using Plots, ImplicitEquations a,b = -1,2 f(x,y) = y^4 - x^4 + a*y^2 + b*x^2 r = (f ⩵ 0) # \Equal[tab] plot(r) ## trident of Newton c,d,e,h = 1,1,1,1 f(x,y) = x*y g(x,y) = c*x^3 + d*x^2 + e*x + h plot(Eq(f,g)) ## aka f ⩵ g (using Unicode\Equal) f(x,y) = x - y plot(f ≪ 0) # \ll[tab] f(x,y) = (y-5)* cos(4sqrt((x-4)^2 +y^2)) g(x,y) = x * sin(2*sqrt(x^2 + y^2)) plot(Ge(f, g), xlims=(-10, 10), ylims=(-10, 10)) a,b = -1,2 f(x,y) = y^4 - x^4 + a*y^2 + b*x^2 r = (f ⩵ 0) plot(r, red=:red) # show undecided regions in red f0(x,y) = ((x/7)^2 + (y/3)^2 - 1) * screen(abs(x)>3) * screen(y > -3*sqrt(33)/7) f1(x,y) = ( abs(x/2)-(3 * sqrt(33)-7) * x^2/112 -3 +sqrt(1-(abs((abs(x)-2))-1)^2)-y) f2(x,y) = y - (9 - 8*abs(x)) * screen((abs(x)>= 3/4) & (abs(x) <= 1) ) f3(x,y) = y - (3*abs(x) + 3/4) * I_((1/2 < abs(x)) & (abs(x) < 3/4)) # alternate name for screen f4(x,y) = y - 2.25 * I_(abs(x) <= 1/2) f5(x,y) = (6 * sqrt(10)/7 + (1.5-.5 * abs(x)) - 6 * sqrt(10)/14 * sqrt(4-(abs(x)-1)^2) -y) * screen(abs(x) >= 1) r = (f0 ⩵ 0) | (f1 ⩵ 0) | (f2 ⩵ 0) | (f3 ⩵ 0) | (f4 ⩵ 0) | (f5 ⩵ 0) plot(r, xlims=(-7, 7), ylims=(-4, 4), red=:black) f(x,y) = x plot(f ≧ 1/2, map=z -> 1/z) f(x,y) = x^2 + y^2 plot(f ⩵ 2*3^2) ## now add tangent at (3,3) a,b = 3,3 dydx(a,b) = -b/a # implicit differentiate to get dy/dx =-y/x tl(x) = b + dydx(a,b)*(x-a) plot!(tl, linewidth=3, -5, 5)