

 COLRED TEST DRIVER RESULTS, EXAMPLE( 1)

 The input polynomial matrix:

 P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s**(dp-1)  + P(dp) * s**dp

 with degree DP = 1 and size MP = 1, NP = 1.

 The tolerance is: 0.000D+00


 P( 0)
            1
  1        1.0000000

 P( 1)
            1
  1        2.0000000
 
 The unimodular polynomial matrix U(s):

 U( 0)
            1
  1        1.0000000
 
 The column reduced polynomial matrix R(s):

 R( 0)
            1
  1        1.0000000

 R( 1)
            1
  1        2.0000000
 
 ZERCOL(j), j = 1, NP: F
 PU - R is the ZERO polynomial matrix.


 COLRED TEST DRIVER RESULTS, EXAMPLE( 2)

 The input polynomial matrix:

 P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s**(dp-1)  + P(dp) * s**dp

 with degree DP = 3 and size MP = 2, NP = 2.

 The tolerance is: 0.100D-09


 P( 0)
            1              2
  1        1.0000000      1.0000000
  2       -2.0000000     -1.0000000

 P( 1)
            1              2
  1        2.0000000      0.0100000
  2       -3.0000000      0.0000000

 P( 2)
            1              2
  1        1.0000000      0.0000000
  2        2.0000000      0.0000000

 P( 3)
            1              2
  1        1.0000000      0.0000000
  2        0.0000000      0.0000000
 
 The unimodular polynomial matrix U(s):

 U( 0)
            1              2
  1        0.0000000      1.4066253
  2      151.9532407      0.0000000

 U( 1)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000   -475.9339805

 U( 2)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000   -140.6625313
 
 The column reduced polynomial matrix R(s):

 R( 0)
            1              2
  1      151.9532407      1.4066253
  2     -151.9532407     -2.8132506

 R( 1)
            1              2
  1        1.5195324   -473.1207299
  2        0.0000000    471.7141046

 R( 2)
            1              2
  1        0.0000000   -144.0152458
  2        0.0000000    143.4757819
 
 ZERCOL(j), j = 1, NP: F F
 The residual matrix P(s) * U(s) - R(s):

 (PU - R)( 0)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000

 (PU - R)( 1)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000

 (PU - R)( 2)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000

 (PU - R)( 3)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000

 (PU - R)( 4)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000

 (PU - R)( 5)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000
 


 COLRED TEST DRIVER RESULTS, EXAMPLE( 3)

 The input polynomial matrix:

 P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s**(dp-1)  + P(dp) * s**dp

 with degree DP = 3 and size MP = 2, NP = 2.

 The tolerance is: 0.100D-11


 P( 0)
            1              2
  1        1.0000000      1.0000000
  2       -2.0000000     -1.0000000

 P( 1)
            1              2
  1        2.0000000      0.0100000
  2       -3.0000000      0.0000000

 P( 2)
            1              2
  1        1.0000000      0.0000000
  2        2.0000000      0.0000000

 P( 3)
            1              2
  1        1.0000000      0.0000000
  2        0.0000000      0.0000000
 
 The unimodular polynomial matrix U(s):

 U( 0)
            1              2
  1        0.0000000      1.4066253
  2      151.9532407      0.0000000

 U( 1)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000   -475.9339805

 U( 2)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000   -140.6625313
 
 The column reduced polynomial matrix R(s):

 R( 0)
            1              2
  1      151.9532407      1.4066253
  2     -151.9532407     -2.8132506

 R( 1)
            1              2
  1        1.5195324   -473.1207299
  2        0.0000000    471.7141046

 R( 2)
            1              2
  1        0.0000000   -144.0152458
  2        0.0000000    143.4757819
 
 ZERCOL(j), j = 1, NP: F F
 The residual matrix P(s) * U(s) - R(s):

 (PU - R)( 0)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000

 (PU - R)( 1)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000

 (PU - R)( 2)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000

 (PU - R)( 3)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000

 (PU - R)( 4)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000

 (PU - R)( 5)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000
 


 COLRED TEST DRIVER RESULTS, EXAMPLE( 4)

 The input polynomial matrix:

 P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s**(dp-1)  + P(dp) * s**dp

 with degree DP = 6 and size MP = 3, NP = 3.

