[Intersection points] Find the roots of functions. #manim #root #intersection #function #math #scipy

20240623_roots.py

# https://discord.com/channels/581738731934056449/1216636172277776435/1216684543042650142
from scipy.optimize import root_scalar

# uwezi intersection method
class question(Scene):
    def construct(self):
        t_dn = DecimalNumber(-5).to_edge(UR)
        # x^3 - 4x
        def f(x):
            return (x-2) * x * (x+2)

        def t(x):
            return -0.1*x**2 + t_dn.get_value()

        axes = Axes()

        fplot = axes.plot(f, color = RED)
        tplot = always_redraw(
            lambda : axes.plot(t, color = WHITE)
        )

        dots = VGroup()
        def dotUpdater(mobj):
            roots = []
            for x0 in np.arange(-4, 4, 0.1):
                root = root_scalar(lambda x: t(x)-f(x), x0 = x0, method = 'newton')
                if root.converged:
                    roots.append(root.root)
            roots = np.unique(np.round(roots,2))
            grp = VGroup(
                *[Dot().set_color(YELLOW).move_to(axes.c2p(root, f(root))) for root in roots]
            )
            mobj.become(grp)
        dots.add_updater(dotUpdater)

        self.add(axes, fplot)
        self.add(tplot, dots)
        self.wait(2)

        self.play(ChangeDecimalToValue(t_dn, 4), run_time = 6, rate_func = linear)
        self.wait(2)

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