Open mohamed-barakat opened 3 years ago
This example is just a place holder. I would like to see Singular supporting GB with Dedekind domains as coefficients rings.
Motivation: Affine rings like
Z[a,b,x,y,z]/( a^2-a+1, 2*b-1 )
appear in applications (e.g., moduli spaces of matroids). GB computations will have to deal with a residue class ring (qring) with 5 indeterminates. With GB over Dedekind domains, one would have a GB in 3 indeterminates over the (free) polynomial ring R[x,y,z], where the coefficients ring R is the Dedekind domain Z[a,b]/( a^2-a+1, 2*b-1 ) = Z[zeta][1/2].
On Fri, Jan 08, 2021 at 05:49:57AM -0800, Mohamed Barakat wrote:
This example is just a place holder. I would like to see Singular supporting GB with Dedekind domains as coefficients rings.
Motivation: Affine rings like
Z[a,b,x,y,z]/( a^2-a+1, 2*b-1 )
appear in applications (e.g., moduli spaces of matroids). GB computations will have to deal with a residue class ring (qring) with 5 indeterminates. With GB over Dedekind domains, one would have a GB in 3 indeterminates over the (free) polynomial ring R[x,y,z], where the coefficients ring R is the Dedekind domain Z[a,b]/( a^2-a+1, 2*b-1 ) = Z[zeta][1/2].
Tommy has special code (in Magma?) and special theory for this. This cannot be done (efficiently) with the Singular generic.
The current chance would be to realize R as an affine algebra (a Singualr quotient ring)...
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On Fri, Jan 08, 2021 at 05:49:57AM -0800, Mohamed Barakat wrote:
This example is just a place holder. I would like to see Singular supporting GB with Dedekind domains as coefficients rings.
Motivation: Affine rings like
Z[a,b,x,y,z]/( a^2-a+1, 2*b-1 )
appear in applications (e.g., moduli spaces of matroids). GB computations will have to deal with a residue class ring (qring) with 5 indeterminates. With GB over Dedekind domains, one would have a GB in 3 indeterminates over the (free) polynomial ring R[x,y,z], where the coefficients ring R is the Dedekind domain Z[a,b]/( a^2-a+1, 2*b-1 ) = Z[zeta][1/2].
I thin offshot:
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The current chance would be to realize R as an affine algebra (a Singualr quotient ring)...
This is what I (almost) do currently, but it is not efficient enough.