I've come up with a rather awkward workaround using the Sage interface to
libSingular. Still I'd be interested to learn about any simpler solution.
Below is the Singular code, followed by Sage code which performs the same
task.
Singular input:
ring R=73, (a,b), dp;
module module1 = [a,a^3], [1,a];
print(groebner(module1));
Singular output:
1,a2-a,
a,0
Sage input:
import sage.libs.singular.function_factory
groebner = sage.libs.singular.function_factory.ff.groebner
from sage.modules.free_module_element import
FreeModuleElement_generic_dense as module_elem
P.<a,b> = PolynomialRing(GF(73))
M=P^2
module1=Sequence(
[module_elem(M, [a,a^3]),
module_elem(M, [1, a])
])
groebner(module1)
Sage output:
[(1, a), (a^2 - a, 0)]
On Friday, October 18, 2019 at 9:43:53 AM UTC+2, Mao Zeng wrote:
>
> As I understand, groebner_basis() in Sage uses Singular as a backend to
> compute the groebner basis of ideals in polynomial rings. However, Singular
> can also compute the groebner basis of modules. Is this functionality
> available in Sage? Similarly, in Singular the "syz" function can compute
> the syzygy module of either an ideal or a module, but the syzygy_module()
> function in Sage seems to work for ideals only. I would like to use Sage
> instead of using Singular directly. Is there an easy workaround?
>
> Thank you!
>
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