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Unformatted text preview: , {1 = 1, 3 = 3}] This method can be valuable if your equation has many solutions, or if you are unsure of the number of solutions that a certain command produces. Restricting Solutions
You can limit solutions by specifying inequalities with the solve command.
> solve({x^2=y^2},{x,y}); 48 • Chapter 3: Finding Solutions {x = −y, y = y }, {y = y, x = y }
> solve({x^2=y^2, x<>y},{x,y}); {x = −y, y = y } Consider this system of ﬁve equations in ﬁve unknowns.
> > > > > eqn1 eqn2 eqn3 eqn4 eqn5 := := := := := x+2*y+3*z+4*t+5*u=41: 5*x+5*y+4*z+3*t+2*u=20: 3*y+4*z8*t+2*u=125: x+y+z+t+u=9: 8*x+4*z+3*t+2*u=11: Solve the system for all variables.
> s1 := solve({eqn1,eqn2,eqn3,eqn4,eqn5}, {x,y,z,t,u}); s1 := {x = 2, t = −11, z = −1, y = 3, u = 16} Solving for a Subset of Unknowns You can also solve for a subset of the unknowns. Maple returns the solutions in terms of the other unknowns.
> s2 := solve({eqn1,eqn2,eqn3}, { x, y, z}); 527 28 70 59 − 7t − u, z = − − 7 t − u, 13 13 13 13 70 635 + 12 t + u} y= 13 13 s2 := {x = − Exploring Solutions
You can explore the parametric solutions found at the end of the previous section. For example, evaluate the solution at u = 1 and t = 1.
> eval( s2, {u=1,t=1} ); {x = 861 −220 −646 ,y= ,z= } 13 13 13 Suppose that you require the solutions from solve in a particular order. Since you cannot ﬁx the order of elements in a set, solve does not necessarily return your solutions in the order x, y, z . However, lists do preserve order. Try the following. 3.1 The Maple solve Command > eval( [x,y,z], s2 ); • 49 [− 28 635 70 70 59 527 − 7t − u, + 12 t + u, − − 7 t − u] 13 13 13 13 13 13 This command ﬁxed the order and extracted the righthand side of the equations. Because the order is ﬁxed, you know the solution for each variable. This capability is particularly useful if you want to plot the solution surface.
> plot3d(%, u=0..2, t=0..2, axes=BOXED); –5 –10 –15 –20 –25 50 55 60 65 –58 –56 –54 –52 –50 –48 –46 –44 –42 70 75 80 The unapply Command
For convenience, deﬁne x = x(u, t), y = y (u, t), and z = z (u, t), that is, convert the solutions to functions. Recall that you can easily select a solution expression for a particular variable using eval.
> eval( x, s2 ); − 527 28 − 7t − u 13 13 However, this is an expression for x and not a function.
> x(1,1); x(1, 1) To convert the expression to a function, use the unapply command. Provide unapply with the expression and the independent variables. For example, 50 • Chapter 3: Finding Solutions > f := unapply(x^2 + y^2 + 4, x, y); f := (x, y ) → x2 + y 2 + 4 produces the function, f , of x and y that maps (x, y ) to x2 + y 2 + 4. This new function is easy to use.
> f(a,b); a2 + b2 + 4 Thus, to make your solution for x a function of both u and t, obtain the expression for x, as above.
> eval(x, s2); − 28 527 − 7t − u 13 13 Use unapply to turn it into a function of u and t.
> x := unapply(%, u, t); x := (u, t...
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 Spring '12
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 Math, Division

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