithmetic/Zp.jl b/src/arithmetic/Zp.jl
index 58745f4e..7f9f72cf 100644
--- a/src/arithmetic/Zp.jl
+++ b/src/arithmetic/Zp.jl
@@ -8,7 +8,7 @@
 # the coefficient. Generally, AccumType should be picked so that the result of
 #   a + b*c
 # is representable exactly in AccumType for feasible  a,b,c of type CoeffType. 
-# One common example is AccumType = UInt64 and CoeffType = UInt32
+# One example is AccumType = UInt64 and CoeffType = UInt32 with prime moduli
 abstract type AbstractArithmetic{AccumType, CoeffType} end
 
 # All implementations of arithmetic in Zp are a subtype of this.
@@ -115,7 +115,7 @@ end
 # a modulo p (addition specialization)
 function mod_p(a::T, mod::SpecializedArithmeticZp{T, C, true}) where {T, C}
     x = _mul_high(a, mod.multiplier)
-    x = convert(T, convert(T, (convert(T, a - x) >>> 1)) + x)
+    x = convert(T, convert(T, (convert(T, a - x) >>> UInt8(1))) + x)
     a - (x >>> mod.shift) * mod.divisor
 end
 # a modulo p (no addition specialization)
@@ -176,7 +176,7 @@ end
 # a modulo p (addition specialization)
 function mod_p(a::A, mod::DelayedArithmeticZp{A, T, true}) where {A, T}
     x = _mul_high(a, mod.multiplier)
-    x = convert(A, convert(A, (convert(A, a - x) >>> 1)) + x)
+    x = convert(A, convert(A, (convert(A, a - x) >>> UInt8(1))) + x)
     a - (x >>> mod.shift) * mod.divisor
 end
 # a modulo p (no addition specialization)
diff --git a/src/f4/basis.jl b/src/f4/basis.jl
index 31c08e1a..e18eb1ac 100644
--- a/src/f4/basis.jl
+++ b/src/f4/basis.jl
@@ -8,7 +8,7 @@
 ###
 # Pairset and Basis
 
-# Pairset is a list of critical pairs (SPairs).
+# Pairset is a list of critical pairs (CriticalPair).
 
 # Basis is a structure that stores a list of polynomials. Each polynomial is
 # represented with a sorted vector of monomials and a vector of coefficients.
@@ -19,7 +19,7 @@
 ###
 # Pairset
 
-# S-pair{Degree}, or, a pair of polynomials,
+# CriticalPair, or, a pair of polynomials,
 struct CriticalPair{Degree}
     # First polynomial given by its index in the basis array
     poly1::Int32
@@ -67,6 +67,41 @@ function pairset_resize_lcms_if_needed!(ps::Pairset, nfilled::Int)
     nothing
 end
 
+function pairset_find_smallest_degree_pair(ps::Pairset)
+    @invariant ps.load > 0 && length(ps.pairs) > 0
+    pairs = ps.pairs
+    pair_idx, pair_min_deg = 1, pairs[1].deg
+    @inbounds for i in 1:(ps.load)
+        if pairs[i].deg <= pair_min_deg
+            pair_min_deg = pairs[i].deg
+            pair_idx = i
+        end
+    end
+    pair_idx, pair_min_deg
+end
+
+function pairset_partition_by_degree!(ps::Pairset)
+    @invariant ps.load > 0
+    _, pair_min_deg = pairset_find_smallest_degree_pair(ps)
+
+    pairs = ps.pairs
+    i, j = 0, ps.load + 1
+    @inbounds while true
+        i += 1
+        j -= 1
+        while i <= ps.load && pairs[i].deg == pair_min_deg
+            i += 1
+        end
+        while j > 1 && pairs[j].deg > pair_min_deg
+            j -= 1
+        end
+        i >= j && break
+        pairs[i], pairs[j] = pairs[j], pairs[i]
+    end
+
+    i - 1
+end
+
 ###
 # Basis
 
diff --git a/src/f4/f4.jl b/src/f4/f4.jl
index 7115407a..eafda901 100644
--- a/src/f4/f4.jl
+++ b/src/f4/f4.jl
@@ -385,14 +385,16 @@ end
 # Returns N, the number of critical pairs of the smallest degree.
 # Sorts the critical pairs so that the first N pairs are the smallest.
 function pairset_lowest_degree_pairs!(pairset::Pairset)
-    sort_pairset_by_degree!(pairset, 1, pairset.load - 1)
-    ps = pairset.pairs
-    @inbounds min_deg = ps[1].deg
-    min_idx = 1
-    @inbounds while min_idx < pairset.load && ps[min_idx + 1].deg == min_deg
-        min_idx += 1
+    cnt = if true
+        n_lowest_degree_pairs = pairset_partition_by_degree!(pairset)
+        n_lowest_degree_pairs
+    else
+        sort_pairset_by_degree!(pairset, 1, pairset.load - 1)
+        pair_idx, _ = pairset_find_smallest_degree_pair(pairset)
+        pair_idx
     end
-    min_idx
+    @invariant cnt > 0
+    cnt
 end
 
 # Returns N, the number of critical pairs of the smallest sugar.
@@ -468,7 +470,8 @@ end
         end
     end
     npairs = min(npairs, maxpairs)
-    @assert npairs > 0
+    @invariant npairs > 0
+
     ps = pairset.pairs
     deg = ps[1].deg
 
@@ -512,8 +515,6 @@ function f4_add_critical_pairs_to_matrix!(
     ht::MonomialHashtable,
     symbol_ht::MonomialHashtable
 )
-
-    #
     matrix_reinitialize!(matrix, npairs)
     pairs = pairset.pairs
     uprows = matrix.upper_rows
diff --git a/src/f4/matrix.jl b/src/f4/matrix.jl
index ec5a4e7d..5ace98e9 100644
--- a/src/f4/matrix.jl
+++ b/src/f4/matrix.jl
@@ -253,7 +253,7 @@ function matrix_resize_lower_part!(matrix::MacaulayMatrix, size::Int)
     resize!(matrix.lower_to_mult, size)
 end
 
-# Refresh and partially initialize the matrix
+# statistics_refresh and partially initialize the matrix
 function matrix_reinitialize!(matrix::MacaulayMatrix, size::Int)
     new_size = size * 2
     matrix_resize_upper_part!(matrix, new_size)
diff --git a/src/fglm/kbase.jl b/src/fglm/kbase.jl
index b17397c9..b9357d70 100644
--- a/src/fglm/kbase.jl
+++ b/src/fglm/kbase.jl
@@ -20,7 +20,7 @@ function _kbase(polynomials, kws)
     ring, _ = set_monomial_ordering!(ring, var_to_index, monoms, coeffs, params)
     m, c = kbase_f4(ring, monoms, coeffs, params)
     res = convert_to_output(ring, polynomials, m, c, params)
-    print_performance_counters(params.statistics)
+    performance_counters_print(params.statistics)
     res
 end
 
diff --git a/src/groebner/groebner.jl b/src/groebner/groebner.jl
index 477fb2d6..ab54cfbb 100644
--- a/src/groebner/groebner.jl
+++ b/src/groebner/groebner.jl
@@ -63,7 +63,7 @@ function _groebner(polynomials, kws::KeywordsHandler, representation)
     # Convert result back to the representation of input
     basis = convert_to_output(ring, polynomials, gbmonoms, gbcoeffs, params)
 
-    print_performance_counters(params.statistics)
+    performance_counters_print(params.statistics)
     print_statistics(params.statistics)
 
     basis
diff --git a/src/groebner/isgroebner.jl b/src/groebner/isgroebner.jl
index 99374e86..53355d24 100644
--- a/src/groebner/isgroebner.jl
+++ b/src/groebner/isgroebner.jl
@@ -15,7 +15,7 @@ function _isgroebner(polynomials, kws::KeywordsHandler)
     params = AlgorithmParameters(ring, polynomial_repr, kws)
     ring, _ = set_monomial_ordering!(ring, var_to_index, monoms, coeffs, params)
     res = _isgroebner(ring, monoms, coeffs, params)
-    print_performance_counters(params.statistics)
+    performance_counters_print(params.statistics)
     res
 end
 
diff --git a/src/groebner/learn-apply.jl b/src/groebner/learn-apply.jl
index a9343824..af138dba 100644
--- a/src/groebner/learn-apply.jl
+++ b/src/groebner/learn-apply.jl
@@ -64,7 +64,7 @@ function _groebner_learn(polynomials, kws, representation)
     Terms: $(term_sorting_permutations)
     Polynomials: $(trace.input_permutation)"""
 
-    print_performance_counters(params.statistics)
+    performance_counters_print(params.statistics)
     print_statistics(params.statistics)
 
     WrappedTraceF4(trace),
@@ -117,10 +117,10 @@ function _groebner_apply!(
         ring, gb_monoms, gb_coeffs =
             dehomogenize_generators!(ring, gb_monoms, gb_coeffs, params)
     end
-    # @print_performance_counters
+    # @performance_counters_print
     !flag && return (flag, polynomials)
 
-    print_performance_counters(params.statistics)
+    performance_counters_print(params.statistics)
     print_statistics(params.statistics)
 
     flag, convert_to_output(ring, polynomials, gb_monoms, gb_coeffs, params)
@@ -151,12 +151,12 @@ function _groebner_apply!(
         ring, gb_monoms, gb_coeffs =
             dehomogenize_generators!(ring, gb_monoms, gb_coeffs, params)
     end
-    # @print_performance_counters
+    # @performance_counters_print
     !flag && return flag, batch
 
     gb_coeffs_unpacked = unpack_composite_coefficients(gb_coeffs)
 
-    print_performance_counters(params.statistics)
+    performance_counters_print(params.statistics)
     print_statistics(params.statistics)
 
     flag,
diff --git a/src/groebner/normalform.jl b/src/groebner/normalform.jl
index 22735047..31a59988 100644
--- a/src/groebner/normalform.jl
+++ b/src/groebner/normalform.jl
@@ -63,7 +63,7 @@ function _normalform(polynomials, to_be_reduced, kws::KeywordsHandler)
     coeffs_reduced = coeffs_to_be_reduced
     # TODO: remove `to_be_reduced` from arguments here
     res = convert_to_output(ring, to_be_reduced, monoms_reduced, coeffs_reduced, params)
-    print_performance_counters(params.statistics)
+    performance_counters_print(params.statistics)
     res
 end
 
diff --git a/src/input-output/AbstractAlgebra.jl b/src/input-output/AbstractAlgebra.jl
index d55d0716..f652e6cb 100644
--- a/src/input-output/AbstractAlgebra.jl
+++ b/src/input-output/AbstractAlgebra.jl
@@ -117,7 +117,7 @@ end
 function extract_coeffs_ff(
     representation::PolynomialRepresentation,
     ring::PolyRing,
-    poly::Union{AbstractAlgebra.Generic.Poly, AbstractAlgebra.PolyElem}
+    poly::Union{AbstractAlgebra.Generic.Poly, AbstractAlgebra.PolyRingElem}
 )
     AbstractAlgebra.iszero(poly) && (return zero_coeffs(representation.coefftype, ring))
     reverse(
@@ -133,7 +133,7 @@ end
 function extract_coeffs_qq(
     representation,
     ring::PolyRing,
-    poly::Union{AbstractAlgebra.Generic.Poly, AbstractAlgebra.PolyElem}
+    poly::Union{AbstractAlgebra.Generic.Poly, AbstractAlgebra.PolyRingElem}
 )
     AbstractAlgebra.iszero(poly) && (return zero_coeffs(representation.coefftype, ring))
     reverse(
@@ -455,7 +455,7 @@ function extract_monoms(
     representation::PolynomialRepresentation,
     ring::PolyRing,
     poly::P
-) where {P <: AbstractAlgebra.Generic.PolyElem}
+) where {P <: AbstractAlgebra.Generic.PolyRingElem}
     exps = Vector{representation.monomtype}(undef, 0)
     @inbounds while !AbstractAlgebra.iszero(poly)
         push!(
diff --git a/src/monomials/packedtuples.jl b/src/monomials/packedtuples.jl
index 4cbc7c95..fd4b64ba 100644
--- a/src/monomials/packedtuples.jl
+++ b/src/monomials/packedtuples.jl
@@ -321,7 +321,6 @@ function monom_isless(
     ord::Ord
 ) where {T, B, Ord <: AbstractInternalOrdering}
     # TODO: Perhaps this should error
-    @unreachable
     s = div(sizeof(T), sizeof(B)) - 1
     tmp1, tmp2 = Vector{T}(undef, s), Vector{T}(undef, s)
     a = monom_construct_from_vector(ExponentVector{T}, monom_to_vector!(tmp1, ea))
@@ -333,7 +332,6 @@ function monom_isless(
     eb::PackedTuple2{T, B},
     ord::Ord
 ) where {T, B, Ord <: AbstractInternalOrdering}
-    @unreachable
     s = 2 * div(sizeof(T), sizeof(B)) - 1
     tmp1, tmp2 = Vector{T}(undef, s), Vector{T}(undef, s)
     a = monom_construct_from_vector(ExponentVector{T}, monom_to_vector!(tmp1, ea))
@@ -345,7 +343,6 @@ function monom_isless(
     eb::PackedTuple3{T, B},
     ord::Ord
 ) where {T, B, Ord <: AbstractInternalOrdering}
-    @unreachable
     s = 3 * div(sizeof(T), sizeof(B)) - 1
     tmp1, tmp2 = Vector{T}(undef, s), Vector{T}(undef, s)
     a = monom_construct_from_vector(ExponentVector{T}, monom_to_vector!(tmp1, ea))
diff --git a/src/monomials/sparsevector.jl b/src/monomials/sparsevector.jl
index 51afe5a0..cc0f7ef0 100644
--- a/src/monomials/sparsevector.jl
+++ b/src/monomials/sparsevector.jl
@@ -201,7 +201,6 @@ function monom_isless(
     eb::SparseExponentVector{T, I, N},
     ord
 ) where {T, I, N}
-    @unreachable
     tmp1, tmp2 = Vector{T}(undef, N), Vector{T}(undef, N)
     a = monom_construct_from_vector(ExponentVector{T}, monom_to_vector!(tmp1, ea))
     b = monom_construct_from_vector(ExponentVector{T}, monom_to_vector!(tmp2, eb))
diff --git a/src/utils/invariants.jl b/src/utils/invariants.jl
index 831bcc00..af67d53a 100644
--- a/src/utils/invariants.jl
+++ b/src/utils/invariants.jl
@@ -1,7 +1,6 @@
 # This file is a part of Groebner.jl. License is GNU GPL v2.
 
-# Custom assertions for Groebner.
-# Provides the @invariant macro
+# Custom assertions for Groebner. Provides the @invariant macro.
 
