Result:

1/2/(X-1)+-1/2/(X+1)

 

 

See also:

PROPFRAC

 

 

PATH

Command

 

 

Type:

 

 

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-name1 ... directory-namen}

 

 

 

 

 

 

 

See also:

CRDIR, HOME, PGDIR, UPDIR

 

 

 

 

 

 

 

 

 

 

 

PCAR

 

 

 

 

 

 

 

 

Type:

Command

 

 

Description:

Returns the characteristic polynomial of an n × n matrix.

 

Access:

Matrices, !Ø LEIGENVECTORS

 

 

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

Command

 

 

Type:

 

 

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:

!ÞPOLYNOMIAL LLPCOEF

( 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 x4 + 2x3 - 25x2 - 26x + 120.

See also:

PEVAL, PROOT

 

 

Full Command and Function Reference 3-165