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sturm

number of real roots of a polynomial in an interval

sturmseq

Sturm sequence of a polynomial

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

sturmseq(p, x)

sturm(s, x, a, b)

Parameters

p

-

polynomial in x with rational, float, or real algebraic coefficients

x

-

variable in polynomial p

s

-

Sturm sequence for polynomial p

a, b

-

rationals, floats, or real algebraic numbers such that ab; a can be  and b can be

Description

• 

The procedure sturmseq computes a Sturm sequence for the polynomial p in x.  It returns the Sturm sequence as a list of polynomials and replaces multiple roots with single roots.

• 

The procedure sturm uses Sturm's theorem to return the number of real roots in the interval (a,b] of polynomial p in x. The first argument to sturm should be a Sturm sequence for p.  This may be computed by sturmseq. Note: The interval excludes the lower endpoint a and includes the upper endpoint b (unless it is ).

Examples

ssturmseqexpandx1x2x3,x

sx36x2+11x6,x24x+113,x2,1

(1)

sturms,x,32,4

2

(2)

sturms,x,1,2

1

(3)

sturms,x,∞,∞

3

(4)

sturmseqx32x+1,x

x32x+1,x223,x324,−1

(5)

Compatibility

• 

The sturm and sturmseq commands were updated in Maple 2018.

• 

The p and a parameters were updated in Maple 2018.

See Also

realroot

RootFinding[Isolate]

roots

solve