def __call__(self, x, coerce=True, hold=False, prec=None,
dont_call_method_on_arg=False):
"""
Note that the ``prec`` argument is deprecated. The precision for
the result is deduced from the precision of the input. Convert
the input to a higher precision explicitly if a result with higher
precision is desired.::
sage: t = exp(RealField(100)(2)); t
7.3890560989306502272304274606
sage: t.prec()
100
TESTS::
sage: exp(2,prec=100)
doctest:...: DeprecationWarning: The prec keyword argument is deprecated. Explicitly set the precision of the input, for example exp(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., exp(1).n(300), instead.
7.3890560989306502272304274606
"""
if prec is not None:
from sage.misc.misc import deprecation
deprecation("The prec keyword argument is deprecated. Explicitly set the precision of the input, for example exp(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., exp(1).n(300), instead.")
x = GinacFunction.__call__(self, x, coerce=coerce, hold=hold,
dont_call_method_on_arg=dont_call_method_on_arg)
return x.n(prec)
return GinacFunction.__call__(self, x, coerce=coerce, hold=hold,
dont_call_method_on_arg=dont_call_method_on_arg)
def __call__(self, x, prec=None, coerce=True, hold=False):
"""
Note that the ``prec`` argument is deprecated. The precision for
the result is deduced from the precision of the input. Convert
the input to a higher precision explicitly if a result with higher
precision is desired.::
sage: t = gamma(RealField(100)(2.5)); t
1.3293403881791370204736256125
sage: t.prec()
100
sage: gamma(6, prec=53)
doctest:...: DeprecationWarning: The prec keyword argument is deprecated. Explicitly set the precision of the input, for example gamma(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., gamma(1).n(300), instead.
120.000000000000
TESTS::
sage: gamma(pi,prec=100)
2.2880377953400324179595889091
sage: gamma(3/4,prec=100)
1.2254167024651776451290983034
"""
if prec is not None:
from sage.misc.misc import deprecation
deprecation(
"The prec keyword argument is deprecated. Explicitly set the precision of the input, for example gamma(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., gamma(1).n(300), instead."
)
import mpmath
return mpmath_utils.call(mpmath.gamma, x, prec=prec)
# this is a kludge to keep
# sage: Q.<i> = NumberField(x^2+1)
# sage: gamma(i)
# working, since number field elements cannot be coerced into SR
# without specifying an explicit embedding into CC any more
try:
res = GinacFunction.__call__(self, x, coerce=coerce, hold=hold)
except TypeError, err:
# the __call__() method returns a TypeError for fast float arguments
# as well, we only proceed if the error message says that
# the arguments cannot be coerced to SR
if not str(err).startswith("cannot coerce"):
raise
from sage.misc.misc import deprecation
deprecation(
"Calling symbolic functions with arguments that cannot be coerced into symbolic expressions is deprecated."
)
parent = RR if prec is None else RealField(prec)
try:
x = parent(x)
except (ValueError, TypeError):
x = parent.complex_field()(x)
res = GinacFunction.__call__(self, x, coerce=coerce, hold=hold)
def __call__(self, x, prec=None, coerce=True, hold=False):
"""
Note that the ``prec`` argument is deprecated. The precision for
the result is deduced from the precision of the input. Convert
the input to a higher precision explicitly if a result with higher
precision is desired.::
sage: t = gamma(RealField(100)(2.5)); t
1.3293403881791370204736256125
sage: t.prec()
100
sage: gamma(6, prec=53)
doctest:...: DeprecationWarning: The prec keyword argument is deprecated. Explicitly set the precision of the input, for example gamma(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., gamma(1).n(300), instead.
