(probably) improve modular arithmetic

Project.toml

@@ -5,6 +5,7 @@ version = "0.5.0"
 
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
+Atomix = "a9b6321e-bd34-4604-b9c9-b65b8de01458"
 Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
 ExprTools = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
 Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"

benchmark/CI-scripts/run-on-nightly/run_benchmarks.jl

@@ -1,4 +1,5 @@
 import Pkg
+Pkg.status()
 Pkg.develop(path=(@__DIR__) * "/../../../")
 
 include("../run_benchmarks.jl")

benchmark/CI-scripts/run-on-stable/run_benchmarks.jl

@@ -1,6 +1,7 @@
 import Pkg
-Pkg.add("Groebner")
-Pkg.update("Groebner")
+Pkg.status()
+Pkg.add(url="https://github.com/sumiya11/Groebner.jl")
+# Pkg.update("Groebner")
 
 include("../run_benchmarks.jl")
 

benchmark/CI-scripts/run_benchmarks.jl

@@ -49,14 +49,37 @@ push!(
     suite,
     (
         problem_name="groebner, AA, GF(2^31-1), katsura 10",
-        result=compute_gb(Groebner.katsuran(10, ordering=:degrevlex, ground=GF(2^31 - 1)))
+        result=compute_gb(
+            Groebner.katsuran(10, ordering=:degrevlex, ground=GF(2^31 - 1)),
+            5
+        )
+    )
+)
+push!(
+    suite,
+    (
+        problem_name="groebner, AA, GF(2^27+29), katsura 10",
+        result=compute_gb(
+            Groebner.katsuran(10, ordering=:degrevlex, ground=GF(2^27 + 29)),
+            5
+        )
+    )
+)
+push!(
+    suite,
+    (
+        problem_name="groebner, AA, GF(2^27+29), cyclic 8",
+        result=compute_gb(
+            Groebner.cyclicn(8, ordering=:degrevlex, ground=GF(2^27 + 29)),
+            5
+        )
     )
 )
 push!(
     suite,
     (
         problem_name="groebner, AA, GF(2^31-1), cyclic 8",
-        result=compute_gb(Groebner.cyclicn(8, ordering=:degrevlex, ground=GF(2^31 - 1)))
+        result=compute_gb(Groebner.cyclicn(8, ordering=:degrevlex, ground=GF(2^31 - 1)), 5)
     )
 )
 push!(
@@ -109,6 +132,15 @@ push!(
         )
     )
 )
+push!(
+    suite,
+    (
+        problem_name="groebner_apply!, AA, GF(2^27+29), katsura 10",
+        result=learn_and_apply(
+            Groebner.katsuran(10, ordering=:degrevlex, ground=GF(2^27 + 29))
+        )
+    )
+)
 push!(
     suite,
     (
@@ -158,7 +190,7 @@ push!(
 
 function multimodular_gb_problem(nbits; np=AbstractAlgebra)
     R, (x1, x2, x3, x4) =
-        PolynomialRing(np.QQ, ["x1", "x2", "x3", "x4"], ordering=:degrevlex)
+        polynomial_ring(np.QQ, ["x1", "x2", "x3", "x4"], ordering=:degrevlex)
     nbits_per_prime = 31
     nprimes = max(div(nbits, nbits_per_prime), 1)
     N = prod(map(BigInt, Primes.nextprimes(2^31 - 100, nprimes)))

benchmark/CI-scripts/runtests.jl

@@ -3,11 +3,13 @@
 using Test
 using TestSetExtensions
 using InteractiveUtils
+using Base.Threads
 
 const MAX_ACCEPTABLE_RELATIVE_DEVIATION = 0.1
 const IGNORE_SMALL_ABSOLUTE_DEVIATION = 1e-3
 
 @info "Start benchmarking.."
+@info "Using $(nthreads()) threads in Groebner.jl"
 
 # Run benchmarks on the latest stable version of Groebner.jl
 dir_stable = (@__DIR__) * "/run-on-stable"

benchmark/benchmark_systems.jl

@@ -61,7 +61,7 @@ function benchmark_set_2()
 end
 
 function dummy_system(ground_field)
-    ring, (x, y) = AbstractAlgebra.PolynomialRing(ground_field, ["x", "y"])
+    ring, (x, y) = AbstractAlgebra.polynomial_ring(ground_field, ["x", "y"])
     ("dummy", [x^2 + y^2 - 1, x + y])
 end
 

benchmark/generate/basis_certificate.jl

@@ -6,7 +6,7 @@ function extract_ring(line1, line2)
     char = parse(BigInt, strip(line2))
     @assert char < typemax(UInt)
     base_field = iszero(char) ? Nemo.QQ : Nemo.GF(UInt(char))
-    ring_nemo, vars_nemo = Nemo.PolynomialRing(base_field, vars_str, ordering=:degrevlex)
+    ring_nemo, vars_nemo = Nemo.polynomial_ring(base_field, vars_str, ordering=:degrevlex)
     base_field, ring_nemo, vars_nemo
 end
 

