function [ x, w ] = ncc_set ( order )

%% NCC_SET sets abscissas and weights for closed Newton-Cotes quadrature.
%
%  Discussion:
%
%    The closed Newton-Cotes rules use equally spaced abscissas, and
%    hence may be used with tabulated function data.
%
%    The rules are called "closed" because they include the endpoints.
%    As a favor, we include an order 1 rule, the midpoint rule, even
%    though this does not satisfy the requirement that the endpoints
%    be included%
%
%    The higher order rules involve negative weights.  These can produce
%    loss of accuracy due to the subtraction of large, nearly equal quantities.
%
%    ORDER = 1 is the midpoint rule (and is not really an NCC rule%)
%    ORDER = 2 is the trapezoidal rule.
%    ORDER = 3 is Simpson's rule.
%    ORDER = 4 is Simpson's 3/8 rule.
%    ORDER = 5 is Bode's rule.
%
%    The Kopal reference for ORDER = 12 lists
%      W(6) = 15494566.0; / 43545600.0D+00
%    but this results in a set of coeffients that don't add up to 2.
%    The correct value is
%      W(6) = 15493566.0; / 43545600.0.
%
%    The integration interval is [ -1, 1 ].
%
%    The weight function is w(x) = 1.0.
%
%    The integral to approximate:
%
%      Integral ( -1 <= X <= 1 ) F(X) dX
%
%    The quadrature rule:
%
%      Sum ( 1 <= I <= ORDER ) W(I) * F ( X(I) )
%
%    In Mathematica, the closed Newton-Cotes weights
%    can be computed by:
%
%      << NumericalMath`NewtonCotes`
%      NewtonCotesWeights [ order, -1, 1, QuadratureType -> Closed ]
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    08 May 2007
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Milton Abramowitz, Irene Stegun,
%    Handbook of Mathematical Functions,
%    National Bureau of Standards, 1964,
%    ISBN: 0-486-61272-4,
%    LC: QA47.A34.
%
%    Johnson,
%    Quarterly Journal of Mathematics,
%    Volume 46, Number 52, 1915.
%
%    Zdenek Kopal,
%    Numerical Analysis,
%    John Wiley, 1955,
%    LC: QA297.K6.
%
%    Stephen Wolfram,
%    The Mathematica Book,
%    Fourth Edition,
%    Cambridge University Press, 1999,
%    ISBN: 0-521-64314-7,
%    LC: QA76.95.W65.
%
%    Daniel Zwillinger, editor,
%    CRC Standard Mathematical Tables and Formulae,
%    30th Edition,
%    CRC Press, 1996,
%    ISBN: 0-8493-2479-3,
%    LC: QA47.M315.
%
%  Parameters:
%
%    Input, integer ORDER, the order of the rule.
%    ORDER must be between 1 and 21.
%
%    Output, real X(ORDER), the abscissas of the rule.
%    The abscissas are uniformly spaced in the interval, and, except
%    for the rule of order 1, include -1 and 1.
%
%    Output, real W(ORDER), the weights of the rule.
%    The weights are symmetric, rational, and should sum to 2.0.
%    Some weights may be negative.
%
  if ( order == 1 )
%
%  2
%
    x(1) = 0.00000000000000000000;

    w(1) = 2.00000000000000000000;

  elseif ( order == 2 )
%
%  1
%  1
%
    x(1) = -1.00000000000000000000;
    x(2) =  1.00000000000000000000;

    w(1) = 1.00000000000000000000;
    w(2) = 1.00000000000000000000;

  elseif ( order == 3 )
%
%  1 / 3
%  4 / 3
%  1 / 3
%
    x(1) = -1.00000000000000000000;
    x(2) =  0.00000000000000000000;
    x(3) =  1.00000000000000000000;

    w(1) = 0.33333333333333333333;
    w(2) = 1.33333333333333333333;
    w(3) = 0.33333333333333333333;

