def Der_Phi_Phi_Basis_Fn(M_Coef,N_Coef, Theta, Phi): # M_Coef < 0 Corresonds to Z^|M|_N Der_Phi_Phi_Val = 0 if(M_Coef < 0): m_sph = -1*M_Coef Der_Phi_Phi_Val += m_sph*(m_sph*(mpmath.cot(Phi)**2) - (mpmath.csc(Phi)**2))*sph_harm(m_sph, N_Coef, Theta, Phi).imag if(m_sph < N_Coef): Der_Phi_Phi_Val += sqrt((N_Coef-m_sph)*(N_Coef+m_sph+1))*(2*m_sph + 1)*mpmath.cot(Phi)*(((e**(-1j*Theta))*sph_harm(m_sph+1, N_Coef, Theta, Phi))).imag if(m_sph < (N_Coef -1) ): Der_Phi_Phi_Val += sqrt((N_Coef-m_sph)*(N_Coef-m_sph-1)*(N_Coef+m_sph+1)*(N_Coef+m_sph+2))*(((e**(-2j*Theta))*sph_harm(m_sph+2, N_Coef, Theta, Phi))).imag else: # M_Coef >= 0 m_sph = M_Coef Der_Phi_Phi_Val += m_sph*(m_sph*(mpmath.cot(Phi)**2) - (mpmath.csc(Phi)**2))*sph_harm(m_sph, N_Coef, Theta, Phi).real if(m_sph < N_Coef): Der_Phi_Phi_Val += sqrt((N_Coef-m_sph)*(N_Coef+m_sph+1))*(2*m_sph + 1)*mpmath.cot(Phi)*(((e**(-1j*Theta))*sph_harm(m_sph+1, N_Coef, Theta, Phi))).real if(m_sph < (N_Coef -1) ): Der_Phi_Phi_Val += sqrt((N_Coef-m_sph)*(N_Coef-m_sph-1)*(N_Coef+m_sph+1)*(N_Coef+m_sph+2))*(((e**(-2j*Theta))*sph_harm(m_sph+2, N_Coef, Theta, Phi))).real return Der_Phi_Phi_Val
def D(k, w):
"""
Henning
"""
two_lambda_j_prime = 2 * (4 - 1.5) * pow(k, 2)
h2f3 = hyp2f3(1, 0.5, 0.5 - 4, 1 + w, 1 - w, two_lambda_j_prime)
print(two_lambda_j_prime)
print(int(h2f3))
result = 1
result -= h2f3
print(result)
third = sqrt(pi) * w
third *= gamma(4 + 1) * gamma(0.5 - 4)
third /= csc(pi * w)
third /= gamma(4 + 1.5 + w) * gamma(4 + 1.5 - w)
third *= pow(two_lambda_j_prime, 4 + 0.5)
third *= hyp1f2(4 + 1, 4 + 1.5 + w, 4 + 1.5 - w, two_lambda_j_prime)
print(int(third))
result += third
print(result)
lambda_kappa_j_p2 = (4 - 1.5) / ((pow(5.099, 2) - 1) * (4 - 0.5))
print(lambda_kappa_j_p2 * pow(k, 2))
result /= pow(k, 2) * lambda_kappa_j_p2
return result
def ddPhiDouble(phi, dPhi, theta, dTheta):
[m] = glob_m.data["val"] # input/
[R] = glob_R.data["val"] # input/
[lam] = glob_lam.data["val"] # input/
if (theta == 0):
return 0
else:
return float(
((g * cos(phi + theta) + R2 * (dTheta + dPhi)**2) / R + dPhi *
(dPhi * cos(theta) - lam * sin(theta) / m)) /
(sin(theta) + csc(theta)))
def CSC(self, a):
x = Argument(int32_t)
y = Argument(int32_t)
try:
with Function("Cosecant", (x, y), int32_t) as asm_csc:
reg_x = GeneralPurposeRegister32()
LOAD.ARGUMENT(reg_x, x)
COS(reg_x)
RETURN(reg_x)
code_csc = asm_csc.finalize(abi.detect()).encode().load()
except:
code_csc = round(mpmath.csc(a), 4)
return (code_csc)
return (code_csc(a))
def eval(self, z):
return mpmath.csc(z)
# -*- coding: utf-8 -*- """ Created by libsedmlscript v0.0.1 """ from sed_roadrunner import model, task, plot from mpmath import csc #---------------------------------------------- csc(0.5)
async def find_csc(event):
input_str = float(event.pattern_match.group(1))
output = mpmath.csc(input_str)
await event.edit(f"**Value of Cosec {input_str}\n==>>**`{output}`")
def run(self, context):
return mpmath.csc(self.body.run(context))
def eval(self, z):
return mpmath.csc(z)
#
'sqrt': ['primitive', [lambda x, y: mp.sqrt(x), None]],
'cbrt': ['primitive', [lambda x, y: mp.cbrt(x), None]],
'root': ['primitive', [lambda x, y: mp.root(x, y[0]), None]], # y's root
'unitroots': ['primitive', [lambda x, y: Vector(mp.unitroots(x)),
None]], #
'hypot': ['primitive', [lambda x, y: mp.hypot(x, y[0]),
None]], # sqrt(x**2+y**2)
#
'sin': ['primitive', [lambda x, y: mp.sin(x), None]],
'cos': ['primitive', [lambda x, y: mp.cos(x), None]],
'tan': ['primitive', [lambda x, y: mp.tan(x), None]],
'sinpi': ['primitive', [lambda x, y: mp.sinpi(x), None]], #sin(x * pi)
'cospi': ['primitive', [lambda x, y: mp.cospi(x), None]],
'sec': ['primitive', [lambda x, y: mp.sec(x), None]],
'csc': ['primitive', [lambda x, y: mp.csc(x), None]],
'cot': ['primitive', [lambda x, y: mp.cot(x), None]],
'asin': ['primitive', [lambda x, y: mp.asin(x), None]],
'acos': ['primitive', [lambda x, y: mp.acos(x), None]],
'atan': ['primitive', [lambda x, y: mp.atan(x), None]],
'atan2': ['primitive', [lambda x, y: mp.atan2(y[0], x), None]],
'asec': ['primitive', [lambda x, y: mp.asec(x), None]],
'acsc': ['primitive', [lambda x, y: mp.acsc(x), None]],
'acot': ['primitive', [lambda x, y: mp.acot(x), None]],
'sinc': ['primitive', [lambda x, y: mp.sinc(x), None]],
'sincpi': ['primitive', [lambda x, y: mp.sincpi(x), None]],
'degrees': ['primitive', [lambda x, y: mp.degrees(x),
None]], #radian - >degree
'radians': ['primitive', [lambda x, y: mp.radians(x),
None]], #degree - >radian
#