On Mar 15, 4:42 am, Dan Schult <dsch...@colgate.edu> wrote:
> > It would be great if you could provide a concrete test case (with your
> > expected result) to work on. You are welcome to open a new issue for
> > this in our issue tracker.
>
> I'll try.... I've simplified my actual problem to get a shorter answer.
> The equations come from circuits and the result we're looking for is
> "p".
> Change the circuit a little and "p" changes.
>
> import sympy
> from sympy.abc import *
>
> all_eqn=[-c+c*a+s*a-m*C-m*P,\
> -H-f+m*P-L*y,\
> c+s-n,\
> p+y-c,\
> y-D*H/R]
>
> solve=[H,c,p,s,y]
>
> soln=sympy.solve(all_eqn,solve)
> for key,val in soln.iteritems():
> print key,":",val
>
> Output is:
> H : (-R*f + P*R*m)/(R + D*L)
> p : (D*f + R*a*n - C*R*m - D*P*m - P*R*m + D*L*a*n - C*D*L*m -
> D*L*P*m)/(R + D*L)
> y : (-D*f + D*P*m)/(R + D*L)
> c : a*n - C*m - P*m
> s : n + C*m + P*m - a*n
>
> I'd like to have
> p: a*n - C*m - P*m + (D*f - D*P*m)/(R+D*L)
>
> In other words, it would be nice to divide the numer by the denom
> leaving any remainder
> as a fraction. In yet other words, I'd like to factor the
> denominator out of the numerator
> to the extent possible.
>
> The expression:
> cancel(collect(expand(val),solve))
> works in some cases, but not in others (I think because
> e.g. C*R*m+C*D*L*m can't factor C*m easily unless you
> tell sympy to factor C*m -- but I'm guessing here as I don't really
> know)
>
I noticed this, too, when working with your expression.
>>> exec("%s=symbols('%s')" % (("n,P,R,D,m,f,a,C,L",)*2))
>>> eq=(D*f + R*a*n - C*R*m - D*P*m - P*R*m + D*L*a*n - C*D*L*m - D*L*P*m)/(R +
>>> D*L)
>>> cancel(collect(eq.expand(mul=1),
>>> list(numer(eq).atoms(Symbol).difference(denom(eq).atoms(Symbol)))))
a*n + (-D*P*m - P*R*m - D*L*P*m)/(R + D*L) - C*m + D*f/(R + D*L)
I think the thing to do is to use polynomial division which is going
to tell you exactly (as in a numerical division) what the whole and
remainder parts are:
>>> n,d = eq.as_numer_denom(); s = eq.atoms(Symbol); w,r =
>>> div(Poly(n,*s),Poly(d, *s))
>>> print (w, r/d)
(a*n - C*m - P*m, (D*f - D*P*m)/(R + D*L))
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