def gammaincc(a, x, dps=50, maxterms=10*10*10*10*10*10*10*10):
"""Compute gammaincc exactly like mpmath does but allow for more
terms in hypercomb. See
mpmath/functions/expintegrals.py#L187
in the mpmath github repository.
"""
with mp.workdps(dps):
z, a = a, x
if mp.isint(z):
try:
# mpmath has a fast integer path
return mpf2float(mp.gammainc(z, a=a, regularized=True))
except mp.libmp.NoConvergence:
pass
nega = mp.fneg(a, exact=True)
G = [z]
# Use 2F0 series when possible; fall back to lower gamma representation
try:
def h(z):
r = z-1
return [([mp.exp(nega), a], [1, r], [], G, [1, -r], [], 1/nega)]
return mpf2float(mp.hypercomb(h, [z], force_series=True))
except mp.libmp.NoConvergence:
def h(z):
T1 = [], [1, z-1], [z], G, [], [], 0
T2 = [-mp.exp(nega), a, z], [1, z, -1], [], G, [1], [1+z], a
return T1, T2
return mpf2float(mp.hypercomb(h, [z], maxterms=maxterms))
def ask_drop(db, tables, name):
if tables:
print "Existing stored {} tables:\n{}\n".format(
name,
"\n".join("{}. {}".format(i + 1, t) for i, t in enumerate(tables)))
if len(tables) > 0:
cont = raw_input(
"{} stored {} tables to drop. Drop all? Y/[n] or list of comma-separated numbers "
.format(len(tables), name))
if cont == "Y":
drop_tables(db, tables)
return
else:
selections = cont.split(",")
if all(isint(s) and int(s) >= 1 for s in selections):
drop_tables(db, [tables[int(s) - 1] for s in selections])
return
print "No {} tables were dropped.".format(name)
else:
print "There are no {} tables.".format(name)
def gammaincc(a, x, dps=50, maxterms=10**8):
"""Compute gammaincc exactly like mpmath does but allow for more
terms in hypercomb. See
mpmath/functions/expintegrals.py#L187
in the mpmath github repository.
"""
with mp.workdps(dps):
z, a = a, x
if mp.isint(z):
try:
# mpmath has a fast integer path
return mpf2float(mp.gammainc(z, a=a, regularized=True))
except mp.libmp.NoConvergence:
pass
nega = mp.fneg(a, exact=True)
G = [z]
# Use 2F0 series when possible; fall back to lower gamma representation
try:
def h(z):
r = z-1
return [([mp.exp(nega), a], [1, r], [], G, [1, -r], [], 1/nega)]
return mpf2float(mp.hypercomb(h, [z], force_series=True))
except mp.libmp.NoConvergence:
def h(z):
T1 = [], [1, z-1], [z], G, [], [], 0
T2 = [-mp.exp(nega), a, z], [1, z, -1], [], G, [1], [1+z], a
return T1, T2
return mpf2float(mp.hypercomb(h, [z], maxterms=maxterms))
def getRoot( n, k ):
if isinstance( n, RPNMeasurement ):
return n.getRoot( k )
if not isint( k ):
return power( n, fdiv( 1, k ) )
else:
return root( n, k )
def getRoot(n, k):
if isinstance(n, RPNMeasurement):
return n.getRoot(k)
if not isint(k):
return power(n, fdiv(1, k))
return root(n, k)
def isKthPower(n, k):
if not isint(k, gaussian=True):
raise ValueError('integer argument expected')
if k == 1:
return 1
if im(n):
# I'm not sure why this is necessary...
if re(n) == 0:
return isKthPower(im(n), k)
# We're looking for a Gaussian integer among any of the roots.
for i in [autoprec(root)(n, k, i) for i in arange(k)]:
if isint(i, gaussian=True):
return 1
return 0
rootN = autoprec(root)(n, k)
return 1 if isint(rootN, gaussian=True) else 0
def isKthPower( n, k ):
if not isint( k, gaussian=True ) and isint( k ):
raise ValueError( 'integer arguments expected' )
if k == 1:
return 1
elif k < 1:
raise ValueError( 'a positive power k is expected' )
if im( n ):
# I'm not sure why this is necessary...
if re( n ) == 0:
return isKthPower( im( n ), k )
# We're looking for a Gaussian integer among any of the roots.
for i in [ autoprec( root )( n, k, i ) for i in arange( k ) ]:
if isint( i, gaussian=True ):
return 1
return 0
else:
rootN = autoprec( root )( n, k )
return 1 if isint( rootN, gaussian=True ) else 0
def _does_have_int_positive_roots(poly):
"""For a poly2sympoly of deg(poly2sympoly) < 3 (after factoring out any power of x^n), check if it has integer
positive roots.
Returns a boolean."""
poly = BasicEnumPolyParams._factor_out_polynom(poly)
if len(poly) == 0:
return True
elif len(poly) == 1:
return False
## # elif len(poly) == 2 and (poly[0] / poly[1]).is_integer() and (poly[0] > 0) != (poly[1] > 0):
elif len(poly) == 2 and isint(poly[0] / poly[1]) and (poly[0] > 0) != (poly[1] > 0):
return True
elif len(poly) == 3:
discrim = (poly[1]**2-4*poly[0]*poly[2])
if discrim < 0:
return False
discrim **= 0.5
## # if ((discrim - poly[1])/(2*poly[0])).is_integer():
if isint((discrim - poly[1])/(2*poly[0])) and ((discrim - poly[1])/(2*poly[0]) > 0):
return True
if isint((-discrim - poly[1])/(2*poly[0])) and ((-discrim - poly[1])/(2*poly[0]) > 0):
return True
return False
def getHardMinYForD3(d):
'''
failed at 61 when used 120 bits for precision (succeeded at 53, 46)
'''
print('trying {}'.format(d))
mp.prec = EULER66_NEEDED_PRECISION_IN_BITS
dRoot = mp.mpf(d).sqrt()
for potentY, dRootMulPotentY in multiplesGenerator2(dRoot):
if EULER66_D_ROOT_MUL_Y_MIN_VAL_AFTER_DEC_POINT < zeroLeftToDecPoint(
dRootMulPotentY):
print(potentY)
if mpmath.isint((d * potentY**2 + 1).sqrt()):
print(d, potentY)
print()
return potentY
d = reduce(operator.mul, [cc[0] for cc in c])
print(f"{d=}")
e = [(d / cc[0], cc[1] * d / cc[0]) for cc in c]
print(f"{e=}")
f = reduce(operator.add, [ee[0] for ee in e])
print(f"{f=}")
g = reduce(operator.add, [ee[1] for ee in e])
print(f"{g=}")
for x in count():
t = (mpmath.mpf(d) * mpmath.mpf(x) - mpmath.mpf(g)) / mpmath.mpf(f)
# if t.is_integer():
if mpmath.isint(t):
# print(x, t, test)
v1 = (mpmath.mpf(f) * t + mpmath.mpf(g)) % mpmath.mpf(d)
if v1 != 0:
v2 = min(v1, d - v1)
print(f"{t=} was close by {v2=}")
continue
printt(a, int(t), t, v1)
exit()
exit()
def f1(t):
return (t + 0) % 67
def safeHasSquareRoot(num):
return mpmath.isint(mpmath.sqrt(num))