 The tolerance is: 0.000D+00


 P( 0)
            1              2              3
  1        0.0000000      0.0000000      1.0000000
  2        0.0000000      1.0000000      0.0000000
  3        1.0000000      0.0000000      1.0000000

 P( 1)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 P( 2)
            1              2              3
  1        0.0000000      1.0000000      0.0000000
  2        1.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 P( 3)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 P( 4)
            1              2              3
  1        1.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      1.0000000
  3        0.0000000      0.0000000      0.0000000

 P( 5)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 P( 6)
            1              2              3
  1        0.0000000      0.0000000      1.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000
 
 The unimodular polynomial matrix U(s):

 U( 0)
            1              2              3
  1        1.0000000     -1.0000000      0.0000000
  2        0.0000000      0.0000000     -1.7029386
  3        0.0000000      1.0000000      0.0000000

 U( 1)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 U( 2)
            1              2              3
  1        0.0000000      0.0000000     -1.7029386
  2       -1.0000000      1.0000000      0.0000000
  3        0.0000000      0.0000000      1.7029386

 U( 3)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 U( 4)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000     -1.0000000      1.7029386
  3        0.0000000      0.0000000      0.0000000

 U( 5)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 U( 6)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000     -1.7029386
  3        0.0000000      0.0000000      0.0000000
 
 The column reduced polynomial matrix R(s):

 R( 0)
            1              2              3
  1        0.0000000      1.0000000      0.0000000
  2        0.0000000      0.0000000     -1.7029386
  3        1.0000000      0.0000000      0.0000000
 
 ZERCOL(j), j = 1, NP: F F F
 The residual matrix P(s) * U(s) - R(s):

 (PU - R)( 0)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)( 1)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)( 2)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)( 3)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)( 4)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)( 5)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)( 6)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)( 7)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)( 8)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)( 9)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)(10)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)(11)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000

 (PU - R)(12)
            1              2              3
  1        0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000
 


 COLRED TEST DRIVER RESULTS, EXAMPLE( 5)

 The input polynomial matrix:

 P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s**(dp-1)  + P(dp) * s**dp

 with degree DP = 2 and size MP = 4, NP = 9.

 The tolerance is: 0.000D+00


 P( 0)
            1              2              3              4              5
  1        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
            6              7              8              9
  1       -1.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000     -1.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000     -1.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000     -1.0000000

 P( 1)
            1              2              3              4              5
  1        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      1.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000      1.0000000
            6              7              8              9
  1        1.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      1.0000000      1.0000000      0.0000000
  3        0.0000000      0.0000000      1.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      1.0000000

 P( 2)
            1              2              3              4              5
  1        1.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
            6              7              8              9
  1        0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000
 
 The unimodular polynomial matrix U(s):

 U( 0)
            1              2              3              4              5
  1        0.0000000      0.0000000      0.0000000      1.4142136      0.0000000
  2       -1.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000     -1.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000      1.7320508
  5        0.0000000      0.0000000      1.0000000      0.0000000      0.0000000
  6        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  7        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  8        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  9        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
            6              7              8              9
  1        1.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000     -1.0000000      2.0000000      0.0000000
  5        0.0000000      0.0000000      0.0000000      1.0000000
  6       -1.0000000      0.0000000      0.0000000      0.0000000
  7        0.0000000      1.0000000      0.0000000      0.0000000
  8        0.0000000      0.0000000     -1.0000000      0.0000000
  9        0.0000000      0.0000000      0.0000000     -1.0000000

