def eval(cls, arg):
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Infinity:
return S.Zero
elif arg is S.NegativeInfinity:
return S.Zero
elif arg is S.Zero:
return S.Pi/ 2
elif arg is S.One:
return S.Pi / 4
elif arg is S.NegativeOne:
return -S.Pi / 4
if arg.could_extract_minus_sign():
return -cls(-arg)
if arg.is_number:
cst_table = {
sqrt(3)/3 : 3,
-sqrt(3)/3 : -3,
1/sqrt(3) : 3,
-1/sqrt(3) : -3,
sqrt(3) : 6,
-sqrt(3) : -6,
}
if arg in cst_table:
return S.Pi / cst_table[arg]
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return -S.ImaginaryUnit * C.acoth(i_coeff)
def eval(cls, arg):
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Infinity:
return S.Zero
elif arg is S.NegativeInfinity:
return S.Zero
elif arg is S.Zero:
return S.Pi / 2
elif arg is S.One:
return S.Pi / 4
elif arg is S.NegativeOne:
return -S.Pi / 4
if arg.could_extract_minus_sign():
return -cls(-arg)
if arg.is_number:
cst_table = {
sqrt(3) / 3: 3,
-sqrt(3) / 3: -3,
1 / sqrt(3): 3,
-1 / sqrt(3): -3,
sqrt(3): 6,
-sqrt(3): -6,
}
if arg in cst_table:
return S.Pi / cst_table[arg]
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return -S.ImaginaryUnit * C.acoth(i_coeff)
def eval(cls, arg):
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Infinity:
return S.Zero
elif arg is S.NegativeInfinity:
return S.Zero
elif arg is S.Zero:
return S.Pi/ 2
elif arg is S.One:
return S.Pi / 4
elif arg is S.NegativeOne:
return -S.Pi / 4
if arg.could_extract_minus_sign():
return -cls(-arg)
if arg.is_number:
cst_table = {
sqrt(3)/3 : 3,
-sqrt(3)/3 : -3,
1/sqrt(3) : 3,
-1/sqrt(3) : -3,
sqrt(3) : 6,
-sqrt(3) : -6,
(1+sqrt(2)) : 8,
-(1+sqrt(2)) : -8,
(1-sqrt(2)) : -S(8)/3,
(sqrt(2)-1) : S(8)/3,
sqrt(5+2*sqrt(5)) : 10,
-sqrt(5+2*sqrt(5)) : -10,
(2+sqrt(3)) : 12,
-(2+sqrt(3)) : -12,
(2-sqrt(3)) : S(12)/5,
-(2-sqrt(3)) : -S(12)/5,
}
if arg in cst_table:
return S.Pi / cst_table[arg]
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return -S.ImaginaryUnit * C.acoth(i_coeff)
def eval(cls, arg):
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Infinity:
return S.Zero
elif arg is S.NegativeInfinity:
return S.Zero
elif arg is S.Zero:
return S.Pi / 2
elif arg is S.One:
return S.Pi / 4
elif arg is S.NegativeOne:
return -S.Pi / 4
if arg.could_extract_minus_sign():
return -cls(-arg)
if arg.is_number:
cst_table = {
sqrt(3) / 3: 3,
-sqrt(3) / 3: -3,
1 / sqrt(3): 3,
-1 / sqrt(3): -3,
sqrt(3): 6,
-sqrt(3): -6,
(1 + sqrt(2)): 8,
-(1 + sqrt(2)): -8,
(1 - sqrt(2)): -S(8) / 3,
(sqrt(2) - 1): S(8) / 3,
sqrt(5 + 2 * sqrt(5)): 10,
-sqrt(5 + 2 * sqrt(5)): -10,
(2 + sqrt(3)): 12,
-(2 + sqrt(3)): -12,
(2 - sqrt(3)): S(12) / 5,
-(2 - sqrt(3)): -S(12) / 5,
}
if arg in cst_table:
return S.Pi / cst_table[arg]
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return -S.ImaginaryUnit * C.acoth(i_coeff)
def canonize(cls, arg):
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Infinity:
return S.Zero
elif arg is S.NegativeInfinity:
return S.Zero
elif arg is S.Zero:
return S.Pi/ 2
elif arg is S.One:
return S.Pi / 4
elif arg is S.NegativeOne:
return -S.Pi / 4
if arg.is_number:
cst_table = {
sqrt(3)/3 : 3,
-sqrt(3)/3 : -3,
1/sqrt(3) : 3,
-1/sqrt(3) : -3,
sqrt(3) : 6,
-sqrt(3) : -6,
}
if arg in cst_table:
return S.Pi / cst_table[arg]
elif arg.is_negative:
return -cls(-arg)
else:
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return -S.ImaginaryUnit * C.acoth(i_coeff)
else:
coeff, terms = arg.as_coeff_terms()
if coeff.is_negative:
return -cls(-arg)
def eval(cls, arg):
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Infinity:
return S.Zero
elif arg is S.NegativeInfinity:
return S.Zero
elif arg is S.Zero:
return S.Pi / 2
elif arg is S.One:
return S.Pi / 4
elif arg is S.NegativeOne:
return -S.Pi / 4
if arg.is_number:
cst_table = {
sqrt(3) / 3: 3,
-sqrt(3) / 3: -3,
1 / sqrt(3): 3,
-1 / sqrt(3): -3,
sqrt(3): 6,
-sqrt(3): -6,
}
if arg in cst_table:
return S.Pi / cst_table[arg]
elif arg.is_negative:
return -cls(-arg)
else:
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return -S.ImaginaryUnit * C.acoth(i_coeff)
else:
coeff, terms = arg.as_coeff_terms()
if coeff.is_negative:
return -cls(-arg)
