Reference Guide

Full Command and Function Reference 3-165
Result: 1/2/(X-1)+-1/2/(X+1)
See also: PROPFRAC
PATH
Type: Command
Description: Current Path Command: Returns a list specifying the path to the current directory.
The first directory is always HOME, and the last directory is always the current directory.
If a program needs to switch to a specific directory, it can do so by evaluating a directory list, such
as one created earlier by PATH.
Access: !° MEMORY DIRECTORY PATH ( °is the left-shift of the Nkey).
Input/Output:
Level 1/Argument 1 Level 1/Item 1
→
{ HOME directory-name
1
... directory-name
n
}
See also: CRDIR, HOME, PGDIR, UPDIR
PCAR
Type: Command
Description: Returns the characteristic polynomial of an n × n matrix.
Access: Matrices, !Ø L EIGENVECTORS
Input: A square matrix.
Output: The characteristic polynomial of the matrix.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example: Find the characteristic polynomial of the following matrix:
5 8 16
4 1 8
4– 4– 11–
Command: PCAR([[5,8,16][4,1,8][-4,-4,-11]])
Result: X^3+5*X^2+3*X-9
See also: JORDAN, PMINI
PCOEF
Type: Command
Description: Monic Polynomial Coefficients Command: Returns the coefficients of a monic polynomial (a
polynomial with a leading coefficient of 1) having specific roots.
The argument must be a real or complex array of length n containing the polynomial’s roots. The
result is a real or complex vector of length n+1 containing the coefficients listed from highest
order to lowest, with a leading coefficient of 1.
Access: !Þ POLYNOMIAL LL PCOEF ( Þis the left-shift of the 1key).
Input/Output:
Level 1/Argument 1 Level 1/Item 1
[ array ]
roots
→
[ array ]
coefficients
Example: Find the polynomial that has the roots 2, –3, 4, –5:
Command: [ 2 –3 4 –5 ] PCOEF
Result: [ 1 2 –25 –26 120 ] , representing the polynomial x
4
+ 2x
3
- 25x
2
- 26x + 120.
See also: PEVAL, PROOT