magma -- boolean ring conversions

[williamstein]

1) This should work (?)

sage: B.<x,y> = BooleanPolynomialRing()
sage: B*[x*y + 1, x + y]
sage: I = B*[x*y + 1, x + y]
sage: I._magma_()

Ideal of Affine Algebra of rank 2 over GF(2)
Lexicographical Order
Variables: x, y
Quotient relations:
[
x^2 + x,
y^2 + y
]
Generating basis:
[
x*y + 1,
x + y
]

sage: Im = I._magma_()
sage: Im.GroebnerBasis()
TypeError: Error evaluation Magma code.
IN:_sage_[21] := GroebnerBasis(_sage_[20]);
OUT:
>> _sage_[21] := GroebnerBasis(_sage_[20]);
                             ^
Runtime error in 'GroebnerBasis': Bad argument types
Argument types given: RngMPolRes

Reported by Martin Albrecht

Component: interfaces

Issue created by migration from https://trac.sagemath.org/ticket/4236

[williamstein]

comment:2

This does not seem like a bug in the Sage/Magma interface. It seems like a misunderstanding of Magma itself, which doesn't have a GroebnerBasis function that takse as input an ideal in a boolean ring. Magma simply doesn't do that. It only has Groebner for ideals in polynomial rings. There are some functions on ideals in boolean rings, but not many. I.e., above

sage: Im.IsMaximal()
true
sage: Im.PrimaryDecomposition()

[
Affine Algebra of rank 2 over GF(2)
Lexicographical Order
Variables: x, y
Quotient relations:
[
x^2 + x,
y^2 + y
]
Generating basis:
[
x + 1,
y + 1
]
]

[malb]

comment:3

We could make Magma better than Magma by

• adding the generators of the quotient to the ideal J = I + Q
• computing gb := GroebnerBasis(J)
• coerce the result to the quotient again.

This is equivalent to computing the GB in the quotient directly.

[malb]

comment:5

This is fixed with #6177