SymPy 用符号代替向量

Question

I have an expression of type Mul called term in the code below. Within term is a type Symbol called zhat . I want to perform something like term.subs(zhat, vec) where vec is of type BaseVector . I am subbing a symbol for a vector. The output is assigned to out_actual in the code.

The issue is that out_actual is of type Mul when I need it to be of type VectorMul . The variable out_ideal is what I would expect from the substitution. Any way to obtain out_ideal ?

import sympy as sp
from sympy.vector import CoordSys3D
N = CoordSys3D('N')
Q, eps, zhat = sp.symbols('Q \epsilon_0 \\hat{\\mathbf{z}}')

vec = N.k
term = Q*eps*zhat
out_ideal = Q*eps*vec
out_actual = term.subs(zhat, vec)

Answer 1

It's not particularly pleasant or generalizable, but you could do the following to convert any Mul into a VectorMul whenever appropriate (and leaving it as a Mul otherwise):

import sympy as sp
from sympy.vector import CoordSys3D
from sympy.core.mul import Mul

N = CoordSys3D('N')

def multiply_args(obj):
    '''Gets the result of multiplying all of the Mul's args together.'''
    if not isinstance(obj, Mul):
        raise ValueError('Input must be an instance of Mul')
    args = obj.args
    prod = args[0]
    for e in args[1:]:
        prod = prod * e
    return prod

Q, eps, zhat = sp.symbols('Q \epsilon_0 \\hat{\\mathbf{z}}')
vec = N.k

term = Q*eps*zhat
sub_result = term.subs(zhat, vec)
sub_result = multiply_args(sub_result)

The reason this is necessary is that subs , a method which belongs to the Basic class, simply looks at all of the arguments (eg Q , eps , zhat ) of the Mul object ( term ) and replaces each that matches the substitution target, and gives the result as a Mul but with an amended list of args (ie zhat has been replaced with vec ). It doesn't do any further evaluation on the result, and leaves the argument as a Mul .

To convert it to a VectorMul , you can just multiply the resulting arguments together manually, like you did to get out_ideal . All multiply_args does is manually multiplies the arguments together, which then promotes to a VectorMul if any of the arguments is a Vector . Obviously this only works because you know you have started with a Mul ; you'd need to generalize this to deal with other types if you needed to.

If could be worth putting in a feature reqeust to the SymPy Github repository for this functionality.