def _evalf_(self, x, y, parent=None, algorithm='mpmath'):
"""
EXAMPLES::
sage: gamma_inc_lower(3,2.)
0.646647167633873
sage: gamma_inc_lower(3,2).n(200)
0.646647167633873081060005050275155...
sage: gamma_inc_lower(0,2.)
+infinity
"""
R = parent or s_parent(x)
# C is the complex version of R
# prec is the precision of R
if R is float:
prec = 53
C = complex
else:
try:
prec = R.precision()
except AttributeError:
prec = 53
try:
C = R.complex_field()
except AttributeError:
C = R
if algorithm == 'pari':
try:
v = ComplexField(prec)(x).gamma() - ComplexField(prec)(
x).gamma_inc(y)
except AttributeError:
if not (is_ComplexNumber(x)):
if is_ComplexNumber(y):
C = y.parent()
else:
C = ComplexField()
x = C(x)
v = ComplexField(prec)(x).gamma() - ComplexField(prec)(
x).gamma_inc(y)
else:
import mpmath
v = ComplexField(prec)(mpmath_utils.call(mpmath.gammainc,
x,
0,
y,
parent=R))
if v.is_real():
return R(v)
else:
return C(v)
def _evalf_(self, x, y, parent=None, algorithm='mpmath'):
"""
EXAMPLES::
sage: gamma_inc_lower(3,2.)
0.646647167633873
sage: gamma_inc_lower(3,2).n(200)
0.646647167633873081060005050275155...
sage: gamma_inc_lower(0,2.)
+infinity
"""
R = parent or s_parent(x)
# C is the complex version of R
# prec is the precision of R
if R is float:
prec = 53
C = complex
else:
try:
prec = R.precision()
except AttributeError:
prec = 53
try:
C = R.complex_field()
except AttributeError:
C = R
if algorithm == 'pari':
try:
v = ComplexField(prec)(x).gamma() - ComplexField(prec)(x).gamma_inc(y)
except AttributeError:
if not (is_ComplexNumber(x)):
if is_ComplexNumber(y):
C = y.parent()
else:
C = ComplexField()
x = C(x)
v = ComplexField(prec)(x).gamma() - ComplexField(prec)(x).gamma_inc(y)
else:
import mpmath
v = ComplexField(prec)(mpmath_utils.call(mpmath.gammainc, x, 0, y, parent=R))
if v.is_real():
return R(v)
else:
return C(v)
def _evalf_(self, x, y, parent=None, algorithm='pari'):
"""
EXAMPLES::
sage: gamma_inc(0,2)
-Ei(-2)
sage: gamma_inc(0,2.)
0.0489005107080611
sage: gamma_inc(0,2).n(algorithm='pari')
0.0489005107080611
sage: gamma_inc(0,2).n(200)
0.048900510708061119567239835228...
sage: gamma_inc(3,2).n()
1.35335283236613
TESTS:
Check that :trac:`7099` is fixed::
sage: R = RealField(1024)
sage: gamma(R(9), R(10^-3)) # rel tol 1e-308
40319.99999999999999999999999999988898884344822911869926361916294165058203634104838326009191542490601781777105678829520585311300510347676330951251563007679436243294653538925717144381702105700908686088851362675381239820118402497959018315224423868693918493033078310647199219674433536605771315869983788442389633
sage: numerical_approx(gamma(9, 10^(-3)) - gamma(9), digits=40) # abs tol 1e-36
-1.110111598370794007949063502542063148294e-28
Check that :trac:`17328` is fixed::
sage: gamma_inc(float(-1), float(-1))
(-0.8231640121031085+3.141592653589793j)
sage: gamma_inc(RR(-1), RR(-1))
-0.823164012103109 + 3.14159265358979*I
sage: gamma_inc(-1, float(-log(3))) - gamma_inc(-1, float(-log(2))) # abs tol 1e-15
(1.2730972164471142+0j)
Check that :trac:`17130` is fixed::
sage: r = gamma_inc(float(0), float(1)); r
0.21938393439552029
sage: type(r)
<... 'float'>
"""
R = parent or s_parent(x)
# C is the complex version of R
# prec is the precision of R
if R is float:
prec = 53
C = complex
else:
try:
prec = R.precision()
except AttributeError:
prec = 53
try:
C = R.complex_field()
except AttributeError:
C = R
if algorithm == 'pari':
v = ComplexField(prec)(x).gamma_inc(y)
else:
import mpmath
v = ComplexField(prec)(mpmath_utils.call(mpmath.gammainc,
x,
y,
parent=R))
if v.is_real():
return R(v)
else:
return C(v)
def _evalf_(self, x, y, parent=None, algorithm='pari'):
"""
EXAMPLES::
sage: gamma_inc(0,2)
-Ei(-2)
sage: gamma_inc(0,2.)
0.0489005107080611
sage: gamma_inc(0,2).n(algorithm='pari')
0.0489005107080611
sage: gamma_inc(0,2).n(200)
0.048900510708061119567239835228...
sage: gamma_inc(3,2).n()
1.35335283236613
TESTS:
Check that :trac:`7099` is fixed::
sage: R = RealField(1024)
sage: gamma(R(9), R(10^-3)) # rel tol 1e-308
40319.99999999999999999999999999988898884344822911869926361916294165058203634104838326009191542490601781777105678829520585311300510347676330951251563007679436243294653538925717144381702105700908686088851362675381239820118402497959018315224423868693918493033078310647199219674433536605771315869983788442389633
sage: numerical_approx(gamma(9, 10^(-3)) - gamma(9), digits=40) # abs tol 1e-36
-1.110111598370794007949063502542063148294e-28
Check that :trac:`17328` is fixed::
sage: gamma_inc(float(-1), float(-1))
(-0.8231640121031085+3.141592653589793j)
sage: gamma_inc(RR(-1), RR(-1))
-0.823164012103109 + 3.14159265358979*I
sage: gamma_inc(-1, float(-log(3))) - gamma_inc(-1, float(-log(2))) # abs tol 1e-15
(1.2730972164471142+0j)
Check that :trac:`17130` is fixed::
sage: r = gamma_inc(float(0), float(1)); r
0.21938393439552029
sage: type(r)
<... 'float'>
"""
R = parent or s_parent(x)
# C is the complex version of R
# prec is the precision of R
if R is float:
prec = 53
C = complex
else:
try:
prec = R.precision()
except AttributeError:
prec = 53
try:
C = R.complex_field()
except AttributeError:
C = R
if algorithm == 'pari':
v = ComplexField(prec)(x).gamma_inc(y)
else:
import mpmath
v = ComplexField(prec)(mpmath_utils.call(mpmath.gammainc, x, y, parent=R))
if v.is_real():
return R(v)
else:
return C(v)
