Merge pull request #19 from RafaelDavidMohr/f5

Signature Gröbner basis implementation

Author: ederc

Project.toml

@@ -1,17 +1,21 @@
 name = "AlgebraicSolving"
 uuid = "66b61cbe-0446-4d5d-9090-1ff510639f9d"
-authors = ["ederc <[email protected]>",
-        "Mohab Safey El Din <[email protected]"]
+authors = ["ederc <[email protected]>", "Mohab Safey El Din <[email protected]", "Rafael Mohr <[email protected]>"]
 version = "0.3.6"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
+LoopVectorization = "bdcacae8-1622-11e9-2a5c-532679323890"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
-msolve_jll = "6d01cc9a-e8f6-580e-8c54-544227e08205"
 Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
+Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+msolve_jll = "6d01cc9a-e8f6-580e-8c54-544227e08205"
 
 [compat]
+Nemo = "0.35.1, 0.36, 0.37"
 julia = "1.6"
 msolve_jll = "0.4.6"
-Nemo = "0.35.1, 0.36, 0.37"

docs/src/groebner-bases.md

@@ -21,7 +21,8 @@ AlgebraicSolving allows to compute Gröbner bases for input generators over fini
 fields of characteristic smaller $2^{31}$ w.r.t. the degree reverse
 lexicographical monomial order.
 
-At the moment different variants of Faugère's F4 Algorithm are implemented.
+At the moment different variants of Faugère's F4 Algorithm are implemented as
+well as a signature based algorithm to compute Gröbner bases.
 
 ## Functionality
 
@@ -56,3 +57,13 @@ variables of the first block via the `eliminate` parameter in the
         info_level::Int=0
         )
 ```
+
+To compute signature Gröbner bases use
+
+```@docs
+   sig_groebner_basis(
+       sys::Vector{T} where T <: MPolyElem,
+	   info_level::Int=0,
+	   degbound::Int=0
+       )
+```

src/AlgebraicSolving.jl

@@ -11,7 +11,10 @@ include("types.jl")
 include("interfaces/nemo.jl")
 include("algorithms/groebner-bases.jl")
 include("algorithms/solvers.jl")
+#= siggb =#
+include("siggb/siggb.jl")
 #= examples =#
 include("examples/katsura.jl")
+include("examples/cyclic.jl")
 
 end # module AlgebraicSolving

src/algorithms/solvers.jl

@@ -171,7 +171,7 @@ function _core_msolve(
     k = 1
     while i <= len
         j = 1
-        tmp = Vector{Nemo.QQFieldElem}(undef, nr_vars)
+        tmp = Vector{QQFieldElem}(undef, nr_vars)
         while j <= nr_vars
             tmp[j]  = QQFieldElem(unsafe_load(jl_sols_num, i)) >> Int64(unsafe_load(jl_sols_den, i))
             tmp[j] += QQFieldElem(unsafe_load(jl_sols_num, i+1)) >> Int64(unsafe_load(jl_sols_den, i+1))

src/examples/cyclic.jl

@@ -0,0 +1,23 @@
+@doc Markdown.doc"""
+    cyclic(R::MPolyRing)
+
+Return the Cyclic ideal in the variables of `R`.
+
+# Example
+```jldoctest
+julia> using AlgebraicSolving
+
+julia> R, vars = polynomial_ring(QQ, ["x$i" for i in 1:4])
+(Multivariate polynomial ring in 4 variables over QQ, QQMPolyRingElem[x1, x2, x3, x4])
+
+julia> cyclic(R)
+QQMPolyRingElem[x1 + x2 + x3 + x4, x1*x2 + x1*x4 + x2*x3 + x3*x4, x1*x2*x3 + x1*x2*x4 + x1*x3*x4 + x2*x3*x4, x1*x2*x3*x4 - 1]
+```
+"""
+function cyclic(R::MPolyRing)
+    vars = gens(R)
+    n = length(vars)
+    pols = [sum(prod(vars[j%n+1] for j in k:k+i) for k in 1:n) for i in 0:n-2]
+    push!(pols, prod(vars[i] for i in 1:n)-1)
+    return Ideal(pols)
+end

src/exports.jl

@@ -1,3 +1,3 @@
 export polynomial_ring, MPolyRing, GFElem, MPolyRingElem, finite_field, GF, fpMPolyRingElem,
        characteristic, degree, ZZ, QQ, vars, nvars, ngens, ZZRingElem, QQFieldElem, QQMPolyRingElem,
-       base_ring, coefficient_ring, evaluate, prime_field
+       base_ring, coefficient_ring, evaluate, prime_field, sig_groebner_basis, cyclic

src/imports.jl

@@ -3,6 +3,12 @@ using Test
 using msolve_jll
 using Nemo
 using LinearAlgebra
+using StaticArrays
+using LoopVectorization
+
+import Random: MersenneTwister
+import Logging: ConsoleLogger, with_logger, Warn, Info
+import Printf: @sprintf
 
 import Nemo:
     bell,