Maple 9 Learning Guide - Maplesoft

170 • Chapter 6: Evaluation and Simplificationexpr := x y z + x y + x z + y z> simplify( expr, { x*z=1 } );x y + y z + y + 1You can give one or more side relations in a set or list. The simplifycommand uses the given equations as additional allowable simplifications.Specifying the order in which simplify performs the simplificationprovides another level of control.> expr := x^3 + y^3;expr := x 3 + y 3> siderel := x^2 + y^2 = 1;siderel := x 2 + y 2 = 1> simplify( expr, {siderel}, [x,y] );y 3 − x y 2 + x> simplify( expr, {siderel}, [y,x] );x 3 − y x 2 + y• In the first case, Maple makes the substitution x 2 = 1 − y 2 in theexpression, then attempts to make substitutions for y 2 terms. Notfinding any, it stops.• In the second case, Maple makes the substitution y 2 = 1 − x 2 in theexpression, then attempts to make substitutions for x 2 terms. Notfinding any, it stops.The simplify routine is based on Gröbner basis manipulations ofpolynomials. For more information, refer to the ?simplify,siderelshelp page.