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Project: I dunno
Views: 42
var('x y'); VF = plot_vector_field([-.06*x+.025*y+.2,.06*x-.075*y],[x,0,10],[y,-3,5]); plot(VF)
(x, y)
f(x,y) = -.06*x+.025*y+.2 g(x,y) = .06*x-.075*y T(x,y) = [f(x,y),g(x,y)] U(x,y) = [f(x,y) / sqrt(f(x,y)^2+g(x,y)^2), g(x,y)/ sqrt(f(x,y)^2+g(x,y)^2)] plot_vector_field(U(x,y), (x,0,10), (y,0,10))
solve([f(x,y)==0, g(x,y)==0], (x,y))
[[x == 5, y == 4]]
f(x,y) = y g(x,y) = -4*x-6*y T(x,y) = [f(x,y),g(x,y)] U(x,y) = [f(x,y) / sqrt(f(x,y)^2+g(x,y)^2), g(x,y)/ sqrt(f(x,y)^2+g(x,y)^2)] plot_vector_field(U(x,y), (x,-10,10), (y,-10,10))
solve([f(x,y)==0, g(x,y)==0], (x,y))
[[x == 0, y == 0]]
f(x,y) = 2*x*(1-x)-x*y g(x,y) = -.5*y+x*y T(x,y) = [f(x,y),g(x,y)] U(x,y) = [f(x,y) / sqrt(f(x,y)^2+g(x,y)^2), g(x,y)/ sqrt(f(x,y)^2+g(x,y)^2)] plot_vector_field(U(x,y), (x,0,2), (y,0,2))
solve([f(x,y)==0, g(x,y)==0], (x,y))
[[x == 0, y == 0], [x == 1, y == 0], [x == (1/2), y == 1]]
f(x,y) = y g(x,y) = -3*y-(x-x^3) T(x,y) = [f(x,y),g(x,y)] U(x,y) = [f(x,y) / sqrt(f(x,y)^2+g(x,y)^2), g(x,y)/ sqrt(f(x,y)^2+g(x,y)^2)] plot_vector_field(U(x,y), (x,-1.5,1.5), (y,-1,1))
solve([f(x,y)==0, g(x,y)==0], (x,y))
[[x == -1, y == 0], [x == 1, y == 0], [x == 0, y == 0]]
f(x,y) = y g(x,y) = -x+y*(1-x^2) T(x,y) = [f(x,y),g(x,y)] U(x,y) = [f(x,y) / sqrt(f(x,y)^2+g(x,y)^2), g(x,y)/ sqrt(f(x,y)^2+g(x,y)^2)] plot_vector_field(U(x,y), (x,-1.5,1.5), (y,-1,1))
solve([f(x,y)==0, g(x,y)==0], (x,y))
[[x == 0, y == 0]]
%typeset_mode True
M = matrix([[1,2],[-2,-2]]) M.eigenvalues()
[-0.50000000000000000? - 1.322875655532296?*I, -0.50000000000000000? + 1.322875655532296?*I]
QQ(1.322875655532296)
258507287/195413141
(1.322875655532296).exact_rational()
5957702309312749/4503599627370496
a=1.322875655532296 a.simplest_rational()
258507287/195413141
f(x,y) = x+2*y g(x,y) = x+3*y T(x,y) = [f(x,y),g(x,y)] U(x,y) = [f(x,y) / sqrt(f(x,y)^2+g(x,y)^2), g(x,y)/ sqrt(f(x,y)^2+g(x,y)^2)] plot_vector_field(U(x,y), (x,-3,3), (y,-3,3))