  elseif ( order == 4 )
%
%  1 / 4
%  3 / 4
%  3 / 4
%  1 / 4
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.33333333333333333333;
    x(3) =  0.33333333333333333333;
    x(4) =  1.00000000000000000000;

    w(1) = 0.25000000000000000000;
    w(2) = 0.75000000000000000000;
    w(3) = 0.75000000000000000000;
    w(4) = 0.25000000000000000000;

  elseif ( order == 5 )
%
%   7 / 45
%  32 / 45
%  12 / 45
%  32 / 45
%   7 / 45
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.50000000000000000000;
    x(3) =  0.00000000000000000000;
    x(4) =  0.50000000000000000000;
    x(5) =  1.00000000000000000000;

    w(1) = 0.15555555555555555556;
    w(2) = 0.71111111111111111111;
    w(3) = 0.26666666666666666667;
    w(4) = 0.71111111111111111111;
    w(5) = 0.15555555555555555556;

  elseif ( order == 6 )
%
%  19 / 144
%  75 / 144
%  50 / 144
%  50 / 144
%  75 / 144
%  19 / 144
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.60000000000000000000;
    x(3) = -0.20000000000000000000;
    x(4) =  0.20000000000000000000;
    x(5) =  0.60000000000000000000;
    x(6) =  1.00000000000000000000;

    w(1) = 0.13194444444444444444;
    w(2) = 0.52083333333333333333;
    w(3) = 0.34722222222222222222;
    w(4) = 0.34722222222222222222;
    w(5) = 0.52083333333333333333;
    w(6) = 0.13194444444444444444;

  elseif ( order == 7 )
%
%   41 / 420
%  216 / 420
%   27 / 420
%  272 / 420
%   27 / 420
%  216 / 420
%   41 / 420
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.66666666666666666667;
    x(3) = -0.33333333333333333333;
    x(4) =  0.00000000000000000000;
    x(5) =  0.33333333333333333333;
    x(6) =  0.66666666666666666667;
    x(7) =  1.00000000000000000000;

    w(1) = 0.097619047619047619048;
    w(2) = 0.51428571428571428571;
    w(3) = 0.064285714285714285714;
    w(4) = 0.64761904761904761905;
    w(5) = 0.064285714285714285714;
    w(6) = 0.51428571428571428571;
    w(7) = 0.097619047619047619048;

  elseif ( order == 8 )
%
%   751 / 8640
%  3577 / 8640
%  1323 / 8640
%  2989 / 8640
%  2989 / 8640
%  1323 / 8640
%  3577 / 8640
%   751 / 8640
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.71428571428571428571;
    x(3) = -0.42857142857142857143;
    x(4) = -0.14285714285714285714;
    x(5) =  0.14285714285714285714;
    x(6) =  0.42857142857142857143;
    x(7) =  0.71428571428571428571;
    x(8) =  1.00000000000000000000;

    w(1) = 0.086921296296296296296;
    w(2) = 0.41400462962962962963;
    w(3) = 0.15312500000000000000;
    w(4) = 0.34594907407407407407;
    w(5) = 0.34594907407407407407;
    w(6) = 0.15312500000000000000;
    w(7) = 0.41400462962962962963;
    w(8) = 0.086921296296296296296;

  elseif ( order == 9 )
%
%    989 / 14175
%   5888 / 14175
%   -928 / 14175
%  10496 / 14175
%  -4540 / 14175
%  10496 / 14175
%   -928 / 14175
%   5888 / 14175
%    989 / 14175
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.75000000000000000000;
    x(3) = -0.50000000000000000000;
    x(4) = -0.25000000000000000000;
    x(5) =  0.00000000000000000000;
    x(6) =  0.25000000000000000000;
    x(7) =  0.50000000000000000000;
    x(8) =  0.75000000000000000000;
    x(9) =  1.00000000000000000000;

