Sorry for a probably naive question.
I have the following expression
s = a g[1, 1] + a g[1, 2] + a g[1, 3] + a g[2, 3] + a q[1] -
b e g[1, 1] q[1] - d e g[1, 1] q[1] - b e g[1, 2] q[1] -
d e g[1, 2] q[1] - b e g[1, 3] q[1] - d e g[1, 3] q[1] -
b g[1, 4] q[1] - b g[1, 5] q[1] - b e g[2, 3] q[1] -
d e g[2, 3] q[1] - b g[3, 4] q[1] - b g[3, 5] q[1] - b e q[1]^2 -
d e q[1]^2 - b e g[1, 1] q[2] - d e g[1, 1] q[2] -
b e g[1, 2] q[2] - d e g[1, 2] q[2] - b e g[1, 3] q[2] -
d e g[1, 3] q[2] - b g[1, 4] q[2] - b g[1, 5] q[2] -
b e g[2, 3] q[2] - d e g[2, 3] q[2] - b g[3, 4] q[2] -
b g[3, 5] q[2] - b e q[1] q[2] - d e q[1] q[2] - d g[1, 1] q[4] -
d g[1, 2] q[4] - d g[1, 3] q[4] - d g[2, 3] q[4] - d q[1] q[4] -
d g[1, 1] q[5] - d g[1, 2] q[5] - d g[1, 3] q[5] - d g[2, 3] q[5] -
d q[1] q[5];
Let's introduce the symbols
h[1] = g[1, 1] + g[1, 2] + g[1, 3] + g[2, 3] + q[1];
h[2] = g[1, 4] + g[1, 5] + g[3, 4] + g[3, 5];
h[3] = q[1] + q[2];
h[4] = q[4] + q[5];
Then once we consider
f = -b h[2] h[3] + a h[1] - (b e + d e) h[1] h[3] - d h[1] h[4];
we conclude that s=f
:
In[244]:= FullSimplify[s - f]
Out[244]= 0
I knew that s
should be expressed through h[1],h[2],h[3],h[4]
(I didn't know about the form of f
as function of those h
though).
I got this explicit form of f
looking at s
and making several Collect
operators (w.r.t. -d e
, -b e
and so on).
My question is whether it is possible to get f
without analysing the structure of s
, but just ask "Represent s
as a polynomial (or a function) of h[1],h[2],h[3],h[4]
"?