Input/Output:

Level 2/Argument 1

Level 1/Argument 2

 

Level 1/Item 1

 

 

 

 

x

y

→

100(y – x)/x

x

'symb'

→

'%CH(x,symb)'

'symb'

x

→

'%CH(symb,x)'

'symb1'

'symb2'

→

'%CH(symb1, symb2)'

x_unit

y_unit

→

100(y_unit – x_unit)/x_unit

x_unit

'symb'

→

'%CH(x_unit,symb)'

'symb'

x_unit

→

'%CH(symb,x_unit)'

Example 1:

1_m 500

_cm %CH returns 400, because 500 cm represents an increase of 400% over 1 m.

Example 2:

100_K 150_K %CH returns 50.

See also:

%, %T

 

 

 

CHINREM

 

 

Type:

Command

Description: Chinese Remainder function. Solves a system of simultaneous polynomial congruences in the ring Z[x].

Access: Arithmetic, !ÞPOLYNOMIAL

Input: Level 2/Argument 1: A vector of the first congruence (expression and modulus). Level 1/Argument 2: A vector of the second congruence (expression and modulus).

Output: A vector of the solution congruence (expression and modulus).

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 simultaneous congruences for the polynomial u: u ≡ x2 + 1 (mod x+2)

u ≡ x – 1 (mod x+3)

Command: CHINREM([X^2+1,X+2],[X-1,X+3])

Result: [X^3+2*X^2+5,-(X^2+5*X+6)]

See also: EGCD, ICHINREM

CHOLESKY

Type: Command

Description: Returns the Cholesky factorization of a square matrix.

Access: Matrices, !Ø QUADRATIC FORM

Input: A positive square matrix, M

Output: An upper triangular matrix, P, such that tP*P=M. (tP is the transpose of P.)

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).

3-34 Full Command and Function Reference