benchmark/generate/benchmark_generators.jl

@@ -16,7 +16,7 @@ function generate_benchmark_source_for_groebner(
         "GF($(characteristic(field)))"
     end
     vars_repr_quoted = map(s -> "$s", map(string, gens(ring)))
-    ring_repr = """ring, ($vars_repr) = PolynomialRing(
+    ring_repr = """ring, ($vars_repr) = polynomial_ring(
         $field_repr, 
         $vars_repr_quoted, 
         ordering=:degrevlex

benchmark/generate/benchmark_systems/MQ/parser.jl

@@ -12,7 +12,7 @@ function read_MQ_GF(filename)
         ne = parse(Int, line3[(findfirst(':', line3) + 1):end])
 
         R, xs =
-            AbstractAlgebra.PolynomialRing(AbstractAlgebra.GF(ch), nv, ordering=:degrevlex)
+            AbstractAlgebra.polynomial_ring(AbstractAlgebra.GF(ch), nv, ordering=:degrevlex)
         @info "Created ring" R xs
 
         labels = sort!(union([x * y for x in xs for y in xs], xs, [R(1)]), rev=true)

benchmark/generate/benchmark_systems/biomodels/parser.jl

@@ -37,7 +37,7 @@ function read_BIOMDs(nspecies)
         symvs = map(x -> Symbol(x), vs)
         expvs = Meta.parse(join(symvs, ","))
         R, xs = eval(
-            :((R, $expvs) = AbstractAlgebra.PolynomialRing(AbstractAlgebra.QQ, $symvs))
+            :((R, $expvs) = AbstractAlgebra.polynomial_ring(AbstractAlgebra.QQ, $symvs))
         )
 
         for p in params

benchmark/generate/benchmark_systems/for_gleb/parser.jl

@@ -11,7 +11,7 @@ function read_SEAIJRC()
         @info "First line" head
         headv = map(x -> Symbol(x), split(head, ", "))
         e = Meta.parse(join(headv, ","))
-        R, xs = eval(:((R, $e) = Nemo.PolynomialRing(Nemo.QQ, $headv)))
+        R, xs = eval(:((R, $e) = Nemo.polynomial_ring(Nemo.QQ, $headv)))
         @info "Created ring" R xs
         rrr = split(body, ",")
         for (i, s) in enumerate(rrr)
@@ -33,7 +33,7 @@ function read_SIWR()
         body = readline(f)
         headv = map(x -> Symbol(x), split(head, ", "))
         e = Meta.parse(join(headv, ","))
-        R, xs = eval(:((R, $e) = Nemo.PolynomialRing(Nemo.QQ, $headv)))
+        R, xs = eval(:((R, $e) = Nemo.polynomial_ring(Nemo.QQ, $headv)))
         @info "Created ring" R xs
         rrr = split(body, ",")
         for (i, s) in enumerate(rrr)
@@ -57,7 +57,7 @@ function read_MAPK()
         @info "First line" head
         headv = map(x -> Symbol(x), split(head, ", "))
         e = Meta.parse(join(headv, ","))
-        R, xs = eval(:((R, $e) = Nemo.PolynomialRing(Nemo.QQ, $headv)))
+        R, xs = eval(:((R, $e) = Nemo.polynomial_ring(Nemo.QQ, $headv)))
         @info "Created ring" R xs
         rrr = split(body, ",")
         l = length(rrr)
@@ -100,7 +100,7 @@ function read_MAPK_include()
     @info "First line" head
     headv = map(x -> Symbol(x), split(head, ", "))
     e = Meta.parse(join(headv, ","))
-    R, xs = eval(:((R, $e) = Nemo.PolynomialRing(Nemo.QQ, $headv)))
+    R, xs = eval(:((R, $e) = Nemo.polynomial_ring(Nemo.QQ, $headv)))
 
     collect(include(apath))
 end
@@ -109,7 +109,7 @@ function parse_include(filename)
     head = "x, y, z"
     headv = map(x -> Symbol(x), split(head, ", "))
     e = Meta.parse("x, y, z")
-    R, xs = eval(:((R, $e) = Nemo.PolynomialRing(Nemo.QQ, $headv)))
+    R, xs = eval(:((R, $e) = Nemo.polynomial_ring(Nemo.QQ, $headv)))
 
