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aliases3(basis[,effect:vec][,length:j]), REAL matrix basis of alias
  generators, REAL vector vec of 0's, 1's and 2's, positive integer j

Keywords: aliasing, design, factorial
aliases3(basis) finds all aliases of I in a 3^(k-p) factional factorial
design and returns a CHARACTER vector of these aliases as its values.  k
must be no larger than 25 and factors are labeled A, B, ..., H, J, ...,
Z (skipping I).

basis is p x k REAL matrix of 0s, 1s and 2s which contains the
generators for the aliasing, one row for each generator and one column
for each factor in the design.  For example 1 0 2 0 0 1 means AC^2F is a
generator (alias of I).

If basis is a (column) vector, it is changed to a row vector (1 by k
matrix) before proceding.

aliases3(basis,effect:vec) returns the aliases of vec, a vector of k 0s,
1s and 2s representing an effect.  When vec:rep(0,k), the result is the
same as aliases3(basis).

aliases3(basis [,effect:vec] , length:j) returns only aliases of length

  Cmd> print(c,format:"2.0f") # Matrix c is 2x4, so 3^(4-2)
  (1,1)  1  2  0  2        [A B^2 D^2 is a generator]
  (2,1)  0  1  2  2        [B C^2 D^2 is a generator]

  Cmd> aliases3(c)  # all aliases of I
  (1) "I"
  (2) "A^1 B^2 D^2 "
  (3) "A^1 B^2 D^2 "
  (4) "B^1 C^2 D^2 "
  (5) "A^1 C^2 D^1 "
  (6) "A^1 B^1 C^1 "
  (7) "B^1 C^2 D^2 "
  (8) "A^1 B^1 C^1 "
  (9) "A^1 C^2 D^1 "

  Cmd> aliases3(c,effect:vector(1,1,0,0)) # aliases of A^1B^1
  (1) "A^1 B^1 "
  (2) "A^1 D^1 "
  (3) "B^1 D^2 "
  (4) "A^1 B^2 C^2 D^2 "
  (5) "A^1 B^2 C^1 D^2 "
  (6) "C^1 "
  (7) "A^1 C^1 D^1 "
  (8) "A^1 B^1 C^2 "
  (9) "B^1 C^1 D^2 "

See also aliases2(), confound3()

Gary Oehlert 2003-01-15