Input/Output:

 

 

Level 1/Argument 1

 

Level 1/Item 1

 

 

 

 

 

 

 

 

 

 

 

 

 

nflag number

 

 

→

0/1

 

If flag –44 is

 

 

Example:

set, -44 FC?C returns 0 to level 1 and clears flag –44.

 

See also:

CF, FC?, FS? FS?C, SF

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FDISTRIB

 

 

 

 

 

 

 

 

Type:

Command

 

 

 

 

 

 

Description:

Performs a full distribution of multiplication and division with respect to addition and subtraction

 

in a single step.

 

 

 

 

 

 

Access:

!Ú REWRITE

 

 

 

 

 

 

Input:

An expression.

 

 

 

 

 

 

Output:

An equivalent expression that results from fully applying the distributive property of

 

multiplication and division over addition and subtraction.

 

Flags:

Exact mode must be set (flag –105 clear).

 

 

 

Numeric mode must not be set (flag –3 clear).

 

Example:

Expand (X+1)(X-1)(X+2):

 

 

 

 

 

 

Command:

FDISTRIB((X+1)*(X-1)*(X+2))

 

 

 

 

Result:

X*(X*X)+2*(X*X)+(-(X*(1*X))+-(2*(1*X)))+ (X*(X*1)+2*(X*1)+

 

(-(X*(1*1))+-(2*(1*1))))

 

 

 

 

See also:

DISTRIB

 

 

 

 

 

 

FFT

Command

 

 

 

 

 

 

Type:

 

 

 

 

 

 

Description:

Discrete Fourier Transform Command: Computes the one- or two-dimensional discrete Fourier

 

transform of an array.

 

 

 

 

 

 

 

If the argument is an N-vector or an N × 1 or 1 × N matrix, FFT computes the one-dimensional

 

transform. If the argument is an M × N matrix, FFT computes the two-dimensional transform. M

 

and N must be integral powers of 2.

 

 

 

 

 

The one-dimensional discrete Fourier transform of an N-vector X is the N-vector Y where:

 

 

 

 

 – 1

 

2πikn

 

 

 

 

 

 

–---------------

 

 

 

Y

k

= ∑ X

n

e

 , i = –1

 

n = 0

for k = 0, 1, …, N – 1.

The two dimensional discrete Fourier transform of an M × N matrix X is the M × N matrix Y where:

 

 

 

M – 1

 – 1

 

2πikm

2πi ln

 

 

 

 

e–----------------M

e–----------------- ,i = –1

Y

kl

=

∑ ∑ x

mn

 

 

m = 0

n = 0

 

 

 

 

 

 

 

 

for k = 0, 1, …, M – 1 and l = 0, 1, …, N – 1.

The discrete Fourier transform and its inverse are defined for any positive sequence length. However, the calculation can be performed very rapidly when the sequence length is a power of two, and the resulting algorithms are called the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT).

The FFT command uses truncated 15-digit arithmetic and intermediate storage, then rounds the result to 12-digit precision.

3-86 Full Command and Function Reference