Learning Guide Learning Guide

5.1 Mathematical Manipulations • 159The option assume=property specifies that simplify assume thatall the unknowns in the expression have that property.> simplify( expr, assume=real );|x y|> simplify( expr, assume=positive );x yYou can also use the general assume facility to place assumptions onindividual variables. See section 5.2.Simplification with Side RelationsSometimes you can simplify an expression using your own special-purposetransformation rule. The simplify command allows you do to this bymeans of side relations.> expr := x*y*z + x*y + x*z + y*z;expr := 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