    w(1) =  0.069770723104056437390;
    w(2) =  0.41537918871252204586;
    w(3) = -0.065467372134038800705;
    w(4) =  0.74045855379188712522;
    w(5) = -0.32028218694885361552;
    w(6) =  0.74045855379188712522;
    w(7) = -0.065467372134038800705;
    w(8) =  0.41537918871252204586;
    w(9) =  0.069770723104056437390;

  elseif ( order == 10 )
%
%   2857 / 44800
%  15741 / 44800
%   1080 / 44800
%  19344 / 44800
%   5778 / 44800
%   5778 / 44800
%  19344 / 44800
%   1080 / 44800
%  15741 / 44800
%   2857 / 44800
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.77777777777777777778;
    x(3) = -0.55555555555555555556;
    x(4) = -0.33333333333333333333;
    x(5) = -0.11111111111111111111;
    x(6) =  0.11111111111111111111;
    x(7) =  0.33333333333333333333;
    x(8) =  0.55555555555555555556;
    x(9) =  0.77777777777777777778;
    x(10) = 1.00000000000000000000;

    w(1) =  0.063772321428571428571;
    w(2) =  0.35136160714285714286;
    w(3) =  0.024107142857142857143;
    w(4) =  0.43178571428571428571;
    w(5) =  0.12897321428571428571;
    w(6) =  0.12897321428571428571;
    w(7) =  0.43178571428571428571;
    w(8) =  0.024107142857142857143;
    w(9) =  0.35136160714285714286;
    w(10) = 0.063772321428571428571;

  elseif ( order == 11 )
%
%     16067 / 299376
%    106300 / 299376
%   - 48525 / 299376
%    272400 / 299376
%  - 260550 / 299376
%    427368 / 299376
%  - 260550 / 299376
%    272400 / 299376
%   - 48525 / 299376
%    106300 / 299376
%     16067 / 299376
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.80000000000000000000;
    x(3) = -0.60000000000000000000;
    x(4) = -0.40000000000000000000;
    x(5) = -0.20000000000000000000;
    x(6) =  0.00000000000000000000;
    x(7) =  0.20000000000000000000;
    x(8) =  0.40000000000000000000;
    x(9) =  0.60000000000000000000;
    x(10) = 0.80000000000000000000;
    x(11) = 1.00000000000000000000;

    w(1) =  0.053668296723852279408;
    w(2) =  0.35507188284966062744;
    w(3) = -0.16208714125380792047;
    w(4) =  0.90989257655924322591;
    w(5) = -0.87031024531024531025;
    w(6) =  1.4275292608625941959;
    w(7) = -0.87031024531024531025;
    w(8) =  0.90989257655924322591;
    w(9) = -0.16208714125380792047;
    w(10) = 0.35507188284966062744;
    w(11) = 0.053668296723852279408;

  elseif ( order == 12 )
%
%     2171465 / 43545600
%    13486539 / 43545600
%   - 3237113 / 43545600
%    25226685 / 43545600
%   - 9595542 / 43545600
%    15493566 / 43545600
%    15493566 / 43545600
%   - 9595542 / 43545600
%    25226685 / 43545600
%   - 3237113 / 43545600
%    13486539 / 43545600
%     2171465 / 43545600
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.81818181818181818182;
    x(3) = -0.63636363636363636364;
    x(4) = -0.45454545454545454545;
    x(5) = -0.27272727272727272727;
    x(6) = -0.090909090909090909091;
    x(7) =  0.090909090909090909091;
    x(8) =  0.27272727272727272727;
    x(9) =  0.45454545454545454545;
    x(10) = 0.63636363636363636364;
    x(11) = 0.81818181818181818182;
    x(12) = 1.00000000000000000000;

    w(1) =   0.049866461823927101705;
    w(2) =   0.30971071704144620811;
    w(3) =  -0.074338463587595532040;
    w(4) =   0.57931650958994708995;
    w(5) =  -0.22035617835097001764;
    w(6) =   0.35580095348324514991;
    w(7) =   0.35580095348324514991;
    w(8) =  -0.22035617835097001764;
    w(9) =   0.57931650958994708995;
    w(10) = -0.074338463587595532040;
    w(11) =  0.30971071704144620811;
    w(12) =  0.049866461823927101705;

