On 04/12/2013 03:53 PM, Prasoon Shukla wrote:
So, after spending a couple of days writing the proposal, I've
uploaded on to the wiki.
https://github.com/sympy/sympy/wiki/GSoC-2013-Application-Prasoon-Shukla:-Vector-Calculus-Module
@All community members: Please give it a read. This is the first draft
of the proposal so it's bound to be rough-ish. Please point out things
that you don't like or would like to see improved. Also, please
suggest any additions that you'd like to see.
Thank you.
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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.
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