# Ver; Vpotential; Xnum - HP 48gII Advanced User's Reference Manual

Graphing calculator.

Example:
Build the row version of the Vandermonde matrix from the following list of objects:
{x, y, z}
Command:
TRAN(VANDERMONDE({x,y,z}))
1 1 1
x y z
2
2
2
x
y
z
Result:
CON, HILBERT, IDN, RANM

## VER

Type:
Command
Description:
Returns the Computer Algebra System version number, and date of release.
Catalog, ...µ
Access:
Input:
No input required.
Output:
A real number giving the version and release date of the Computer Algebra System software.
Flags:
The version and release date are given as a number of the form V.YYYYMMDD, so a display
mode showing at least 8 digits after the fraction mark is needed to display the result in full.

### VPOTENTIAL

Type:
Command
Description:
Find a vector potential function describing a field whose curl (or "rot") is the input. This
command is the opposite of CURL. Given a vector V it attempts to return a function U such
that curl 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 vector U of the variables that is the potential from which V is obtained. 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 see if this command is the opposite of CURL, use the output of the example in CURL as
input to VPOTENTIAL. Find a vector in the spatial variables x, y, and z whose curl is:
i
(2yz)
+ (0)
Command:
VPOTENTIAL([2*Y*Z, 0, 2*X*Y-X^2], [X,Y,Z])
EXPAND(ANS(1))
Result:
[0, -((X^3-3*Y*X^2)/3), Z*Y^2]
This shows that the reversal is not unique – more than one vector can have the same curl.
However, obtaining the curl of the above result, and then applying VPOTENTIAL to it again
will give the same result.
CURL, POTENTIAL

### XNUM

Type:
Command
U
V
j
k
+ (2xy – x
)
2
. For this to be possible, DIV(V) must be zero,
Computer Algebra Commands 4-79  