  elseif ( order == 13 )
%
%      1364651 / 31531500
%      9903168 / 31531500
%    - 7587864 / 31531500
%     35725120 / 31531500
%   - 51491295 / 31531500
%     87516288 / 31531500
%   - 87797136 / 31531500
%     87516288 / 31531500
%   - 51491295 / 31531500
%     35725120 / 31531500
%    - 7587864 / 31531500
%      9903168 / 31531500
%      1364651 / 31531500
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.83333333333333333333;
    x(3) = -0.66666666666666666667;
    x(4) = -0.50000000000000000000;
    x(5) = -0.33333333333333333333;
    x(6) = -0.16666666666666666667;
    x(7) =  0.00000000000000000000;
    x(8) =  0.16666666666666666667;
    x(9) =  0.33333333333333333333;
    x(10) = 0.50000000000000000000;
    x(11) = 0.66666666666666666667;
    x(12) = 0.83333333333333333333;
    x(13) = 1.00000000000000000000;

    w(1) =   0.043278974993260707546;
    w(2) =   0.31407221350078492936;
    w(3) =  -0.24064392750107035821;
    w(4) =   1.1329977958549387121;
    w(5) =  -1.6330112744398458684;
    w(6) =   2.7755193378050520908;
    w(7) =  -2.7844262404262404262;
    w(8) =   2.7755193378050520908;
    w(9) =  -1.6330112744398458684;
    w(10) =  1.1329977958549387121;
    w(11) = -0.24064392750107035821;
    w(12) =  0.31407221350078492936;
    w(13) =  0.043278974993260707546;

  elseif ( order == 14 )
%
%      6137698213 / 150885504000
%     42194238652 / 150885504000
%   - 23361540993 / 150885504000
%    116778274403 / 150885504000
%  - 113219777650 / 150885504000
%    154424590209 / 150885504000
%   - 32067978834 / 150885504000
%   - 32067978834 / 150885504000
%    154424590209 / 150885504000
%  - 113219777650 / 150885504000
%    116778274403 / 150885504000
%   - 23361540993 / 150885504000
%     42194238652 / 150885504000
%      6137698213 / 150885504000
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.84615384615384615385;
    x(3) = -0.69230769230769230769;
    x(4) = -0.53846153846153846154;
    x(5) = -0.38461538461538461538;
    x(6) = -0.23076923076923076923;
    x(7) = -0.076923076923076923077;
    x(8) =  0.076923076923076923077;
    x(9) =  0.23076923076923076923;
    x(10) = 0.38461538461538461538;
    x(11) = 0.53846153846153846154;
    x(12) = 0.69230769230769230769;
    x(13) = 0.84615384615384615385;
    x(14) = 1.00000000000000000000;

    w(1) =   0.040669438210247155353;
    w(2) =   0.27975217053157074652;
    w(3) =  -0.15542374057682837445;
    w(4) =   0.77579230848776566369;
    w(5) =  -0.75384763266423526013;
    w(6) =   1.0273523591123107492;
    w(7) =  -0.21429490310083068020;
    w(8) =  -0.21429490310083068020;
    w(9) =   1.0273523591123107492;
    w(10) = -0.75384763266423526013;
    w(11) =  0.77579230848776566369;
    w(12) = -0.15542374057682837445;
    w(13) =  0.27975217053157074652;
    w(14) =  0.040669438210247155353;

