Cholesky; Circ - HP 48gII Advanced User's Reference Manual

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:
2
u x + 1
u x 1 –
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.
Matrices, !Ø
Access:
Input: A positive square matrix, M
Output: An upper triangular matrix, P, such that
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 the Cholesky factorization of:
1 1
1 5
CHOLESKY 1 1
Command:
1 1
0 2
Result:

CIRC

Type: Command
Description: Composes two permutations.
Arithmetic, !Þ
Access:
Input: Two lists, L1 and L2, representing two permutations. The composition L1○L2 is the
permutation equivalent to performing permutation L2 first and L1 second.
Level 2/Argument 1: L1
Level 1/Argument 2: L2
Output: A list representing the single equivalent permutation, L = L1○L2
Example: Compose the permutations given by {3,4,5,2,1} and {2,1,4,3,5}
Command: CIRC({3,4,5,2,1},{2,1,4,3,5})
Result: {4,3,2,5,1}
See also: C2P, P2C
4-18 Computer Algebra Commands
(mod x+2)
(mod x+3)
QUADRATIC FORM
⎛ ⎞
⎜ ⎟
⎝ ⎠
1 5
PERMUTATION
P*P=M. ( P is the transpose of P.)
t t