Comment #2 on issue 2750 by smi...@gmail.com: solve could do a better job
with over determined systems
http://code.google.com/p/sympy/issues/detail?id=2750
When you don't tell it what to do, it gives you the first valid solution it
finds. It used to give *all* valid solutions for symbols it could find but
Ronan said this wasn't the job of solve (and I agree). If solve were an
object, not giving symbols is like using the pop() method: you get
something. The same applies to systems: if you don't supply symbols you
just get *some* solution:
>>> for e in eqs:
... print Eq(e, 0)
...
I1 - I2 - I3 == 0
I3 - I4 - I5 == 0
I4 + I5 - I6 == 0
-I1 + I2 + I6 == 0
-2*I1 - 2*I3 - 2*I5 - 3*I6 - dI1/2 + 12 == 0
-I4 + dQ4 == 0
-I2 + dQ2 == 0
2*I3 + 2*I5 + 3*I6 - Q2 == 0
I4 - 2*I5 + 2*Q4 + dI4 == 0
>>> ans=solve(eqs)
>>> for k in sorted(ans.keys()):
... print Eq(k, ans[k])
...
I1 == -dI1/18 + 7*dQ2/9 + 2*dQ4/9 + 4/3
I2 == dQ2
I3 == -dI1/18 - 2*dQ2/9 + 2*dQ4/9 + 4/3
I4 == dQ4
I5 == -dI1/18 - 2*dQ2/9 - 7*dQ4/9 + 4/3
I6 == -dI1/18 - 2*dQ2/9 + 2*dQ4/9 + 4/3
Q2 == -7*dI1/18 - 14*dQ2/9 - 4*dQ4/9 + 28/3
Q4 == -dI1/18 - dI4/2 - 2*dQ2/9 - 23*dQ4/18 + 4/3
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