  elseif ( order == 15 )
%
%       90241897 / 2501928000
%      710986864 / 2501928000
%    - 770720657 / 2501928000
%     3501442784 / 2501928000
%   - 6625093363 / 2501928000
%    12630121616 / 2501928000
%  - 16802270373 / 2501928000
%    19534438464 / 2501928000
%  - 16802270373 / 2501928000
%    12630121616 / 2501928000
%   - 6625093363 / 2501928000
%     3501442784 / 2501928000
%    - 770720657 / 2501928000
%      710986864 / 2501928000
%       90241897 / 2501928000
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.85714285714285714286;
    x(3) = -0.71428571428571428571;
    x(4) = -0.57142857142857142857;
    x(5) = -0.42857142857142857143;
    x(6) = -0.28571428571428571429;
    x(7) = -0.14285714285714285714;
    x(8) =  0.00000000000000000000;
    x(9) =  0.14285714285714285714;
    x(10) = 0.28571428571428571429;
    x(11) = 0.42857142857142857143;
    x(12) = 0.57142857142857142857;
    x(13) = 0.71428571428571428571;
    x(14) = 0.85714285714285714286;
    x(15) = 1.00000000000000000000;

    w(1) =   0.036068942431596752584;
    w(2) =   0.28417558938546592868;
    w(3) =  -0.30805069410470645039;
    w(4) =   1.3994978208805369299;
    w(5) =  -2.6479952112930507992;
    w(6) =   5.0481555088715582543;
    w(7) =  -6.7157289790113864188;
    w(8) =   7.8077540456799716059;
    w(9) =  -6.7157289790113864188;
    w(10) =  5.0481555088715582543;
    w(11) = -2.6479952112930507992;
    w(12) =  1.3994978208805369299;
    w(13) = -0.30805069410470645039;
    w(14) =  0.28417558938546592868;
    w(15) =  0.036068942431596752584;

  elseif ( order == 16 )
%
%     105930069 / 3099672576
%     796661595 / 3099672576
%   - 698808195 / 3099672576
%    3143332755 / 3099672576
%  - 4688522055 / 3099672576
%    7385654007 / 3099672576
%  - 6000998415 / 3099672576
%    3056422815 / 3099672576
%    3056422815 / 3099672576
%  - 6000998415 / 3099672576
%    7385654007 / 3099672576
%  - 4688522055 / 3099672576
%    3143332755 / 3099672576
%   - 698808195 / 3099672576
%     796661595 / 3099672576
%     105930069 / 3099672576
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.86666666666666666667;
    x(3) = -0.73333333333333333333;
    x(4) = -0.60000000000000000000;
    x(5) = -0.46666666666666666667;
    x(6) = -0.33333333333333333333;
    x(7) = -0.20000000000000000000;
    x(8) = -0.066666666666666666667;
    x(9) =  0.066666666666666666667;
    x(10) = 0.20000000000000000000;
    x(11) = 0.33333333333333333333;
    x(12) = 0.46666666666666666667;
    x(13) = 0.60000000000000000000;
    x(14) = 0.73333333333333333333;
    x(15) = 0.86666666666666666667;
    x(16) = 1.00000000000000000000;

    w(1) =   0.034174599543251887002;
    w(2) =   0.25701475735481036820;
    w(3) =  -0.22544581011901045383;
    w(4) =   1.0140854164204471124;
    w(5) =  -1.5125862296882804695;
    w(6) =   2.3827206990135980091;
    w(7) =  -1.9360104229924960952;
    w(8) =   0.98604699046767964179;
    w(9) =   0.98604699046767964179;
    w(10) = -1.9360104229924960952;
    w(11) =  2.3827206990135980091;
    w(12) = -1.5125862296882804695;
    w(13) =  1.0140854164204471124;
    w(14) = -0.22544581011901045383;
    w(15) =  0.25701475735481036820;
    w(16) =  0.034174599543251887002;

