from lj import lj_pot
from specialize_n2d2 import n2, V12, r_12
from derivation_modeling.derivation import replace, compute_children, all_to_xhtml
from derivation_modeling.util.vector_utils import replace_func
from sympy import Symbol, sqrt, Integral
lj_n2 = n2.new_derivation()
lj_n2.set_name('lj_n2')
lj_n2.set_title('Using LJ potential with N=2')
lj_eqn = lj_pot.final()
lj_n2.add_step(replace_func(V12, lj_eqn), 'Specialize to the LJ potential')
L = 4.0
lj_n2.add_step(replace('L', L), 'Insert value for box size')
lj_n2.add_step(replace('Omega', L * L), 'Insert value for box volume')
lj_n2.add_step(replace('beta', 1.0), 'Insert value for temperature')
# Could evaluate now in sympy
#i1 = lj_n2.final().rhs
#print 'Z = ',i1.evalf()
# Could replace the last three steps with the following code
# to evaluate parameter scan in sympy
#for i in range(10):
# for j in range(10):
# box_len = 0.6 + j*.02
# beta = 0.5 + i*.1
# i1 = lj_n2.final().rhs
# i1 = i1.subs('L',box_len)
from sympy import Symbol, Integral, exp, Function, Abs, Eq
from derivation_modeling.util.vector import Vector, VectorMagnitude
from derivation_modeling.util.vector_utils import decompose, add_limits, replace_func
from derivation_modeling.derivation import derivation, definition, replace_definition, specialize_integral, replace, do_integral, identity
from partition import partition_function, beta_def, R, V
r1 = Vector('r1',dim=2)
r2 = Vector('r2',dim=2)
V2 = Function('V')
n2 = partition_function.new_derivation()
n2.set_name('specialize_n2d2')
n2.set_title('Specialized to N=2, D=2')
#n2.do_print()
n2.add_step(specialize_integral(R,(r1,r2)),'specialize to N=2')
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
from lj import lj_pot
from specialize_n2d2 import n2,V12,r_12
from derivation_modeling.derivation import replace, compute_children, all_to_xhtml
from derivation_modeling.util.vector_utils import replace_func
from sympy import Symbol, sqrt, Integral
lj_n2 = n2.new_derivation()
lj_n2.set_name('lj_n2')
lj_n2.set_title('Using LJ potential with N=2')
lj_eqn = lj_pot.final()
lj_n2.add_step(replace_func(V12,lj_eqn),'Specialize to the LJ potential')
L = 4.0
lj_n2.add_step(replace('L',L),'Insert value for box size')
lj_n2.add_step(replace('Omega',L*L),'Insert value for box volume')
lj_n2.add_step(replace('beta',1.0),'Insert value for temperature')
# Could evaluate now in sympy
#i1 = lj_n2.final().rhs
#print 'Z = ',i1.evalf()
# Could replace the last three steps with the following code
# to evaluate parameter scan in sympy
#for i in range(10):
# for j in range(10):
# box_len = 0.6 + j*.02
