Updates:
Summary: sqrt(6)/2*sqrt(2) does not auto-simplify properly
Comment #10 on issue 415 by asmeurer: sqrt(6)/2*sqrt(2) does not
auto-simplify properly
http://code.google.com/p/sympy/issues/detail?id=415
Remembering that Python associates * and / to the left:
In [12]: S(1)/2*sqrt(6)*sqrt(2)
Out[12]:
⎽⎽⎽
2⋅╲╱ 3
───────
2
In [13]: sqrt(6)/2*sqrt(2)
Out[13]:
⎽⎽⎽
2⋅╲╱ 3
───────
2
In [14]: sqrt(6)*sqrt(2)/2
Out[14]:
⎽⎽⎽
╲╱ 3
In [15]: sqrt(6)*sqrt(2)
Out[15]:
⎽⎽⎽
2⋅╲╱ 3
In [16]: sqrt(6)/2
Out[16]:
⎽⎽⎽
╲╱ 6
─────
2
So I guess the problem is clear. It doesn't pull out a sqrt()2 from the
sqrt(6) until after it finds the sqrt(2) to match it, which may
happen after it has checked to see if the 2 can cancel. I have worked on
the auto-simplification of Mul before, so I may check
this out some more and see if I can find a fix.
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