`grassmann_pluecker_ideal` saved GB wrong #4018

YueRen · 2024-08-17T17:48:07Z

I'm very happy that OSCAR has a constructor for Pluecker ideals, but the output is not very usable. For example, asking for its dim raises and error and asking for its degree returns something wrong:

julia> I = grassmann_pluecker_ideal(2,5)
Ideal generated by
  x[1]*x[8] - x[2]*x[6] + x[3]*x[5]
  x[1]*x[9] - x[2]*x[7] + x[4]*x[5]
  x[1]*x[10] - x[3]*x[7] + x[4]*x[6]
  x[2]*x[10] - x[3]*x[9] + x[4]*x[8]
  x[5]*x[10] - x[6]*x[9] + x[7]*x[8]

julia> dim(I)
ERROR: Not a Groebner basis
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] dimension(I::Singular.sideal{Singular.spoly{Singular.n_Q}})
   @ Singular ~/.julia/packages/Singular/A4riV/src/ideal/ideal.jl:105
 [3] __compute_dim__(I::MPolyIdeal{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}})
   @ Oscar ~/.julia/dev/Oscar/src/Rings/mpoly-ideals.jl:1811
 [4] #379
   @ ~/.julia/packages/AbstractAlgebra/tABFQ/src/Attributes.jl:357 [inlined]
 [5] get!(default::Oscar.var"#379#380"{MPolyIdeal{MPolyDecRingElem{…}}}, h::Dict{Symbol, Any}, key::Symbol)
   @ Base ./dict.jl:479
 [6] get_attribute!
   @ ~/.julia/packages/AbstractAlgebra/tABFQ/src/Attributes.jl:230 [inlined]
 [7] dim(I::MPolyIdeal{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}})
   @ Oscar ~/.julia/dev/Oscar/src/Rings/mpoly-ideals.jl:1806
 [8] top-level scope
   @ REPL[19]:1
Some type information was truncated. Use `show(err)` to see complete types.

julia> degree(I)
1

The text was updated successfully, but these errors were encountered:

thofma · 2024-08-17T17:56:43Z

We started saving knowledge about a groebner basis in #3382. Maybe related to this?

YueRen · 2024-08-17T18:20:47Z

Good point, so either the fact that the generating set is a GB is wrong, or the GB does not match the ordering.

To me, the generators look pretty unassuming (the default "easy" generators that I would expect). I don't think they form a GB.

wdecker · 2024-08-17T21:37:31Z

Sorry, I do not understand the discussion, may be since I did not follow the history of this:
We can easily check whether the stored generating set is a GB with respect to some ordering.
If not, why not storing the correct GB?

YueRen · 2024-08-18T06:00:41Z

@wdecker The error is exactly because the stored generating set is no GB with the stored ordering. The construction of the generating set follows the usual formula for Pluecker relations, and there are two options:

the resulting generating said is no GB with respect to any ordering (then fix: remove groebner basis information for grassmann_pluecker_ideal #4019 should be merged)
the ordering is wrong (then the right ordering should be provided)

I think (1) is the case, but only because if the standard construction would result in a GB in some ordering, I would have learned it by now.

wdecker · 2024-08-18T08:17:16Z

I did not have the time to check details here. But here are a guess or rather some questions to @antonydellavecchia:

From the documentation, I guess that you make use of the straightening algorithm. True?
If true, why do you use variables indexed by just one number as default:
julia> I = grassmann_pluecker_ideal(2, 5)
Ideal generated by
x[1]*x[8] - x[2]*x[6] + x[3]*x[5]
x[1]*x[9] - x[2]*x[7] + x[4]*x[5]
x[1]*x[10] - x[3]*x[7] + x[4]*x[6]
x[2]*x[10] - x[3]*x[9] + x[4]*x[8]
x[5]*x[10] - x[6]*x[9] + x[7]*x[8]
This does not reflect the straightening algorithm.
Here, you do better:
julia> II = flag_pluecker_ideal([2], 5)
Ideal generated by
-x[[1, 4]]*x[[2, 3]] + x[[2, 4]]*x[[1, 3]] - x[[3, 4]]*x[[1, 2]]
-x[[1, 5]]*x[[2, 3]] + x[[2, 5]]*x[[1, 3]] - x[[3, 5]]*x[[1, 2]]
-x[[2, 5]]*x[[3, 4]] + x[[3, 5]]*x[[2, 4]] - x[[4, 5]]*x[[2, 3]]
-x[[1, 5]]*x[[3, 4]] + x[[3, 5]]*x[[1, 4]] - x[[4, 5]]*x[[1, 3]]
-x[[1, 5]]*x[[2, 4]] + x[[2, 5]]*x[[1, 4]] - x[[4, 5]]*x[[1, 2]]
The result of the straightening algorithm is indeed a degrevlex GB but only when you order the variables in a specific way. Quite likely, this is not the case in the polymake implementation. True?