 U( 1)
            1              2              3              4              5
  1        0.0000000      0.0000000      0.0000000     -1.4142136      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000     -3.4641016
  5        0.0000000      0.0000000     -1.0000000      0.0000000      0.0000000
  6        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  7        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  8        0.0000000      0.0000000      0.0000000      0.0000000      1.7320508
  9        0.0000000      0.0000000      1.0000000      0.0000000      0.0000000
            6              7              8              9
  1        0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      1.0000000     -1.0000000      0.0000000
  5        0.0000000      0.0000000      0.0000000      0.0000000
  6       -1.0000000      0.0000000      0.0000000      0.0000000
  7        0.0000000      1.0000000     -1.0000000      0.0000000
  8        0.0000000     -1.0000000      1.0000000      0.0000000
  9        0.0000000      0.0000000      0.0000000      0.0000000

 U( 2)
            1              2              3              4              5
  1        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000      1.7320508
  5        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  6        0.0000000      0.0000000      0.0000000      1.4142136      0.0000000
  7        0.0000000      0.0000000      0.0000000      0.0000000      1.7320508
  8        0.0000000      0.0000000      0.0000000      0.0000000     -1.7320508
  9        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
            6              7              8              9
  1        0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000
  5        0.0000000      0.0000000      0.0000000      0.0000000
  6        0.0000000      0.0000000      0.0000000      0.0000000
  7        0.0000000      0.0000000      0.0000000      0.0000000
  8        0.0000000      0.0000000      0.0000000      0.0000000
  9        0.0000000      0.0000000      0.0000000      0.0000000
 
 The column reduced polynomial matrix R(s):

 R( 0)
            1              2              3              4              5
  1        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
            6              7              8              9
  1        1.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000     -1.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      1.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      1.0000000
 
 ZERCOL(j), j = 1, NP: T T T T T F F F F
 The residual matrix P(s) * U(s) - R(s):

 (PU - R)( 0)
            1              2              3              4              5
  1        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
            6              7              8              9
  1        0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000

 (PU - R)( 1)
            1              2              3              4              5
  1        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
            6              7              8              9
  1        0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000

 (PU - R)( 2)
            1              2              3              4              5
  1        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
            6              7              8              9
  1        0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000

 (PU - R)( 3)
            1              2              3              4              5
  1        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
            6              7              8              9
  1        0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000
 


 COLRED TEST DRIVER RESULTS, EXAMPLE( 6)

 The input polynomial matrix:

 P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s**(dp-1)  + P(dp) * s**dp

 with degree DP = 1 and size MP = 2, NP = 2.

 The tolerance is: 0.000D+00


 P( 0)
            1              2
  1        1.0000000      1.0000000
  2       -2.0000000     -2.0000000

 P( 1)
            1              2
  1        1.0000000      1.0000000
  2        0.0000000      0.0000000
 
 The unimodular polynomial matrix U(s):

 U( 0)
            1              2
  1        1.0000000     -1.0954451
  2       -1.0000000      0.0000000
 
 The column reduced polynomial matrix R(s):

 R( 0)
            1              2
  1        0.0000000     -1.0954451
  2        0.0000000      2.1908902

 R( 1)
            1              2
  1        0.0000000     -1.0954451
  2        0.0000000      0.0000000
 
 ZERCOL(j), j = 1, NP: T F
 The residual matrix P(s) * U(s) - R(s):

 (PU - R)( 0)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000

 (PU - R)( 1)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000
 


 COLRED TEST DRIVER RESULTS, EXAMPLE( 7)

 The input polynomial matrix:

 P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s**(dp-1)  + P(dp) * s**dp

 with degree DP = 0 and size MP = 3, NP = 2.

