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problem identification for vectors and my current responses

Published 2020-09-20T19:38:00.003Z by Physics Derivation Graph

I encountered a few issues with SymPy today. I'll explain what I found and what I plan to do about it.

I have an expression (1158485859) that, in Latex, is

\frac{-\hbar^2}{2m} \nabla^2 = {\cal H}

The \nabla^2 is represented in SymPy as Laplacian(), though an argument is required for the operator.

My solution: leave the SymPy representation as Pow(Symbol('nabla'), Integer(2))

Also on the topic of vectors, I encountered the expression

\vec{p} \cdot \vec{F}(\vec{r}, t) = a

In order to convert that to SymPy, I'd need to specify a basis for `\vec{p}` (e.g., `from sympy.vector import CoordSys3D`). For example, 

>>> N = CoordSys3D('N')
>>> p = Symbol('p_x')*N.i + Symbol('p_y')*N.j + Symbol('p_z')*N.k
>>> F = Symbol('F_x')*N.i + Symbol('F_y')*N.j + Symbol('F_z')*N.k
F_x*p_x + F_y*p_y + F_z*p_z

However, that doesn't seem to extend to functions:

>>>'r'), Symbol('t')))
Traceback (most recent call last):
TypeError: expecting string or Symbol for name

My solution: leave the SymPy representation as incorrect, using "multiplication" instead of "dot"