sturmseq takes as argument, a polynomial expression P or a rationnal fraction P/Q and returns the list of the Sturm sequences of the square-free factors of odd multiplicity of P (or of P/Q). For F a square-free factor of odd multiplicity, the Sturm sequence R_{1},R_{2},... is made from F, F′ by a recurrence relation :
Input :
^
3+2)or
^
3+2,y)Output :
The first term gives the content of the numerator (here 2),
then the Sturm sequence (in list representation) [x^{3}+1,3x^{2},−9].
Input :
^
3+2)/(3*x^
2+2),x)Output :
The first term gives the content of the numerator (here 2),
then the Sturm sequence of the numerator ([[1,0,0,1],[3,0,0],-9]),
then the content of the denominator (here 1) and the Sturm
sequence of the denominator ([[3,0,2],[6,0],-72]). As expressions,
[x^{3}+1,3x^{2}, −9] is the Sturm sequence of the numerator and
[3x^{2}+2,6x,−72] is the Sturm sequence of the denominator.
Input :
^
3+1)^
2,x)Output :
Indeed F=1.
Input :
^
3+1)/(2*x+2),x)Output :
The first term gives the content of the numerator
(here 3),
the second term gives the Sturm sequence of the numerator
(here 3x^
3+1, 9x^
2, -81),
the third term gives the content of the denominator (here
2),
the fourth term gives the Sturm sequence of the denominator
(x+1,1).
Warning !!!!
P is defined by its symbolic expression.
Input :
sturmseq([1,0,0,1],x),
Output :
Bad argument type.