 """
     @invariant expr
@@ -20,8 +19,7 @@ long as the code is compiled with `invariants_enabled() = false`.
 ```
 """
 macro invariant(arg)
-    # NOTE: This formulation of @invariant does not propagate the error source
-    # path out of the macro
+    # NOTE: does not propagate the error source path
     expr = quote
         if $(@__MODULE__).invariants_enabled()
             @assert $arg
@@ -33,7 +31,7 @@ macro invariant(arg)
 end
 
 macro unreachable()
-    @invariant false
+    :(@invariant false)
 end
 
 # Invokes undefined behavior in LLVM. 
diff --git a/src/utils/keywords.jl b/src/utils/keywords.jl
index 030c8b3c..2728f20a 100644
--- a/src/utils/keywords.jl
+++ b/src/utils/keywords.jl
@@ -217,14 +217,14 @@ struct KeywordsHandler{Ord}
 end
 
 function setup_logging(keywords::KeywordsHandler)
-    update_logger(loglevel=keywords.loglevel)
+    logger_update(loglevel=keywords.loglevel)
     nothing
 end
 
 function setup_statistics(keywords::KeywordsHandler)
     if keywords.loglevel <= 0
-        refresh_performance_counters()
-        refresh_statistics()
+        performance_counters_refresh()
+        statistics_refresh()
     end
     nothing
 end
diff --git a/src/utils/logging.jl b/src/utils/logging.jl
index f6bfdc71..b90c4d5a 100644
--- a/src/utils/logging.jl
+++ b/src/utils/logging.jl
@@ -6,8 +6,6 @@
 # message to console. The macro @log wraps Logging.@logmsg from the standard
 # library.
 
-# Logging is disabled on all threads except the one with threadid() == 1.
-
 """
     @log expr
     @log level=N expr
@@ -27,6 +25,8 @@ macro log end
 ###
 # Some aux. definitions
 
+const _groebner_log_lock = Ref{ReentrantLock}(ReentrantLock())
+
 function meta_formatter_groebner end
 
 @static if VERSION >= v"1.7.0"
@@ -104,14 +104,24 @@ end
 const _groebner_logger = Ref{GroebnerLogger}(GroebnerLogger())
 
 # Updates the global logging parameters in the Groebner module. 
-function update_logger(; loglevel=nothing)
+function logger_update(; loglevel=nothing)
     # Do nothing if logging is disabled
     !logging_enabled() && return nothing
-    # Do nothing if run from a worker thread
+    # Do nothing if nothing is being updated
+    loglevel === nothing && return nothing
+    # Do nothing if run from a worker thread.
+    # NOTE: this does not always do what is intended. It is still correct, since
+    # we lock the logger anyway.
     threadid() != 1 && return nothing
-    if loglevel !== nothing
-        _groebner_logger[] = Groebner.GroebnerLogger(stderr, Logging.LogLevel(loglevel))
+
+    new_logger = Groebner.GroebnerLogger(stderr, Logging.LogLevel(loglevel))
+    lock(_groebner_log_lock[])
+    try
+        _groebner_logger[] = new_logger
+    finally
+        unlock(_groebner_log_lock[])
     end
+
     nothing
 end
 
@@ -147,10 +157,8 @@ macro log(args...)
     level, msgs = log_macro_pruneargs(file, line, args)
     esc(:(
         if $(@__MODULE__).logging_enabled()
-            if threadid() == 1
-                with_logger($(@__MODULE__)._groebner_logger[]) do
-                    @logmsg LogLevel($level) $(msgs...) _file = $file _line = $line
-                end
+            with_logger($(@__MODULE__)._groebner_logger[]) do
+                @logmsg LogLevel($level) $(msgs...) _file = $file _line = $line
             end
         else
             nothing
diff --git a/src/utils/statistics.jl b/src/utils/statistics.jl
index 46eee74d..4d635d7b 100644
--- a/src/utils/statistics.jl
+++ b/src/utils/statistics.jl
@@ -78,7 +78,7 @@ function update_statistic!(
     nothing
 end
 
-function refresh_statistics!(stat::GroebnerStatistics)
+function statistics_refresh!(stat::GroebnerStatistics)
     stat.stopwatch_start = time_ns()
     empty!(stat.F4_stats)
     nothing
@@ -119,10 +119,10 @@ function update_statistic(file, line, args, key, value)
     update_statistic!(_groebner_statistics, file, line, args, key, value)
 end
 
-function refresh_statistics()
+function statistics_refresh()
     !statistics_enabled() && return nothing
     threadid() != 1 && return nothing
-    refresh_statistics!(_groebner_statistics)
+    statistics_refresh!(_groebner_statistics)
     nothing
 end
 
diff --git a/src/utils/test_systems.jl b/src/utils/test_systems.jl
index a2a52bc7..cdda71b7 100644
--- a/src/utils/test_systems.jl
+++ b/src/utils/test_systems.jl
@@ -5,11 +5,9 @@
 #! format: off
 # Syntax formatting is off in this file.
 
-# The cyclic-n system
-#
-# Göran Björck and Ralf Fröberg: 
-# `A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots', 
-# in J. Symbolic Computation (1991) 12, pp 329–336.
+# Göran Björck and Ralf Fröberg: `A faster way to count the solutions of
+# inhomogeneous systems of algebraic equations, with applications to cyclic
+# n-roots', in J. Symbolic Computation (1991) 12, pp 329–336.
 function cyclicn(n; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     _, z = np.polynomial_ring(ground, ["z$i" for i in 1:n], ordering=ordering)
     [
@@ -20,8 +18,7 @@ function cyclicn(n; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     ]
 end
 
-# The root-n system
-# (not to be confused with cyclic-n system)!!
+# Not to be confused with cyclic-n !!
 function rootn(n; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     _, xs = np.polynomial_ring(ground, ["x$i" for i in 1:n], ordering=ordering)
     ans = [sum(map(prod, Combinatorics.combinations(xs, i))) for i in 1:n]
@@ -29,14 +26,11 @@ function rootn(n; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     ans
 end
 
-# The reimer-n system
 function reimern(n; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     _, xs = np.polynomial_ring(ground, ["x$i" for i in 1:n], ordering=ordering)
     [sum((-1)^(i + 1) * 2 * xs[i]^j for i in 1:n) - 1 for j in 2:(n + 1)]
 end
 
-# The katsura-n system
-#
 # S. Katsura, W. Fukuda, S. Inawashiro, N.M. Fujiki and R. Gebauer,
 #  Cell Biophysics, Vol 11, pages 309–319, 1987.
 function katsuran(n; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
@@ -50,8 +44,6 @@ function katsuran(n; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     ]
 end
 
-# The noon-n system
-# 
 function noonn(n; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     without(x, k) = x[1:end .!= k]
 
@@ -64,8 +56,9 @@ function noonn(n; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     fs
 end
 
-# The henrion-5 system
-#
+###
+# Henrion
+
 # Source:
 # https://gitlab.lip6.fr/eder/msolve-examples/-/raw/master/zero-dimensional/henrion5.ms
 function henrion5(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
@@ -103,8 +96,6 @@ function henrion5(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     ]
 end
 
-# The henrion-6 system
-#
 # Source:
 # https://gitlab.lip6.fr/eder/msolve-examples/-/raw/master/zero-dimensional/henrion6.ms
 function henrion6(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
@@ -173,8 +164,6 @@ function henrion6(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     ]
 end
 
-# The henrion-7 system
-#
 # Source:
 # https://gitlab.lip6.fr/eder/msolve-examples/-/raw/master/zero-dimensional/henrion7.ms
 function henrion7(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
@@ -310,24 +299,48 @@ function henrion7(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     ]
 end
 
+# Source:
+# https://gitlab.lip6.fr/eder/msolve-examples/-/raw/master/zero-dimensional/henrion8.ms
 function henrion8(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     _, (f1, f2, f3, f4, f5, f6, f7, f8) = np.polynomial_ring(
         ground,
         ["f1", "f2", "f3", "f4", "f5", "f6", "f7", "f8"],
-        ordering=ordering)
-        [
-            ground(2)*f1*f2*f3*f4*f5*f6*f7*f8-ground(69850115960625),
-            ground(8)*f7*f6*f5*f4*f3*f1*f2+ground(15)//ground(8)*f2*f3*f4*f5*f6*f7*f8+ground(15)//ground(2)*f1*f2*f3*f4*f5*f7*f8+ground(55)//ground(8)*f1*f2*f3*f4*f6*f7*f8+ground(6)*f1*f2*f3*f5*f6*f7*f8+ground(39)//ground(8)*f1*f2*f4*f5*f6*f7*f8+ground(7)//ground(2)*f1*f3*f4*f5*f6*f7*f8+ground(63)//ground(8)*f1*f2*f3*f4*f5*f6*f8-ground(32870642805000),
-            -ground(3654447799500)+ground(27)//ground(2)*f1*f2*f4*f5*f6*f8+ground(45)//ground(4)*f1*f3*f4*f5*f6*f8+ground(27)//ground(4)*f2*f3*f4*f5*f6*f8+ground(7)//ground(4)*f3*f4*f5*f6*f7*f8+ground(12)*f1*f2*f3*f4*f5*f7+ground(15)*f1*f2*f3*f4*f6*f7+ground(16)*f1*f2*f3*f5*f6*f7+ground(15)*f1*f2*f4*f5*f6*f7+ground(12)*f1*f3*f4*f5*f6*f7+ground(25)//ground(4)*f1*f2*f3*f4*f7*f8+ground(10)*f1*f2*f3*f5*f7*f8+ground(11)//ground(2)*f1*f2*f3*f6*f7*f8+ground(45)//ground(4)*f1*f2*f4*f5*f7*f8+ground(33)//ground(4)*f1*f2*f4*f6*f7*f8+ground(9)//ground(2)*f1*f2*f5*f6*f7*f8+ground(10)*f1*f3*f4*f5*f7*f8+ground(33)//ground(4)*f1*f3*f4*f6*f7*f8+ground(6)*f1*f3*f5*f6*f7*f8+ground(13)//ground(4)*f1*f4*f5*f6*f7*f8+ground(25)//ground(4)*f2*f3*f4*f5*f7*f8+ground(11)//ground(2)*f2*f3*f4*f6*f7*f8+ground(9)//ground(2)*f2*f3*f5*f6*f7*f8+ground(13)//ground(4)*f2*f4*f5*f6*f7*f8+ground(27)//ground(4)*f1*f2*f3*f4*f5*f8+ground(45)//ground(4)*f1*f2*f3*f4*f6*f8+ground(27)//ground(2)*f1*f2*f3*f5*f6*f8+ground(7)*f6*f5*f4*f3*f1*f2+ground(7)*f2*f3*f4*f5*f6*f7,
-            -ground(163221399000)+ground(6)*f5*f4*f3*f1*f2+ground(6)*f2*f3*f4*f5*f6+ground(6)*f3*f4*f5*f6*f7+ground(10)*f1*f2*f3*f4*f6+ground(12)*f1*f2*f3*f5*f6+ground(12)*f1*f2*f4*f5*f6+ground(10)*f1*f3*f4*f5*f6+ground(13)//ground(8)*f4*f5*f6*f7*f8+ground(10)*f1*f2*f3*f4*f7+ground(16)*f1*f2*f3*f5*f7+ground(12)*f1*f2*f3*f6*f7+ground(18)*f1*f2*f4*f5*f7+ground(18)*f1*f2*f4*f6*f7+ground(12)*f1*f2*f5*f6*f7+ground(16)*f1*f3*f4*f5*f7+ground(18)*f1*f3*f4*f6*f7+ground(16)*f1*f3*f5*f6*f7+ground(10)*f1*f4*f5*f6*f7+ground(10)*f2*f3*f4*f5*f7+ground(12)*f2*f3*f4*f6*f7+ground(12)*f2*f3*f5*f6*f7+ground(10)*f2*f4*f5*f6*f7+ground(5)*f1*f2*f3*f7*f8+ground(15)//ground(2)*f1*f2*f4*f7*f8+ground(15)//ground(2)*f1*f2*f5*f7*f8+ground(33)//ground(8)*f1*f2*f6*f7*f8+ground(15)//ground(2)*f1*f3*f4*f7*f8+ground(10)*f1*f3*f5*f7*f8+ground(11)//ground(2)*f1*f3*f6*f7*f8+ground(15)//ground(2)*f1*f4*f5*f7*f8+ground(11)//ground(2)*f1*f4*f6*f7*f8+ground(3)*f1*f5*f6*f7*f8+ground(5)*f2*f3*f4*f7*f8+ground(15)//ground(2)*f2*f3*f5*f7*f8+ground(33)//ground(8)*f2*f3*f6*f7*f8+ground(15)//ground(2)*f2*f4*f5*f7*f8+ground(11)//ground(2)*f2*f4*f6*f7*f8+ground(3)*f2*f5*f6*f7*f8+ground(5)*f3*f4*f5*f7*f8+ground(33)//ground(8)*f3*f4*f6*f7*f8+ground(3)*f3*f5*f6*f7*f8+ground(45)//ground(8)*f1*f2*f3*f4*f8+ground(9)*f1*f2*f3*f5*f8+ground(9)*f1*f2*f3*f6*f8+ground(81)//ground(8)*f1*f2*f4*f5*f8+ground(27)//ground(2)*f1*f2*f4*f6*f8+ground(81)//ground(8)*f1*f2*f5*f6*f8+ground(9)*f1*f3*f4*f5*f8+ground(27)//ground(2)*f1*f3*f4*f6*f8+ground(27)//ground(2)*f1*f3*f5*f6*f8+ground(9)*f1*f4*f5*f6*f8+ground(45)//ground(8)*f2*f3*f4*f5*f8+ground(9)*f2*f3*f4*f6*f8+ground(81)//ground(8)*f2*f3*f5*f6*f8+ground(9)*f2*f4*f5*f6*f8+ground(45)//ground(8)*f3*f4*f5*f6*f8,
-            -ground(3562995798)+ground(5)*f4*f3*f1*f2+ground(5)*f2*f3*f4*f5+ground(5)*f3*f4*f5*f6+ground(8)*f1*f2*f3*f5+ground(9)*f1*f2*f4*f5+ground(8)*f1*f3*f4*f5+ground(5)*f4*f5*f6*f7+ground(8)*f1*f2*f3*f6+ground(12)*f1*f2*f4*f6+ground(9)*f1*f2*f5*f6+ground(12)*f1*f3*f4*f6+ground(12)*f1*f3*f5*f6+ground(8)*f1*f4*f5*f6+ground(8)*f2*f3*f4*f6+ground(9)*f2*f3*f5*f6+ground(8)*f2*f4*f5*f6+ground(3)//ground(2)*f5*f6*f7*f8+ground(8)*f1*f2*f3*f7+ground(12)*f1*f2*f4*f7+ground(12)*f1*f2*f5*f7+ground(9)*f1*f2*f6*f7+ground(12)*f1*f3*f4*f7+ground(16)*f1*f3*f5*f7+ground(12)*f1*f3*f6*f7+ground(12)*f1*f4*f5*f7+ground(12)*f1*f4*f6*f7+ground(8)*f1*f5*f6*f7+ground(8)*f2*f3*f4*f7+ground(12)*f2*f3*f5*f7+ground(9)*f2*f3*f6*f7+ground(12)*f2*f4*f5*f7+ground(12)*f2*f4*f6*f7+ground(8)*f2*f5*f6*f7+ground(8)*f3*f4*f5*f7+ground(9)*f3*f4*f6*f7+ground(8)*f3*f5*f6*f7+ground(15)//ground(4)*f1*f2*f7*f8+ground(5)*f1*f3*f7*f8+ground(5)*f1*f4*f7*f8+ground(5)*f1*f5*f7*f8+ground(11)//ground(4)*f1*f6*f7*f8+ground(15)//ground(4)*f2*f3*f7*f8+ground(5)*f2*f4*f7*f8+ground(5)*f2*f5*f7*f8+ground(11)//ground(4)*f2*f6*f7*f8+ground(15)//ground(4)*f3*f4*f7*f8+ground(5)*f3*f5*f7*f8+ground(11)//ground(4)*f3*f6*f7*f8+ground(15)//ground(4)*f4*f5*f7*f8+ground(11)//ground(4)*f4*f6*f7*f8+ground(9)//ground(2)*f1*f2*f3*f8+ground(27)//ground(4)*f1*f2*f4*f8+ground(27)//ground(4)*f1*f2*f5*f8+ground(27)//ground(4)*f1*f2*f6*f8+ground(27)//ground(4)*f1*f3*f4*f8+ground(9)*f1*f3*f5*f8+ground(9)*f1*f3*f6*f8+ground(27)//ground(4)*f1*f4*f5*f8+ground(9)*f1*f4*f6*f8+ground(27)//ground(4)*f1*f5*f6*f8+ground(9)//ground(2)*f2*f3*f4*f8+ground(27)//ground(4)*f2*f3*f5*f8+ground(27)//ground(4)*f2*f3*f6*f8+ground(27)//ground(4)*f2*f4*f5*f8+ground(9)*f2*f4*f6*f8+ground(27)//ground(4)*f2*f5*f6*f8+ground(9)//ground(2)*f3*f4*f5*f8+ground(27)//ground(4)*f3*f4*f6*f8+ground(27)//ground(4)*f3*f5*f6*f8+ground(9)//ground(2)*f4*f5*f6*f8,
-            -ground(41268600)+ground(4)*f2*f3*f4+ground(6)*f3*f4*f1+ground(4)*f3*f4*f5+ground(6)*f1*f2*f4+ground(6)*f4*f5*f2+ground(6)*f4*f5*f1+ground(4)*f4*f5*f6+ground(6)*f1*f2*f5+ground(8)*f1*f3*f5+ground(6)*f2*f3*f5+ground(6)*f5*f6*f3+ground(6)*f5*f6*f2+ground(6)*f5*f6*f1+ground(4)*f5*f6*f7+ground(6)*f1*f2*f6+ground(8)*f1*f3*f6+ground(8)*f1*f4*f6+ground(6)*f2*f3*f6+ground(8)*f2*f4*f6+ground(6)*f3*f4*f6+ground(6)*f6*f7*f4+ground(6)*f6*f7*f3+ground(6)*f6*f7*f2+ground(6)*f6*f7*f1+ground(11)//ground(8)*f6*f7*f8+ground(6)*f1*f2*f7+ground(8)*f1*f3*f7+ground(8)*f1*f4*f7+ground(8)*f1*f5*f7+ground(6)*f2*f3*f7+ground(8)*f2*f4*f7+ground(8)*f2*f5*f7+ground(6)*f3*f4*f7+ground(8)*f3*f5*f7+ground(6)*f4*f5*f7+ground(5)//ground(2)*f7*f8*f5+ground(5)//ground(2)*f7*f8*f4+ground(5)//ground(2)*f7*f8*f3+ground(5)//ground(2)*f7*f8*f2+ground(5)//ground(2)*f7*f8*f1+ground(27)//ground(8)*f1*f2*f8+ground(9)//ground(2)*f1*f3*f8+ground(9)//ground(2)*f1*f4*f8+ground(9)//ground(2)*f1*f5*f8+ground(9)//ground(2)*f1*f6*f8+ground(27)//ground(8)*f2*f3*f8+ground(9)//ground(2)*f2*f4*f8+ground(9)//ground(2)*f2*f5*f8+ground(9)//ground(2)*f2*f6*f8+ground(27)//ground(8)*f3*f4*f8+ground(9)//ground(2)*f3*f5*f8+ground(9)//ground(2)*f3*f6*f8+ground(27)//ground(8)*f4*f5*f8+ground(9)//ground(2)*f4*f6*f8+ground(27)//ground(8)*f5*f6*f8+ground(4)*f3*f1*f2,