     include(abspath("benchmark\\data\\$filename"))
 end

benchmark/generate/benchmark_systems/standard/parser.jl

@@ -11,7 +11,7 @@ function read_SEAIJRC()
         @info "First line" head
         headv = map(x -> Symbol(x), split(head, ", "))
         e = Meta.parse(join(headv, ","))
-        R, xs = eval(:((R, $e) = Nemo.PolynomialRing(Nemo.QQ, $headv)))
+        R, xs = eval(:((R, $e) = Nemo.polynomial_ring(Nemo.QQ, $headv)))
         @info "Created ring" R xs
         rrr = split(body, ",")
         for (i, s) in enumerate(rrr)
@@ -33,7 +33,7 @@ function read_SIWR()
         body = readline(f)
         headv = map(x -> Symbol(x), split(head, ", "))
         e = Meta.parse(join(headv, ","))
-        R, xs = eval(:((R, $e) = Nemo.PolynomialRing(Nemo.QQ, $headv)))
+        R, xs = eval(:((R, $e) = Nemo.polynomial_ring(Nemo.QQ, $headv)))
         @info "Created ring" R xs
         rrr = split(body, ",")
         for (i, s) in enumerate(rrr)
@@ -57,7 +57,7 @@ function read_MAPK()
         @info "First line" head
         headv = map(x -> Symbol(x), split(head, ", "))
         e = Meta.parse(join(headv, ","))
-        R, xs = eval(:((R, $e) = Nemo.PolynomialRing(Nemo.QQ, $headv)))
+        R, xs = eval(:((R, $e) = Nemo.polynomial_ring(Nemo.QQ, $headv)))
         @info "Created ring" R xs
         rrr = split(body, ",")
         l = length(rrr)
@@ -100,7 +100,7 @@ function read_MAPK_include()
     @info "First line" head
     headv = map(x -> Symbol(x), split(head, ", "))
     e = Meta.parse(join(headv, ","))
-    R, xs = eval(:((R, $e) = Nemo.PolynomialRing(Nemo.QQ, $headv)))
+    R, xs = eval(:((R, $e) = Nemo.polynomial_ring(Nemo.QQ, $headv)))
 
     collect(include(apath))
 end
@@ -109,7 +109,7 @@ function parse_include(filename)
     head = "x, y, z"
     headv = map(x -> Symbol(x), split(head, ", "))
     e = Meta.parse("x, y, z")
-    R, xs = eval(:((R, $e) = Nemo.PolynomialRing(Nemo.QQ, $headv)))
+    R, xs = eval(:((R, $e) = Nemo.polynomial_ring(Nemo.QQ, $headv)))
 
     include(abspath("benchmark\\data\\$filename"))
 end

docs/index.md

@@ -44,7 +44,7 @@ Pkg.add("AbstractAlgebra") # hide
 ```julia:aaimport
 using AbstractAlgebra
 
-R, (x, y, z) = PolynomialRing(GF(2^31 - 1), ["x", "y", "z"])
+R, (x, y, z) = polynomial_ring(GF(2^31 - 1), ["x", "y", "z"])
 polys = [x^2 + y + z, x*y + z];
 ```
 

docs/tutorial.md

@@ -237,7 +237,7 @@ The Groebner basis of the above with $t > x > y$ in lexicographic order is
 
 ```julia:impl1
 using AbstractAlgebra
-_, (t, x, y) = PolynomialRing(QQ, ["t", "x", "y"], ordering=:lex)
+_, (t, x, y) = polynomial_ring(QQ, ["t", "x", "y"], ordering=:lex)
 
 groebner([t^2*y - 2t + y, t^2*x + t^2 + x - 1])
 ```
@@ -257,7 +257,7 @@ Groebner bases can be used to solve systems *exactly*, given the number of solut
 In this section we assume the usual lexicographic ordering of variables and consider the case with three variables (i.e, $x > y > z$). Same method generalizes naturally for $n$ indeterminates.
 
 ```julia:sys0
-_, (x, y, z) = PolynomialRing(QQ, ["x", "y", "z"], ordering=:lex);
+_, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"], ordering=:lex);
 ```
 
 To illustrate the method, we consider the following polynomial system to solve
@@ -316,7 +316,7 @@ F = \{p^5 - n, p^10 - d, p^25 - q\}
 The idea is to construct a more useful set of constraints using a Groebner basis
 
 ```julia:coins1
-_, (p, n, d, q) = PolynomialRing(QQ, ["p","n","d","q"], ordering=:deglex)
+_, (p, n, d, q) = polynomial_ring(QQ, ["p","n","d","q"], ordering=:deglex)
 
 F = [p^5 - n, p^10 - d, p^25 - q]   # initial constraints
 

experimental/SI/si.jl

@@ -88,7 +88,7 @@ flag, gb_2 = Groebner.groebner_apply!(graph, G_zp)
     end
 end
 
-R, x = PolynomialRing(Nemo.GF(2^31 - 1), ["x$i" for i in 1:15], ordering=:degrevlex)
+R, x = polynomial_ring(Nemo.GF(2^31 - 1), ["x$i" for i in 1:15], ordering=:degrevlex)
 
 f = [a^rand(1:3) * b^rand(1:3) + c^rand(1:2) for a in x for b in x for c in x];