Merge pull request #59 from linus-md/block

Add block orderings

Author: ederc

docs/src/groebner-bases.md

@@ -34,6 +34,7 @@ well as a signature based algorithm to compute Gröbner bases.
         max_nr_pairs::Int=0,
         la_option::Int=2,
         eliminate::Int=0,
+        intersect::Bool=true,
         complete_reduction::Bool=true,
         info_level::Int=0
         )
@@ -43,12 +44,15 @@ The engine supports the elimination of one block of variables considering the
 product monomial ordering of two blocks, both ordered w.r.t. the degree
 reverse lexicographical order. One can either directly add the number of
 variables of the first block via the `eliminate` parameter in the
-`groebner_basis` call. We have also implemented an alias for this call:
+`groebner_basis` call. By using `intersect=false` it is possible to only 
+use block ordering without intersecting. We have also implemented an alias 
+for this call:
 
 ```@docs
     eliminate(
         I::Ideal{T} where T <: MPolyRingElem,
         eliminate::Int;
+        intersect::Bool=true,
         initial_hts::Int=17,
         nr_thrds::Int=1,
         max_nr_pairs::Int=0,

src/algorithms/groebner-bases.jl

@@ -15,6 +15,8 @@ At the moment the underlying algorithm is based on variants of Faugère's F4 Alg
 
 # Arguments
 - `I::Ideal{T} where T <: MPolyRingElem`: input generators.
+- `eliminate::Int=0`: size of first block of variables to be eliminated.
+- `intersect::Bool=true`: compute the `eliminate`-th elimination ideal.
 - `initial_hts::Int=17`: initial hash table size `log_2`.
 - `nr_thrds::Int=1`: number of threads for parallel linear algebra.
 - `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`.
@@ -40,6 +42,7 @@ julia> eliminate(I, 2)
 function eliminate(
         I::Ideal{T} where T <: MPolyRingElem,
         eliminate::Int;
+        intersect::Bool=true,
         initial_hts::Int=17,
         nr_thrds::Int=1,
         max_nr_pairs::Int=0,
@@ -50,9 +53,9 @@ function eliminate(
     if eliminate <= 0
         error("Number of variables to be eliminated is <= 0.")
     else
-        return groebner_basis(I, initial_hts=initial_hts, nr_thrds=nr_thrds,
+        return groebner_basis(I, initial_hts=initial_hts,nr_thrds=nr_thrds,
                               max_nr_pairs=max_nr_pairs, la_option=la_option,
-                              eliminate=eliminate,
+                              eliminate=eliminate, intersect=intersect,
                               complete_reduction=complete_reduction,
                               info_level=info_level)
     end
@@ -73,6 +76,7 @@ At the moment the underlying algorithm is based on variants of Faugère's F4 Alg
 - `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`.
 - `la_option::Int=2`: linear algebra option: exact sparse-dense (`1`), exact sparse (`2`, default), probabilistic sparse-dense (`42`), probabilistic sparse(`44`).
 - `eliminate::Int=0`: size of first block of variables to be eliminated.
+- `intersect::Bool=true`: compute the `eliminate`-th elimination ideal.
 - `complete_reduction::Bool=true`: compute a reduced Gröbner basis for `I`
 - `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`).
 
@@ -105,14 +109,15 @@ function groebner_basis(
         max_nr_pairs::Int=0,
         la_option::Int=2,
         eliminate::Int=0,
+        intersect::Bool=true,
         complete_reduction::Bool=true,
         info_level::Int=0
         )
 
     return get!(I.gb, eliminate) do
         _core_groebner_basis(I, initial_hts = initial_hts, nr_thrds = nr_thrds, 
                              max_nr_pairs = max_nr_pairs, la_option = la_option,
-                             eliminate = eliminate,
+                             eliminate = eliminate, intersect = intersect,
                              complete_reduction = complete_reduction,
                              info_level = info_level)
     end
@@ -125,6 +130,7 @@ function _core_groebner_basis(
         max_nr_pairs::Int=0,
         la_option::Int=2,
         eliminate::Int=0,
+        intersect::Bool=true,
         complete_reduction::Bool=true,
         info_level::Int=0
         )
@@ -170,9 +176,13 @@ function _core_groebner_basis(
     ptr     = reinterpret(Ptr{Int32}, gb_cf[])
     jl_cf   = Base.unsafe_wrap(Array, ptr, nr_terms)
 
-    basis = _convert_finite_field_array_to_abstract_algebra(
-                jl_ld, jl_len, jl_cf, jl_exp, R, eliminate)
-
+    if intersect == true
+        basis = _convert_finite_field_array_to_abstract_algebra(
+            jl_ld, jl_len, jl_cf, jl_exp, R, eliminate)
+    else
+        basis = _convert_finite_field_array_to_abstract_algebra(
+            jl_ld, jl_len, jl_cf, jl_exp, R, 0)
+    end
 
     ccall((:free_f4_julia_result_data, libneogb), Nothing ,
           (Ptr{Nothing}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}},

test/algorithms/groebner-bases.jl

@@ -20,6 +20,15 @@
          z^4 + 38*z^3 + 95*z^2 + 95*z
         ]
     @test G == H
+    
+    I = Ideal([x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y])
+    G = groebner_basis(I, eliminate=2, intersect=false)
+    H = MPolyRingElem[
+        z^4 + 38*z^3 + 95*z^2 + 95*z
+        30*z^3 + 32*z^2 + y + 87*z
+        41*z^3 + 37*z^2 + x + 30*z + 100
+        ]
+    @test G == H
 
     @test_throws ErrorException eliminate(I,0)
     L = eliminate(I,2)