# Author: Alex Gezerlis

# Numerical Methods in Physics with Python (CUP, 2020)

from kahansum import kahansum

from chargearray import chargearray, vecmag

from legendre import legendre

def decomp(rs,ris):

rmag = vecmag(rs); rimag = vecmag(ris)

prs = [r*ri for r,ri in zip(rs,ris)]

vecdot = kahansum(prs)

costheta = vecdot/(rmag*rimag)

return rmag, rimag, costheta

def multicoes(rs,qtopos,nmax=60):

coes = [0. for n in range(nmax+1)]

for n in range(nmax+1):

for q,pos in qtopos.items():

rmag, rimag, costheta = decomp(rs,pos)

val = q*(rimag**n)*legendre(n,costheta)[0]

coes[n] += val

return coes

def multifullpot(rs,qtopos):

coes = multicoes(rs,qtopos)

rmag = vecmag(rs)

contribs = [coe/rmag**(n+1) for n,coe in enumerate(coes)]

return kahansum(contribs)

if __name__ == '__main__':

qtopos = chargearray(6)

for y in 1,-1:

rs = [0.,y]

potval = multifullpot(rs,qtopos)

print(rs, potval)