  elseif ( order == 17 )
%
%       15043611773 / 488462349375
%      127626606592 / 488462349375
%    - 179731134720 / 488462349375
%      832211855360 / 488462349375
%   - 1929498607520 / 488462349375
%     4177588893696 / 488462349375
%   - 6806534407936 / 488462349375
%     9368875018240 / 488462349375
%  - 10234238972220 / 488462349375
%     9368875018240 / 488462349375
%   - 6806534407936 / 488462349375
%     4177588893696 / 488462349375
%   - 1929498607520 / 488462349375
%      832211855360 / 488462349375
%    - 179731134720 / 488462349375
%      127626606592 / 488462349375
%       15043611773 / 488462349375
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.87500000000000000000;
    x(3) = -0.75000000000000000000;
    x(4) = -0.62500000000000000000;
    x(5) = -0.50000000000000000000;
    x(6) = -0.37500000000000000000;
    x(7) = -0.25000000000000000000;
    x(8) = -0.12500000000000000000;
    x(9) =  0.00000000000000000000;
    x(10) = 0.12500000000000000000;
    x(11) = 0.25000000000000000000;
    x(12) = 0.37500000000000000000;
    x(13) = 0.50000000000000000000;
    x(14) = 0.62500000000000000000;
    x(15) = 0.75000000000000000000;
    x(16) = 0.87500000000000000000;
    x(17) = 1.00000000000000000000;

    w(1)  =   0.030797894233299012495;
    w(2)  =   0.26128238288028031086;
    w(3)  =  -0.36795289329867605622;
    w(4)  =   1.7037379778090086905;
    w(5)  =  -3.9501480717783930427;
    w(6)  =   8.5525299934402953388;
    w(7)  = -13.934614237197880038;
    w(8)  =  19.180342211078732848;
    w(9)  = -20.951950514333334128;
    w(10) =  19.180342211078732848;
    w(11) = -13.934614237197880038;
    w(12) =   8.5525299934402953388;
    w(13) =  -3.9501480717783930427;
    w(14) =   1.7037379778090086905;
    w(15) =  -0.36795289329867605622;
    w(16) =   0.26128238288028031086;
    w(17) =   0.030797894233299012495;

  elseif ( order == 18 )
%
%       55294720874657 / 1883051089920000
%      450185515446285 / 1883051089920000
%    - 542023437008852 / 1883051089920000
%     2428636525764260 / 1883051089920000
%   - 4768916800123440 / 1883051089920000
%     8855416648684984 / 1883051089920000
%  - 10905371859796660 / 1883051089920000
%    10069615750132836 / 1883051089920000
%   - 3759785974054070 / 1883051089920000
%   - 3759785974054070 / 1883051089920000
%    10069615750132836 / 1883051089920000
%  - 10905371859796660 / 1883051089920000
%     8855416648684984 / 1883051089920000
%   - 4768916800123440 / 1883051089920000
%     2428636525764260 / 1883051089920000
%    - 542023437008852 / 1883051089920000
%      450185515446285 / 1883051089920000
%       55294720874657 / 1883051089920000
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.88235294117647058824;
    x(3) = -0.76470588235294117647;
    x(4) = -0.64705882352941176471;
    x(5) = -0.52941176470588235294;
    x(6) = -0.41176470588235294118;
    x(7) = -0.29411764705882352941;
    x(8) = -0.17647058823529411765;
    x(9) = -0.058823529411764705882;
    x(10) = 0.058823529411764705882;
    x(11) = 0.17647058823529411765;
    x(12) = 0.29411764705882352941;
    x(13) = 0.41176470588235294118;
    x(14) = 0.52941176470588235294;
    x(15) = 0.64705882352941176471;
    x(16) = 0.76470588235294117647;
    x(17) = 0.88235294117647058824;
    x(18) = 1.00000000000000000000;

    w(1) =   0.029364429446790078519;
    w(2) =   0.23907238516051669677;
    w(3) =  -0.28784319231183443641;
    w(4) =   1.2897348026109258587;
    w(5) =  -2.5325477495812627261;
    w(6) =   4.7026959045817496499;
    w(7) =  -5.7913308450170443690;
    w(8) =   5.3475000248456540826;
    w(9) =  -1.9966457597354948350;
    w(10) = -1.9966457597354948350;
    w(11) =  5.3475000248456540826;
    w(12) = -5.7913308450170443690;
    w(13) =  4.7026959045817496499;
    w(14) = -2.5325477495812627261;
    w(15) =  1.2897348026109258587;
    w(16) = -0.28784319231183443641;
    w(17) =  0.23907238516051669677;
    w(18) =  0.029364429446790078519;