benlorenz · 2024-08-18T09:13:16Z

This does look very much like a groebner basis:

julia> I = grassmann_pluecker_ideal(2,5);

julia> Icopy = ideal(gens(I));

julia> Icopy.gens.isGB
false

julia> is_groebner_basis(Icopy.gens)
true

julia> I.gens
Gröbner basis with elements
  1 -> x[3]*x[5] - x[2]*x[6] + x[1]*x[8]
  2 -> x[4]*x[5] - x[2]*x[7] + x[1]*x[9]
  3 -> x[4]*x[6] - x[3]*x[7] + x[1]*x[10]
  4 -> x[4]*x[8] - x[3]*x[9] + x[2]*x[10]
  5 -> x[7]*x[8] - x[6]*x[9] + x[5]*x[10]
with respect to the ordering
  degrevlex([x[1], x[2], x[3], x[4], x[5], x[6], x[7], x[8], x[9], x[10]])

julia> Icopy.gens
Gröbner basis with elements
  1 -> x[3]*x[5] - x[2]*x[6] + x[1]*x[8]
  2 -> x[4]*x[5] - x[2]*x[7] + x[1]*x[9]
  3 -> x[4]*x[6] - x[3]*x[7] + x[1]*x[10]
  4 -> x[4]*x[8] - x[3]*x[9] + x[2]*x[10]
  5 -> x[7]*x[8] - x[6]*x[9] + x[5]*x[10]
with respect to the ordering
  degrevlex([x[1], x[2], x[3], x[4], x[5], x[6], x[7], x[8], x[9], x[10]])

julia> dim(Icopy)
7

julia> degree(Icopy)
5

The same works for other dimensions as well.

The reference in the polymake code is:

Sturmfels: Algorithms in invariant theory, Springer, 2nd ed., 2008

There is also code that generates variable names but that function is not straightforward to use from Oscar, for the $2,5$ case it looks like this:

p_(0,1) p_(0,2) p_(0,3) p_(0,4) p_(1,2) p_(1,3) p_(1,4) p_(2,3) p_(2,4) p_(3,4)

But these are 0-based and not 1-based as one would expect in Oscar.

YueRen · 2024-08-18T10:22:03Z

This is weird, as dim claims that it isn't. Here is an example summing up the issue:

R,p = polynomial_ring(QQ,"p"=>sort(AbstractAlgebra.combinations(5,2)))
I = grassmann_pluecker_ideal(R,2,5)
dim(I) # error due to missing GB
issetequal(groebner_basis(ideal(gens(I))),gens(I)) # confirms that gens are GB

wdecker · 2024-08-18T10:39:26Z

p_(0,1) p_(0,2) p_(0,3) p_(0,4) p_(1,2) p_(1,3) p_(1,4) p_(2,3) p_(2,4) p_(3,4)

Yes, precisely, the indices must be lex ordered. How about using p12 etc in Oscar

YueRen · 2024-08-18T12:39:16Z

There is another problem with the output of grassamann_pluecker_ideal, it doesn't live in the polynomial ring it is supposed to:

julia> R,x = polynomial_ring(QQ,10);

julia> I = grassmann_pluecker_ideal(R,2,5); # should live in R

julia> phi = hom(R,R,gens(R)); # identitiy on R

julia> phi(I) # Error
ERROR: ideal not defined over the domain of the map
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] (::Oscar.MPolyAnyMap{QQMPolyRing, QQMPolyRing, Nothing, QQMPolyRingElem})(I::MPolyIdeal{MPolyDecRingElem{…}})
   @ Oscar ~/.julia/dev/Oscar/experimental/Schemes/src/IdealSheaves.jl:1094
 [3] top-level scope
   @ REPL[24]:1
Some type information was truncated. Use `show(err)` to see complete types.

benlorenz · 2024-08-18T12:51:12Z

There is another problem with the output of grassamann_pluecker_ideal, it doesn't live in the polynomial ring it is supposed to:

help?> grassmann_pluecker_ideal
...
 If the input ring is not graded, return the ideal in the ring with the standard grading.

