Thue Interactive.sagews

# Algorithm to plot Thue equation, solutions and roots given a thue equation
def thue_graph_finder(thue_input, c):
    R.<x,y> = QQbar[]
    ts = []
    thue_eq = thue_input(y=1)
    thue_eq2 = thue_eq.univariate_polynomial()
    print thue_eq2
    thue_eq_roots = thue_eq2.roots()
    eq_roots = []
    for p in thue_eq_roots:
        eq_roots.append(CC(p[0]))
    th_init = gp.thueinit(thue_eq2,1)
    sols = gp.thue(th_init,c)

    for p in sols:
        print p
        if p[1] != 0 and p[2] != 0:
            t = p[1] / p[2]
            ts.append(CC(t))

    approx_plot = plot([0,0], xmin = -100, ymin = -100, xmax = 100, ymax = 100)
    if len(ts) > 0:
        approx_plot = point(ts, pointsize=100, color = "red")
    root_plot = point(eq_roots, pointsize=100)
    show(root_plot + approx_plot)

from sage.misc.html import HtmlFragment
R.<x,y> = QQbar[]
F.<x> = ZZ[]
p = F.random_element(3).homogenize(y)
@interact
def _(thue_input = input_box(p, label = '$f$'), c = input_box(ZZ.random_element(1, 50))):
    print(thue_graph_finder(thue_input, c))

Interact: please open in CoCalc

def plane_curve_finder(thue_input,c):
    ts = []
    thue_eq = thue_input(y=1)
    thue_eq2 = thue_eq.univariate_polynomial()
    th_init = gp.thueinit(thue_eq2,1)
    # what gp returns is "gp integers", which are not sage integers.
    # This line will convert "gp integers" to the usual sage ZZ elements.
    sols = [map(ZZ,a) for a in gp.thue(th_init,c)]
    for p in sols:
            ts.append(p)

    approx_plot = point([0,0], color = "white")
    if len(ts) > 0:
        approx_plot += point(ts, pointsize=100, color = "red")
    curve_plot = implicit_plot(thue_input - c, (x,-10,10), (y,-10,10))
    show(curve_plot + approx_plot)


from sage.misc.html import HtmlFragment
R.<x,y> = QQbar[]
F.<x,y> = ZZ[]
p = F.random_element(3)

@interact
def _(thue_input = input_box(p, label = '$f$'), c = input_box(17)):
    print(plane_curve_finder(thue_input, c))

Interact: please open in CoCalc