1309.sagews

var('x,y,z,a')
f(x,y)= (-1/a^2)*(x*y)^(1/a-1)+(1/a)*x^(1/a-1)+(1/a)*y^(1/a-1)

f(a=2)

-1/4/sqrt(x*y) + 1/2/sqrt(x) + 1/2/sqrt(y)

implicit_plot(f(a=.5)==0,(x,-2,2),(y,-2,2))

contour_plot(f(a=.5),(x,-2,2),(y,-2,2),labels=True,fill=False)

f(a=0.5)==0

-4.00000000000000*x*y + 2.00000000000000*x + 2.00000000000000*y == 0

solve(f(a=1/2)==0,x,y)

([x == y/(2*y - 1)], [1])

@interact
def my_solve(a_val=slider([.1,.2,..,3])):
    show(implicit_plot(f(a=a_val),(x,0,5),(y,0,5)))
    print solve(f(a=a_val)==0,x,y)

a_val