#### 6.16 algebraic relation (11.9.97)

Is there a way in Maple to perform systematic algebraic simpliﬁcations in complex
calculations ? I would like to diagonalize a matrix which depends on a parameter r. It is
known that this parameter satisﬁes an algebraic relation, `r^2 = r+1`

, say.

How could I teach Maple to use this relation in combination with the eigenvals routine ? Is
there a way through the assume facility ?

You need to look at the help pages for simplify (use `?simplify,siderels`

). This will show
you how to simplify with respect to side relationships speciﬁed as a set of equations. Thus a
simple example based on your query would be

> simplify(r^2+r^3+4*r^4,{r^2=r+1});
15 r + 10