-            -ground(257068)+ground(3)*f1*f2+ground(3)*f2*f3+ground(4)*f3*f1+ground(3)*f3*f4+ground(4)*f4*f2+ground(4)*f4*f1+ground(3)*f4*f5+ground(4)*f5*f3+ground(4)*f5*f2+ground(4)*f5*f1+ground(3)*f5*f6+ground(4)*f6*f4+ground(4)*f6*f3+ground(4)*f6*f2+ground(4)*f6*f1+ground(3)*f6*f7+ground(4)*f7*f5+ground(4)*f7*f4+ground(4)*f7*f3+ground(4)*f7*f2+ground(4)*f7*f1+ground(5)//ground(4)*f7*f8+ground(9)//ground(4)*f8*f6+ground(9)//ground(4)*f8*f5+ground(9)//ground(4)*f8*f4+ground(9)//ground(4)*f8*f3+ground(9)//ground(4)*f8*f2+ground(9)//ground(4)*f8*f1,ground(9)//ground(8)*f8+ground(2)*f7+ground(2)*f6+ground(2)*f5+ground(2)*f4+ground(2)*f3+ground(2)*f2+ground(2)*f1-ground(808)
-        ]
+        ordering=ordering
+    )
+    [
+        ground(2)*f1*f2*f3*f4*f5*f6*f7*f8-ground(69850115960625),
+        ground(8)*f7*f6*f5*f4*f3*f1*f2+ground(15)//ground(8)*f2*f3*f4*f5*f6*f7*f8+ground(15)//ground(2)*f1*f2*f3*f4*f5*f7*f8+ground(55)//ground(8)*f1*f2*f3*f4*f6*f7*f8+ground(6)*f1*f2*f3*f5*f6*f7*f8+ground(39)//ground(8)*f1*f2*f4*f5*f6*f7*f8+ground(7)//ground(2)*f1*f3*f4*f5*f6*f7*f8+ground(63)//ground(8)*f1*f2*f3*f4*f5*f6*f8-ground(32870642805000),
+        -ground(3654447799500)+ground(27)//ground(2)*f1*f2*f4*f5*f6*f8+ground(45)//ground(4)*f1*f3*f4*f5*f6*f8+ground(27)//ground(4)*f2*f3*f4*f5*f6*f8+ground(7)//ground(4)*f3*f4*f5*f6*f7*f8+ground(12)*f1*f2*f3*f4*f5*f7+ground(15)*f1*f2*f3*f4*f6*f7+ground(16)*f1*f2*f3*f5*f6*f7+ground(15)*f1*f2*f4*f5*f6*f7+ground(12)*f1*f3*f4*f5*f6*f7+ground(25)//ground(4)*f1*f2*f3*f4*f7*f8+ground(10)*f1*f2*f3*f5*f7*f8+ground(11)//ground(2)*f1*f2*f3*f6*f7*f8+ground(45)//ground(4)*f1*f2*f4*f5*f7*f8+ground(33)//ground(4)*f1*f2*f4*f6*f7*f8+ground(9)//ground(2)*f1*f2*f5*f6*f7*f8+ground(10)*f1*f3*f4*f5*f7*f8+ground(33)//ground(4)*f1*f3*f4*f6*f7*f8+ground(6)*f1*f3*f5*f6*f7*f8+ground(13)//ground(4)*f1*f4*f5*f6*f7*f8+ground(25)//ground(4)*f2*f3*f4*f5*f7*f8+ground(11)//ground(2)*f2*f3*f4*f6*f7*f8+ground(9)//ground(2)*f2*f3*f5*f6*f7*f8+ground(13)//ground(4)*f2*f4*f5*f6*f7*f8+ground(27)//ground(4)*f1*f2*f3*f4*f5*f8+ground(45)//ground(4)*f1*f2*f3*f4*f6*f8+ground(27)//ground(2)*f1*f2*f3*f5*f6*f8+ground(7)*f6*f5*f4*f3*f1*f2+ground(7)*f2*f3*f4*f5*f6*f7,
+        -ground(163221399000)+ground(6)*f5*f4*f3*f1*f2+ground(6)*f2*f3*f4*f5*f6+ground(6)*f3*f4*f5*f6*f7+ground(10)*f1*f2*f3*f4*f6+ground(12)*f1*f2*f3*f5*f6+ground(12)*f1*f2*f4*f5*f6+ground(10)*f1*f3*f4*f5*f6+ground(13)//ground(8)*f4*f5*f6*f7*f8+ground(10)*f1*f2*f3*f4*f7+ground(16)*f1*f2*f3*f5*f7+ground(12)*f1*f2*f3*f6*f7+ground(18)*f1*f2*f4*f5*f7+ground(18)*f1*f2*f4*f6*f7+ground(12)*f1*f2*f5*f6*f7+ground(16)*f1*f3*f4*f5*f7+ground(18)*f1*f3*f4*f6*f7+ground(16)*f1*f3*f5*f6*f7+ground(10)*f1*f4*f5*f6*f7+ground(10)*f2*f3*f4*f5*f7+ground(12)*f2*f3*f4*f6*f7+ground(12)*f2*f3*f5*f6*f7+ground(10)*f2*f4*f5*f6*f7+ground(5)*f1*f2*f3*f7*f8+ground(15)//ground(2)*f1*f2*f4*f7*f8+ground(15)//ground(2)*f1*f2*f5*f7*f8+ground(33)//ground(8)*f1*f2*f6*f7*f8+ground(15)//ground(2)*f1*f3*f4*f7*f8+ground(10)*f1*f3*f5*f7*f8+ground(11)//ground(2)*f1*f3*f6*f7*f8+ground(15)//ground(2)*f1*f4*f5*f7*f8+ground(11)//ground(2)*f1*f4*f6*f7*f8+ground(3)*f1*f5*f6*f7*f8+ground(5)*f2*f3*f4*f7*f8+ground(15)//ground(2)*f2*f3*f5*f7*f8+ground(33)//ground(8)*f2*f3*f6*f7*f8+ground(15)//ground(2)*f2*f4*f5*f7*f8+ground(11)//ground(2)*f2*f4*f6*f7*f8+ground(3)*f2*f5*f6*f7*f8+ground(5)*f3*f4*f5*f7*f8+ground(33)//ground(8)*f3*f4*f6*f7*f8+ground(3)*f3*f5*f6*f7*f8+ground(45)//ground(8)*f1*f2*f3*f4*f8+ground(9)*f1*f2*f3*f5*f8+ground(9)*f1*f2*f3*f6*f8+ground(81)//ground(8)*f1*f2*f4*f5*f8+ground(27)//ground(2)*f1*f2*f4*f6*f8+ground(81)//ground(8)*f1*f2*f5*f6*f8+ground(9)*f1*f3*f4*f5*f8+ground(27)//ground(2)*f1*f3*f4*f6*f8+ground(27)//ground(2)*f1*f3*f5*f6*f8+ground(9)*f1*f4*f5*f6*f8+ground(45)//ground(8)*f2*f3*f4*f5*f8+ground(9)*f2*f3*f4*f6*f8+ground(81)//ground(8)*f2*f3*f5*f6*f8+ground(9)*f2*f4*f5*f6*f8+ground(45)//ground(8)*f3*f4*f5*f6*f8,
+        -ground(3562995798)+ground(5)*f4*f3*f1*f2+ground(5)*f2*f3*f4*f5+ground(5)*f3*f4*f5*f6+ground(8)*f1*f2*f3*f5+ground(9)*f1*f2*f4*f5+ground(8)*f1*f3*f4*f5+ground(5)*f4*f5*f6*f7+ground(8)*f1*f2*f3*f6+ground(12)*f1*f2*f4*f6+ground(9)*f1*f2*f5*f6+ground(12)*f1*f3*f4*f6+ground(12)*f1*f3*f5*f6+ground(8)*f1*f4*f5*f6+ground(8)*f2*f3*f4*f6+ground(9)*f2*f3*f5*f6+ground(8)*f2*f4*f5*f6+ground(3)//ground(2)*f5*f6*f7*f8+ground(8)*f1*f2*f3*f7+ground(12)*f1*f2*f4*f7+ground(12)*f1*f2*f5*f7+ground(9)*f1*f2*f6*f7+ground(12)*f1*f3*f4*f7+ground(16)*f1*f3*f5*f7+ground(12)*f1*f3*f6*f7+ground(12)*f1*f4*f5*f7+ground(12)*f1*f4*f6*f7+ground(8)*f1*f5*f6*f7+ground(8)*f2*f3*f4*f7+ground(12)*f2*f3*f5*f7+ground(9)*f2*f3*f6*f7+ground(12)*f2*f4*f5*f7+ground(12)*f2*f4*f6*f7+ground(8)*f2*f5*f6*f7+ground(8)*f3*f4*f5*f7+ground(9)*f3*f4*f6*f7+ground(8)*f3*f5*f6*f7+ground(15)//ground(4)*f1*f2*f7*f8+ground(5)*f1*f3*f7*f8+ground(5)*f1*f4*f7*f8+ground(5)*f1*f5*f7*f8+ground(11)//ground(4)*f1*f6*f7*f8+ground(15)//ground(4)*f2*f3*f7*f8+ground(5)*f2*f4*f7*f8+ground(5)*f2*f5*f7*f8+ground(11)//ground(4)*f2*f6*f7*f8+ground(15)//ground(4)*f3*f4*f7*f8+ground(5)*f3*f5*f7*f8+ground(11)//ground(4)*f3*f6*f7*f8+ground(15)//ground(4)*f4*f5*f7*f8+ground(11)//ground(4)*f4*f6*f7*f8+ground(9)//ground(2)*f1*f2*f3*f8+ground(27)//ground(4)*f1*f2*f4*f8+ground(27)//ground(4)*f1*f2*f5*f8+ground(27)//ground(4)*f1*f2*f6*f8+ground(27)//ground(4)*f1*f3*f4*f8+ground(9)*f1*f3*f5*f8+ground(9)*f1*f3*f6*f8+ground(27)//ground(4)*f1*f4*f5*f8+ground(9)*f1*f4*f6*f8+ground(27)//ground(4)*f1*f5*f6*f8+ground(9)//ground(2)*f2*f3*f4*f8+ground(27)//ground(4)*f2*f3*f5*f8+ground(27)//ground(4)*f2*f3*f6*f8+ground(27)//ground(4)*f2*f4*f5*f8+ground(9)*f2*f4*f6*f8+ground(27)//ground(4)*f2*f5*f6*f8+ground(9)//ground(2)*f3*f4*f5*f8+ground(27)//ground(4)*f3*f4*f6*f8+ground(27)//ground(4)*f3*f5*f6*f8+ground(9)//ground(2)*f4*f5*f6*f8,
+        -ground(41268600)+ground(4)*f2*f3*f4+ground(6)*f3*f4*f1+ground(4)*f3*f4*f5+ground(6)*f1*f2*f4+ground(6)*f4*f5*f2+ground(6)*f4*f5*f1+ground(4)*f4*f5*f6+ground(6)*f1*f2*f5+ground(8)*f1*f3*f5+ground(6)*f2*f3*f5+ground(6)*f5*f6*f3+ground(6)*f5*f6*f2+ground(6)*f5*f6*f1+ground(4)*f5*f6*f7+ground(6)*f1*f2*f6+ground(8)*f1*f3*f6+ground(8)*f1*f4*f6+ground(6)*f2*f3*f6+ground(8)*f2*f4*f6+ground(6)*f3*f4*f6+ground(6)*f6*f7*f4+ground(6)*f6*f7*f3+ground(6)*f6*f7*f2+ground(6)*f6*f7*f1+ground(11)//ground(8)*f6*f7*f8+ground(6)*f1*f2*f7+ground(8)*f1*f3*f7+ground(8)*f1*f4*f7+ground(8)*f1*f5*f7+ground(6)*f2*f3*f7+ground(8)*f2*f4*f7+ground(8)*f2*f5*f7+ground(6)*f3*f4*f7+ground(8)*f3*f5*f7+ground(6)*f4*f5*f7+ground(5)//ground(2)*f7*f8*f5+ground(5)//ground(2)*f7*f8*f4+ground(5)//ground(2)*f7*f8*f3+ground(5)//ground(2)*f7*f8*f2+ground(5)//ground(2)*f7*f8*f1+ground(27)//ground(8)*f1*f2*f8+ground(9)//ground(2)*f1*f3*f8+ground(9)//ground(2)*f1*f4*f8+ground(9)//ground(2)*f1*f5*f8+ground(9)//ground(2)*f1*f6*f8+ground(27)//ground(8)*f2*f3*f8+ground(9)//ground(2)*f2*f4*f8+ground(9)//ground(2)*f2*f5*f8+ground(9)//ground(2)*f2*f6*f8+ground(27)//ground(8)*f3*f4*f8+ground(9)//ground(2)*f3*f5*f8+ground(9)//ground(2)*f3*f6*f8+ground(27)//ground(8)*f4*f5*f8+ground(9)//ground(2)*f4*f6*f8+ground(27)//ground(8)*f5*f6*f8+ground(4)*f3*f1*f2,
+        -ground(257068)+ground(3)*f1*f2+ground(3)*f2*f3+ground(4)*f3*f1+ground(3)*f3*f4+ground(4)*f4*f2+ground(4)*f4*f1+ground(3)*f4*f5+ground(4)*f5*f3+ground(4)*f5*f2+ground(4)*f5*f1+ground(3)*f5*f6+ground(4)*f6*f4+ground(4)*f6*f3+ground(4)*f6*f2+ground(4)*f6*f1+ground(3)*f6*f7+ground(4)*f7*f5+ground(4)*f7*f4+ground(4)*f7*f3+ground(4)*f7*f2+ground(4)*f7*f1+ground(5)//ground(4)*f7*f8+ground(9)//ground(4)*f8*f6+ground(9)//ground(4)*f8*f5+ground(9)//ground(4)*f8*f4+ground(9)//ground(4)*f8*f3+ground(9)//ground(4)*f8*f2+ground(9)//ground(4)*f8*f1,ground(9)//ground(8)*f8+ground(2)*f7+ground(2)*f6+ground(2)*f5+ground(2)*f4+ground(2)*f3+ground(2)*f2+ground(2)*f1-ground(808)
+    ]
 end
 
-#
-# Eco-n systems
+# Source:
+# https://gitlab.lip6.fr/eder/msolve-examples/-/raw/master/zero-dimensional/henrion9.ms
+function henrion9(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
+    _, (f1, f2, f3, f4, f5, f6, f7, f8, f9) = np.polynomial_ring(
+        ground,
+        ["f1", "f2", "f3", "f4", "f5", "f6", "f7", "f8", "f9"],
+        ordering=ordering
+    )
+    [
+        2*f1*f2*f3*f4*f5*f6*f7*f8*f9-22561587455281875,
+        9*f8*f7*f6*f5*f4*f3*f1*f2+17//ground(9)*f2*f3*f4*f5*f6*f7*f8*f9+77//ground(9)*f1*f2*f3*f4*f5*f6*f8*f9+8*f1*f2*f3*f4*f5*f7*f8*f9+65//ground(9)*f1*f2*f3*f4*f6*f7*f8*f9+56//ground(9)*f1*f2*f3*f5*f6*f7*f8*f9+5*f1*f2*f4*f5*f6*f7*f8*f9+32//ground(9)*f1*f3*f4*f5*f6*f7*f8*f9+80//ground(9)*f1*f2*f3*f4*f5*f6*f7*f9-10687067741975625,
+        -1213257282043500+44//ground(3)*f1*f2*f3*f5*f6*f8*f9+32//ground(3)*f1*f2*f3*f5*f7*f8*f9+52//ground(9)*f1*f2*f3*f6*f7*f8*f9+44//ground(3)*f1*f2*f4*f5*f6*f8*f9+12*f1*f2*f4*f5*f7*f8*f9+26//ground(3)*f1*f2*f4*f6*f7*f8*f9+14//ground(3)*f1*f2*f5*f6*f7*f8*f9+110//ground(9)*f1*f3*f4*f5*f6*f8*f9+32//ground(3)*f1*f3*f4*f5*f7*f8*f9+26//ground(3)*f1*f3*f4*f6*f7*f8*f9+56//ground(9)*f1*f3*f5*f6*f7*f8*f9+10//ground(3)*f1*f4*f5*f6*f7*f8*f9+22//ground(3)*f2*f3*f4*f5*f6*f8*f9+20//ground(3)*f2*f3*f4*f5*f7*f8*f9+52//ground(9)*f2*f3*f4*f6*f7*f8*f9+14//ground(3)*f2*f3*f5*f6*f7*f8*f9+10//ground(3)*f2*f4*f5*f6*f7*f8*f9+70//ground(9)*f1*f2*f3*f4*f5*f6*f9+40//ground(3)*f1*f2*f3*f4*f5*f7*f9+50//ground(3)*f1*f2*f3*f4*f6*f7*f9+160//ground(9)*f1*f2*f3*f5*f6*f7*f9+50//ground(3)*f1*f2*f4*f5*f6*f7*f9+40//ground(3)*f1*f3*f4*f5*f6*f7*f9+70//ground(9)*f2*f3*f4*f5*f6*f7*f9+8*f7*f6*f5*f4*f3*f1*f2+8*f2*f3*f4*f5*f6*f7*f8+16//ground(9)*f3*f4*f5*f6*f7*f8*f9+14*f1*f2*f3*f4*f5*f6*f8+18*f1*f2*f3*f4*f5*f7*f8+20*f1*f2*f3*f4*f6*f7*f8+20*f1*f2*f3*f5*f6*f7*f8+18*f1*f2*f4*f5*f6*f7*f8+14*f1*f3*f4*f5*f6*f7*f8+22//ground(3)*f1*f2*f3*f4*f5*f8*f9+110//ground(9)*f1*f2*f3*f4*f6*f8*f9+20//ground(3)*f1*f2*f3*f4*f7*f8*f9,
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+        -124301564+4*f3*f1*f2+4*f2*f3*f4+6*f3*f4*f1+4*f3*f4*f5+6*f1*f2*f4+6*f4*f5*f2+6*f4*f5*f1+4*f4*f5*f6+6*f1*f2*f5+8*f1*f3*f5+6*f2*f3*f5+6*f5*f6*f3+6*f5*f6*f2+6*f5*f6*f1+4*f5*f6*f7+6*f1*f2*f6+8*f1*f3*f6+8*f1*f4*f6+6*f2*f3*f6+8*f2*f4*f6+6*f3*f4*f6+6*f6*f7*f4+6*f6*f7*f3+6*f6*f7*f2+6*f6*f7*f1+4*f6*f7*f8+6*f1*f2*f7+8*f1*f3*f7+8*f1*f4*f7+8*f1*f5*f7+6*f2*f3*f7+8*f2*f4*f7+8*f2*f5*f7+6*f3*f4*f7+8*f3*f5*f7+6*f4*f5*f7+6*f7*f8*f5+6*f7*f8*f4+6*f7*f8*f3+6*f7*f8*f2+6*f7*f8*f1+4//ground(3)*f7*f8*f9+6*f1*f2*f8+8*f1*f3*f8+8*f1*f4*f8+8*f1*f5*f8+8*f1*f6*f8+6*f2*f3*f8+8*f2*f4*f8+8*f2*f5*f8+8*f2*f6*f8+6*f3*f4*f8+8*f3*f5*f8+8*f3*f6*f8+6*f4*f5*f8+8*f4*f6*f8+6*f5*f6*f8+22//ground(9)*f8*f9*f6+22//ground(9)*f8*f9*f5+22//ground(9)*f8*f9*f4+22//ground(9)*f8*f9*f3+22//ground(9)*f8*f9*f2+22//ground(9)*f8*f9*f1+10//ground(3)*f1*f2*f9+40//ground(9)*f1*f3*f9+40//ground(9)*f1*f4*f9+40//ground(9)*f1*f5*f9+40//ground(9)*f1*f6*f9+40//ground(9)*f1*f7*f9+10//ground(3)*f2*f3*f9+40//ground(9)*f2*f4*f9+40//ground(9)*f2*f5*f9+40//ground(9)*f2*f6*f9+40//ground(9)*f2*f7*f9+10//ground(3)*f3*f4*f9+40//ground(9)*f3*f5*f9+40//ground(9)*f3*f6*f9+40//ground(9)*f3*f7*f9+10//ground(3)*f4*f5*f9+40//ground(9)*f4*f6*f9+40//ground(9)*f4*f7*f9+10//ground(3)*f5*f6*f9+40//ground(9)*f5*f7*f9+10//ground(3)*f6*f7*f9,
+        -518052+3*f1*f2+3*f2*f3+4*f3*f1+3*f3*f4+4*f4*f2+4*f4*f1+3*f4*f5+4*f5*f3+4*f5*f2+4*f5*f1+3*f5*f6+4*f6*f4+4*f6*f3+4*f6*f2+4*f6*f1+3*f6*f7+4*f7*f5+4*f7*f4+4*f7*f3+4*f7*f2+4*f7*f1+3*f7*f8+4*f8*f6+4*f8*f5+4*f8*f4+4*f8*f3+4*f8*f2+4*f8*f1+11//ground(9)*f8*f9+20//ground(9)*f9*f7+20//ground(9)*f9*f6+20//ground(9)*f9*f5+20//ground(9)*f9*f4+20//ground(9)*f9*f3+20//ground(9)*f9*f2+20//ground(9)*f9*f1,
+        10//ground(9)*f9+2*f8+2*f7+2*f6+2*f5+2*f4+2*f3+2*f2+2*f1-1131
+    ]
+end
+
+###
+# Eco
 
 function eco5(; np=AbstractAlgebra, ground=np.GF(2^31 - 1), ordering=:lex)
     _, (x1, x2, x3, x4, x5) =
@@ -604,11 +617,76 @@ function eco14(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
         x0*x12*x13+x11*x13-12,
         x12*x13-13,
         x0+x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+1
-]
+    ]
+end
+
+function eco15(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
+    _, (x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14) = np.polynomial_ring(ground, ["x$i" for i in 1:15], ordering=ordering)
+    [
+        x0*x1*x14+x1*x2*x14+x2*x3*x14+x3*x4*x14+x4*x5*x14+x5*x6*x14+x6*x7*x14+x7*x8*x14+x8*x9*x14+x9*x10*x14+x10*x11*x14+x11*x12*x14+x12*x13*x14+x0*x14-1,
+        x0*x2*x14+x1*x3*x14+x2*x4*x14+x3*x5*x14+x4*x6*x14+x5*x7*x14+x6*x8*x14+x7*x9*x14+x8*x10*x14+x9*x11*x14+x10*x12*x14+x11*x13*x14+x1*x14-2,
+        x0*x3*x14+x1*x4*x14+x2*x5*x14+x3*x6*x14+x4*x7*x14+x5*x8*x14+x6*x9*x14+x7*x10*x14+x8*x11*x14+x9*x12*x14+x10*x13*x14+x2*x14-3,
+        x0*x4*x14+x1*x5*x14+x2*x6*x14+x3*x7*x14+x4*x8*x14+x5*x9*x14+x6*x10*x14+x7*x11*x14+x8*x12*x14+x9*x13*x14+x3*x14-4,
+        x0*x5*x14+x1*x6*x14+x2*x7*x14+x3*x8*x14+x4*x9*x14+x5*x10*x14+x6*x11*x14+x7*x12*x14+x8*x13*x14+x4*x14-5,
+        x0*x6*x14+x1*x7*x14+x2*x8*x14+x3*x9*x14+x4*x10*x14+x5*x11*x14+x6*x12*x14+x7*x13*x14+x5*x14-6,
+        x0*x7*x14+x1*x8*x14+x2*x9*x14+x3*x10*x14+x4*x11*x14+x5*x12*x14+x6*x13*x14+x6*x14-7,
+        x0*x8*x14+x1*x9*x14+x2*x10*x14+x3*x11*x14+x4*x12*x14+x5*x13*x14+x7*x14-8,
+        x0*x9*x14+x1*x10*x14+x2*x11*x14+x3*x12*x14+x4*x13*x14+x8*x14-9,
+        x0*x10*x14+x1*x11*x14+x2*x12*x14+x3*x13*x14+x9*x14-10,
+        x0*x11*x14+x1*x12*x14+x2*x13*x14+x10*x14-11,
+        x0*x12*x14+x1*x13*x14+x11*x14-12,
+        x0*x13*x14+x12*x14-13,
+        x13*x14-14,
+        x0+x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13+1
+    ]
+end
+
+# Source:
+# https://github.com/JuliaHomotopyContinuation/PolynomialTestSystems.jl/blob/master/src/rps10.jl
+function rps10(; tol=0, np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
+    _, (g1, g2, g3, p1, p2, p3, q0, q1, q2, q3) = np.polynomial_ring(ground, ["g1", "g2", "g3", "p1", "p2", "p3", "q0", "q1", "q2", "q3",], ordering=ordering)
+    equations = [