See #3765 and #3632

wdecker · 2024-08-19T05:53:20Z

@benlorenz Thx for the explanation. We will check and correct the problem.

joschmitt · 2024-08-21T07:43:41Z

I tried this with Singular.jl master, so including oscar-system/Singular.jl#820, and this is not completely fixed.

julia> I = grassmann_pluecker_ideal(2,5)
Ideal generated by
  x[1]*x[8] - x[2]*x[6] + x[3]*x[5]
  x[1]*x[9] - x[2]*x[7] + x[4]*x[5]
  x[1]*x[10] - x[3]*x[7] + x[4]*x[6]
  x[2]*x[10] - x[3]*x[9] + x[4]*x[8]
  x[5]*x[10] - x[6]*x[9] + x[7]*x[8]

julia> dim(I)
7

julia> degree(I)
1

The dimension is fine, but the degree should be:

julia> degree(ideal(gens(I)))
5

If I compute the degree without computing the dimension first, I actually get an error:

julia> I = grassmann_pluecker_ideal(2,5)
Ideal generated by
  x[1]*x[8] - x[2]*x[6] + x[3]*x[5]
  x[1]*x[9] - x[2]*x[7] + x[4]*x[5]
  x[1]*x[10] - x[3]*x[7] + x[4]*x[6]
  x[2]*x[10] - x[3]*x[9] + x[4]*x[8]
  x[5]*x[10] - x[6]*x[9] + x[7]*x[8]

julia> degree(I)
ERROR: UndefRefError: access to undefined reference
Stacktrace:
  [1] getproperty
    @ ./Base.jl:37 [inlined]
  [2] getproperty
    @ ~/.julia/dev/Oscar/src/Rings/mpoly.jl:220 [inlined]
  [3] HilbertData(I::MPolyIdeal{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}})
    @ Oscar ~/.julia/dev/Oscar/src/Rings/mpoly-graded.jl:1506
  [4] degree(A::MPolyQuoRing{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}})
    @ Oscar ~/.julia/dev/Oscar/src/Rings/mpoly-affine-algebras.jl:461
  [5] __compute_degree__(I::MPolyIdeal{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}})
    @ Oscar ~/.julia/dev/Oscar/src/Rings/mpoly-graded.jl:2439
  [6] #246
    @ ~/.julia/packages/AbstractAlgebra/bB5QU/src/Attributes.jl:357 [inlined]
  [7] get!(default::Oscar.var"#246#247"{MPolyIdeal{MPolyDecRingElem{…}}}, h::Dict{Symbol, Any}, key::Symbol)
    @ Base ./dict.jl:479
  [8] get_attribute!
    @ ~/.julia/packages/AbstractAlgebra/bB5QU/src/Attributes.jl:230 [inlined]
  [9] degree(I::MPolyIdeal{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}})
    @ Oscar ~/.julia/dev/Oscar/src/Rings/mpoly-graded.jl:2432
 [10] top-level scope
    @ REPL[33]:1
Some type information was truncated. Use `show(err)` to see complete types.

This also happens without oscar-system/Singular.jl#820.

jankoboehm · 2024-08-22T09:33:56Z

We should change groebner_assure to the following (adding the missing else)

function groebner_assure(I::MPolyIdeal, complete_reduction::Bool = false, need_global::Bool = false)
  if !isempty(I.gb)
    for G in values(I.gb)
      need_global || return G
      is_global(G.ord) || continue
      complete_reduction || return G
      if !G.isReduced
        I.gb[G.ord] = _compute_standard_basis(G, G.ord, true)
        return I.gb[G.ord]
      else
        return G
      end
    end
  end
  ord = default_ordering(base_ring(I))
  (need_global <= is_global(ord)) || error("Monomial ordering must be global.")
  I.gb[ord] = groebner_assure(I, ord, complete_reduction)
  return I.gb[ord]
end

joschmitt · 2024-08-22T10:09:34Z

I'm sorry, but I don't understand. With this change

diff --git a/src/Rings/groebner.jl b/src/Rings/groebner.jl
index 8496956053..58007d35d5 100644
--- a/src/Rings/groebner.jl
+++ b/src/Rings/groebner.jl
@@ -41,6 +41,8 @@ function groebner_assure(I::MPolyIdeal, complete_reduction::Bool = false, need_g
       if !G.isReduced
         I.gb[G.ord] = _compute_standard_basis(G, G.ord, true)
         return I.gb[G.ord]
+      else
+        return G
       end
     end
   end

