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Merge pull request #26 from ederc/normal-form
Adds normal form interface for msolve -> prepares v0.4.0
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‎Project.toml‎

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@@ -1,7 +1,7 @@
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name = "AlgebraicSolving"
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uuid = "66b61cbe-0446-4d5d-9090-1ff510639f9d"
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authors = ["ederc <[email protected]>", "Mohab Safey El Din <[email protected]", "Rafael Mohr <[email protected]>"]
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version = "0.3.7"
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version = "0.4.0"
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[deps]
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -20,4 +20,4 @@ LoopVectorization = "0.12"
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Nemo = "0.35.1, 0.36, 0.37"
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StaticArrays = "1"
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julia = "1.6"
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msolve_jll = "0.4.6"
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msolve_jll = "0.6.1"

‎docs/Project.toml‎

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@@ -8,5 +8,5 @@ Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
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[compat]
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Documenter = "0.26"
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msolve_jll = "0.4.1"
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msolve_jll = "0.6.1"
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Nemo = "0.35.1"

‎docs/make.jl‎

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@@ -20,6 +20,7 @@ makedocs(
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"index.md",
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"types.md",
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"Algorithms" => ["groebner-bases.md",
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"normal-forms.md",
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"solvers.md"],
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"Examples" => "katsura.md"
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]

‎docs/src/groebner-bases.md‎

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@@ -61,9 +61,5 @@ variables of the first block via the `eliminate` parameter in the
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To compute signature Gröbner bases use
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```@docs
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sig_groebner_basis(
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sys::Vector{T} where T <: MPolyElem,
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info_level::Int=0,
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degbound::Int=0
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)
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sig_groebner_basis(sys::Vector{T}; info_level::Int = 0, degbound::Int = 0) where {T <: MPolyRingElem}
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```

‎docs/src/normal-forms.md‎

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```@meta
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CurrentModule = AlgebraicSolving
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DocTestSetup = quote
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using AlgebraicSolving
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end
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```
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```@setup algebraicsolving
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using AlgebraicSolving
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```
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```@contents
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Pages = ["normal-forms.md"]
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```
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# Gröbner bases
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## Introduction
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AlgebraicSolving allows to compute normal forms of a polynomial resp. a finite
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array of polynomials w.r.t. some given ideal over a finite field of
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characteristic smaller $2^{31}$ w.r.t. the degree reverse lexicographical
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monomial order.
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**Note:** It therefore might first compute a Gröbner bases for the ideal.
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## Functionality
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```@docs
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normal_form(
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f::T,
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I::Ideal{T};
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nr_thrds::Int=1,
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info_level::Int=0
34+
) where T <: MPolyRingElem
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```
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```@docs
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normal_form(
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F::Vector{T},
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I::Ideal{T};
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nr_thrds::Int=1,
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info_level::Int=0
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) where T <: MPolyRingElem
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```

‎src/AlgebraicSolving.jl‎

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@@ -10,6 +10,7 @@ include("types.jl")
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#= functionality =#
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include("interfaces/nemo.jl")
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include("algorithms/groebner-bases.jl")
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include("algorithms/normal-forms.jl")
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include("algorithms/solvers.jl")
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#= siggb =#
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include("siggb/siggb.jl")

‎src/algorithms/groebner-bases.jl‎

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@@ -151,7 +151,7 @@ function _core_groebner_basis(
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gb_exp = Ref(Ptr{Cint}(0))
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gb_cf = Ref(Ptr{Cvoid}(0))
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154-
nr_terms = ccall((:f4_julia, libneogb), Int,
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nr_terms = ccall((:export_f4, libneogb), Int,
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(Ptr{Nothing}, Ptr{Cint}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cvoid}},
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Ptr{Cint}, Ptr{Cint}, Ptr{Cvoid}, Cint, Cint, Cint, Cint, Cint, Cint,
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Cint, Cint, Cint, Cint, Cint, Cint, Cint),
@@ -166,7 +166,7 @@ function _core_groebner_basis(
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ptr = reinterpret(Ptr{Int32}, gb_cf[])
167167
jl_cf = Base.unsafe_wrap(Array, ptr, nr_terms)
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169-
basis = _convert_finite_field_gb_to_abstract_algebra(
169+
basis = _convert_finite_field_array_to_abstract_algebra(
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jl_ld, jl_len, jl_cf, jl_exp, R, eliminate)
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‎src/algorithms/normal-forms.jl‎

