On 11/09/2010 3:46 PM, Aaron S. Meurer wrote:
I think you want the collect() function and the .as_independent
method. The easiest way to manipulate Equalities is to first convert
them into regular expressions. Then, you would call collect on the
expression using x**2. collect collects all powers of the argument by
default, but you can use the exact=False flag to turn this off (see
the docstring of collect). Actually, collect is optional, and is only
if you want (A + D)*x**2 instead of A*x**2 + D*x**2.
Then, you can gather the independent and dependent parts using
as_independent. Here is an example of how you would do it with your
expression:
In [1]: var('A B C D E F')
Out[1]: (A, B, C, D, E, F)
In [2]: expr = Eq(A*x**2 + B*y**2 + C*x*y + D*x**2, E*z**2 + F)
In [3]: expr
Out[3]:
2 2 2 2
C⋅x⋅y + A⋅x + B⋅y + D⋅x = F + E⋅z
In [4]: expr = expr.lhs - expr.rhs
In [5]: expr
Out[5]:
2 2 2 2
-F + C⋅x⋅y + A⋅x + B⋅y + D⋅x - E⋅z
In [6]: expr = collect(expr, x**2, exact=True)
In [7]: expr
Out[7]:
2 2 2
-F + x ⋅(A + D) + C⋅x⋅y + B⋅y - E⋅z
In [8]: expr.as_independent(x**2, y**2)
Out[8]:
⎛ 2 2 2⎞
⎝-F + C⋅x⋅y - E⋅z , x ⋅(A + D) + B⋅y ⎠
In [9]: expr = Eq(*reversed(expr.as_independent(x**2, y**2)))
In [10]: expr
Out[10]:
2 2 2
x ⋅(A + D) + B⋅y = -F + C⋅x⋅y - E⋅z
It shouldn't be too hard to write a simple function that is passed an
Equality and some variables and returns the result like in [10].
Aaron Meurer
Thanks, Aaron; that's exactly what I wanted and it is very exciting to
realize that this can be done. I've just started playing with sympy
and exploring its possibilities, so thank you very much for helping to
guide me and for your response!
Nicholas
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