Sturm; Sturmab; Subst - HP 48gII Advanced User's Reference Manual

Graphing calculator.

Description:
Stores a name or list of names in the current CAS variable. This is the same as storing into the
VX variable in the CASDIR directory. By default, the CAS variable is called X; this command
allows a program to change that name.
Catalog, ...µ
Access:
Input:
Level 1/Argument 1: A name or list of names.
Output:
None in RPN mode, NOVAL in Algebraic mode.
RCLVX

STURM

Type:
Command
Description:
For a polynomial
multiplicities
Arithmetic, !Þ
Access:
Input:
A polynomial
Output:
A list containing the Sturm's sequences for
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Find the Sturm sequences and their multiplicities for the polynomial:
3
x
1
+
Command:
STURM(X^3+1)
Result:
{[1],-1.,[1],1.,[X^3+1,-(3*X^2),-1],1.}

STURMAB

STURMAB
Type:
Command
Description:
For a polynomial
has in [
P
Arithmetic, !Þ
Access:
Input:
A polynomial
Output:
A list containing a number that is the same sign as
].
b
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
For the polynomial:
3
x
+
2
in the interval [-2,0] find the sign at the lower bound, and the number of zeroes
Command:
STURMAB(X^3+2, -2, 0)
Result:
{-6,1}
STURM, ZEROS

SUBST

Type:
Function
, STURM returns a list containing Sturm's sequences of
P
POLYNOMIAL
P
and a closed interval [
P
]
a, b
POLYNOMIAL
P
, and the multiplicity for each (as a real number).
P
], STURMAB determines the number of zeroes
a, b
) and the number of zeroes
P(a
Computer Algebra Commands 4-69
and their
P
has in [
P
a,