Automatic recognize the bilinear form and the linear form

General
1

Can ngsolve automatically recognize the linear form & bilinear form from a given weak form Instead of compute them manually?

(I mean the following fenicsx codes can automatically recognize the linear form & bilinear form.

u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
F = u * v * ufl.dx + dt * ufl.dot(ufl.grad(u), ufl.grad(v)) * ufl.dx - (u_n + dt * f) * v * ufl.dx
a = fem.form(ufl.lhs(F))
L = fem.form(ufl.rhs(F))
2

Here are suggestions for ufl-like rhs/lhs functions:
all trial-functions are found with equ.GetProxies().
For the lhs, we take the directional derivatives with respect to proxies, into the direction of proxies. Since grad(u).Diff(grad(u), grad(u)) returns grad(u), as well as grad(u).Diff(u,u) returns the same, we take only the derivatives with proxies having a named derivative (a hack, for the moment).
For the rhs, we replace all trial-functions by zero.

from ngsolve import *
mesh = Mesh(unit_square.GenerateMesh(maxh=0.2))

fes = H1(mesh, order=1)
u,v = fes.TnT()

def lhs(equ):
    return sum(equ.Diff(proxy,proxy) for proxy in equ.GetProxies(trial=True) if proxy.derivname!='')

def rhs(equ):
    repl = dict((proxy, CF((0,)*proxy.dim).Reshape(proxy.shape)) for proxy in equ.GetProxies(trial=True))
    return equ.Replace(repl)

dt = 0.1
u_n = GridFunction(fes)
f = x*y
F = u * v * dx + dt * InnerProduct(grad(u), grad(v)) * dx - (u_n + dt * f) * v * dx
a = lhs(F)
print ("lhs = ", a)
L = rhs(F)
print ("rhs =", L)```