%% m21_newtonsystemChebfun2.m - same as m20 but with Chebfun2
%          See chapter 14 of Chebfun Guide at www.chebfun.org

%% Two scalar functions on unit square:
cheb.xy                                   % chebfun2 objects x and y
F1 = sin(x+y) - exp(-x.^2);
F2 = 3*x - x.*y.^2-1;
contour(F1,20), axis equal, colorbar
hold on
plot(roots(F1),'k','linewidth',2)
plot(roots(F2),'r','linewidth',2)
roots(F1,F2)

%% Alternatively, one vector function:
F = chebfun2v(F1,F2);
figure, quiver(F,'k','numpts',20)
roots(F)
hold on, plot(ans(1),ans(2),'.','markersize',30)