+    -rationalize(BigInt, rationalize(BigInt, 0.1279703687075118, tol=tol), tol=tol)*g1^2 - rationalize(BigInt, rationalize(BigInt, 0.48596123125526264, tol=tol), tol=tol)*g1*g2 + rationalize(BigInt, 0.30699556370717496, tol=tol)*g2^2 + rationalize(BigInt, 0.3778977698527674, tol=tol)*g1*g3 - rationalize(BigInt, 0.23404544076569642, tol=tol)*g2*g3 + rationalize(BigInt, 0.01563626178508072, tol=tol)*g3^2 + rationalize(BigInt, 0.327228678790004, tol=tol)*g1^2*p1 + rationalize(BigInt, 0.8426829275672494, tol=tol)*g1*g2*p1 + rationalize(BigInt, 0.6075645757034159, tol=tol)*g2^2*p1 - rationalize(BigInt, 1.1371405598667543, tol=tol)*g1*g3*p1 + rationalize(BigInt, 0.229293271620915, tol=tol)*g2*g3*p1 - rationalize(BigInt, 0.21948911177437957, tol=tol)*g3^2*p1 - rationalize(BigInt, 0.2075154964282774, tol=tol)*g1^2*p1^2 - rationalize(BigInt, 0.37702968479068544, tol=tol)*g1*g2*p1^2 - rationalize(BigInt, 0.16688906819159421, tol=tol)*g2^2*p1^2 + rationalize(BigInt, 0.7986954318323025, tol=tol)*g1*g3*p1^2 + rationalize(BigInt, 0.866826144775651, tol=tol)*g2*g3*p1^2 + rationalize(BigInt, 0.37440456461987165, tol=tol)*g3^2*p1^2 + rationalize(BigInt, 1.5614616440131446, tol=tol)*g1^2*p2 - rationalize(BigInt, 1.7388380675822595, tol=tol)*g1*g2*p2 + rationalize(BigInt, 0.06790915713070725, tol=tol)*g2^2*p2 - rationalize(BigInt, 0.4309121044684771, tol=tol)*g1*g3*p2 + rationalize(BigInt, 0.9086272006283425, tol=tol)*g2*g3*p2 - rationalize(BigInt, 0.2764931751394603, tol=tol)*g3^2*p2 - rationalize(BigInt, 1.8163349832174116, tol=tol)*g1^2*p1*p2 - rationalize(BigInt, 0.9167144057621401, tol=tol)*g1*g2*p1*p2 + rationalize(BigInt, 1.0203368504488892, tol=tol)*g2^2*p1*p2 - rationalize(BigInt, 0.23194646823111892, tol=tol)*g1*g3*p1*p2 + rationalize(BigInt, 0.539670777307627, tol=tol)*g2*g3*p1*p2 + rationalize(BigInt, 0.7959981327685224, tol=tol)*g3^2*p1*p2 + rationalize(BigInt, 0.08717268867521591, tol=tol)*g1^2*p2^2 + rationalize(BigInt, 0.9504154644263471, tol=tol)*g1*g2*p2^2 - rationalize(BigInt, 0.48206756571420756, tol=tol)*g2^2*p2^2 - rationalize(BigInt, 1.065062423127697, tol=tol)*g1*g3*p2^2 + rationalize(BigInt, 0.1209952909274163, tol=tol)*g2*g3*p2^2 + rationalize(BigInt, 0.3948948770389917, tol=tol)*g3^2*p2^2 + rationalize(BigInt, 0.289766299873838, tol=tol)*g1^2*p3 - rationalize(BigInt, 1.2778927965251532, tol=tol)*g1*g2*p3 + rationalize(BigInt, 0.9087896778886251, tol=tol)*g2^2*p3 - rationalize(BigInt, 0.5812612591154215, tol=tol)*g1*g3*p3 - rationalize(BigInt, 0.7595904624983555, tol=tol)*g2*g3*p3 + rationalize(BigInt, 0.5084892760496751, tol=tol)*g3^2*p3 - rationalize(BigInt, 0.3268802641947883, tol=tol)*g1^2*p1*p3 + rationalize(BigInt, 0.657630238424344, tol=tol)*g1*g2*p1*p3 + rationalize(BigInt, 1.1093919363972093, tol=tol)*g2^2*p1*p3 + rationalize(BigInt, 0.4551393419480071, tol=tol)*g1*g3*p1*p3 + rationalize(BigInt, 1.8553852513069364, tol=tol)*g2*g3*p1*p3 - rationalize(BigInt, 0.7825116722024211, tol=tol)*g3^2*p1*p3 + rationalize(BigInt, 0.5810469298461638, tol=tol)*g1^2*p2*p3 - rationalize(BigInt, 1.1557382363783264, tol=tol)*g1*g2*p2*p3 - rationalize(BigInt, 0.11367961187637783, tol=tol)*g2^2*p2*p3 + rationalize(BigInt, 1.7077140933509898, tol=tol)*g1*g3*p2*p3 - rationalize(BigInt, 0.36547942767108677, tol=tol)*g2*g3*p2*p3 - rationalize(BigInt, 0.4673673179697859, tol=tol)*g3^2*p2*p3 + rationalize(BigInt, 0.12034280775306151, tol=tol)*g1^2*p3^2 - rationalize(BigInt, 0.5733857796356615, tol=tol)*g1*g2*p3^2 + rationalize(BigInt, 0.6489566339058018, tol=tol)*g2^2*p3^2 + rationalize(BigInt, 0.2663669912953945, tol=tol)*g1*g3*p3^2 - rationalize(BigInt, 0.9878214357030672, tol=tol)*g2*g3*p3^2 - rationalize(BigInt, 0.7692994416588633, tol=tol)*g3^2*p3^2 - rationalize(BigInt, 0.19466145678474384, tol=tol)*q0 - rationalize(BigInt, 0.7153041427190404, tol=tol)*p1*q0 - rationalize(BigInt, 1.3528776260043915, tol=tol)*p2*q0 - rationalize(BigInt, 1.7070452538121381, tol=tol)*p3*q0 - rationalize(BigInt, 1.0516635822669562, tol=tol)*q1 + rationalize(BigInt, 1.2244185478631853, tol=tol)*p1*q1 - rationalize(BigInt, 0.05844567698552443, tol=tol)*p2*q1 - rationalize(BigInt, 0.37706149953585283, tol=tol)*p3*q1 + rationalize(BigInt, 0.580102254517945, tol=tol)*q2 + rationalize(BigInt, 1.2898860704586343, tol=tol)*p1*q2 - rationalize(BigInt, 0.6655948497180294, tol=tol)*p2*q2 + rationalize(BigInt, 0.697758704890495, tol=tol)*p3*q2 - rationalize(BigInt, 0.042921436747585445, tol=tol)*q3 + rationalize(BigInt, 0.5172073855756967, tol=tol)*p1*q3 + rationalize(BigInt, 0.6917094054122289, tol=tol)*p2*q3 - rationalize(BigInt, 1.4579672250860476, tol=tol)*p3*q3,
+    rationalize(BigInt, 0.16011034303688113, tol=tol)*g1^2 - rationalize(BigInt, 0.9005468824403076, tol=tol)*g1*g2 - rationalize(BigInt, 0.3519015838689263, tol=tol)*g2^2 + rationalize(BigInt, 0.5202586158306898, tol=tol)*g1*g3 + rationalize(BigInt, 0.908682123022068, tol=tol)*g2*g3 - rationalize(BigInt, 0.4464562170645777, tol=tol)*g3^2 - rationalize(BigInt, 0.13844524415679324, tol=tol)*g1^2*p1 + rationalize(BigInt, 1.5568085644333742, tol=tol)*g1*g2*p1 + rationalize(BigInt, 1.6863862382239232, tol=tol)*g2^2*p1 - rationalize(BigInt, 1.7409458121154344, tol=tol)*g1*g3*p1 - rationalize(BigInt, 0.13872356093602894, tol=tol)*g2*g3*p1 - rationalize(BigInt, 0.5159047084859331, tol=tol)*g3^2*p1 - rationalize(BigInt, 0.2741643484200128, tol=tol)*g1^2*p1^2 - rationalize(BigInt, 0.34212012775550327, tol=tol)*g1*g2*p1^2 - rationalize(BigInt, 0.07542436599114127, tol=tol)*g2^2*p1^2 + rationalize(BigInt, 0.37458987278720324, tol=tol)*g1*g3*p1^2 + rationalize(BigInt, 0.4782561996467687, tol=tol)*g2*g3*p1^2 + rationalize(BigInt, 0.3495887144111541, tol=tol)*g3^2*p1^2 + rationalize(BigInt, 0.41377445473869573, tol=tol)*g1^2*p2 - rationalize(BigInt, 1.5789383736211624, tol=tol)*g1*g2*p2 + rationalize(BigInt, 1.268319517294935, tol=tol)*g2^2*p2 + rationalize(BigInt, 0.6163793667190677, tol=tol)*g1*g3*p2 - rationalize(BigInt, 0.43374574206406646, tol=tol)*g2*g3*p2 - rationalize(BigInt, 0.2061458017243186, tol=tol)*g3^2*p2 + rationalize(BigInt, 0.14555549639831628, tol=tol)*g1^2*p1*p2 - rationalize(BigInt, 1.1674745895517964, tol=tol)*g1*g2*p1*p2 - rationalize(BigInt, 0.9428064489876502, tol=tol)*g2^2*p1*p2 + rationalize(BigInt, 0.0024916775818734295, tol=tol)*g1*g3*p1*p2 + rationalize(BigInt, 0.5291621555283466, tol=tol)*g2*g3*p1*p2 + rationalize(BigInt, 0.7972509525893339, tol=tol)*g3^2*p1*p2 + rationalize(BigInt, 0.1807885464109201, tol=tol)*g1^2*p2^2 + rationalize(BigInt, 0.9404541869824675, tol=tol)*g1*g2*p2^2 - rationalize(BigInt, 0.5780030515551372, tol=tol)*g2^2*p2^2 - rationalize(BigInt, 1.0257418447585547, tol=tol)*g1*g3*p2^2 + rationalize(BigInt, 0.09251778173989315, tol=tol)*g2*g3*p2^2 + rationalize(BigInt, 0.39721450514421713, tol=tol)*g3^2*p2^2 + rationalize(BigInt, 0.40272988912109214, tol=tol)*g1^2*p3 - rationalize(BigInt, 0.8272484673958682, tol=tol)*g1*g2*p3 + rationalize(BigInt, 1.057139636924469, tol=tol)*g2^2*p3 - rationalize(BigInt, 0.12353226665002319, tol=tol)*g1*g3*p3 - rationalize(BigInt, 2.5741855761862396, tol=tol)*g2*g3*p3 + rationalize(BigInt, 1.560474007685759, tol=tol)*g3^2*p3 - rationalize(BigInt, 0.6150996832616941, tol=tol)*g1^2*p1*p3 + rationalize(BigInt, 0.09937192239106099, tol=tol)*g1*g2*p1*p3 + rationalize(BigInt, 0.8226042775491553, tol=tol)*g2^2*p1*p3 + rationalize(BigInt, 0.4732438203631739, tol=tol)*g1*g3*p1*p3 + rationalize(BigInt, 1.6946050580334677, tol=tol)*g2*g3*p1*p3 - rationalize(BigInt, 0.20750459428746135, tol=tol)*g3^2*p1*p3 + rationalize(BigInt, 0.7556396990592089, tol=tol)*g1^2*p2*p3 - rationalize(BigInt, 1.412614951501404, tol=tol)*g1*g2*p2*p3 - rationalize(BigInt, 0.09676545515565128, tol=tol)*g2^2*p2*p3 - rationalize(BigInt, 0.9781576342585658, tol=tol)*g1*g3*p2*p3 + rationalize(BigInt, 2.5006617995144724, tol=tol)*g2*g3*p2*p3 - rationalize(BigInt, 0.6588742439035575, tol=tol)*g3^2*p2*p3 + rationalize(BigInt, 0.09337580200909272, tol=tol)*g1^2*p3^2 - rationalize(BigInt, 0.5983340592269643, tol=tol)*g1*g2*p3^2 + rationalize(BigInt, 0.6534274175462785, tol=tol)*g2^2*p3^2 + rationalize(BigInt, 0.6511519719713513, tol=tol)*g1*g3*p3^2 - rationalize(BigInt, 0.5707739813866619, tol=tol)*g2*g3*p3^2 - rationalize(BigInt, 0.7468032195553712, tol=tol)*g3^2*p3^2 + rationalize(BigInt, 0.6382474578966228, tol=tol)*q0 - rationalize(BigInt, 1.032036285581197, tol=tol)*p1*q0 - rationalize(BigInt, 1.4759481703093122, tol=tol)*p2*q0 - rationalize(BigInt, 3.0203435337313205, tol=tol)*p3*q0 - rationalize(BigInt, 0.22812438675350769, tol=tol)*q1 - rationalize(BigInt, 0.2157590670168509, tol=tol)*p1*q1 - rationalize(BigInt, 0.1270558344695696, tol=tol)*p2*q1 - rationalize(BigInt, 0.5148593639524484, tol=tol)*p3*q1 + rationalize(BigInt, 1.3667793800860086, tol=tol)*q2 - rationalize(BigInt, 0.06171123442924746, tol=tol)*p1*q2 - rationalize(BigInt, 0.7314954155886625, tol=tol)*p2*q2 + rationalize(BigInt, 0.7189348075213543, tol=tol)*p3*q2 - rationalize(BigInt, 0.902118536026858, tol=tol)*q3 + rationalize(BigInt, 0.43214823742186254, tol=tol)*p1*q3 + rationalize(BigInt, 0.6677624868260497, tol=tol)*p2*q3 + rationalize(BigInt, 0.5162571144422815, tol=tol)*p3*q3,
+    rationalize(BigInt, 0.20816475809219404, tol=tol)*g1^2 - rationalize(BigInt, 0.44624795696445435, tol=tol)*g1*g2 + rationalize(BigInt, 0.1573457781818856, tol=tol)*g2^2 + rationalize(BigInt, 0.2432511536576595, tol=tol)*g1*g3 - rationalize(BigInt, 0.4587424991969163, tol=tol)*g2*g3 - rationalize(BigInt, 0.048748564896809544, tol=tol)*g3^2 - rationalize(BigInt, 0.542424299098038, tol=tol)*g1^2*p1 + rationalize(BigInt, 0.412606879197033, tol=tol)*g1*g2*p1 + rationalize(BigInt, 0.026228493490255755, tol=tol)*g2^2*p1 - rationalize(BigInt, 0.7135454436169615, tol=tol)*g1*g3*p1 + rationalize(BigInt, 0.38566725023570736, tol=tol)*g2*g3*p1 + rationalize(BigInt, 0.06641935708182738, tol=tol)*g3^2*p1 + rationalize(BigInt, 0.1946156279601214, tol=tol)*g1^2*p1^2 + rationalize(BigInt, 1.0726514255671113, tol=tol)*g1*g2*p1^2 - rationalize(BigInt, 0.29746151974577967, tol=tol)*g2^2*p1^2 + rationalize(BigInt, 0.3474150051655493, tol=tol)*g1*g3*p1^2 + rationalize(BigInt, 1.5662794253637933, tol=tol)*g2*g3*p1^2 + rationalize(BigInt, 0.10284589178565828, tol=tol)*g3^2*p1^2 + rationalize(BigInt, 0.8655281158446179, tol=tol)*g1^2*p2 - rationalize(BigInt, 1.4227007533612923, tol=tol)*g1*g2*p2  - rationalize(BigInt, 0.3561608986253729, tol=tol)*g2^2*p2 - rationalize(BigInt, 0.7002053827479838, tol=tol)*g1*g3*p2 + rationalize(BigInt, 0.1451263721376322, tol=tol)*g2*g3*p2 - rationalize(BigInt, 0.4446427929457582, tol=tol)*g3^2*p2  - rationalize(BigInt, 0.35089234105147404, tol=tol)*g1^2*p1*p2 - rationalize(BigInt, 1.8637325747105546, tol=tol)*g1*g2*p1*p2 - rationalize(BigInt, 0.7643910878410862, tol=tol)*g2^2*p1*p2 + rationalize(BigInt, 0.7421389633104346, tol=tol)*g1*g3*p1*p2 + rationalize(BigInt, 0.8043890896223826, tol=tol)*g2*g3*p1*p2 + rationalize(BigInt, 1.1152834288925604, tol=tol)*g3^2*p1*p2 - rationalize(BigInt, 0.05058692105297476, tol=tol)*g1^2*p2^2 - rationalize(BigInt, 0.8545531093164939, tol=tol)*g1*g2*p2^2 - rationalize(BigInt, 0.25045809562785276, tol=tol)*g2^2*p2^2 - rationalize(BigInt, 1.482438556873845, tol=tol)*g1*g3*p2^2 - rationalize(BigInt, 0.2760311985894717, tol=tol)*g2*g3*p2^2 + rationalize(BigInt, 0.30104501668082756, tol=tol)*g3^2*p2^2 + rationalize(BigInt, 0.41615153726461007, tol=tol)*g1^2*p3 - rationalize(BigInt, 1.6031132124173149, tol=tol)*g1*g2*p3 + rationalize(BigInt, 1.1652768530802575, tol=tol)*g2^2*p3 + rationalize(BigInt, 0.1236694347662175, tol=tol)*g1*g3*p3  - rationalize(BigInt, 0.033510271732486586, tol=tol)*g2*g3*p3 + rationalize(BigInt, 0.6625023868605743, tol=tol)*g3^2*p3 - rationalize(BigInt, 0.06941899872446193, tol=tol)*g1^2*p1*p3 - rationalize(BigInt, 0.5612725019588681, tol=tol)*g1*g2*p1*p3 + rationalize(BigInt, 1.4835363108262836, tol=tol)*g2^2*p1*p3 - rationalize(BigInt, 0.8310204341509994, tol=tol)*g1*g3*p1*p3 + rationalize(BigInt, 1.3650887611787323, tol=tol)*g2*g3*p1*p3 - rationalize(BigInt, 1.4141173121018216, tol=tol)*g3^2*p1*p3 - rationalize(BigInt, 0.2915853970368523, tol=tol)*g1^2*p2*p3 - rationalize(BigInt, 1.2521117933146961, tol=tol)*g1*g2*p2*p3 + rationalize(BigInt, 0.38706376702247, tol=tol)*g2^2*p2*p3 + rationalize(BigInt, 1.2309129178715645, tol=tol)*g1*g3*p2*p3 + rationalize(BigInt, 2.001338697637118, tol=tol)*g2*g3*p2*p3 - rationalize(BigInt, 0.09547836998561768, tol=tol)*g3^2*p2*p3 - rationalize(BigInt, 0.14402870690714664, tol=tol)*g1^2*p3^2 - rationalize(BigInt, 0.2180983162506176, tol=tol)*g1*g2*p3^2 + rationalize(BigInt, 0.5479196153736324, tol=tol)*g2^2*p3^2 + rationalize(BigInt, 1.1350235517082958, tol=tol)*g1*g3*p3^2 - rationalize(BigInt, 1.2902482267743214, tol=tol)*g2*g3*p3^2 - rationalize(BigInt, 0.40389090846648584, tol=tol)*g3^2*p3^2 - rationalize(BigInt, 0.31676197137727014, tol=tol)*q0 + rationalize(BigInt, 0.44977644852595483, tol=tol)*p1*q0 - rationalize(BigInt, 0.06472442427348668, tol=tol)*p2*q0 - rationalize(BigInt, 2.2439307772054415, tol=tol)*p3*q0 - rationalize(BigInt, 0.5547165223690258, tol=tol)*q1 + rationalize(BigInt, 0.23831878651082344, tol=tol)*p1*q1 + rationalize(BigInt, 0.031977776730485255, tol=tol)*p2*q1 + rationalize(BigInt, 0.16687455406564522, tol=tol)*p3*q1 + rationalize(BigInt, 0.9423377906275198, tol=tol)*q2 + rationalize(BigInt, 1.376589178886685, tol=tol)*p1*q2 + rationalize(BigInt, 0.5306523901876015, tol=tol)*p2*q2 + rationalize(BigInt, 0.4754891181933043, tol=tol)*p3*q2 + rationalize(BigInt, 0.09673230093655334, tol=tol)*q3 + rationalize(BigInt, 0.0892904130224598, tol=tol)*p1*q3 + rationalize(BigInt, 0.943551163213123, tol=tol)*p2*q3 - rationalize(BigInt, 1.2527250130712726, tol=tol)*p3*q3,