 The tolerance is: 0.000D+00


 P( 0)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000
  3        0.0000000      0.0000000
 
 The unimodular polynomial matrix U(s):

 U( 0)
            1              2
  1        1.0000000      0.0000000
  2        0.0000000      1.0000000
 
 The column reduced polynomial matrix R(s):

 R( 0)
            1              2
  1        0.0000000      0.0000000
  2        0.0000000      0.0000000
  3        0.0000000      0.0000000
 
 ZERCOL(j), j = 1, NP: F F
 PU - R is the ZERO polynomial matrix.


 COLRED TEST DRIVER RESULTS, EXAMPLE( 8)

 The input polynomial matrix:

 P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s**(dp-1)  + P(dp) * s**dp

 with degree DP = 0 and size MP = 1, NP = 2.

 The tolerance is: 0.000D+00


 P( 0)
            1              2
  1        1.5000000      2.7000000
 
 The unimodular polynomial matrix U(s):

 U( 0)
            1              2
  1        1.8000000     -0.6666667
  2       -1.0000000      0.0000000
 
 The column reduced polynomial matrix R(s):

 R( 0)
            1              2
  1        0.0000000     -1.0000000
 
 ZERCOL(j), j = 1, NP: T F
 PU - R is the ZERO polynomial matrix.


 COLRED TEST DRIVER RESULTS, EXAMPLE( 9)

 The input polynomial matrix:

 P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s**(dp-1)  + P(dp) * s**dp

 with degree DP = 0 and size MP = 1, NP = 3.

 The tolerance is: 0.000D+00


 P( 0)
            1              2              3
  1        1.2000000      1.5600000     -0.3610000
 
 The unimodular polynomial matrix U(s):

 U( 0)
            1              2              3
  1        1.3000000     -0.3008333     -0.8333333
  2       -1.0000000      0.0000000      0.0000000
  3        0.0000000     -1.0000000      0.0000000
 
 The column reduced polynomial matrix R(s):

 R( 0)
            1              2              3
  1        0.0000000      0.0000000     -1.0000000
 
 ZERCOL(j), j = 1, NP: T T F
 PU - R is the ZERO polynomial matrix.


 COLRED TEST DRIVER RESULTS, EXAMPLE(10)

 The input polynomial matrix:

 P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s**(dp-1)  + P(dp) * s**dp

 with degree DP = 0 and size MP = 4, NP = 4.

 The tolerance is: 0.000D+00


 P( 0)
            1              2              3              4
  1        0.0000000      0.0000000      1.0000000      1.0000000
  2        1.0000000      1.0000000      2.0000000      2.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000
  4        1.0000000      1.0000000     -3.0000000     -3.0000000
 
 The unimodular polynomial matrix U(s):

 U( 0)
            1              2              3              4
  1        1.0000000      0.0000000      0.7071068      0.1360828
  2       -1.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      1.0000000      0.0000000      0.2721655
  4        0.0000000     -1.0000000      0.0000000      0.0000000
 
 The column reduced polynomial matrix R(s):

 R( 0)
            1              2              3              4
  1        0.0000000      0.0000000      0.0000000      0.2721655
  2        0.0000000      0.0000000      0.7071068      0.6804138
  3        0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.7071068     -0.6804138
 
 ZERCOL(j), j = 1, NP: T T F F
 The residual matrix P(s) * U(s) - R(s):

 (PU - R)( 0)
            1              2              3              4
  1        0.0000000      0.0000000      0.0000000      0.0000000
  2        0.0000000      0.0000000      0.0000000      0.0000000
  3        0.0000000      0.0000000      0.0000000      0.0000000
  4        0.0000000      0.0000000      0.0000000      0.0000000
 


 COLRED TEST DRIVER RESULTS, EXAMPLE(11)

 The input polynomial matrix:

 P(s) = P(0) + P(1) * s + . . . + P(dp-1) * s**(dp-1)  + P(dp) * s**dp

 with degree DP = 0 and size MP = 0, NP = 0.

 The tolerance is: 0.000D+00

 COLRED has failed: IERR = 1
