Isprime; Jordan - HP 48gII Advanced User's Reference Manual

Example 1: Analyze the isometry given by the matrix
0 1 –
1 – 0
Command:
ISOM([[0,-1] [-1,0]])
Result: { [1, 1]
–
isometry.
Example 2: Analyze the isometry given by the matrix
Command:
ISOM([[1/2, - 3/2][ 3/2, 1/2]])
Result:
{ /3, 1 },
See also: MKISOM

ISPRIME?

Type: Function
Description: Tests if a number is prime. For numbers of the order of 10
than 341550071728321), tests if the number is a pseudoprime; this has a chance of less than 1
in 10 of wrongly identifying a number as a prime.
12
P
Access:
ARITH
Input: An object that evaluates to an integer or a whole real number.
Output: 1 (True) if the number is prime, 0 (False) if it is not.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
See also: NEXTPRIME, PREVPRIME

JORDAN

Type: Command
Description: Diagonalization, or Jordan cycle decomposition, of a matrix. Computes the eigenvalues,
eigenvectors, minimum polynomial, and characteristic polynomial of a matrix.
Matrices, !Ø L
Access:
Input: An n × n matrix.
Output: Level 4/Item 1: The minimum polynomial.
Level 3/Item 2: The characteristic polynomial.
Level 2/Item 3: A list of characteristic spaces tagged by the corresponding eigenvalue (either a
vector or a list of Jordan chains, each of them ending with an "Eigen:"-tagged eigenvector).
Level 1/Item 4: An array of the eigenvalues, with multiplicities
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: Perform the following diagonalization:
Command:
JORDAN([1,1][1,1])
Result:
{X^2-2*X,
X^2-2*X,
4-44 Computer Algebra Commands
1}, meaning the matrix represents a symmetry in the line
meaning the matrix represents a rotation of
or Arithmetic, !Þ
EIGENVECTORS
1 – 3
-- - --------- -
2 2
3 1
------ - -- -
2 2
radians, and this is a direct isometry.
/3
or greater (to be exact, greater
14
L
INTEGER
, and this is an indirect
y = –x