+     -rationalize(BigInt, 0.04095049824628835, tol=tol)*g1^2 + rationalize(BigInt, 0.043116025511842154, tol=tol)*g1*g2 + rationalize(BigInt, 0.003940499198786224, tol=tol)*g2^2 + rationalize(BigInt, 0.7629770334036455, tol=tol)*g1*g3 - rationalize(BigInt, 0.8492350760146794, tol=tol)*g2*g3 - rationalize(BigInt, 0.2784174783424625, tol=tol)*g3^2 + rationalize(BigInt, 0.4281444292173086, tol=tol)*g1^2*p1 - rationalize(BigInt, 0.8828960936117035, tol=tol)*g1*g2*p1 + rationalize(BigInt, 0.5676682886279524, tol=tol)*g2^2*p1 - rationalize(BigInt, 1.3924527881029736, tol=tol)*g1*g3*p1 - rationalize(BigInt, 0.08671339002537767, tol=tol)*g2*g3*p1 - rationalize(BigInt, 0.7256104095984146, tol=tol)*g3^2*p1 - rationalize(BigInt, 0.5422313181564682, tol=tol)*g1^2*p1^2 + rationalize(BigInt, 0.4871946471731439, tol=tol)*g1*g2*p1^2 + rationalize(BigInt, 0.33193585698170985, tol=tol)*g2^2*p1^2 - rationalize(BigInt, 0.10273772900088107, tol=tol)*g1*g3*p1^2 + rationalize(BigInt, 0.6624874115365778, tol=tol)*g2*g3*p1^2 + rationalize(BigInt, 0.21029546117475836, tol=tol)*g3^2*p1^2 + rationalize(BigInt, 1.1356911567255628, tol=tol)*g1^2*p2 - rationalize(BigInt, 1.222100685178249, tol=tol)*g1*g2*p2 - rationalize(BigInt, 0.09334002143332033, tol=tol)*g2^2*p2 - rationalize(BigInt, 1.6524959396527132, tol=tol)*g1*g3*p2 + rationalize(BigInt, 1.5569725124184146, tol=tol)*g2*g3*p2 + rationalize(BigInt, 0.7669386068453008, tol=tol)*g3^2*p2 - rationalize(BigInt, 1.5587675264538823, tol=tol)*g1^2*p1*p2 - rationalize(BigInt, 1.1317581527003464, tol=tol)*g1*g2*p1*p2 + rationalize(BigInt, 0.01829080736739283, tol=tol)*g2^2*p1*p2 + rationalize(BigInt, 1.0020439814840232, tol=tol)*g1*g3*p1*p2 + rationalize(BigInt, 0.7984049760283556, tol=tol)*g2*g3*p1*p2 + rationalize(BigInt, 1.5404767190864894, tol=tol)*g3^2*p1*p2 + rationalize(BigInt, 0.4331904808414006, tol=tol)*g1^2*p2^2 - rationalize(BigInt, 0.1389285705830233, tol=tol)*g1*g2*p2^2 - rationalize(BigInt, 0.012183710127155694, tol=tol)*g2^2*p2^2 - rationalize(BigInt, 0.23769385136664706, tol=tol)*g1*g3*p2^2 + rationalize(BigInt, 0.24382837068218804, tol=tol)*g2*g3*p2^2 - rationalize(BigInt, 0.4210067707142449, tol=tol)*g3^2*p2^2 + rationalize(BigInt, 0.21198555697618326, tol=tol)*g1^2*p3 - rationalize(BigInt, 0.01647709154129892, tol=tol)*g1*g2*p3 - rationalize(BigInt, 0.18945218115272705, tol=tol)*g2^2*p3 + rationalize(BigInt, 0.77528301920843, tol=tol)*g1*g3*p3 - rationalize(BigInt, 2.0514046696465, tol=tol)*g2*g3*p3 + rationalize(BigInt, 0.10432028494512646, tol=tol)*g3^2*p3 - rationalize(BigInt, 0.1676311045685404, tol=tol)*g1^2*p1*p3 - rationalize(BigInt, 1.325546381572095, tol=tol)*g1*g2*p1*p3 + rationalize(BigInt, 0.8078478514339609, tol=tol)*g2^2*p1*p3 - rationalize(BigInt, 0.9669176278885212, tol=tol)*g1*g3*p1*p3 - rationalize(BigInt, 0.36872926793739896, tol=tol)*g2*g3*p1*p3 - rationalize(BigInt, 0.6402167468654205, tol=tol)*g3^2*p1*p3 + rationalize(BigInt, 0.6297207100844667, tol=tol)*g1^2*p2*p3 - rationalize(BigInt, 2.067771321161895, tol=tol)*g1*g2*p2*p3  - rationalize(BigInt, 0.17862819697751522, tol=tol)*g2^2*p2*p3 + rationalize(BigInt, 0.020391323549034297, tol=tol)*g1*g3*p2*p3  + rationalize(BigInt, 2.777563669744398, tol=tol)*g2*g3*p2*p3 - rationalize(BigInt, 0.45109251310695153, tol=tol)*g3^2*p2*p3 + rationalize(BigInt, 0.10904083731506761, tol=tol)*g1^2*p3^2 - rationalize(BigInt, 0.3482660765901206, tol=tol)*g1*g2*p3^2 - rationalize(BigInt, 0.31975214685455416, tol=tol)*g2^2*p3^2 + rationalize(BigInt, 0.34043158036752813, tol=tol)*g1*g3*p3^2 - rationalize(BigInt, 0.9063157822187657, tol=tol)*g2*g3*p3^2 + rationalize(BigInt, 0.21071130953948652, tol=tol)*g3^2*p3^2 + rationalize(BigInt, 0.31542747738996463, tol=tol)*q0 - rationalize(BigInt, 0.27020230824684643, tol=tol)*p1*q0 - rationalize(BigInt, 1.8092897421375431, tol=tol)*p2*q0 - rationalize(BigInt, 0.12685366076858268, tol=tol)*p3*q0 - rationalize(BigInt, 0.9721054060313574, tol=tol)*q1 + rationalize(BigInt, 1.4332583965298273, tol=tol)*p1*q1 - rationalize(BigInt, 0.3658292969614953, tol=tol)*p2*q1 - rationalize(BigInt, 0.458292808629767, tol=tol)*p3*q1 + rationalize(BigInt, 1.1057480001700448, tol=tol)*q2 + rationalize(BigInt, 0.649216154064302, tol=tol)*p1*q2 + rationalize(BigInt, 0.1435470147844548, tol=tol)*p2*q2 + rationalize(BigInt, 1.8049686045262234, tol=tol)*p3*q2 + rationalize(BigInt, 0.3619641675513017, tol=tol)*q3 + rationalize(BigInt, 1.0386298649000567, tol=tol)*p1*q3 - rationalize(BigInt, 0.2739870731830222, tol=tol)*p2*q3 - rationalize(BigInt, 0.38992289294835114, tol=tol)*p3*q3,
+     -rationalize(BigInt, 0.41615764608945516, tol=tol)*g1^2 - rationalize(BigInt, 1.2331171001793817, tol=tol)*g1*g2 + rationalize(BigInt, 0.10423594498637195, tol=tol)*g2^2 + rationalize(BigInt, 0.4451741240918564, tol=tol)*g1*g3 - rationalize(BigInt, 0.0807794759847403, tol=tol)*g2*g3 + rationalize(BigInt, 0.015584822151867354, tol=tol)*g3^2 + rationalize(BigInt, 0.5169791211840113, tol=tol)*g1^2*p1 - rationalize(BigInt, 0.3281633186673521, tol=tol)*g1*g2*p1 + rationalize(BigInt, 0.10768082059655043, tol=tol)*g2^2*p1 - rationalize(BigInt, 1.78387184821123, tol=tol)*g1*g3*p1 + rationalize(BigInt, 0.1962385955438586, tol=tol)*g2*g3*p1 - rationalize(BigInt, 0.0932755727182936, tol=tol)*g3^2*p1 - rationalize(BigInt, 0.12307658314371513, tol=tol)*g1^2*p1^2 + rationalize(BigInt, 1.3649915585405705, tol=tol)*g1*g2*p1^2 - rationalize(BigInt, 0.01641144275933561, tol=tol)*g2^2*p1^2 + rationalize(BigInt, 1.282522294958988, tol=tol)*g1*g3*p1^2 + rationalize(BigInt, 0.13118389677242223, tol=tol)*g2*g3*p1^2 + rationalize(BigInt, 0.13948802590305073, tol=tol)*g3^2*p1^2 - rationalize(BigInt, 0.4784260518169776, tol=tol)*g1^2*p2 - rationalize(BigInt, 2.092134198423298, tol=tol)*g1*g2*p2 - rationalize(BigInt, 0.2652478875380973, tol=tol)*g2^2*p2 - rationalize(BigInt, 0.9322070346912057, tol=tol)*g1*g3*p2 + rationalize(BigInt, 0.28229645793462466, tol=tol)*g2*g3*p2 - rationalize(BigInt, 0.07438003692790207, tol=tol)*g3^2*p2 + rationalize(BigInt, 0.1376969425780227, tol=tol)*g1^2*p1*p2 - rationalize(BigInt, 1.3462021315216954, tol=tol)*g1*g2*p1*p2 - rationalize(BigInt, 0.35831006800801096, tol=tol)*g2^2*p1*p2 - rationalize(BigInt, 0.3236078908735904, tol=tol)*g1*g3*p1*p2 - rationalize(BigInt, 0.23312973570099904, tol=tol)*g2*g3*p1*p2 + rationalize(BigInt, 0.2206131254299883, tol=tol)*g3^2*p1*p2 + rationalize(BigInt, 0.03212463900566726, tol=tol)*g1^2*p2^2 - rationalize(BigInt, 0.543299069419884, tol=tol)*g1*g2*p2^2 - rationalize(BigInt, 0.1081313237618179, tol=tol)*g2^2*p2^2 - rationalize(BigInt, 1.8348908578280814, tol=tol)*g1*g3*p2^2 - rationalize(BigInt, 0.3379484782876818, tol=tol)*g2*g3*p2^2 + rationalize(BigInt, 0.07600668475615065, tol=tol)*g3^2*p2^2 + rationalize(BigInt, 0.6002572265406737, tol=tol)*g1^2*p3 + rationalize(BigInt, 0.1802055521069689, tol=tol)*g1*g2*p3 + rationalize(BigInt, 1.5644331744196656, tol=tol)*g2^2*p3 - rationalize(BigInt, 0.5267676534246675, tol=tol)*g1*g3*p3 - rationalize(BigInt, 1.676157338774887, tol=tol)*g2*g3*p3 + rationalize(BigInt, 0.4008307913692461, tol=tol)*g3^2*p3 - rationalize(BigInt, 0.5875157312206984, tol=tol)*g1^2*p1*p3 - rationalize(BigInt, 0.26794777918572443, tol=tol)*g1*g2*p1*p3 + rationalize(BigInt, 1.8161766879761405, tol=tol)*g2^2*p1*p3 + rationalize(BigInt, 0.08217873131336825, tol=tol)*g1*g3*p1*p3 + rationalize(BigInt, 0.41625228622759664, tol=tol)*g2*g3*p1*p3 - rationalize(BigInt, 1.228660956755442, tol=tol)*g3^2*p1*p3 + rationalize(BigInt, 0.801736157469905, tol=tol)*g1^2*p2*p3 - rationalize(BigInt, 0.06119905069237429, tol=tol)*g1*g2*p2*p3 + rationalize(BigInt, 0.5320140756032581, tol=tol)*g2^2*p2*p3 - rationalize(BigInt, 0.5120321678148483, tol=tol)*g1*g3*p2*p3 + rationalize(BigInt, 1.3994959245799465, tol=tol)*g2*g3*p2*p3 - rationalize(BigInt, 1.3337502330731632, tol=tol)*g3^2*p2*p3 + rationalize(BigInt, 0.09095194413804787, tol=tol)*g1^2*p3^2 - rationalize(BigInt, 0.8216924891206866, tol=tol)*g1*g2*p3^2 + rationalize(BigInt, 0.12454276652115351, tol=tol)*g2^2*p3^2 + rationalize(BigInt, 0.5523685628690934, tol=tol)*g1*g3*p3^2 + rationalize(BigInt, 0.20676458151525956, tol=tol)*g2*g3*p3^2 - rationalize(BigInt, 0.2154947106592014, tol=tol)*g3^2*p3^2 + rationalize(BigInt, 0.29633687895121585, tol=tol)*q0 - rationalize(BigInt, 0.5313843690622682, tol=tol)*p1*q0 + rationalize(BigInt, 0.8180539762829769, tol=tol)*p2*q0 - rationalize(BigInt, 2.5655211923295855, tol=tol)*p3*q0 - rationalize(BigInt, 1.2602089223582702, tol=tol)*q1 + rationalize(BigInt, 1.1609512634985952, tol=tol)*p1*q1 - rationalize(BigInt, 1.5289512288758575, tol=tol)*p2*q1 - rationalize(BigInt, 0.17424561505966216, tol=tol)*p3*q1 + rationalize(BigInt, 0.10364901876603111, tol=tol)*q2 - rationalize(BigInt, 0.013973408764994696, tol=tol)*p1*q2 - rationalize(BigInt, 0.30080374272031296, tol=tol)*p2*q2 + rationalize(BigInt, 1.5473286276087392, tol=tol)*p3*q2 - rationalize(BigInt, 0.04276145686338927, tol=tol)*q3 + rationalize(BigInt, 0.12497482938060817, tol=tol)*p1*q3 + rationalize(BigInt, 0.06337974500071619, tol=tol)*p2*q3 - rationalize(BigInt, 1.1223229062458282, tol=tol)*p3*q3,
+    rationalize(BigInt, 0.0995239208560676, tol=tol)*g1^2 - rationalize(BigInt, 0.4069835646127759, tol=tol)*g1*g2 + rationalize(BigInt, 0.2822661867004282, tol=tol)*g2^2 + rationalize(BigInt, 0.8451107786883508, tol=tol)*g1*g3 - rationalize(BigInt, 0.5316708978452792, tol=tol)*g2*g3 - rationalize(BigInt, 0.8798108963881374, tol=tol)*g3^2 - rationalize(BigInt, 0.08841286657967666, tol=tol)*g1^2*p1 - rationalize(BigInt, 0.5437440767827946, tol=tol)*g1*g2*p1 + rationalize(BigInt, 0.8310187547943032, tol=tol)*g2^2*p1 - rationalize(BigInt, 2.300828301805621, tol=tol)*g1*g3*p1 + rationalize(BigInt, 1.7576212044508612, tol=tol)*g2*g3*p1 + rationalize(BigInt, 0.8123567734335738, tol=tol)*g3^2*p1 - rationalize(BigInt, 0.06820768665581543, tol=tol)*g1^2*p1^2 + rationalize(BigInt, 1.3043060864108098, tol=tol)*g1*g2*p1^2 - rationalize(BigInt, 0.009054065062096384, tol=tol)*g2^2*p1^2 + rationalize(BigInt, 1.3077574118576432, tol=tol)*g1*g3*p1^2 + rationalize(BigInt, 0.06768474224643237, tol=tol)*g2*g3*p1^2 + rationalize(BigInt, 0.07726175171791182, tol=tol)*g3^2*p1^2 + rationalize(BigInt, 0.21964796928975452, tol=tol)*g1^2*p2 - rationalize(BigInt, 0.7213869971382741, tol=tol)*g1*g2*p2 + rationalize(BigInt, 0.06428880062023586, tol=tol)*g2^2*p2 + rationalize(BigInt, 0.6769693907722261, tol=tol)*g1*g3*p2 + rationalize(BigInt, 1.0938889186830445, tol=tol)*g2*g3*p2 + rationalize(BigInt, 1.033778176369894, tol=tol)*g3^2*p2 + rationalize(BigInt, 0.04579106142198317, tol=tol)*g1^2*p1*p2 - rationalize(BigInt, 1.6136177673887118, tol=tol)*g1*g2*p1*p2 - rationalize(BigInt, 0.08313705215573315, tol=tol)*g2^2*p1*p2 - rationalize(BigInt, 0.3180870028357637, tol=tol)*g1*g3*p1*p2 - rationalize(BigInt, 0.1323253404673372, tol=tol)*g2*g3*p1*p2 + rationalize(BigInt, 0.03734599073374998, tol=tol)*g3^2*p1*p2 + rationalize(BigInt, 0.06270407236710761, tol=tol)*g1^2*p2^2 - rationalize(BigInt, 0.19162792586107563, tol=tol)*g1*g2*p2^2 - rationalize(BigInt, 0.009068232422623026, tol=tol)*g2^2*p2^2 - rationalize(BigInt, 1.9648502282295741, tol=tol)*g1*g3*p2^2 - rationalize(BigInt, 0.09696983966017489, tol=tol)*g2*g3*p2^2 - rationalize(BigInt, 0.053635839944484585, tol=tol)*g3^2*p2^2 + rationalize(BigInt, 0.09136896607569936, tol=tol)*g1^2*p3 - rationalize(BigInt, 1.5831271499881143, tol=tol)*g1*g2*p3  + rationalize(BigInt, 1.1586203238882382, tol=tol)*g2^2*p3 + rationalize(BigInt, 1.561944037084699, tol=tol)*g1*g3*p3 + rationalize(BigInt, 0.5373765622781439, tol=tol)*g2*g3*p3 - rationalize(BigInt, 0.7510078085771675, tol=tol)*g3^2*p3 + rationalize(BigInt, 0.03313601431114031, tol=tol)*g1^2*p1*p3 + rationalize(BigInt, 0.999575794109116, tol=tol)*g1*g2*p1*p3 + rationalize(BigInt, 0.0005673645755714211, tol=tol)*g2^2*p1*p3 - rationalize(BigInt, 1.8768450822200746, tol=tol)*g1*g3*p1*p3 + rationalize(BigInt, 0.15574381848783894, tol=tol)*g2*g3*p1*p3 - rationalize(BigInt, 0.03370337888671173, tol=tol)*g3^2*p1*p3 + rationalize(BigInt, 0.040671941002624216, tol=tol)*g1^2*p2*p3 - rationalize(BigInt, 2.5271478321380254, tol=tol)*g1*g2*p2*p3 - rationalize(BigInt, 0.11221443152128503, tol=tol)*g2^2*p2*p3 + rationalize(BigInt, 0.5426249873354888, tol=tol)*g1*g3*p2*p3 + rationalize(BigInt, 0.01844664972668835, tol=tol)*g2*g3*p2*p3 + rationalize(BigInt, 0.07154249051866082, tol=tol)*g3^2*p2*p3 + rationalize(BigInt, 0.005503614288707821, tol=tol)*g1^2*p3^2 - rationalize(BigInt, 1.1126781605497342, tol=tol)*g1*g2*p3^2 + rationalize(BigInt, 0.01812229748471941, tol=tol)*g2^2*p3^2 + rationalize(BigInt, 0.657092816371931, tol=tol)*g1*g3*p3^2 + rationalize(BigInt, 0.029285097413742515, tol=tol)*g2*g3*p3^2 - rationalize(BigInt, 0.02362591177342723, tol=tol)*g3^2*p3^2 + rationalize(BigInt, 0.49802078883164164, tol=tol)*q0 - rationalize(BigInt, 1.5549626616482004, tol=tol)*p1*q0 - rationalize(BigInt, 1.3177149462798845, tol=tol)*p2*q0 - rationalize(BigInt, 0.49898148138677, tol=tol)*p3*q0 - rationalize(BigInt, 0.12338824573791841, tol=tol)*q1 - rationalize(BigInt, 0.06111510706623446, tol=tol)*p1*q1 - rationalize(BigInt, 0.04157014428073322, tol=tol)*p2*q1 - rationalize(BigInt, 0.007996832327295606, tol=tol)*p3*q1 + rationalize(BigInt, 0.3953545453627241, tol=tol)*q2 + rationalize(BigInt, 1.168253359907005, tol=tol)*p1*q2 + rationalize(BigInt, 0.1289788318383644, tol=tol)*p2*q2 + rationalize(BigInt, 1.6166074402033737, tol=tol)*p3*q2 - rationalize(BigInt, 1.1634376524391858, tol=tol)*q3 + rationalize(BigInt, 1.1753697910765462, tol=tol)*p1*q3 + rationalize(BigInt, 1.303746265623441, tol=tol)*p2*q3 - rationalize(BigInt, 0.9550529463247988, tol=tol)*p3*q3,