120.000000000000
TESTS::
sage: gamma(pi,prec=100)
2.2880377953400324179595889091
sage: gamma(3/4,prec=100)
1.2254167024651776451290983034
"""
if prec is not None:
from sage.misc.misc import deprecation
deprecation("The prec keyword argument is deprecated. Explicitly set the precision of the input, for example gamma(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., gamma(1).n(300), instead.")
import mpmath
return mpmath_utils.call(mpmath.gamma, x, prec=prec)
# this is a kludge to keep
# sage: Q.<i> = NumberField(x^2+1)
# sage: gamma(i)
# working, since number field elements cannot be coerced into SR
# without specifying an explicit embedding into CC any more
try:
res = GinacFunction.__call__(self, x, coerce=coerce, hold=hold)
except TypeError, err:
# the __call__() method returns a TypeError for fast float arguments
# as well, we only proceed if the error message says that
# the arguments cannot be coerced to SR
if not str(err).startswith("cannot coerce"):
raise
from sage.misc.misc import deprecation
deprecation("Calling symbolic functions with arguments that cannot be coerced into symbolic expressions is deprecated.")
parent = RR if prec is None else RealField(prec)
try:
x = parent(x)
except (ValueError, TypeError):
x = parent.complex_field()(x)
res = GinacFunction.__call__(self, x, coerce=coerce, hold=hold)
def __call__(self,
x,
coerce=True,
hold=False,
prec=None,
dont_call_method_on_arg=False):
"""
Note that the ``prec`` argument is deprecated. The precision for
the result is deduced from the precision of the input. Convert
the input to a higher precision explicitly if a result with higher
precision is desired.::
sage: t = exp(RealField(100)(2)); t
7.3890560989306502272304274606
sage: t.prec()
100
TESTS::
sage: exp(2,prec=100)
doctest:...: DeprecationWarning: The prec keyword argument is deprecated. Explicitly set the precision of the input, for example exp(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., exp(1).n(300), instead.
See http://trac.sagemath.org/7490 for details.
7.3890560989306502272304274606
Ensure that :trac:`13608` is fixed::
sage: import mpmath
sage: a = mpmath.mpf('0.5')
sage: exp(a)
mpf('1.6487212707001282')
sage: a.exp
-1
"""
if prec is not None:
from sage.misc.superseded import deprecation
deprecation(
7490,
"The prec keyword argument is deprecated. Explicitly set the precision of the input, for example exp(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., exp(1).n(300), instead."
)
x = GinacFunction.__call__(
self,
x,
coerce=coerce,
hold=hold,
dont_call_method_on_arg=dont_call_method_on_arg)
return x.n(prec)
return GinacFunction.__call__(
self,
x,
coerce=coerce,
hold=hold,
dont_call_method_on_arg=dont_call_method_on_arg)
def __call__(self,
x,
coerce=True,
hold=False,
prec=None,
dont_call_method_on_arg=False):
"""
Note that the ``prec`` argument is deprecated. The precision for
the result is deduced from the precision of the input. Convert
the input to a higher precision explicitly if a result with higher
precision is desired.::
sage: t = exp(RealField(100)(2)); t
7.3890560989306502272304274606
sage: t.prec()
100
TESTS::
sage: exp(2,prec=100)
doctest:...: DeprecationWarning: The prec keyword argument is deprecated. Explicitly set the precision of the input, for example exp(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., exp(1).n(300), instead.
7.3890560989306502272304274606
"""
if prec is not None:
from sage.misc.misc import deprecation
deprecation(
"The prec keyword argument is deprecated. Explicitly set the precision of the input, for example exp(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., exp(1).n(300), instead."
)
x = GinacFunction.__call__(
self,
x,
coerce=coerce,
hold=hold,
dont_call_method_on_arg=dont_call_method_on_arg)
return x.n(prec)
return GinacFunction.__call__(
self,
x,
coerce=coerce,
hold=hold,
dont_call_method_on_arg=dont_call_method_on_arg)
def __call__(self, x, coerce=True, hold=False, prec=None,
dont_call_method_on_arg=False):
"""
Note that the ``prec`` argument is deprecated. The precision for
the result is deduced from the precision of the input. Convert
the input to a higher precision explicitly if a result with higher
precision is desired.::
sage: t = exp(RealField(100)(2)); t
7.3890560989306502272304274606
sage: t.prec()
100
TESTS::
sage: exp(2,prec=100)
doctest:...: DeprecationWarning: The prec keyword argument is deprecated. Explicitly set the precision of the input, for example exp(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., exp(1).n(300), instead.
