def _real_str(y, exact_form, prec_offset):
''' Convert a Real number to a string, with nice display.
Returns a tuple containing the string an a bool indicating whether changes
have been made. The function works in floats and is cached for speed. '''
small = 5 * 10**(-5)
x = float(y)
if abs(x - int(x)) < small:
return (str(int(x)), False)
if exact_form and abs(x) > small:
# Show pi in full
if abs(x - float(pi())) < small: return ('pi', True)
# Display small fractions as such
a, b = nm.to_fraction(x)
if b < 50: return ('{}/{}'.format(a,b), True) if b != 1\
else (str(a), False)
# Display small fractional coefficients of pi in exact form
q = x / float(pi())
a, b = nm.to_fraction(q)
if b <= 12:
return ((str(a) if a != 1 else '') + 'pi'\
+ ('/' + str(b) if b != 1 else ''), True)
# Sort out square roots
for n in [2, 3, 5, 6, 7, 10, 11, 13]:
q = x / n**0.5
a, b = nm.to_fraction(q)
if b <= 100:
return ((str(a) + '*' if a != 1 else '') + str(n) + '^(1/2)'\
+ ('/' + str(b) if b != 1 else ''), True)
# Otherwise display as a decimal
with localcontext():
getcontext().prec -= prec_offset
return (str(Decimal(y).normalize()), False)
def _real_str(y, exact_form, prec_offset):
''' Convert a Real number to a string, with nice display.
Returns a tuple containing the string an a bool indicating whether changes
have been made. The function works in floats and is cached for speed. '''
small = 5 * 10**(-5)
x = float(y)
if abs(x - int(x)) < small:
return (str(int(x)), False)
if exact_form and abs(x) > small:
# Show pi in full
if abs(x - float(pi())) < small: return ('pi', True)
# Display small fractions as such
a, b = nm.to_fraction(x)
if b < 50: return ('{}/{}'.format(a,b), True) if b != 1\
else (str(a), False)
# Display small fractional coefficients of pi in exact form
q = x / float(pi()); a, b = nm.to_fraction(q);
if b <= 12:
return ((str(a) if a != 1 else '') + 'pi'\
+ ('/' + str(b) if b != 1 else ''), True)
# Sort out square roots
for n in [2,3,5,6,7,10,11,13]:
q = x / n ** 0.5
a, b = nm.to_fraction(q)
if b <= 100:
return ((str(a) + '*' if a != 1 else '') + str(n) + '^(1/2)'\
+ ('/' + str(b) if b != 1 else ''), True)
# Otherwise display as a decimal
with localcontext():
getcontext().prec -= prec_offset
return (str(Decimal(y).normalize()), False)
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
# Public License for more details.
#
# You should have received a copy of the GNU General Public License along with
# C1000 Intelligent Calculator. If not, see <http://www.gnu.org/licenses/>.
# Third party modules
from dmath import e, pi
# Project modules
from .core import handle_type as ht
from .numerical_methods import romberg_integral
# Calculate constants
e = ht(e())
pi = ht(pi())
def factorial(x):
''' An iterative factorial function. '''
if x < 0 or not isinstance(x, int):
raise ValueError('The factorial of negative numbers in not defined')
ans = x.__class__(1)
while x > 0:
ans *= x
x -= 1
return ans
# return x * factorial(x - 1) if x > 0 else 1
def nCr(n, r):
''' n combinations of r. '''
return factorial(n) / ( factorial(r) * factorial(n - r) )
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
# Public License for more details.
#
# You should have received a copy of the GNU General Public License along with
# C1000 Intelligent Calculator. If not, see <http://www.gnu.org/licenses/>.
# Third party modules
from dmath import e, pi
# Project modules
from .core import handle_type as ht
from .numerical_methods import romberg_integral
# Calculate constants
e = ht(e())
pi = ht(pi())
def factorial(x):
''' An iterative factorial function. '''
if x < 0 or not isinstance(x, int):
raise ValueError('The factorial of negative numbers in not defined')
ans = x.__class__(1)
while x > 0:
ans *= x
x -= 1
return ans
# return x * factorial(x - 1) if x > 0 else 1
def nCr(n, r):