+     -rationalize(BigInt, 0.43946259392041137, tol=tol)*g1^2 - rationalize(BigInt, 0.2794194400312886, tol=tol)*g1*g2 + rationalize(BigInt, 0.28633513817241923, tol=tol)*g2^2 + rationalize(BigInt, 0.4837842932289669, tol=tol)*g1*g3 - rationalize(BigInt, 0.2789447622513483, tol=tol)*g2*g3 + rationalize(BigInt, 0.00840391192868436, tol=tol)*g3^2 - rationalize(BigInt, 1.5744202005495247, tol=tol)*g1^2*p1 - rationalize(BigInt, 0.2861663506179279, tol=tol)*g1*g2*p1 + rationalize(BigInt, 0.7386941869051702, tol=tol)*g2^2*p1 + rationalize(BigInt, 0.5331769017373268, tol=tol)*g1*g3*p1 + rationalize(BigInt, 0.3754313238644043, tol=tol)*g2*g3*p1 - rationalize(BigInt, 0.49557272342979514, tol=tol)*g3^2*p1 - rationalize(BigInt, 0.1697121445535322, tol=tol)*g1^2*p1^2 + rationalize(BigInt, 0.17649121044520624, tol=tol)*g1*g2*p1^2 + rationalize(BigInt, 0.230772384999563, tol=tol)*g2^2*p1^2 + rationalize(BigInt, 1.5487222154552227, tol=tol)*g1*g3*p1^2 + rationalize(BigInt, 1.1549190062177301, tol=tol)*g2*g3*p1^2 - rationalize(BigInt, 0.061060240446030825, tol=tol)*g3^2*p1^2 + rationalize(BigInt, 0.3428887153466959, tol=tol)*g1^2*p2 - rationalize(BigInt, 2.0520172954900926, tol=tol)*g1*g2*p2 + rationalize(BigInt, 0.2548434377395737, tol=tol)*g2^2*p2 - rationalize(BigInt, 1.1661156986017325, tol=tol)*g1*g3*p2 + rationalize(BigInt, 1.1418016311188108, tol=tol)*g2*g3*p2 - rationalize(BigInt, 0.03717326023724154, tol=tol)*g3^2*p2 - rationalize(BigInt, 1.1298456541690676, tol=tol)*g1^2*p1*p2 - rationalize(BigInt, 2.0395244570443807, tol=tol)*g1*g2*p1*p2 - rationalize(BigInt, 0.46158802071478294, tol=tol)*g2^2*p1*p2 - rationalize(BigInt, 0.7937227851031279, tol=tol)*g1*g3*p1*p2 + rationalize(BigInt, 1.3925863980743391, tol=tol)*g2*g3*p1*p2 + rationalize(BigInt, 1.5914336748838505, tol=tol)*g3^2*p1*p2 + rationalize(BigInt, 0.5461657368466324, tol=tol)*g1^2*p2^2 - rationalize(BigInt, 0.40076456254394, tol=tol)*g1*g2*p2^2 - rationalize(BigInt, 0.5789448963236655, tol=tol)*g2^2*p2^2 - rationalize(BigInt, 1.2606913391501393, tol=tol)*g1*g3*p2^2 - rationalize(BigInt, 0.8839870841626388, tol=tol)*g2*g3*p2^2 + rationalize(BigInt, 0.03277915947703309, tol=tol)*g3^2*p2^2 - rationalize(BigInt, 0.8186969313136523, tol=tol)*g1^2*p3 - rationalize(BigInt, 0.02925076747851844, tol=tol)*g1*g2*p3 + rationalize(BigInt, 0.7392135200738452, tol=tol)*g2^2*p3 + rationalize(BigInt, 0.12848993732517067, tol=tol)*g1*g3*p3 - rationalize(BigInt, 0.9246721961161062, tol=tol)*g2*g3*p3 + rationalize(BigInt, 0.34711806557393554, tol=tol)*g3^2*p3 - rationalize(BigInt, 1.3114980542204153, tol=tol)*g1^2*p1*p3 + rationalize(BigInt, 0.7458693987541652, tol=tol)*g1*g2*p1*p3  + rationalize(BigInt, 1.309443056027262, tol=tol)*g2^2*p1*p3 - rationalize(BigInt, 0.5609050703954811, tol=tol)*g1*g3*p1*p3 - rationalize(BigInt, 0.560863866588139, tol=tol)*g2*g3*p1*p3 + rationalize(BigInt, 0.0020549981931533984, tol=tol)*g3^2*p1*p3 + rationalize(BigInt, 0.21040044489655793, tol=tol)*g1^2*p2*p3 - rationalize(BigInt, 2.094674294769259, tol=tol)*g1*g2*p2*p3 + rationalize(BigInt, 0.9014935747766074, tol=tol)*g2^2*p2*p3 - rationalize(BigInt, 0.7741828342315165, tol=tol)*g1*g3*p2*p3 + rationalize(BigInt, 1.0179705141740856, tol=tol)*g2*g3*p2*p3 - rationalize(BigInt, 1.1118940196731655, tol=tol)*g3^2*p2*p3 - rationalize(BigInt, 0.37645359229310016, tol=tol)*g1^2*p3^2 + rationalize(BigInt, 0.22427335209873375, tol=tol)*g1*g2*p3^2 + rationalize(BigInt, 0.34817251132410243, tol=tol)*g2^2*p3^2 - rationalize(BigInt, 0.2880308763050832, tol=tol)*g1*g3*p3^2 - rationalize(BigInt, 0.27093192205509137, tol=tol)*g2*g3*p3^2 + rationalize(BigInt, 0.028281080968997733, tol=tol)*g3^2*p3^2 + rationalize(BigInt, 0.14472354381930777, tol=tol)*q0 + rationalize(BigInt, 1.3312987370741496, tol=tol)*p1*q0 - rationalize(BigInt, 0.560558892849028, tol=tol)*p2*q0 - rationalize(BigInt, 0.26763465433412853, tol=tol)*p3*q0 + rationalize(BigInt, 0.34474968158768826, tol=tol)*q1 + rationalize(BigInt, 1.1967487089081013, tol=tol)*p1*q1 - rationalize(BigInt, 0.5416788729536276, tol=tol)*p2*q1 + rationalize(BigInt, 0.35732161373948407, tol=tol)*p3*q1 + rationalize(BigInt, 0.4086834090152563, tol=tol)*q2 + rationalize(BigInt, 0.9057045158335053, tol=tol)*p1*q2 + rationalize(BigInt, 0.790785041402257, tol=tol)*p2*q2 + rationalize(BigInt, 0.25330644272284614, tol=tol)*p3*q2 - rationalize(BigInt, 0.3854162586341408, tol=tol)*q3 - rationalize(BigInt, 0.04738889206888738, tol=tol)*p1*q3 + rationalize(BigInt, 1.2360880142692436, tol=tol)*p2*q3 - rationalize(BigInt, 0.03146357181747231, tol=tol)*p3*q3,
+     -rationalize(BigInt, 0.3364985136694329, tol=tol)*g1^2 - rationalize(BigInt, 0.6220713377668979, tol=tol)*g1*g2  + rationalize(BigInt, 0.30253663989085705, tol=tol)*g2^2 + rationalize(BigInt, 0.09691241616903694, tol=tol)*g1*g3 - rationalize(BigInt, 0.23475287081412524, tol=tol)*g2*g3 + rationalize(BigInt, 0.03759204880218851, tol=tol)*g3^2 - rationalize(BigInt, 1.0655428995245861, tol=tol)*g1^2*p1 + rationalize(BigInt, 1.2015525036653503, tol=tol)*g1*g2*p1 + rationalize(BigInt, 0.7601103825805371, tol=tol)*g2^2*p1 - rationalize(BigInt, 0.19738187400246698, tol=tol)*g1*g3*p1 + rationalize(BigInt, 0.6151569823342218, tol=tol)*g2*g3*p1 - rationalize(BigInt, 0.19896444557080828, tol=tol)*g3^2*p1 + rationalize(BigInt, 0.12867336914719074, tol=tol)*g1^2*p1^2 + rationalize(BigInt, 1.2422164684570598, tol=tol)*g1*g2*p1^2 - rationalize(BigInt, 0.32698199621342966, tol=tol)*g2^2*p1^2 + rationalize(BigInt, 0.988903111633841, tol=tol)*g1*g3*p1^2 + rationalize(BigInt, 0.015998020944011523, tol=tol)*g2*g3*p1^2 + rationalize(BigInt, 0.19830862706623895, tol=tol)*g3^2*p1^2 - rationalize(BigInt, 0.36506543203523656, tol=tol)*g1^2*p2 - rationalize(BigInt, 1.8191248166962, tol=tol)*g1*g2*p2 - rationalize(BigInt, 0.04702353062492582, tol=tol)*g2^2*p2 + rationalize(BigInt, 0.22650992191881464, tol=tol)*g1*g3*p2 + rationalize(BigInt, 0.6757394159618821, tol=tol)*g2*g3*p2 - rationalize(BigInt, 0.20784006514510822, tol=tol)*g3^2*p2 - rationalize(BigInt, 1.3823450011564475, tol=tol)*g1^2*p1*p2 - rationalize(BigInt, 0.10921823662847378, tol=tol)*g1*g2*p1*p2 + rationalize(BigInt, 0.9411204746791397, tol=tol)*g2^2*p1*p2 + rationalize(BigInt, 0.6416176172245012, tol=tol)*g1*g3*p1*p2 + rationalize(BigInt, 0.6050178988297725, tol=tol)*g2*g3*p1*p2 + rationalize(BigInt, 0.4412245264773078, tol=tol)*g3^2*p1*p2 + rationalize(BigInt, 0.06735301456610396, tol=tol)*g1^2*p2^2 - rationalize(BigInt, 0.8585408362609629, tol=tol)*g1*g2*p2^2 - rationalize(BigInt, 0.3090762258515019, tol=tol)*g2^2*p2^2 - rationalize(BigInt, 0.4001418483728859, tol=tol)*g1*g3*p2^2 + rationalize(BigInt, 0.4779675484647562, tol=tol)*g2*g3*p2^2 + rationalize(BigInt, 0.24172321128539795, tol=tol)*g3^2*p2^2 - rationalize(BigInt, 0.5137007261636957, tol=tol)*g1^2*p3 - rationalize(BigInt, 0.9820327320175907, tol=tol)*g1*g2*p3 + rationalize(BigInt, 0.926095293449879, tol=tol)*g2^2*p3 - rationalize(BigInt, 0.7003487284409724, tol=tol)*g1*g3*p3 - rationalize(BigInt, 0.9430374895060032, tol=tol)*g2*g3*p3 + rationalize(BigInt, 0.08868217302851986, tol=tol)*g3^2*p3 - rationalize(BigInt, 0.8028419556001375, tol=tol)*g1^2*p1*p3 + rationalize(BigInt, 1.4979362188623169, tol=tol)*g1*g2*p1*p3 + rationalize(BigInt, 0.6798639272820932, tol=tol)*g2^2*p1*p3 - rationalize(BigInt, 1.0625669164194511, tol=tol)*g1*g3*p1*p3  + rationalize(BigInt, 1.6499737530190743, tol=tol)*g2*g3*p1*p3 + rationalize(BigInt, 0.12297802831804432, tol=tol)*g3^2*p1*p3 - rationalize(BigInt, 0.2829951083769471, tol=tol)*g1^2*p2*p3 - rationalize(BigInt, 1.67180387717421, tol=tol)*g1*g2*p2*p3 + rationalize(BigInt, 0.22862840829725906, tol=tol)*g2^2*p2*p3 - rationalize(BigInt, 0.45573353517584536, tol=tol)*g1*g3*p2*p3 - rationalize(BigInt, 0.030399560249614144, tol=tol)*g2*g3*p2*p3 + rationalize(BigInt, 0.05436670007968804, tol=tol)*g3^2*p2*p3 - rationalize(BigInt, 0.1960263837132947, tol=tol)*g1^2*p3^2 - rationalize(BigInt, 0.3836756321960968, tol=tol)*g1*g2*p3^2 + rationalize(BigInt, 0.6360582220649316, tol=tol)*g2^2*p3^2 - rationalize(BigInt, 0.5887612632609552, tol=tol)*g1*g3*p3^2 - rationalize(BigInt, 0.49396556940876774, tol=tol)*g2*g3*p3^2 - rationalize(BigInt, 0.4400318383516369, tol=tol)*g3^2*p3^2 - rationalize(BigInt, 0.0036301750236126602, tol=tol)*q0 + rationalize(BigInt, 0.5043969625148573, tol=tol)*p1*q0 + rationalize(BigInt, 0.6199290278052706, tol=tol)*p2*q0 - rationalize(BigInt, 0.5010767403147031, tol=tol)*p3*q0 + rationalize(BigInt, 0.27845755063810307, tol=tol)*q1 + rationalize(BigInt, 0.9141858220671707, tol=tol)*p1*q1 - rationalize(BigInt, 0.04474642022970836, tol=tol)*p2*q1 + rationalize(BigInt, 0.21510107355697375, tol=tol)*p3*q1 + rationalize(BigInt, 0.6261152163591358, tol=tol)*q2 - rationalize(BigInt, 0.23441023070199246, tol=tol)*p1*q2  + rationalize(BigInt, 0.5860551333365724, tol=tol)*p2*q2 + rationalize(BigInt, 0.6514610848268766, tol=tol)*p3*q2 - rationalize(BigInt, 0.1414398428437503, tol=tol)*q3 + rationalize(BigInt, 0.18837597417330545, tol=tol)*p1*q3 + rationalize(BigInt, 0.23529746996939166, tol=tol)*p2*q3 + rationalize(BigInt, 0.34502969365002717, tol=tol)*p3*q3,
+     -rationalize(BigInt, 0.4997153826800627, tol=tol)*g1^2 + rationalize(BigInt, 1.1379854833548109, tol=tol)*g1*g2 - rationalize(BigInt, 0.6474309248194395, tol=tol)*g2^2 + rationalize(BigInt, 0.5441177673182162, tol=tol)*g1*g3  - rationalize(BigInt, 0.6356209362624222, tol=tol)*g2*g3 - rationalize(BigInt, 0.00249167421336129, tol=tol)*g3^2 - rationalize(BigInt, 1.5544041627556424, tol=tol)*g1^2*p1 + rationalize(BigInt, 2.3739950333676623, tol=tol)*g1*g2*p1  - rationalize(BigInt, 0.626498203472872, tol=tol)*g2^2*p1 - rationalize(BigInt, 1.251167893581656, tol=tol)*g1*g3*p1 + rationalize(BigInt, 1.014528145879352, tol=tol)*g2*g3*p1 - rationalize(BigInt, 0.07360314669929015, tol=tol)*g3^2*p1 - rationalize(BigInt, 0.11700211538167525, tol=tol)*g1^2*p1^2 + rationalize(BigInt, 1.4292168664824174, tol=tol)*g1*g2*p1^2 - rationalize(BigInt, 0.08561887506760898, tol=tol)*g2^2*p1^2 + rationalize(BigInt, 0.11756149787203274, tol=tol)*g1*g3*p1^2 + rationalize(BigInt, 1.2753331275027957, tol=tol)*g2*g3*p1^2 + rationalize(BigInt, 0.20262099044928422, tol=tol)*g3^2*p1^2 - rationalize(BigInt, 0.5322121916934887, tol=tol)*g1^2*p2 - rationalize(BigInt, 0.5705836762208184, tol=tol)*g1*g2*p2 + rationalize(BigInt, 1.338552997747994, tol=tol)*g2^2*p2 + rationalize(BigInt, 0.1626686039427204, tol=tol)*g1*g3*p2 + rationalize(BigInt, 0.8255938648528275, tol=tol)*g2*g3*p2 - rationalize(BigInt, 0.2877403739032339, tol=tol)*g3^2*p2 - rationalize(BigInt, 1.7484788356484942, tol=tol)*g1^2*p1*p2 - rationalize(BigInt, 0.7462669895235802, tol=tol)*g1*g2*p1*p2 + rationalize(BigInt, 0.9024930142580471, tol=tol)*g2^2*p1*p2 - rationalize(BigInt, 0.836428661723292, tol=tol)*g1*g3*p1*p2 + rationalize(BigInt, 0.10315211869079574, tol=tol)*g2*g3*p1*p2 + rationalize(BigInt, 0.8459858213904471, tol=tol)*g3^2*p1*p2 + rationalize(BigInt, 0.0524174914208927, tol=tol)*g1^2*p2^2 - rationalize(BigInt, 1.0349080883999526, tol=tol)*g1*g2*p2^2 - rationalize(BigInt, 0.4456138068634661, tol=tol)*g2^2*p2^2 - rationalize(BigInt, 0.8702119648626987, tol=tol)*g1*g3*p2^2 + rationalize(BigInt, 0.1347633798985455, tol=tol)*g2*g3*p2^2 + rationalize(BigInt, 0.3931963154425734, tol=tol)*g3^2*p2^2 + rationalize(BigInt, 0.7263228121576023, tol=tol)*g1^2*p3 - rationalize(BigInt, 2.2210658961930227, tol=tol)*g1*g2*p3 + rationalize(BigInt, 1.6108892968930464, tol=tol)*g2^2*p3 - rationalize(BigInt, 1.0504867050871953, tol=tol)*g1*g3*p3 + rationalize(BigInt, 1.0659099359741329, tol=tol)*g2*g3*p3 + rationalize(BigInt, 0.5672833993063003, tol=tol)*g3^2*p3 - rationalize(BigInt, 0.06811413086649659, tol=tol)*g1^2*p1*p3 - rationalize(BigInt, 0.31001429706461026, tol=tol)*g1*g2*p1*p3 + rationalize(BigInt, 1.4153449120254278, tol=tol)*g2^2*p1*p3 - rationalize(BigInt, 1.8526453839326555, tol=tol)*g1*g3*p1*p3 + rationalize(BigInt, 1.3321822393355465, tol=tol)*g2*g3*p1*p3 - rationalize(BigInt, 1.3472307811589312, tol=tol)*g3^2*p1*p3 + rationalize(BigInt, 0.8918357940981352, tol=tol)*g1^2*p2*p3 - rationalize(BigInt, 1.500420306224534, tol=tol)*g1*g2*p2*p3 - rationalize(BigInt, 0.43633002867072346, tol=tol)*g2^2*p2*p3 - rationalize(BigInt, 1.087845994748532, tol=tol)*g1*g3*p2*p3 - rationalize(BigInt, 0.15102803926606495, tol=tol)*g2*g3*p2*p3 - rationalize(BigInt, 0.4555057654274117, tol=tol)*g3^2*p2*p3 + rationalize(BigInt, 0.06458462396078254, tol=tol)*g1^2*p3^2 - rationalize(BigInt, 0.39430877808246473, tol=tol)*g1*g2*p3^2 + rationalize(BigInt, 0.5312326819310751, tol=tol)*g2^2*p3^2 + rationalize(BigInt, 0.752650466990666, tol=tol)*g1*g3*p3^2 - rationalize(BigInt, 1.4100965074013412, tol=tol)*g2*g3*p3^2 - rationalize(BigInt, 0.5958173058918577, tol=tol)*g3^2*p3^2 + rationalize(BigInt, 1.1496379817128635, tol=tol)*q0 + rationalize(BigInt, 2.2545055129278047, tol=tol)*p1*q0 - rationalize(BigInt, 0.5186004321512713, tol=tol)*p2*q0 - rationalize(BigInt, 2.904495508356949, tol=tol)*p3*q0 + rationalize(BigInt, 0.3811371457709, tol=tol)*q1 + rationalize(BigInt, 1.1561384774363503, tol=tol)*p1*q1 - rationalize(BigInt, 0.03459051968276095, tol=tol)*p2*q1 - rationalize(BigInt, 0.5860104174434722, tol=tol)*p3*q1 - rationalize(BigInt, 0.42262305475993184, tol=tol)*q2 - rationalize(BigInt, 0.06960283700014054, tol=tol)*p1*q2 + rationalize(BigInt, 0.6975228406191866, tol=tol)*p2*q2 + rationalize(BigInt, 1.1761445768437886, tol=tol)*p3*q2 - rationalize(BigInt, 0.4132504788764938, tol=tol)*q3 + rationalize(BigInt, 1.0477095469315294, tol=tol)*p1*q3 + rationalize(BigInt, 0.5581768684334514, tol=tol)*p2*q3 + rationalize(BigInt, 0.4360576481532085, tol=tol)*p3*q3,
+    -1. + rationalize(BigInt, 0.9336143308746049, tol=tol)*g1 + rationalize(BigInt, 1.1781580271766483, tol=tol)*g2 + rationalize(BigInt, 0.551650235747964, tol=tol)*g3
+    ]
+    equations
+end
+
+# Source:
+# https://github.com/JuliaHomotopyContinuation/PolynomialTestSystems.jl/blob/master/src/systems.jl
+function chandran(n; tol=0, np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
+    _, H = np.polynomial_ring(ground, ["H$i" for i in 1:n], ordering=ordering)
+    c = rationalize(BigInt, 0.51234, tol=tol)
+    c = ground(numerator(c)) // ground(denominator(c))
+    eqs = [(2n*H[i] - c*H[i]*(1 + sum(ground(i) // (j+i) * H[j] for j=1:(n-1))) - 2n) for i=1:n]
+    eqs
+end
+
+# Source:
+# https://github.com/JuliaHomotopyContinuation/PolynomialTestSystems.jl/blob/master/src/systems.jl
+function boon(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
+    _, (s1, g1, s2, g2, C1, C2) = np.polynomial_ring(ground, ["s1", "g1", "s2", "g2", "C1", "C2"], ordering=ordering)
+    eqs = [
+        s1^2+g1^2 - 1,
+        s2^2+g2^2 - 1,
+        C1*g1^3+C2*g2^3 - ground(12)//10,
+        C1*s1^3+C2*s2^3 - ground(12)//10,
+        C1*g1^2*s1+C2*g2^2*s2 - ground(7)//10,
+        C1*g1*s1^2+C2*g2*s2^2 - ground(7)//10
+    ]
+    eqs
 end
 
 ###
-# Some other tiny systems
+# Some other examples
 
 function ku10(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     _, (x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) =
@@ -744,6 +822,9 @@ function ojika4_d1R2_d2R5(; np=AbstractAlgebra, ground=np.QQ, ordering=:lex)
     ]
 end
 
+###
+# Random generation
+
 # generate a random polynomial system with:
 # . `nvariables` variables, 
 # . monomial exponents in range `exps`,
diff --git a/src/utils/timeit.jl b/src/utils/timeit.jl
index e2610292..2f93b915 100644
--- a/src/utils/timeit.jl
+++ b/src/utils/timeit.jl
@@ -14,13 +14,13 @@
 # code, since they do not affect performance when inactive.
 
 const _groebner_timer = TimerOutputs.TimerOutput()
+const _groebner_timer_lock = Ref{ReentrantLock}(ReentrantLock())
 
 @noinline __throw_timeit_error() = throw(ArgumentError("""
     Invalid usage of macro @timeit in Groebner.jl. Use it as:
     @timeit label expr
     @timeit function foo() ... end"""))
 
-# TODO: @timeit macro is broken in combination with Base.Threads.@threads..
 """
     @timeit label expr
     @timeit function foo() ... end
@@ -53,6 +53,7 @@ end
 ```
 
