2647.sagews

x,y = var('x y')
maxima.eval('load("plotdf");')
eq='(x+y)/(x-y)'
x0,x1,y0,y1=-3,3,-3,3
eq=sage_eval(eq,locals={'x':x,'y':y})
#p=plot_slope_field(eq, (x,x0,x1), (y, y0, y1))
p=implicit_plot(eq==0, (x, x0, x1), (y, y0, y1), color="red")
p=p+implicit_plot(1/(eq)==0,(x, x0, x1),(y, y0, y1),color="yellow")    
show(p)
@interact 
def df(eq='-x/y',usemaxima=False,window=matrix(2,2,[-3,3,-3,3]),IVP=False,xinit=0,yinit=1):
    x0=window[0,0]
    x1=window[0,1]
    y0=window[1,0]
    y1=window[1,1]
    eq=sage_eval(eq,locals={'x':x,'y':y})
    html(r'This is the vector field corresponding to $\frac{dy}{dx}='+latex(eq)+'$')
    if not usemaxima:
        p=implicit_plot(eq==0, (x, x0, x1), (y, y0, y1), color="red")
        p=p+plot_slope_field(eq, (x,x0,x1), (y, y0, y1))
        p=p+implicit_plot(1/eq==0,(x, x0, x1),(y, y0, y1),color="yellow")    
        if IVP:
            p+=list_plot(desolve_rk4(eq,y,ics=[xinit,yinit],ivar=x,end_points=[x0,x1])
            ,ymin=y0,ymax=y1)
        p.show(aspect_ratio=1)
    else:
        if IVP:
            maxima.plotdf(eq,str([y,y0,y1]),str([x,x0,x1]),
            '[trajectory_at, %s, %s]'%(str(xinit), str(yinit) ))
        else:
            maxima.plotdf(str(eq),str([y,y0,y1]),str([x,x0,x1]))

x,y=var('x y')
@interact
def iso(eq=-x/y,isofrom =-2,isoto=2,isostep=.5,xmin=-3,xmax=3,ymin=-3,ymax=3):
    print html('This interact plots the slope field for $\\frac{dy}{dx}='+str(eq)+'$')
    print html('It also shows the isoclines given by the  from, to and step numbers')
    print html('as well as the isocline corresponding to the vertical slopes')
    p=plot_slope_field(eq, (x,xmin,xmax), (y,ymin,ymax))
    for k in srange(isofrom,isoto,isostep):
        p+=implicit_plot(eq==k, (x, xmin, xmax), (y, ymin, ymax), cmap='autumn')
    p+implicit_plot(1/eq==0,(x, xmin, xmax), (y, ymin, ymax), cmap='autumn')
    show(p,aspect_ratio=1)

#Is this a bug?
x,y=var('x y')
q=implicit_plot((x-y)/(x+y)==0,(x,-2,2),(y,-2,2),color='red')
p=implicit_plot((x+y)/(x-y)==0,(x,-2,2),(y,-2,2),color='yellow')
show(q)
show(p)
show(p+q)