Previous Up Next

5.30.15  Sturm sequences and number of sign changes of P on (a, b]: sturm

sturm takes two or four arguments: P a polynomial expression or P/Q a rational fraction and a variable name or P a polynomial expression, a variable name and two real or complex numbers a and b.

If sturm takes two arguments, sturm returns the list of the Sturm sequences and multiplicities of the square-free factors of P (or P/Q) (in this case sturm behaves like sturmseq).

If sturm takes four arguments, it behaves like sturmab:

Input:

sturm(2*x^3+2,x)

Output:

[2,[[1,0,0,1],[3,0,0],-9],1]

Input:

sturm((2*x^3+2)/(x+2),x)

Output:

[2,[[1,0,0,1],[3,0,0],-9],1,[[1,2],1]]

Input:

sturm(x^2*(x^3+2),x,-2,0)

Output:

1

Previous Up Next