ABCUV

Type:

Command

 

 

 

 

 

 

 

 

Description:

Returns a solution in polynomials u and v of au+bv =c where a and b are polynomials in the

 

current CAS independent variable, and c is a value.

 

 

 

 

Access:

Arithmetic, !ÞPOLYNOMIAL

 

 

 

 

 

 

Input:

Level 3/Argument 1: The polynomial corresponding to a.

 

 

 

 

 

Level 2/Argument 2: The polynomial corresponding to b.

 

 

 

 

 

Level 1/Argument 3: The value corresponding to c.

 

 

 

 

Output:

Level 2/Item 1: The solution corresponding to u.

 

 

 

 

 

Level 1/Item 2: The solution corresponding to v.

 

 

 

 

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).

 

 

 

 

 

 

Example:

Find a solution in polynomials u and v for the following equation:

 

 

 

 

 

(x2 + x + 1)u + (x2 + 4)V = 13

 

 

 

 

 

 

 

 

Command:

ABCUV(X^2+X+1,X^2+4,13)

 

 

 

 

 

 

 

 

Result:

{-(X+3),X+4}

 

 

 

 

 

 

 

 

See also:

IABCUV, EGCD

 

 

 

 

 

 

 

 

ABS

Function

 

 

 

 

 

 

 

 

Type:

 

 

 

 

 

 

 

 

Description:

Absolute Value Function: Returns the absolute value of its argument.

 

 

 

 

 

ABS has a derivative (SIGN) but not an inverse.

 

 

 

 

 

In the case of an array, ABS returns the Frobenius (Euclidean) norm of the array, defined as the

 

square root of the sum of the squares of the absolute values of all n elements. That is:

 

 

 

n

 

2

 

 

 

 

 

 

 

∑

z

i

 

 

 

 

 

 

 

i = 1

 

 

 

 

 

 

 

Access:

!Ê

 

( Ê is the left-shift of the /key).

 

 

Flags:

Numerical Results (–3)

 

 

 

 

 

 

 

 

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 1/Argument 1

 

 

Level 1/Item 1

 

 

 

 

 

 

 

 

 

 

 

x

 

 

 

→

x

 

 

 

(x,y)

 

 

 

→

x

2

+ y

2

 

 

 

 

 

 

 

 

 

 

 

x_unit

 

 

 

→

x_unit

 

 

[array]

 

 

 

→

array

 

 

'symb'

 

 

 

→

'ABS(symb)'

See also:

NEG, SIGN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ACK

Command

 

 

 

 

 

 

 

 

Type:

 

 

 

 

 

 

 

 

Description: Acknowledge Alarm Command: Acknowledges the oldest past-due alarm.

ACK clears the alert annunciator if there are both no other past-due alarms and no other active alert sources (such as a low battery condition).

Full Command and Function Reference 3-5