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import msolve_jll: libneogb
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export normal_form
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@doc Markdown.doc"""
6+
normal_form(
7+
f::T,
8+
I::Ideal{T};
9+
nr_thrds::Int=1,
10+
info_level::Int=0
11+
) where T <: MPolyRingElem
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13+
Compute the normal forms of the elements of `F` w.r.t. a degree reverse
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lexicographical Gröbner basis of `I`.
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**Note:** If `I` has not already cached a degree reverse lexicographical
17+
Gröbner basis, then this one is first computed.
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# Arguments
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- `F::Vector{T} where T <: MPolyRingElem`: elements to be reduced.
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- `I::Ideal{T} where T <: MPolyRingElem`: ideal data to reduce with.
22+
- `nr_thrds::Int=1`: number of threads for parallel linear algebra.
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- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`).
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# Examples
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```jldoctest
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julia> using AlgebraicSolving
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julia> R, (x,y) = polynomial_ring(GF(101),["x","y"])
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(Multivariate polynomial ring in 2 variables over GF(101), fpMPolyRingElem[x, y])
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julia> I = Ideal([y*x^3+12-y, x+y])
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fpMPolyRingElem[x^3*y + 100*y + 12, x + y]
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julia> f = 2*x^2+7*x*y
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2*x^2 + 7*x*y
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julia> normal_form(f, I)
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96*y^2
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```
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"""
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function normal_form(
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f::T,
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I::Ideal{T};
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nr_thrds::Int=1,
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info_level::Int=0
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) where T <: MPolyRingElem
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nf = _core_normal_form([f], I; nr_thrds, info_level)
49+
return nf[1]
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end
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@doc Markdown.doc"""
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normal_form(
54+
F::Vector{T},
55+
I::Ideal{T};
56+
nr_thrds::Int=1,
57+
info_level::Int=0
58+
) where T <: MPolyRingElem
59+
60+
Compute the normal forms of the elements of `F` w.r.t. a degree reverse
61+
lexicographical Gröbner basis of `I`.
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63+
**Note:** If `I` has not already cached a degree reverse lexicographical
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Gröbner basis, then this one is first computed.
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# Arguments
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- `F::Vector{T} where T <: MPolyRingElem`: elements to be reduced.
68+
- `I::Ideal{T} where T <: MPolyRingElem`: ideal data to reduce with.
69+
- `nr_thrds::Int=1`: number of threads for parallel linear algebra.
70+
- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`).
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# Examples
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```jldoctest
74+
julia> using AlgebraicSolving
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76+
julia> R, (x,y) = polynomial_ring(GF(101),["x","y"])
77+
(Multivariate polynomial ring in 2 variables over GF(101), fpMPolyRingElem[x, y])
78+
79+
julia> I = Ideal([y*x^3+12-y, x+y])
80+
fpMPolyRingElem[x^3*y + 100*y + 12, x + y]
81+
82+
julia> F = [2*x^2+7*x*y, x+y]
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2-element Vector{fpMPolyRingElem}:
84+
2*x^2 + 7*x*y
85+
x + y
86+
87+
julia> normal_form(F,I)
88+
2-element Vector{fpMPolyRingElem}:
89+
96*y^2
90+
0
91+
```
92+
"""
93+
function normal_form(
94+
F::Vector{T},
95+
I::Ideal{T};
96+
nr_thrds::Int=1,
97+
info_level::Int=0
98+
) where T <: MPolyRingElem
99+
return _core_normal_form(F, I; nr_thrds, info_level)
100+
end
101+
102+
function _core_normal_form(
103+
F::Vector{T},
104+
I::Ideal{T};
105+
nr_thrds::Int=1,
106+
info_level::Int=0
107+
) where T <: MPolyRingElem
108+
109+
110+
if (length(F) == 0 || length(I.gens) == 0)
111+
error("Input data not valid.")
112+
end
113+
114+
R = first(F).parent
115+
nr_vars = nvars(R)
116+
field_char = Int(characteristic(R))
117+
118+
if !(is_probable_prime(field_char))
119+
error("At the moment we only supports finite fields.")
120+
end
121+
122+
#= first get a degree reverse lexicographical Gröbner basis for I =#
123+
G = groebner_basis(I, eliminate = 0, la_option = 44, info_level = info_level)
124+
125+
tbr_nr_gens = length(F)
126+
bs_nr_gens = length(G)
127+
is_gb = 1
128+
129+
# convert ideal to flattened arrays of ints
130+
tbr_lens, tbr_cfs, tbr_exps = _convert_to_msolve(F)
131+
bs_lens, bs_cfs, bs_exps = _convert_to_msolve(G)
132+
133+
nf_ld = Ref(Cint(0))
134+
nf_len = Ref(Ptr{Cint}(0))
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nf_exp = Ref(Ptr{Cint}(0))
136+
nf_cf = Ref(Ptr{Cvoid}(0))
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138+
nr_terms = ccall((:export_nf, libneogb), Int,
139+
(Ptr{Nothing}, Ptr{Cint}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cvoid}},
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Cint, Ptr{Cint}, Ptr{Cint}, Ptr{Cvoid}, Cint, Ptr{Cint}, Ptr{Cint}, Ptr{Cvoid},
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Cint, Cint, Cint, Cint, Cint, Cint, Cint),
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cglobal(:jl_malloc), nf_ld, nf_len, nf_exp, nf_cf, tbr_nr_gens, tbr_lens, tbr_exps,
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tbr_cfs, bs_nr_gens, bs_lens, bs_exps, bs_cfs, field_char, 0, 0, nr_vars, is_gb,
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nr_thrds, info_level)
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146+
# convert to julia array, also give memory management to julia
147+
jl_ld = nf_ld[]
148+
jl_len = Base.unsafe_wrap(Array, nf_len[], jl_ld)
149+
jl_exp = Base.unsafe_wrap(Array, nf_exp[], nr_terms*nr_vars)
150+
ptr = reinterpret(Ptr{Int32}, nf_cf[])
151+
jl_cf = Base.unsafe_wrap(Array, ptr, nr_terms)
152+
153+
basis = _convert_finite_field_array_to_abstract_algebra(
154+
jl_ld, jl_len, jl_cf, jl_exp, R, 0)
155+
156+
ccall((:free_f4_julia_result_data, libneogb), Nothing ,
157+
(Ptr{Nothing}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}},
158+
Ptr{Ptr{Cvoid}}, Int, Int),
159+
cglobal(:jl_free), nf_len, nf_exp, nf_cf, jl_ld, field_char)
160+
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return basis
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end
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‎src/exports.jl‎

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

‎src/imports.jl‎

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@@ -34,6 +34,7 @@ import Nemo:
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is_unit,
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isqrtrem,
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jacobi_symbol,
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leading_coefficient,
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matrix_space,
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moebius_mu,
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MPolyRing,

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