n2.add_step(replace(V,V2(r1,r2)),'replace potential with N=2')
#n2.do_print()
r_cm = Vector('r_cm',dim=2)
r_12 = Vector('r_12',dim=2)
r_12_def = definition(r_12, r2-r1)
r_cm_def = definition(r_cm, (r1+r2)/2)
V12 = Function('V')
# replace r1,r2 with r_12 and r_cm
# tranformation of limit region is hard, but the square box should be equivalent in periodic
# boundary conditions
# Jacobian is 1
n2.add_step(specialize_integral(r1,(r_12,r_cm)),'Switch variables')
n2.add_step(replace(V2(r1,r2),V12(r_12)),'Specialize to a potential that depends only on interparticle distance')
n2.add_step(replace(V12(r_12),V12(Abs(r_12))),'Depend only on the magnitude of the distance')
#n2.add_step(replace_func(V12(r_12),Eq(V12,V12(Abs(r_12)))),'Depend only on the magnitude of the distance')
n2.do_print()
Vol = Symbol('Omega')
n2.add_step(do_integral(Vol, [r_12]),'Integrate out r_cm (this step is still a hack)')
L = Symbol('L')
n2.add_step(identity(decompose),'Decompose into vector components')
# Lower limit is adjusted by small amount to avoid a division by zero error at the origin.
n2.add_step(identity(add_limits(-L/2+0.000000001,L/2)),'Add integration limits')
def peel_terms(s):
lim_min = None
lim_max = None
for p in preorder_traversal(s):
if isinstance(p, Sum):
lmin = p.limits[0][1]
lmax = p.limits[0][2]
if lim_min:
lim_min = max(lmin, lim_min)
else:
lim_min = lmin
if lim_max:
lim_max = min(lmax, lim_max)
else:
lim_max = lmax
p = peel_sum_terms(lim_min, lim_max)
new_s = rewrite(s, [(Sum, p)])
return new_s
trap.add_step(identity(split_sum), 'Split sum')
trap.add_step(identity(adjust_limits), 'Adjust limits')
trap.add_step(identity(peel_terms), 'Peel terms')
#trap.to_xhtml()
trap.to_mathjax()
if __name__ == '__main__':
trap.do_print()
lim_min = None
lim_max = None
for p in preorder_traversal(s):
if isinstance(p,Sum):
lmin = p.limits[0][1]
lmax = p.limits[0][2]
if lim_min:
lim_min = max(lmin,lim_min)
else:
lim_min = lmin
if lim_max:
lim_max = min(lmax,lim_max)
else:
lim_max = lmax
p = peel_sum_terms(lim_min, lim_max)
new_s = rewrite(s,[(Sum,p)])
return new_s
trap.add_step(identity(split_sum),'Split sum')
trap.add_step(identity(adjust_limits),'Adjust limits')
trap.add_step(identity(peel_terms),'Peel terms')
#trap.to_xhtml()
trap.to_mathjax()
if __name__ == '__main__':
trap.do_print()
