simplify regression in newer versions

[unknownuser75]

S,K,T,t,r,sigma=symbols('S K T t r sigma')
simplify(-sqrt(2)*K*exp(-r*(T - t))*exp(-(sigma*sqrt(T - t)/2 - log(S*exp(r*(T - t))/K)/(sigma*sqrt(T - t)))**2/2)/(2*sqrt(pi)*S*sigma*sqrt(T - t)) + sqrt(2)*exp(-(sigma*sqrt(T - t)/2 + log(S*exp(r*(T - t))/K)/(sigma*sqrt(T - t)))**2/2)/(2*sqrt(pi)*sigma*sqrt(T - t)))

The above expression is 0. I've just started using sympy and this was one of the first examples I tried. On my older Ubuntu 12.04 with sympy 0.7.1.rc1 this correctly simplifies to zero. On newer sympy versions (0.7.4, 0.7.5) it does not simplify to zero.

[debugger22]

This change was introduced in 3305c73b265691be4a411971cdbbd8e39e8810ca. @smichr

[smichr]

It's good to see that nothing too heroic has to be done to show that this is zero. How to put this into simplify in a meaningful way will take some thought:

>>> ok
-sqrt(2)*K*exp(-8*r*sigma**2*(T - t)**2/(8*T*sigma**2 - 8*sigma**2*t) - (T*sigma**2 - sigma**2*t - 2*log(S*exp(T*r - r*t)/K))**2/(8*T*sigma**2 - 8*sigma**2*t))/(2*sqrt(pi)*S*sigma*sqrt(T - t)) + sqrt(2)*exp(-(T*sigma**2 - sigma**2*t + 2*log(S*exp(T*r - r*t)/K))**2/(8*T*sigma**2 - 8*sigma**2*t))/(2*sqrt(pi)*sigma*sqrt(T - t))
>>> bottom_up(ok, factor_terms)
sqrt(2)*(-K*exp(-r*(T - t) - (T*sigma**2 - sigma**2*t - 2*log(S*exp(r*(T - t))/K))**2/(8*sigma**2*(T - t)))/S + exp(-(T*sigma**2 - sigma**2*t + 2*log(S*exp(r*(T - t))/K))**2/(8*sigma**2*(T - t))))/(2*sqrt(pi)*sigma*sqrt(T - t))
>>> r,e = cse(_); e=factor_terms(e[0].expand().as_numer_denom()[0]);e
sqrt(2)*sqrt(pi)*sigma*sqrt(x0)*(-K*exp(4*x2*x4*x5) + S*exp(x1))*exp(x2**2*x5)*exp(x4**2*x5)
>>> _.args
(sigma, sqrt(2), sqrt(pi), sqrt(x0), -K*exp(4*x2*x4*x5) + S*exp(x1), exp(x2**2*x5), exp(x4**2*x5))
>>> _[4].subs(reversed(r))
-K*exp((T*sigma**2 - sigma**2*t)*log(S*exp(r*(T - t))/K)/(sigma**2*(T - t))) + S*exp(r*(T - t))
>>> factor_terms(_)
0

That last factor_terms is important: if you don't eliminate that factor then things get out of control again with expansion.

>>> e.args[4].subs(reversed(r)).expand()
-K*exp(T*sigma**2*log(S*exp(T*r)*exp(-r*t)/K)/(T*sigma**2 - sigma**2*t))*exp(-sigma**2*t*log(S*exp(T*r)*exp(-r*t)/K)/(T*sigma**2 - sigma**2*t)) + S*exp(T*r)*exp(-r*t)

A point to consider:

• work with numer and denom separately and for each of them, work with factors independently