 NOTE: `@timeit` cannot wrap code blocks that contain `@label` or `@goto`.
+NOTE: `@timeit` is broken in combination with `Base.Threads.@threads`.
 """
 macro timeit(args...)
     if isempty(args) || length(args) > 2
@@ -96,14 +97,25 @@ function _timeit_expr(m, label, expr)
     end
 end
 
-function refresh_performance_counters()
+function performance_counters_refresh()
+    # Do nothing if counters are disabled
     !performance_counters_enabled() && return nothing
+    # Do nothing if run from a worker thread.
+    # NOTE: this does not always do what is intended. It is still correct, since
+    # we lock the timer anyway.
     threadid() != 1 && return nothing
-    TimerOutputs.reset_timer!(_groebner_timer)
+
+    lock(_groebner_timer_lock[])
+    try
+        TimerOutputs.reset_timer!(_groebner_timer)
+    finally
+        unlock(_groebner_timer_lock[])
+    end
+
     nothing
 end
 
-function print_performance_counters(statistics)
+function performance_counters_print(statistics)
     (statistics in (:no, :stats)) && return nothing
     if statistics in (:timings, :all) && !performance_counters_enabled()
         @log level = 1_000 """
diff --git a/src/utils/versioninfo.jl b/src/utils/versioninfo.jl
index f4d0c717..4c0322cf 100644
--- a/src/utils/versioninfo.jl
+++ b/src/utils/versioninfo.jl
@@ -2,9 +2,7 @@
 
