randomIntegerSymmetric -- constructs a random integer symmetric matrix

Synopsis

Usage:

randomIntegerSymmetric n

randomIntegerSymmetric(n, R)
Inputs:
- n, an integer,
- R, a ring, or RR or CC (of type InexactFieldFamily)
Outputs:
- a matrix, a random $n\times n$ symmetric matrix with integer entries, over the ring $R$

Description

This method returns a random symmetric matrix of a given size $n$ with integer entries. This can in turn be specialized to any ring, which may be provided as an argument.

i1 : randomIntegerSymmetric 5

o1 = | 16 4  8  10 14 |
     | 4  6  14 14 17 |
     | 8  14 16 8  5  |
     | 10 14 8  12 15 |
     | 14 17 5  15 12 |

              5       5
o1 : Matrix ZZ  <-- ZZ

i2 : randomIntegerSymmetric 20

o2 = | 18 9  3  10 9  5  13 14 8  10 10 10 11 7  11 16 8  8  6  13 |
     | 9  2  16 14 4  3  12 6  11 6  10 9  6  10 17 7  11 11 6  14 |
     | 3  16 4  6  7  15 5  10 14 13 5  9  2  4  13 10 8  6  10 5  |
     | 10 14 6  18 16 11 7  13 15 11 10 16 18 1  13 10 5  10 14 10 |
     | 9  4  7  16 6  8  15 5  9  7  14 13 10 13 12 6  16 12 9  9  |
     | 5  3  15 11 8  16 3  5  15 10 8  13 10 7  9  1  16 10 9  7  |
     | 13 12 5  7  15 3  4  13 9  11 18 10 4  4  8  15 9  8  10 14 |
     | 14 6  10 13 5  5  13 4  16 14 4  14 15 7  4  17 9  7  8  5  |
     | 8  11 14 15 9  15 9  16 0  8  10 6  5  11 3  12 2  14 15 7  |
     | 10 6  13 11 7  10 11 14 8  16 12 6  6  6  9  10 11 9  9  12 |
     | 10 10 5  10 14 8  18 4  10 12 18 9  6  8  5  9  3  9  12 11 |
     | 10 9  9  16 13 13 10 14 6  6  9  8  14 6  12 6  6  4  8  11 |
     | 11 6  2  18 10 10 4  15 5  6  6  14 16 12 2  13 5  7  4  5  |
     | 7  10 4  1  13 7  4  7  11 6  8  6  12 4  9  10 10 12 12 4  |
     | 11 17 13 13 12 9  8  4  3  9  5  12 2  9  4  4  3  11 8  11 |
     | 16 7  10 10 6  1  15 17 12 10 9  6  13 10 4  4  3  15 13 7  |
     | 8  11 8  5  16 16 9  9  2  11 3  6  5  10 3  3  0  10 14 10 |
     | 8  11 6  10 12 10 8  7  14 9  9  4  7  12 11 15 10 18 7  14 |
     | 6  6  10 14 9  9  10 8  15 9  12 8  4  12 8  13 14 7  10 11 |
     | 13 14 5  10 9  7  14 5  7  12 11 11 5  4  11 7  10 14 11 4  |

              20       20
o2 : Matrix ZZ   <-- ZZ

i3 : R = RR[x,y]

o3 = R

o3 : PolynomialRing

i4 : randomIntegerSymmetric(3, R)

o4 = | 14 13 6  |
     | 13 0  13 |
     | 6  13 2  |

             3      3
o4 : Matrix R  <-- R

Caveat

The entries of the constructed matrix will be integers between 0 and 18, inclusive.

Ways to use randomIntegerSymmetric :

randomIntegerSymmetric(ZZ)
randomIntegerSymmetric(ZZ,Ring)

For the programmer