def test_comparison(ring):
"""
Check comparison with infinity
INPUT:
- ``ring`` -- a sub-ring of the real numbers
OUTPUT:
Various attempts are made to generate elements of ``ring``. An
assertion is triggered if one of these elements does not compare
correctly with plus/minus infinity.
EXAMPLES::
sage: from sage.rings.infinity import test_comparison
sage: rings = [ZZ, QQ, RR, RealField(200), RDF, RLF, AA, RIF]
sage: for R in rings:
....: print('testing {}'.format(R))
....: test_comparison(R)
testing Integer Ring
testing Rational Field
testing Real Field with 53 bits of precision
testing Real Field with 200 bits of precision
testing Real Double Field
testing Real Lazy Field
testing Algebraic Real Field
testing Real Interval Field with 53 bits of precision
Comparison with number fields does not work::
sage: K.<sqrt3> = NumberField(x^2-3)
sage: (-oo < 1+sqrt3) and (1+sqrt3 < oo) # known bug
False
The symbolic ring handles its own infinities, but answers
``False`` (meaning: cannot decide) already for some very
elementary comparisons::
sage: test_comparison(SR) # known bug
Traceback (most recent call last):
...
AssertionError: testing -1000.0 in Symbolic Ring: id = ...
"""
from sage.symbolic.ring import SR
from sage.rings.rational_field import QQ
elements = [
-1e3, 99.9999, -SR(2).sqrt(), 0, 1, 3**(-QQ.one() / 3),
SR.pi(), 100000
]
elements.append(ring.an_element())
elements.extend(ring.some_elements())
for z in elements:
try:
z = ring(z)
except (ValueError, TypeError):
continue # ignore if z is not in ring
msg = 'testing {} in {}: id = {}, {}, {}'.format(
z, ring, id(z), id(infinity), id(minus_infinity))
assert minus_infinity < z, msg
assert z > minus_infinity, msg
assert z < infinity, msg
assert infinity > z, msg
assert minus_infinity <= z, msg
assert z >= minus_infinity, msg
assert z <= infinity, msg
assert infinity >= z, msg
def test_comparison(ring):
"""
Check comparison with infinity
INPUT:
- ``ring`` -- a sub-ring of the real numbers
OUTPUT:
Various attempts are made to generate elements of ``ring``. An
assertion is triggered if one of these elements does not compare
correctly with plus/minus infinity.
EXAMPLES::
sage: from sage.rings.infinity import test_comparison
sage: rings = [ZZ, QQ, RR, RealField(200), RDF, RLF, AA, RIF]
sage: for R in rings:
....: print('testing {}'.format(R))
....: test_comparison(R)
testing Integer Ring
testing Rational Field
testing Real Field with 53 bits of precision
testing Real Field with 200 bits of precision
testing Real Double Field
testing Real Lazy Field
testing Algebraic Real Field
testing Real Interval Field with 53 bits of precision
Comparison with number fields does not work::
sage: K.<sqrt3> = NumberField(x^2-3)
sage: (-oo < 1+sqrt3) and (1+sqrt3 < oo) # known bug
False
The symbolic ring handles its own infinities, but answers
``False`` (meaning: cannot decide) already for some very
elementary comparisons::
sage: test_comparison(SR) # known bug
Traceback (most recent call last):
...
AssertionError: testing -1000.0 in Symbolic Ring: id = ...
"""
from sage.symbolic.ring import SR
elements = [-1e3, 99.9999, -SR(2).sqrt(), 0, 1, 3^(-1/3), SR.pi(), 100000]
elements.append(ring.an_element())
elements.extend(ring.some_elements())
for z in elements:
try:
z = ring(z)
except (ValueError, TypeError):
continue # ignore if z is not in ring
msg = 'testing {} in {}: id = {}, {}, {}'.format(z, ring, id(z), id(infinity), id(minus_infinity))
assert minus_infinity < z, msg
assert z > minus_infinity, msg
assert z < infinity, msg
assert infinity > z, msg
assert minus_infinity <= z, msg
assert z >= minus_infinity, msg
assert z <= infinity, msg
assert infinity >= z, msg
