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# allaliases2()

Usage:
 ```allaliases2(basis), REAL matrix basis of alias generators ```

Keywords: aliasing, design, factorial
```allaliases2(basis) finds the full set of aliases in a 2^(k-p) fractional
factorial and returns a CHARACTER vector of these aliases as its value.
k must be no larger than 25, and factors are labeled A, B, ..., H, J,
..., Z (skipping I).

The p x k matrix basis contains the generators for the aliasing, one row
for each generator and one column for each factor in the design.  The
elements in basis are 0, -1, or 1.  A nonzero entry indicates that a
factor is present in the generator for that row. The sign of a generator
is the product of the signs of the nonzero elements of the generator.
For example, 1 0 1 0 0 -1 means -ACF is a generator (alias of I).

Examples:
Cmd> print(b,format:"2.0f")  # Matrix b is 2x5, so 2^(5-2) design
b:
(1,1)  1  1  1  0  0     [ABC is a generator]
(2,1)  0  0  1  1 -1     [-CDE is a generator]

Cmd> allaliases2(b)  # alias table
(1) "I = ABC = -CDE = -ABDE"
(2) "A = BC = -ACDE = -BDE"
(3) "B = AC = -BCDE = -ADE"
(4) "AB = C = -ABCDE = -DE"
(5) "D = ABCD = -CE = -ABE"
(6) "AD = BCD = -ACE = -BE"
(7) "BD = ACD = -BCE = -AE"
(8) "ABD = CD = -ABCE = -E"
```

Gary Oehlert 2003-01-15