  elseif ( order == 19 )
%
%       203732352169 / 7604556960000
%      1848730221900 / 7604556960000
%    - 3212744374395 / 7604556960000
%     15529830312096 / 7604556960000
%   - 42368630685840 / 7604556960000
%    103680563465808 / 7604556960000
%  - 198648429867720 / 7604556960000
%    319035784479840 / 7604556960000
%  - 419127951114198 / 7604556960000
%    461327344340680 / 7604556960000
%  - 419127951114198 / 7604556960000
%    319035784479840 / 7604556960000
%  - 198648429867720 / 7604556960000
%    103680563465808 / 7604556960000
%   - 42368630685840 / 7604556960000
%     15529830312096 / 7604556960000
%    - 3212744374395 / 7604556960000
%      1848730221900 / 7604556960000
%       203732352169 / 7604556960000
%
    x(1) = -1.00000000000000000000;
    x(2) = -0.88888888888888888889;
    x(3) = -0.77777777777777777778;
    x(4) = -0.66666666666666666667;
    x(5) = -0.55555555555555555556;
    x(6) = -0.44444444444444444444;
    x(7) = -0.33333333333333333333;
    x(8) = -0.22222222222222222222;
    x(9) = -0.11111111111111111111;
    x(10) = 0.00000000000000000000;
    x(11) = 0.11111111111111111111;
    x(12) = 0.22222222222222222222;
    x(13) = 0.33333333333333333333;
    x(14) = 0.44444444444444444444;
    x(15) = 0.55555555555555555556;
    x(16) = 0.66666666666666666667;
    x(17) = 0.77777777777777777778;
    x(18) = 0.88888888888888888889;
    x(19) = 1.00000000000000000000;

    w(1) =    0.026790824664820447344;
    w(2) =    0.24310820888374278151;
    w(3) =   -0.42247620621346493274;
    w(4) =    2.0421742376029227612;
    w(5) =   -5.5714791681749728126;
    w(6) =   13.634004454324976218;
    w(7) =  -26.122288374274995239;
    w(8) =   41.953237533490708445;
    w(9) =  -55.115367445968607749;
    w(10) =  60.664591871329740161;
    w(11) = -55.115367445968607749;
    w(12) =  41.953237533490708445;
    w(13) = -26.122288374274995239;
    w(14) =  13.634004454324976218;
    w(15) =  -5.5714791681749728126;
    w(16) =   2.0421742376029227612;
    w(17) =  -0.42247620621346493274;
    w(18) =   0.24310820888374278151;
    w(19) =   0.026790824664820447344;

  elseif ( order == 20 )
%
%       69028763155644023 / 2688996956405760000
%      603652082270808125 / 2688996956405760000
%    - 926840515700222955 / 2688996956405760000
%     4301581538450500095 / 2688996956405760000
%  - 10343692234243192788 / 2688996956405760000
%    22336420328479961316 / 2688996956405760000
%  - 35331888421114781580 / 2688996956405760000
%    43920768370565135580 / 2688996956405760000
%  - 37088370261379851390 / 2688996956405760000
%    15148337305921759574 / 2688996956405760000
%    15148337305921759574 / 2688996956405760000
%  - 37088370261379851390 / 2688996956405760000
%    43920768370565135580 / 2688996956405760000
%  - 35331888421114781580 / 2688996956405760000
%    22336420328479961316 / 2688996956405760000
%  - 10343692234243192788 / 2688996956405760000
%     4301581538450500095 / 2688996956405760000
%    - 926840515700222955 / 2688996956405760000
%      603652082270808125 / 2688996956405760000
%       69028763155644023 / 2688996956405760000
%
    x(1) =  -1.00000000000000000000;
    x(2) =  -0.89473684210526315789;
    x(3) =  -0.78947368421052631579;
    x(4) =  -0.68421052631578947368;
    x(5) =  -0.57894736842105263158;
    x(6) =  -0.47368421052631578947;
    x(7) =  -0.36842105263157894737;
    x(8) =  -0.26315789473684210526;
    x(9) =  -0.15789473684210526316;
    x(10) = -0.052631578947368421053;
    x(11) =  0.052631578947368421053;
    x(12) =  0.15789473684210526316;
    x(13) =  0.26315789473684210526;
    x(14) =  0.36842105263157894737;
    x(15) =  0.47368421052631578947;
    x(16) =  0.57894736842105263158;
    x(17) =  0.68421052631578947368;
    x(18) =  0.78947368421052631579;
    x(19) =  0.89473684210526315789;
    x(20) =  1.00000000000000000000;