 # Adapted from Nemo.jl
 # The license is Simplified "2-clause" BSD License
-# https://github.com/Nemocas/Nemo.jl/blob/master/LICENSE.md
-
-# NOTE: Currently not used
+#   https://github.com/Nemocas/Nemo.jl/blob/master/LICENSE.md
 
 import Pkg
 import LibGit2
@@ -14,7 +12,7 @@ const Groebner_uuid = Base.UUID("0b43b601-686d-58a3-8a1c-6623616c7cd4")
 
 deps = Pkg.dependencies()
 if !haskey(deps, Groebner_uuid)
-    version() = "building"
+    version() = "build"
 else
     ver = deps[Groebner_uuid]
     if occursin("/dev/", ver.source)
@@ -42,11 +40,12 @@ function versioninfo()
 
     println()
     println("Switches:")
-    println("  invariants_enabled = $(invariants_enabled())")
-    println("  logging_enabled    = $(logging_enabled())")
+    println("  invariants_enabled           = $(invariants_enabled())")
+    println("  logging_enabled              = $(logging_enabled())")
+    println("  performance_counters_enabled = $(performance_counters_enabled())")
 
     println("Environment:")
     println("  GROEBNER_NO_THREADED = $(get(ENV, "GROEBNER_NO_THREADED", "0"))")
 
-    return nothing
+    nothing
 end
diff --git a/test/input-output/Nemo.jl b/test/input-output/Nemo.jl
index 3526a520..122977e7 100644
--- a/test/input-output/Nemo.jl
+++ b/test/input-output/Nemo.jl
@@ -16,7 +16,7 @@ import Primes
 end
 
 @testset "Nemo.jl, input-output" begin
-    R, (x, y) = Nemo.GF(Nemo.fmpz(Primes.nextprime(BigInt(2)^100)))["x", "y"]
+    R, (x, y) = Nemo.GF(Nemo.ZZRingElem(Primes.nextprime(BigInt(2)^100)))["x", "y"]
     @test_throws DomainError Groebner.groebner([x, y])
 
     R, (x, y) = Nemo.GF(2, 2)["x", "y"]
diff --git a/test/runtests.jl b/test/runtests.jl
index cd23d002..bcfe8e3a 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -3,12 +3,12 @@ using TestSetExtensions
 
 using AbstractAlgebra
 using Random
-using Groebner
+# using Groebner
 
 # Check invariants during testing.
 # NOTE: it's good to turn this on!
 Groebner.invariants_enabled() = true
-Groebner.update_logger(loglevel=0)
+Groebner.logger_update(loglevel=0)
 
 # Taken from JuMP/test/solvers.jl
 function try_import(name::Symbol)
@@ -26,6 +26,8 @@ end
 ⊂(xs, ys) = all(in(ys), xs)
 ≂(xs, ys) = ⊂(xs, ys) && ⊂(ys, xs)
 
+Groebner.versioninfo()
+
 @time @testset "All tests" verbose = true begin
     # Different implementations of a monomial 
     @includetests ["monoms/exponentvector", "monoms/packedtuples", "monoms/sparsevector"]