def arithmetic(t = None):
"""
Controls the default proof strategy for integer arithmetic algorithms (such as primality testing).
INPUT:
t -- boolean or None
OUTPUT:
If t == True, requires integer arithmetic operations to (by default) return results that are true unconditionally: the correctness will not depend on an algorithm with a nonzero probability of returning an incorrect answer or on the truth of any unproven conjectures.
If t == False, allows integer arithmetic operations to (by default) return results that may depend on unproven conjectures or on probabilistic algorithms. Such algorithms often have a substantial speed improvement over those requiring proof.
If t is None, returns the integer arithmetic proof status.
EXAMPLES:
sage: proof.arithmetic()
True
sage: proof.arithmetic(False)
sage: proof.arithmetic()
False
sage: proof.arithmetic(True)
sage: proof.arithmetic()
True
"""
from proof import _proof_prefs
return _proof_prefs.arithmetic(t)
def elliptic_curve(t = None):
"""
Controls the default proof strategy for elliptic curve algorithms.
INPUT:
t -- boolean or None
OUTPUT:
If t == True, requires elliptic curve algorithms to (by default) return results that are true unconditionally: the correctness will not depend on an algorithm with a nonzero probability of returning an incorrect answer or on the truth of any unproven conjectures.
If t == False, allows elliptic curve algorithms to (by default) return results that may depend on unproven conjectures or on probabilistic algorithms. Such algorithms often have a substantial speed improvement over those requiring proof.
If t is None, returns the current elliptic curve proof status.
EXAMPLES:
sage: proof.elliptic_curve()
True
sage: proof.elliptic_curve(False)
sage: proof.elliptic_curve()
False
sage: proof.elliptic_curve(True)
sage: proof.elliptic_curve()
True
"""
from proof import _proof_prefs
return _proof_prefs.elliptic_curve(t)
def linear_algebra(t = None):
"""
Controls the default proof strategy for linear algebra algorithms.
INPUT:
t -- boolean or None
OUTPUT:
If t == True, requires linear algebra algorithms to (by default) return results that are true unconditionally: the correctness will not depend on an algorithm with a nonzero probability of returning an incorrect answer or on the truth of any unproven conjectures.
If t == False, allows linear algebra algorithms to (by default) return results that may depend on unproven conjectures or on probabilistic algorithms. Such algorithms often have a substantial speed improvement over those requiring proof.
If t is None, returns the current linear algebra proof status.
EXAMPLES:
sage: proof.linear_algebra()
True
sage: proof.linear_algebra(False)
sage: proof.linear_algebra()
False
sage: proof.linear_algebra(True)
sage: proof.linear_algebra()
True
"""
from proof import _proof_prefs
return _proof_prefs.linear_algebra(t)
def number_field(t = None):
"""
Controls the default proof strategy for number field algorithms.
INPUT:
t -- boolean or None
OUTPUT:
If t == True, requires number field algorithms to (by default) return results that are true unconditionally: the correctness will not depend on an algorithm with a nonzero probability of returning an incorrect answer or on the truth of any unproven conjectures.
If t == False, allows number field algorithms to (by default) return results that may depend on unproven conjectures or on probabilistic algorithms. Such algorithms often have a substantial speed improvement over those requiring proof.
If t is None, returns the current number field proof status.
EXAMPLES:
sage: proof.number_field()
True
sage: proof.number_field(False)
sage: proof.number_field()
False
sage: proof.number_field(True)
sage: proof.number_field()
True
"""
from proof import _proof_prefs
return _proof_prefs.number_field(t)
def polynomial(t = None):
"""
Controls the default proof strategy for polynomial algorithms.
INPUT:
t -- boolean or None
OUTPUT:
If t == True, requires polynomial algorithms to (by default) return results that are true unconditionally: the correctness will not depend on an algorithm with a nonzero probability of returning an incorrect answer or on the truth of any unproven conjectures.
If t == False, allows polynomial algorithms to (by default) return results that may depend on unproven conjectures or on probabilistic algorithms. Such algorithms often have a substantial speed improvement over those requiring proof.
If t is None, returns the current polynomial proof status.
EXAMPLES:
sage: proof.polynomial()
True
sage: proof.polynomial(False)
sage: proof.polynomial()
False
sage: proof.polynomial(True)
sage: proof.polynomial()
True
"""
from proof import _proof_prefs
return _proof_prefs.polynomial(t)
def all(t = None):
"""
Controls the default proof strategy throughout Sage.
INPUT:
t -- boolean or None
OUTPUT:
If t == True, requires Sage algorithms to (by default) return results that are true unconditionally: the correctness will not depend on an algorithm with a nonzero probability of returning an incorrect answer or on the truth of any unproven conjectures.
If t == False, allows Sage algorithms to (by default) return results that may depend on unproven conjectures or on probabilistic algorithms. Such algorithms often have a substantial speed improvement over those requiring proof.
If t is None, returns the current global Sage proof status.
EXAMPLES:
sage: proof.all()
{'polynomial': True, 'other': True, 'elliptic_curve': True, 'number_field': True, 'linear_algebra': True, 'arithmetic': True}
sage: proof.number_field(False)
sage: proof.number_field()
False
sage: proof.all()
{'polynomial': True, 'other': True, 'elliptic_curve': True, 'number_field': False, 'linear_algebra': True, 'arithmetic': True}
sage: proof.number_field(True)
sage: proof.number_field()
True
"""
from proof import _proof_prefs
if t is None:
return _proof_prefs._require_proof.copy()
for s in _proof_prefs._require_proof.iterkeys():
_proof_prefs._require_proof[s] = bool(t)
from proof import WithProof
