Closed YueRen closed 5 months ago
There are already plans to do this, @hannes14 is preparing to provide the corresponding functionality via Singular.jl
which can then be used in Oscar
.
At current state, in the case of a global ordering, all returned remainders are fully reduced.
@wdecker Thanks for the tip! That is more than enough for me for now (and what I thought was a non-tailreduced polynomial turned out to me a mistake on my end).
Appears to be resolved. An example from the documentation:
julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);
julia> f1 = x^2+x^2*y; f2 = y^3+x*y*z; f3 = x^3*y^2+z^4;
julia> g = x^3*y+x^5+x^2*y^2*z^2+z^6;
julia> reduce(g, [f1, f2, f3], ordering = lex(R))
x^5 + x^3*y + x^2*y^2*z^2 + z^6
julia> reduce(g, [f1,f2, f3], ordering = lex(R), complete_reduction = true)
x^5 - x^3 + y^6 + z^6
groebner_basis
has an optioncomplete_reduction
, which if set totrue
ensures that the returned Groebner basis is reduced.Can we equip
reduce
with the same option? The default would befalse
, but if set totrue
thenreduce
would also perform tail reductions. I would need it to read off the inequalities and equations of the Groebner cone.