    w(1) =    0.025670822345560078100;
    w(2) =    0.22448968595251886556;
    w(3) =   -0.34467890099030890987;
    w(4) =    1.5996974366978074270;
    w(5) =   -3.8466730910952978835;
    w(6) =    8.3065993344729824120;
    w(7) =  -13.139430424771119113;
    w(8) =   16.333513604742678295;
    w(9) =  -13.792641220001198577;
    w(10) =   5.6334527526463774045;
    w(11) =   5.6334527526463774045;
    w(12) = -13.792641220001198577;
    w(13) =  16.333513604742678295;
    w(14) = -13.139430424771119113;
    w(15) =   8.3065993344729824120;
    w(16) =  -3.8466730910952978835;
    w(17) =   1.5996974366978074270;
    w(18) =  -0.34467890099030890987;
    w(19) =   0.22448968595251886556;
    w(20) =   0.025670822345560078100;

  elseif ( order == 21 )

    x(1) =  -1.00000000000000000000;
    x(2) =  -0.90000000000000000000;
    x(3) =  -0.80000000000000000000;
    x(4) =  -0.70000000000000000000;
    x(5) =  -0.60000000000000000000;
    x(6) =  -0.50000000000000000000;
    x(7) =  -0.40000000000000000000;
    x(8) =  -0.30000000000000000000;
    x(9) =  -0.20000000000000000000;
    x(10) = -0.10000000000000000000;
    x(11) =  0.00000000000000000000;
    x(12) =  0.10000000000000000000;
    x(13) =  0.20000000000000000000;
    x(14) =  0.30000000000000000000;
    x(15) =  0.40000000000000000000;
    x(16) =  0.50000000000000000000;
    x(17) =  0.60000000000000000000;
    x(18) =  0.70000000000000000000;
    x(19) =  0.80000000000000000000;
    x(20) =  0.90000000000000000000;
    x(21) =  1.00000000000000000000;

    w(1) =     0.023650546498063206389;
    w(2) =     0.22827543528921394997;
    w(3) =    -0.47295674102285392846;
    w(4) =     2.4123737869637513288;
    w(5) =    -7.5420634534306609355;
    w(6) =    20.673596439879602287;
    w(7) =   -45.417631687959024596;
    w(8) =    83.656114844387109207;
    w(9) =  -128.15055898030800930;
    w(10) =  165.59456694494570344;
    w(11) = -180.01073427048578932;
    w(12) =  165.59456694494570344;
    w(13) = -128.15055898030800930;
    w(14) =   83.656114844387109207;
    w(15) =  -45.417631687959024596;
    w(16) =   20.673596439879602287;
    w(17) =   -7.5420634534306609355;
    w(18) =    2.4123737869637513288;
    w(19) =   -0.47295674102285392846;
    w(20) =    0.22827543528921394997;
    w(21) =    0.023650546498063206389;

  else

    fprintf ( 1, '\n' );
    fprintf ( 1, 'NCC_SET - Fatal error!\n' );
    fprintf ( 1, '  Illegal value of ORDER = %d\n', order );
    fprintf ( 1, '  Legal values are 1 through 21.\n' );
    error ( 'NCC_SET - Fatal error!\n' )

  end