You should also know about pre/post_order_traversal (both must be imported from
sympy.utilities.iterables), which let you dig all the way down in an expression
tree.
In [109]: from sympy.utilities.iterables import preorder_traversal,
postorder_traversal
In [110]: preorder_traversal(sin(x**2) + 4*x**3)
Out[110]: <generator object preorder_traversal at 0x102415a00>
In [111]: list(preorder_traversal(sin(x**2) + 4*x**3))
Out[111]:
⎡ ⎛ 2⎞ 3 3 3 ⎛ 2⎞ 2 ⎤
⎣sin⎝x ⎠ + 4⋅x , 4⋅x , 4, x , x, 3, sin⎝x ⎠, x , x, 2⎦
In [112]: list(postorder_traversal(sin(x**2) + 4*x**3))
Out[112]:
⎡ 3 3 2 ⎛ 2⎞ ⎛ 2⎞ 3⎤
⎣4, x, 3, x , 4⋅x , x, 2, x , sin⎝x ⎠, sin⎝x ⎠ + 4⋅x ⎦
Also, as Chris said, using .atoms() to find what IndexedElements there are is
useful. There maybe ought to be some .is_IndexedElement attribute on
IndexedElement, just as there is for every other major class. Øyvind, what do
you think?
Aaron Meurer
On Sep 23, 2010, at 3:26 PM, Nicholas Kinar wrote:
>
>> h[1]>>> from sympy.tensor import *
>> h[1]>>> M=Indexed('M')
>> h[1]>>> var('i j k', integer=1)
>> (i, j, k)
>> h[2]>>> eq=1+2*M(i,1)+3*j+4*M(i,2); eq
>> 1 + 2*M(i, 1) + 3*j + 4*M(i, 2)
>> h[3]>>> for a in eq.as_Add():
>> ... ie = []
>> ... co = []
>> ... for m in a.as_Mul():
>> ... if isinstance(m, IndexedElement):
>> ... ie.append(m)
>> ... else:
>> ... co.append(m)
>> ... if ie:
>> ... print Mul(*co), Mul(*ie)
>> ...
>> 4 M(i, 2)
>> 2 M(i, 1)
>> h[3]>>>
>>
>> If there's always only going to be one IndexedElement per term then
>> you could find them all with atoms and then find their coefficients
>> with coeff. But if you are worried about efficiency then you could
>> just check for an IndexedElement atom in a given term and find the
>> coeff of it when found:
>>
>> h[3]>>> for a in eq.as_Add():
>> ... ie = a.atoms(IndexedElement)
>> ... if ie:
>> ... assert len(ie) == 1
>> ... ie = ie.pop()
>> ... print a.coeff(ie), ie
>> ...
>> 4 M(i, 2)
>> 2 M(i, 1)
>>
>> If you need to know which argument it was then you can use the
>> enumerate to keep track of which "a" it was that had that term:
>>
>> h[3]>>> for i, a in enumerate(eq.as_Add()):
>> ... ie = a.atoms(IndexedElement)
>> ... if ie:
>> ... assert len(ie) == 1
>> ... ie = ie.pop()
>> ... print i, a.coeff(ie), ie
>> ...
>> 2 4 M(i, 2)
>> 3 2 M(i, 1)
>> h[3]>>> print eq.args
>> (1, 3*j, 4*M(i, 2), 2*M(i, 1))
>>
>>
> Thanks Chris; that is exactly what I wanted, and the code snippets that you
> gave demonstrates quite a few exciting features of sympy.
>
> Nicholas
>
>
>
>
>
>
>
>
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