def eval(cls, arg):
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Infinity:
return S.NegativeInfinity * S.ImaginaryUnit
elif arg is S.NegativeInfinity:
return S.Infinity * S.ImaginaryUnit
elif arg is S.Zero:
return S.Zero
elif arg is S.One:
return S.Pi / 2
elif arg is S.NegativeOne:
return -S.Pi / 2
if arg.could_extract_minus_sign():
return -cls(-arg)
if arg.is_number:
cst_table = {
sqrt(3)/2 : 3,
-sqrt(3)/2 : -3,
sqrt(2)/2 : 4,
-sqrt(2)/2 : -4,
1/sqrt(2) : 4,
-1/sqrt(2) : -4,
sqrt((5-sqrt(5))/8) : 5,
-sqrt((5-sqrt(5))/8) : -5,
S.Half : 6,
-S.Half : -6,
sqrt(2-sqrt(2))/2 : 8,
-sqrt(2-sqrt(2))/2 : -8,
(sqrt(5)-1)/4 : 10,
(1-sqrt(5))/4 : -10,
(sqrt(3)-1)/sqrt(2**3) : 12,
(1-sqrt(3))/sqrt(2**3) : -12,
(sqrt(5)+1)/4 : S(10)/3,
-(sqrt(5)+1)/4 : -S(10)/3
}
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.asinh(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.NegativeInfinity * S.ImaginaryUnit
elif arg is S.NegativeInfinity:
return S.Infinity * S.ImaginaryUnit
elif arg is S.Zero:
return S.Zero
elif arg is S.One:
return S.Pi / 2
elif arg is S.NegativeOne:
return -S.Pi / 2
if arg.could_extract_minus_sign():
return -cls(-arg)
if arg.is_number:
cst_table = {
sqrt(3) / 2: 3,
-sqrt(3) / 2: -3,
sqrt(2) / 2: 4,
-sqrt(2) / 2: -4,
1 / sqrt(2): 4,
-1 / sqrt(2): -4,
sqrt((5 - sqrt(5)) / 8): 5,
-sqrt((5 - sqrt(5)) / 8): -5,
S.Half: 6,
-S.Half: -6,
sqrt(2 - sqrt(2)) / 2: 8,
-sqrt(2 - sqrt(2)) / 2: -8,
(sqrt(5) - 1) / 4: 10,
(1 - sqrt(5)) / 4: -10,
(sqrt(3) - 1) / sqrt(2**3): 12,
(1 - sqrt(3)) / sqrt(2**3): -12,
(sqrt(5) + 1) / 4: S(10) / 3,
-(sqrt(5) + 1) / 4: -S(10) / 3
}
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.asinh(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.NegativeInfinity * S.ImaginaryUnit
elif arg is S.NegativeInfinity:
return S.Infinity * S.ImaginaryUnit
elif arg is S.Zero:
return S.Zero
elif arg is S.One:
return S.Pi / 2
elif arg is S.NegativeOne:
return -S.Pi / 2
if arg.is_number:
cst_table = {
S.Half : 6,
-S.Half : -6,
sqrt(2)/2 : 4,
-sqrt(2)/2 : -4,
1/sqrt(2) : 4,
-1/sqrt(2) : -4,
sqrt(3)/2 : 3,
-sqrt(3)/2 : -3,
}
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.asinh(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.NegativeInfinity * S.ImaginaryUnit
elif arg is S.NegativeInfinity:
return S.Infinity * S.ImaginaryUnit
elif arg is S.Zero:
return S.Zero
elif arg is S.One:
return S.Pi / 2
elif arg is S.NegativeOne:
return -S.Pi / 2
if arg.is_number:
cst_table = {
S.Half: 6,
-S.Half: -6,
sqrt(2) / 2: 4,
-sqrt(2) / 2: -4,
1 / sqrt(2): 4,
-1 / sqrt(2): -4,
sqrt(3) / 2: 3,
-sqrt(3) / 2: -3,
}
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.asinh(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.NegativeInfinity * S.ImaginaryUnit
elif arg is S.NegativeInfinity:
return S.Infinity * S.ImaginaryUnit
elif arg is S.Zero:
return S.Zero
elif arg is S.One:
return S.Pi / 2
elif arg is S.NegativeOne:
return -S.Pi / 2
if arg.could_extract_minus_sign():
return -cls(-arg)
if arg.is_number:
cst_table = {
S.Half : 6,
-S.Half : -6,
sqrt(2)/2 : 4,
-sqrt(2)/2 : -4,
1/sqrt(2) : 4,
-1/sqrt(2) : -4,
sqrt(3)/2 : 3,
-sqrt(3)/2 : -3,
}
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.asinh(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.NegativeInfinity * S.ImaginaryUnit
elif arg is S.NegativeInfinity:
return S.Infinity * S.ImaginaryUnit
elif arg is S.Zero:
return S.Zero
elif arg is S.One:
return S.Pi / 2
elif arg is S.NegativeOne:
return -S.Pi / 2
if arg.could_extract_minus_sign():
return -cls(-arg)
if arg.is_number:
cst_table = {
S.Half: 6,
-S.Half: -6,
sqrt(2) / 2: 4,
-sqrt(2) / 2: -4,
1 / sqrt(2): 4,
-1 / sqrt(2): -4,
sqrt(3) / 2: 3,
-sqrt(3) / 2: -3,
}
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.asinh(i_coeff)
