I'm working with polynomials of 5 variables $a,b,p,q,r$ which have a condition $a+b=p+q+r$. I'd like to minimize the number of variables in the answer. However, FullSimplify can't handle even simple example:

FullSimplify[pol, Assumptions -> a + b == p + q + r]


-b + p + q + r

instead of a. Is there a way to do it?

  • $\begingroup$ That ain't how assumptions work. Here's a possibility: do you prefer expressing in terms of $a,b$, or $p,q,r$? $\endgroup$ Commented May 8, 2016 at 17:05
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    – Michael E2
    Commented May 8, 2016 at 18:46
  • $\begingroup$ Are your examples all linear? That could simplify matters if so. $\endgroup$ Commented May 8, 2016 at 21:27
  • $\begingroup$ @DanielLichtblau In general, I need to decompose homogeneous polynomials of degree n-1 which variables satisfy equation $a+b=p_1+...+p_n$ (at least for n=4,5,6). The polynomial I actually needed to simplify was 2*b*(-b+p+q+r). I'm thinking of introducing additional variable $d=a+b=p_1+...+p_n$, substitute sums for $d$, then substitute expressions of the type $d-p$. $\endgroup$
    – Ingvar
    Commented May 9, 2016 at 9:38

2 Answers 2


The equality may be used to eliminate one variable of your choice. It may be done by the way used in the @happy fish answer, or by a direct substitution:

 pol = p + q + r - b;
pol /. b -> p + q + r - a

(*  a  *)

Have fun!


You can use

Solve[pol == p + q + r - b && a + b == p + q + r, pol, {b, q, p, r}]


Eliminate[pol == p + q + r - b && a + b == p + q + r, {b, q, p, r}]

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