Example 2: Find the matrix for a rotation with axis [1 1 1] and angle π/3 radians combined with a reflection in the plane x + y + z = 0

Command: MKISOM({ [1, 1, 1],π/3}, -1) then simplify with EXPAND(ANS(1))

 

 

0

–1

0

 

 

 

 

 

 

 

0

0

–1

 

 

 

 

 

Result:

 

–1

0

0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ISOM

 

 

 

 

 

 

See also:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MOD

Function

 

 

 

Type:

 

 

 

Description:

Modulo Function: Returns a remainder defined by: x mod y = x – y floor (x/y)

 

Mod (x, y) is periodic in x with period y. Mod (x, y) lies in the interval [0, y) for y > 0 and in (y, 0]

 

for y < 0.

 

 

 

 

Algebraic syntax: argument 1 MOD argument 2

 

 

Access:

!´REAL MOD

( ´is the left-shift of the Pkey).

 

!ÞMODUL LMOD

( Þis the left-shift of the 1key).

Flags:

Numerical Results (–3)

 

 

 

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 2/Argument 1

Level 1/Argument 2

 

Level 1/Item 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x

y

→

x mod y

 

 

 

 

 

 

x

'symb'

→

'MOD(x, symb)'

 

 

 

 

 

 

'symb'

x

→

'MOD(symb, x)'

 

 

 

 

 

 

'symb1'

'symb2'

→

'MOD(symb1, symb2)'

See also:

FLOOR, /

 

 

 

 

 

 

 

 

MODSTO

 

 

 

 

 

 

 

 

 

Type:

Command

 

 

 

Description:

Changes the modulo setting to the specified number. The number that you set is reflected in the

 

CAS Modes input form. Negative numbers are replaced by their positive value, 0 and 1 are

 

replaced by 2.

 

 

 

Access:

Arithmetic, !ÞMODULO L

 

 

Input:

The modulo value that you want to set, an integer or an expression that evaluates to an integer.

Output:

The modulo setting is changed to the specified number. In Algebraic mode, NOVAL is returned

 

as argument 1.

 

 

 

Flags:

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

 

 

 

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

 

 

 

 

 

 

 

 

 

 

 

 

MODULAR

 

 

 

 

 

 

 

 

 

Type:

Command

 

 

 

Description:

Displays a menu or list of the CAS modulo operations.

 

Access:

Catalog, …µ

 

 

 

Flags:

If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If

 

the flag is set, displays the operations as a menu of function keys.

 

See also:

ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR,

 

POLYNOMIAL, REWRITE, TESTS, TRIGO

 

 

 

 

 

 

 

 

 

 

 

 

3-150 Full Command and Function Reference