See http://trac.sagemath.org/7490 for details.
7.3890560989306502272304274606
Ensure that :trac:`13608` is fixed::
sage: import mpmath
sage: a = mpmath.mpf('0.5')
sage: exp(a)
mpf('1.6487212707001282')
sage: a.exp
-1
"""
if prec is not None:
from sage.misc.superseded import deprecation
deprecation(7490, "The prec keyword argument is deprecated. Explicitly set the precision of the input, for example exp(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., exp(1).n(300), instead.")
x = GinacFunction.__call__(self, x, coerce=coerce, hold=hold,
dont_call_method_on_arg=dont_call_method_on_arg)
return x.n(prec)
return GinacFunction.__call__(self, x, coerce=coerce, hold=hold,
dont_call_method_on_arg=dont_call_method_on_arg)
def __call__(self, *args, **kwds):
"""
Return the logarithm of x to the given base.
Calls the ``log`` method of the object x when computing
the logarithm, thus allowing use of logarithm on any object
containing a ``log`` method. In other words, log works
on more than just real numbers.
EXAMPLES::
sage: log(e^2)
2
To change the base of the logarithm, add a second parameter::
sage: log(1000,10)
3
You can use
:class:`RDF<sage.rings.real_double.RealDoubleField_class>`,
:class:`~sage.rings.real_mpfr.RealField` or ``n`` to get a
numerical real approximation::
sage: log(1024, 2)
10
sage: RDF(log(1024, 2))
10.0
sage: log(10, 4)
log(10)/log(4)
sage: RDF(log(10, 4))
1.6609640474436813
sage: log(10, 2)
log(10)/log(2)
sage: n(log(10, 2))
3.32192809488736
sage: log(10, e)
log(10)
sage: n(log(10, e))
2.30258509299405
The log function works for negative numbers, complex
numbers, and symbolic numbers too, picking the branch
with angle between `-pi` and `pi`::
sage: log(-1+0*I)
I*pi
sage: log(CC(-1))
3.14159265358979*I
sage: log(-1.0)
3.14159265358979*I
For input zero, the following behavior occurs::
sage: log(0)
-Infinity
sage: log(CC(0))
-infinity
sage: log(0.0)
-infinity
The log function also works in finite fields as long as the
argument lies in the multiplicative group generated by the base::
sage: F = GF(13); g = F.multiplicative_generator(); g
2
sage: a = F(8)
sage: log(a,g); g^log(a,g)
3
8
sage: log(a,3)
Traceback (most recent call last):
...
ValueError: No discrete log of 8 found to base 3
sage: log(F(9), 3)
2
The log function also works for p-adics (see documentation for
p-adics for more information)::
sage: R = Zp(5); R
5-adic Ring with capped relative precision 20
sage: a = R(16); a
1 + 3*5 + O(5^20)
sage: log(a)
3*5 + 3*5^2 + 3*5^4 + 3*5^5 + 3*5^6 + 4*5^7 + 2*5^8 + 5^9 +
5^11 + 2*5^12 + 5^13 + 3*5^15 + 2*5^16 + 4*5^17 + 3*5^18 +
3*5^19 + O(5^20)
TESTS:
Check if :trac:`10136` is fixed::
sage: log(x).operator() is log
True
sage: log(x).operator() is ln
True
sage: log(1000, 10, base=5)
Traceback (most recent call last):
...
TypeError: Symbolic function log must be called as log(x),
log(x, base=b) or log(x, b)
"""
base = kwds.pop('base', None)
if base is None:
if len(args) == 1:
return GinacFunction.__call__(self, *args, **kwds)
# second argument is base
base = args[1]
args = args[:1]
if len(args) != 1:
raise TypeError("Symbolic function log must be called as "
"log(x), log(x, base=b) or log(x, b)")
try:
return args[0].log(base)
except (AttributeError, TypeError):
return GinacFunction.__call__(self, *args, **kwds) / \
GinacFunction.__call__(self, base, **kwds)
