On Saturday, April 13, 2013 2:40:52 AM UTC+5:30, brombo wrote:
>
> Analogous to term pythonic code I would use sympythonic code and make
> the following suggestions -
>
> Start by defining you basis vectors as noncommutative symbols -
>
> (e1,e2,e3) = symbols('e_1 e_2 e_3',commutative=False)
>
> Then if a1, a2, and a3 are commutative sympy expressions (symbols) any
> vector a is -
>
> a = a1*e1+a2*e2+a3*e3
>
> Then you automatically get vector addition, subtraction, and scalar
> multiplication (if c, b1, b2, and b3 are scalars)
>
> b = b1*e1+b2*e2+b3*e3
>
> and
>
> a+b = (a1+b1)*e1+(a2+b2)*e2+(a3+b3)*e3
>
> a-b = (a1-b1)*e1+(a2-b2)*e2+(a3-b3)*e3
>
> c*a = c*a1*e1+c*a2*e2+c*a3*e3
>
> Then if you define dictionaries for the dot and cross products, dot
> product
>
> dot_dict =
> {e1**2:1,e1*e2:0,e1*e3:0,e2*e1:0,e2**2:1,e2*e3:0,e3*e1:0,e3*e2:0,e3**2:1}
>
> then -
>
> dot(a,b) = (a*b).subs(dot_dict)
>
> cross product
>
> cross_dict =
> {e1**2:0,e1*e2:e3,e1*e3:-e2,e2*e1:-e3,e2**2:0,e2*e3:e1,e3*e1:e2,e3*e2:-e1,e3**2:0}
>
>
>
> cross(a,b) = (a*b).subs(cross_dict)
>
> Like wise for coordinate transformations -
>
> Let the bases be e1,e2,e3 ang g1,g2,g3 be related by g1 = f1(e1,e2,e3),
> g1 = f2(e1,e2,e3), g1 = f2(e1,e2,e3)
> where f1, f2, and f3 could also be functions of the coordinates then
>
> g_to_e_dict = {g1:f1,g2:f2,g3:f3}
>
> a = a1*g1+a2*g2+a3*g3
>
> a_in_terms_of_e = a.subs(g_to_e_dict)
>
> etc.
>
Thanks a lot. I'll make the changes soon.
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