Polynomial; Potential; Powexpand - HP 48gII Advanced User's Reference Manual

Graphing calculator.

Example:
Find the minimal polynomial of
Command:
PMINI([[0,1][1,0]])
1 0 0 1
0 1 1 0
0 0 0 0 X
Result:
zeros, except for the result.
JORDAN, PCAR

POLYNOMIAL

Type:
Command
Description:
Displays a menu or list of CAS operations with polynomials.
Catalog, ...µ
Access:
Flags:
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered
list. If the flag is set, displays the operations as a menu of function keys.
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR,
MODULAR, REWRITE, TESTS, TRIGO

POTENTIAL

Type:
Command
Description:
Find the potential field function describing a field whose vector gradient is input. This
command is the opposite of DERIV. Given a vector V it attempts to return a function U
such that grad U is equal to V;
otherwise the command reports a "Bad Argument Value" error. Step-by-step mode is
available with this command.
Catalog, ...µ
Access:
Input:
Level 2/Argument 1: A vector V of expressions.
Level 1/Argument 2: A vector of the names of the variables.
Output:
Level 1/Item 1: A function U of the variables that is the potential from which V is derived.
An arbitrary constant can be added, the command does not do this.
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).
Step-by-step mode can be set (flag –100 set).
Example:
To confirm that this command is the opposite of DERIV, use the output of the example in
DERIV, and show that the result is the same as the input given in the DERIV example. Find
the function of the spatial variables x, y, and z whose gradient is:
i
(4xy+z)
Command:
POTENTIAL([4*X*Y+Z, 2*X^2+6*Y*Z, X+3*Y^2], [X,Y,Z])
EXPAND(ANS(1))
Result:
2*Y*X^2+Z*X+3*Z*Y^2
DERIV, VPOTENTIAL

POWEXPAND

Type:
Function
0 1
1 0
1
X
2
1
So, the minimal polynomial is
U
j
k
+ (2x
+ 6yz)
+ (x+3y
)
2
2
:
2
, as it is in the first row to contain entirely
-1
X
V
. For this to be possible, CURL(V) must be zero,
Computer Algebra Commands 4-57  