On 03/13/2012 09:02 AM, Alan Bromborsky wrote:
First a question on noncommutative multiplication. The following code -
from sympy import *
(a1,a2,b1,b2) = symbols('a1 a2 b1 b2')
(e1,e2) = symbols('e1 e2',commutative=False)
x = expand(a1*(e1+e2)*a2*b1*(e1+e2)*b2)
print x
gives -
a1*a2*b1*b2*e1*e2 + a1*a2*b1*b2*e1**2 + a1*a2*b1*b2*e2*e1 +
a1*a2*b1*b2*e2**2
Are the products of the noncommutative symbols always grouped together?
This is important so that if one defines a multiplication table for
the noncommutative symbols a complex product could be evaluated with a
simple
x = x.subs(mul_table)
where the keys of the mul_table dictionary are e1**2, e1*e2, e2*e1,
e2**2. Would e1*e1 work as a key as well as e1**2?
The second question is if one uses a function rather than a table to
calculate the product of noncommuting symbols what class should be
subclassed in order to overload the __mul__() operator? Should it be
the Basic class?
Would this be a good way of implementing a noncommutative product -
from sympy import *
Expr_mul = Expr.__mul__
def mymul(a,b):
if not a.is_commutative and not b.is_commutative:
if isinstance(a,Symbol) and isinstance(b,Symbol):
print 'a =',a,'b =',b
return(Expr_mul(a,b))
else:
return(Expr_mul(a,b))
else:
return(Expr_mul(a,b))
Expr.__mul__ = mymul
(a1,a2,b1,b2) = symbols('a1 a2 b1 b2')
(e1,e2) = symbols('e1 e2',commutative=False)
print expand(a1*(e1+e2)*a2*b1*(e1+e2)*b2)
the output is -
a = e2 b = e2
a = e2 b = e1
a = e1 b = e2
a = e1 b = e1
a1*a2*b1*b2*e1*e2 + a1*a2*b1*b2*e1**2 + a1*a2*b1*b2*e2*e1 +
a1*a2*b1*b2*e2**2
In the real implementation there would be no print statments a and b and
the first instance of Expr_mul(a,b) would be replaced by the actual
function for multiplying noncommutative symbols.
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