#13103: Makes BooleanPolynomial more compatible with MPolynomial
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Reporter: Bouillaguet | Owner: malb
Type: enhancement | Status: new
Priority: minor | Milestone: sage-5.1
Component: commutative algebra | Resolution:
Keywords: polybori | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Charles Bouillaguet | Merged in:
Dependencies: | Stopgaps:
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Comment (by Bouillaguet):
With the patch, the variety() function "works":
{{{
sage: R.<x,y,z> = BooleanPolynomialRing()
sage: I = ideal( [ x*y*z + x*z + y + 1, x*y+x*z+y*z, x+y+z+1 ] )
sage: I.variety()
verbose 0 (3293: multi_polynomial_ideal.py, groebner_basis) Warning:
falling back to very slow toy implementation.
verbose 0 (2364: multi_polynomial_ideal.py, variety) Warning: falling back
to very slow toy implementation.
[{y: 1, z: 0, x: 0}]
}}}
However, it returns a '''mathematically wrong result''' when the
polynomials do not generate a zero-dimensional ideal without the field
equations. In this case, the variety() function normally fails (because on
non-finite fields, the variety would be infinite).
Example:
{{{
sage: R.<x,y,z> = GF(2)[]
sage: I = ideal( [ x*y*z + x*z + y + 1, x+y+z+1 ] )
sage: I.variety()
...
ValueError: The dimension of the ideal is 1, but it should be 0
}}}
If we add the field equations, then the ideal becomes zero-dimensional,
and the variety() function works normally:
{{{
sage: J = I + sage.rings.ideal.FieldIdeal(R)
sage: J.variety()
[{y: 1, z: 0, x: 0}, {y: 1, z: 1, x: 1}]
}}}
But over BooleanPolynomial things go wrong:
{{{
sage: R.<x,y,z> = BooleanPolynomialRing()
sage: I = ideal( [ x*y*z + x*z + y + 1, x+y+z+1 ] )
sage: I.variety()
verbose 0 (3293: multi_polynomial_ideal.py, groebner_basis) Warning:
falling back to very slow toy implementation.
verbose 0 (2364: multi_polynomial_ideal.py, variety) Warning: falling back
to very slow toy implementation.
[{y: 1}]
}}}
This result does not make sense. Of course ideals of BooleanPolynomials
should have dimension zero, so that the variety() function should always
work. But it should always return the right result!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13103#comment:1>
Sage <http://www.sagemath.org>
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