HP 50g Graphing, 48gII Graphing manual Chinrem, Cholesky

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).

334 Full Command and Function Reference