Reference Guide

3-122 Full Command and Function Reference
Example 1: Analyze the isometry given by the matrix
0 1–
1– 0
Command: ISOM([[0,-1] [-1,0]])
Result: { [1, 1] – 1}, meaning the matrix represents a symmetry in the line y = –x , and this is an indirect
isometry.
Example 2: Analyze the isometry given by the matrix
1
2
---
3–
2
----------
3
2
-------
1
2
---
Command: ISOM([[1/2, - √ 3/2][ √ 3/2, 1/2]])
Result: { π /3, 1 }, meaning the matrix represents a rotation of π /3 radians, and this is a direct isometry.
See also: MKISOM
ISPRIME?
Type: Function
Description: Tests if a number is prime. For numbers of the order of 10
14
or greater (to be exact, greater than
341550071728321), tests if the number is a pseudoprime; this has a chance of less than 1 in 10
12
of wrongly identifying a number as a prime.
Access: P ARITH or Arithmetic, !Þ INTEGER L
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
I→R
Type: Function
Description: Converts an integer into a real number.
Access: …Ú REWRITE
Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). The flags
affect the output only if the input is not an integer.
Input: Level 1/Argument 1: An integer or real number.
Output: Level 1/Item 1: The integer converted to a real number.
See also: →NUM, R→I, XNUM
JORDAN
Type: Command
Description: Diagonalization, or Jordan cycle decomposition, of a matrix. Computes the eigenvalues,
eigenvectors, minimum polynomial, and characteristic polynomial of a matrix.
Access: Matrices, !Ø L EIGENVECTORS
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