#### algebraic relation (11.9.97)

##### Malte Henkel

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 ?

##### Stanley J Houghton (21.9.97)

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