I'm reading/studying on my own a book about algebraic curves.

I'm trying to find a way for Mathematica help me with the following (the book, ISBN: 038731802X, allows me to use any CAS / program.

Here is a question:


  How many times do the two given curves intersect at the origin?  
  
  $\quad(a)\quad y = x^3$  
  
  which I can rewrite as $y-x^3 = 0$  
  
  $\quad(b)\quad y^4 + 6x^3*y + x^8 == 0 $


I can view both curves using:

ContourPlot[{y^4 + 6 x^3*y + x^8 == 0, y - x^3 == 0}, {x, -5, 5}, {y, -5, 5}]


However, I have no idea how to find the the multiplicity of the zeros at the origin. I'm really stuck.


Question: Passing data from Controller, to View, and back to Controller
Answer: You are not supposed to do that in a classical MVC app. You are supposed to create and fill out the model once in the controller then feed it to the view in a single pass and after that forget about it till the next round trip to the server. You should not toss it back and forth to the controller.

What you are trying to do is supposed to be done by either an iframe or a subsequent ajax call from the client.