slope field solution for my class

[ttja]

does anyone know how to create the code for making a slope field? so if i insert a function using gui or something it'll graph the slopes for the function on the graphic screen. here's wat i have so far:

import math
from livewires import *
begin_graphics()
x1=random_between(1,639)
y1=random_between(1,479)
plot(x1,y1)
a=5
while a==5 :
corner= float(random_between(1,3))
if corner == 1:
x2=320
y2=480
elif corner == 2:
x2=0
y2=0
else:
x2=640
y2=0
x1=(x1+x2)/2
y1=(y1+y2)/2
plot(x1,y1)

i know im missing the yend. and probably some other stuff too, but if anyone can help me out finding the missing codes and errors, i'll appreciate it a lot.

[ttja]

does anyone know how to create the code for making a slope field? so if i insert a function using gui or something it'll graph the slopes for the function on the graphic screen. here's wat i have so far:

from livewires import*
import math
begin_graphics()
def slope(x,y):
    return float(x*y)
def xend (x,r,m):
    return [r-r/math.sqrt(1+m**2),x+r/math.sqrt(1+m**2)]
def yend (x,r1,m1,r,m)
        return [r-r/math
r=0.25
y=4
while y>=-4:
    x=-4
    while x<=4:
        m=slope(x,y)
        xnd=xend(x,r,m)
        ynd=yend(x,y,xnd[0],xnd[1],m)
        line(50*xnd[0]+200,50*ynd[0]+200,50*xnd[1]+200,50*ynd[1]+200)
        x=x+1
y=y-1
 

i know im missing the yend. and probably some other stuff too, but if anyone can help me out finding the missing codes and errors, i'll appreciate it a lot.

[ttja]

how would you go about making a slope field using python?

[bartonc]

For those interested:
Given a system of differential equations,

    {du}/{dt}=f(t,u,...y,z)
 
         ...
 
    {dy}/{dt}=j(t,u,...y,z)
    {dz}/{dt}=k(t,u,...y,z)
 

the slope field is an array of slope marks in the phase space (the preceding equations imply seven dimensions, but can be any number depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (t,u,...y,z) and is parallel to the vector

    ( 1 \\ f(t,u,...y,z) \\ ... \\ j(t,u,...y,z) \\ k(t,u,...y,z). 

Much prettier here.

[bartonc]

how would you go about making a slope field using python?

For solving Differential Equations, you'll probably want to check out the scipy extensions.
Also, this IEEE Computer Society article looks interesting.