I still get the very same error(s):

julia> I = grassmann_pluecker_ideal(2, 5)
Ideal generated by
  x[1]*x[8] - x[2]*x[6] + x[3]*x[5]
  x[1]*x[9] - x[2]*x[7] + x[4]*x[5]
  x[1]*x[10] - x[3]*x[7] + x[4]*x[6]
  x[2]*x[10] - x[3]*x[9] + x[4]*x[8]
  x[5]*x[10] - x[6]*x[9] + x[7]*x[8]

julia> degree(I)
ERROR: UndefRefError: access to undefined reference
[...]

julia> dim(I)
ERROR: Not a Groebner basis
[...]

julia> degree(I)
1

…d to issue #4018) (#4074) * change variable labeling for default grassmann pluecker ideal * Update src/Rings/mpoly-ideals.jl --------- Co-authored-by: Lars Göttgens <lars.goettgens@rwth-aachen.de> Co-authored-by: Lars Göttgens <lars.goettgens@gmail.com>

…d to issue oscar-system#4018) (oscar-system#4074) * change variable labeling for default grassmann pluecker ideal * Update src/Rings/mpoly-ideals.jl --------- Co-authored-by: Lars Göttgens <lars.goettgens@rwth-aachen.de> Co-authored-by: Lars Göttgens <lars.goettgens@gmail.com>

YueRen added the bug Something isn't working label Aug 17, 2024

YueRen changed the title ~~dim(grassmann_pluecker_ideal(2,5)) fails~~ grassmann_pluecker_ideal saved GB wrong Aug 17, 2024

YueRen mentioned this issue Aug 17, 2024

fix: remove groebner basis information for grassmann_pluecker_ideal #4019

Closed

hannes14 added a commit to hannes14/Singular.jl that referenced this issue Aug 20, 2024

keep isGB in map_ideal (oscar-system/Oscar.jl#4018)

ace5147

hannes14 mentioned this issue Aug 20, 2024

keep isGB in map_ideal (https://github.com/oscar-system/Oscar.jl/issu… oscar-system/Singular.jl#820

Merged

hannes14 added a commit to oscar-system/Singular.jl that referenced this issue Aug 21, 2024

keep isGB in map_ideal (oscar-system/Oscar.jl#4018) (#820)

3dac87e

hannes14 closed this as completed in oscar-system/Singular.jl#820 Aug 21, 2024

joschmitt reopened this Aug 21, 2024

hannes14 mentioned this issue Aug 21, 2024

also check for equal orderings in map_ideal oscar-system/Singular.jl#821

Merged

joschmitt mentioned this issue Aug 21, 2024

Fix #4018 #4037

Closed

joschmitt added a commit to joschmitt/Oscar.jl that referenced this issue Aug 21, 2024

Fix oscar-system#4018

a24b598

joschmitt added a commit to joschmitt/Oscar.jl that referenced this issue Aug 21, 2024

Fix oscar-system#4018

d3ec96e

joschmitt mentioned this issue Aug 21, 2024

Fix #4018 #4038

Merged

joschmitt added a commit to joschmitt/Oscar.jl that referenced this issue Aug 21, 2024

Fix oscar-system#4018

25bd99e

joschmitt added a commit to joschmitt/Oscar.jl that referenced this issue Aug 21, 2024

Fix oscar-system#4018

c38c14b

danteluber mentioned this issue Sep 4, 2024

change variable labeling for default grassmann pluecker ideal (Related to issue #4018) #4074

Merged

ederc added a commit to ederc/Oscar.jl that referenced this issue Sep 9, 2024

adds issue oscar-system#4018 as test

7ab1be1

fingolfin closed this as completed in #4038 Sep 10, 2024

fingolfin closed this as completed in 0a1d296 Sep 10, 2024

HechtiDerLachs pushed a commit to HechtiDerLachs/Oscar.jl that referenced this issue Sep 13, 2024

Fix oscar-system#4018 (oscar-system#4038)

e4c3ef2

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`grassmann_pluecker_ideal` saved GB wrong #4018

`grassmann_pluecker_ideal` saved GB wrong #4018

YueRen commented Aug 17, 2024

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grassmann_pluecker_ideal saved GB wrong #4018

grassmann_pluecker_ideal saved GB wrong #4018

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`grassmann_pluecker_ideal` saved GB wrong #4018

`grassmann_pluecker_ideal` saved GB wrong #4018

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