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There is no doubt that there is a possibility of having the function inverted from LambertW to a normal transcendental equation.
# code from `invert` function.
if isinstance(f, LambertW):
return _invert_real(f.args[0], imageset(Lambda(n, n*exp(n)), g_ys), symbol)
return (f, g_ys)
But I don't think that the reverse could be possible. Because of the following reasons.
There are many forms of representation and many different ways of solving lambert equations, I think it's not necessary to rewrite it again in invert function as it's already in _solve_lambert. (also see different types of lambert representation and #20545 (comment))
Maybe more than 12 ways of representation
1. x*exp(x)=a
2. x*a**x = b
3. x**(x+c) = a
4. x*log(x) = c
5. X**X = C
6. X*(B*log(X) + D)**A = C
7. A*log(B*X + A) + d*X = C
8. (B*X + A)*exp(d*X + g) = C
9. g*exp(B*X + h) - B*X = C
10. A*D**(E*X + g) - B*X = C
11. A*cos(X) + B*sin(X) - D*X = C
12. A*cosh(X) + B*sinh(X) - D*X = C
etc...
Where X is any variable,
A, B, C, D, E are any constants,
g, h are linear functions or log terms.
If anyone has an idea how to handle such a case please do give your suggestions on this.
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There is no doubt that there is a possibility of having the function inverted from
LambertW
to a normal transcendental equation.But I don't think that the reverse could be possible. Because of the following reasons.
There are many forms of representation and many different ways of solving lambert equations, I think it's not necessary to rewrite it again in
invert
function as it's already in_solve_lambert
. (also see different types of lambert representation and #20545 (comment))Maybe more than 12 ways of representation
If anyone has an idea how to handle such a case please do give your suggestions on this.
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