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2015-10-23 02:38:10 +0200

asked a question

Variable not found while trying to plot a parametric phase portrait

I'm trying to plot a parametric phase portrait of a differential equations system, but i get the following error:

ValueError: Variable 't' not found

Here's what I'm trying to do:

@interact
def _(a1 = slider(-30, 30, 0.001, default=0, label='a1'), 
  b1 = slider(-30, 30, 0.001, default=0, label='b1'), 
  a2 = slider(-30, 30, 0.001, default=0, label='a2'), 
  b2 = slider(-30, 30, 0.001, default=0, label='b2'), 
  g1 = slider(-30, 30, 0.001, default=0, label='g1'), 
  g2 = slider(-30, 30, 0.001, default=0, label='g2'), 
  auto_update=True):
    discriminant = b2^2-2*b1*b2+b1^2+4*a1*a2

    pretty_print("discriminant = " + str(discriminant))
    if discriminant >= 0:
        t = var('t')

        M1 = function('M_1', t)
        M2 = function('M_2', t)

        de1 = diff(M1,t) == a1 * M2 - b1 * M1 + g1
        de2 = diff(M2,t) == a2 * M1 - b2 * M2 + g2

        plot_vector_field((de1.rhs(),de2.rhs()),(M1,-3,3),(M2,-3,3))
    else:
        pretty_print("discriminant is negative. adjust parameters")

Can't really figure out why is t not found and how to fix it