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# Checking 'newt2' using numerical root finding capablities 
# of Maple.
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einstein% maple
    |\^/|     Maple V Release 3 (University of Texas - Austin)
._|\|   |/|_. Copyright (c) 1981-1994 by Waterloo Maple Software and the
 \  MAPLE  /  University of Waterloo. All rights reserved. Maple and Maple V
 <____ ____>  are registered trademarks of Waterloo Maple Software.
      |       Type ? for help.
> f1 := sin(x*y) - 1/2;

                              f1 := sin(x y) - 1/2

> f2 := y^2 - 6*x - 2;

                                      2
                               f2 := y  - 6 x - 2

> ans := fsolve({f1,f2},{x,y});

                   ans := {y = 1.909297746, x = .2742363137}

> r1 := evalf(subs(ans,f1));

                                    r1 := 0

> r2 := evalf(subs(ans,f2));

                                            -8
                                 r2 := .1*10
> quit;