# What on earth is a Subresultant?

• Jun 23rd 2010, 07:40 AM
slevvio
What on earth is a Subresultant?
I am investigating polynomial roots, for example a quartic can have several root configurations (1,1,1,1),(2,1,1),(2,2),(3,1),(4)

I have used resultants and determinants to study when we get repeated roots, but for example in the (2,2) case when there are 2 repeated roots it is a bit more complicated, I was pointed in the direction of thinking about subresultants, but I can't even find a definition of a subresultant anywhere! Mathematica can calculate them, but MathWorld doesn't explain what a subresultant actually is. Does anyone know?

Thanks
• Jun 24th 2010, 11:02 AM
Ackbeet
I don't really have an idea myself. However, here are some links that might help:

Paper on subresultants.

From the Mathematica Documentation Center

Resultants and Subresultants

Check out this book on Amazon, and search within for subresultants.

Subresultants appear to factor largely in symbolic algebra.

Good luck!
• Jun 25th 2010, 06:12 AM
slevvio
thanks!