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