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: Use integration by parts to calculate the following:

∫xcos (x)dx

Command 1: Apply the IBP command in RPN mode:

Level 2: X*COS(X)

Level 1: SIN(X)

Result: Level 2: SIN(X)*X

Level 1: -SIN(X)

Command 2: Apply the INTVX command to level 1, -SIN(X)

Result: Level 2: SIN(X)*X Level 1: COS(X)

Command 3: Press +to add the result to the value at level 2 to obtain the final result.

Result: SIN(X)*(X)+COS(X)

See also: INTVX, INT, PREVAL, RISCH

ICHINREM

Type:

Command

Description:

Solves a system of two congruences in integers using the Chinese Remainder theorem.

Access:

Arithmetic, !ÞINTEGER

Input:

Level 2/Argument 1: A vector of the first value and the modulus.

 

Level 1/Argument 2: A vector of the second value and the modulus.

Output:

A vector of the solution.

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:

Solve the following system of congruences:

 

 

x ≡ 2

Modulo 3

 

 

x ≡ 1

Modulo 5

Command:

ICHINREM([2,3],[1,5])

Results:

[-4, 15]

See also:

CHINREM

IDN

Command

Type:

Description:

Identity Matrix Command: Returns an identity matrix; that is, a square matrix with its diagonal

 

elements equal to 1 and its off-diagonal elements equal to 0.

 

The result is either a new square matrix, or an existing square matrix with its elements replaced by

 

the elements of the identity matrix, according to the argument.

 

•

Creating a new matrix: If the argument is a real number n, a new real identity matrix is returned,

 

 

with its number of rows and number of columns equal to n.

 

•

Replacing the elements of an existing matrix: If the argument is a square matrix, an identity

 

 

matrix of the same dimensions is returned. If the original matrix is complex, the resulting

 

 

identity matrix will also be complex, with diagonal values (1,0).

3-110 Full Command and Function Reference