Cody

# Problem 1465. Generalized Laguerre polynomials

Solution 1466182

Submitted on 19 Mar 2018 by Philipp Doblhofer
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### Test Suite

Test Status Code Input and Output
1   Pass
user_solution = fileread('genLaguerrePoly.m'); assert(isempty(strfind(user_solution,'regexp'))); assert(isempty(strfind(user_solution,'2str'))); assert(isempty(strfind(user_solution,'str2'))); assert(isempty(strfind(user_solution,'interp'))); assert(isempty(strfind(user_solution,'printf'))); assert(isempty(strfind(user_solution,'assert')));

2   Pass
n = 0; a = 0; P_correct = [1]/1; assert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));

a = 0

3   Pass
n = 1; a = 0; P_correct = [-1 1]/1; assert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));

a = 0 0

4   Pass
n = 2; a = 0; P_correct = [1 -4 2]/2; assert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));

a = 0 0 0 a = 0 0 0 a = 0 0 0 a = 0.5000 -2.0000 1.0000

5   Pass
n = 3; a = 0; P_correct = [-1 9 -18 6]/6; assert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));

a = 0 0 0 0 a = 0 0 0 0 a = 0 0 0 0 a = 0 0 0 0 a = 0 0.5000 -2.0000 1.0000 a = 0 0 0 0 a = -0.1667 1.5000 -3.0000 1.0000

6   Pass
n = 4; a = 0; P_correct = [1 -16 72 -96 24]/24; assert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));

a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0.5000 -2.0000 1.0000 a = 0 0 0 0 0 a = 0 -0.1667 1.5000 -3.0000 1.0000 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0.5000 -2.0000 1.0000 a = 0.0417 -0.6667 3.0000 -4.0000 1.0000

7   Pass
n = 5; a = 0; P_correct = [-1 25 -200 600 -600 120]/120; assert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));

a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -2.0000 1.0000 a = 0 0 0 0 0 0 a = 0 0 -0.1667 1.5000 -3.0000 1.0000 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -2.0000 1.0000 a = 0 0.0417 -0.6667 3.0000 -4.0000 1.0000 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -2.0000 1.0000 a = 0 0 0 0 0 0 a = 0 0 -0.1667 1.5000 -3.0000 1.0000 a = -0.0083 0.2083 -1.6667 5.0000 -5.0000 1.0000

8   Pass
n = 6; a = 0; P_correct = [1 -36 450 -2400 5400 -4320 720]/720; assert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));

a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -2.0000 1.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 1.5000 -3.0000 1.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -2.0000 1.0000 a = 0 0 0.0417 -0.6667 3.0000 -4.0000 1.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -2.0000 1.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 1.5000 -3.0000 1.0000 a = 0 -0.0083 0.2083 -1.6667 5.0000 -5.0000 1.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -2.0000 1.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 1.5000 -3.0000 1.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -2.0000 1.0000 a = 0 0 0.0417 -0.6667 3.0000 -4.0000 1.0000 a = 0.0014 -0.0500 0.6250 -3.3333 7.5000 -6.0000 1.0000

9   Pass
n = 0; a = 1; P_correct = [1]/1; assert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));

a = 0

10   Pass
n = 1; a = 1; P_correct = [-1 2]/1; assert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));

a = 0 0

11   Pass
n = 2; a = 1; P_correct = [1 -6 6]/2; assert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));

a = 0 0 0 a = 0 0 0 a = 0 0 0 a = 0.5000 -3.0000 3.0000

12   Pass
n = 3; a = 1; P_correct = [-1 12 -36 24]/6; assert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));

a = 0 0 0 0 a = 0 0 0 0 a = 0 0 0 0 a = 0 0 0 0 a = 0 0.5000 -3.0000 3.0000 a = 0 0 0 0 a = -0.1667 2.0000 -6.0000 4.0000

13   Pass
n = 4; a = 1; P_correct = [1 -20 120 -240 120]/24; assert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));

a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0.5000 -3.0000 3.0000 a = 0 0 0 0 0 a = 0 -0.1667 2.0000 -6.0000 4.0000 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0.5000 -3.0000 3.0000 a = 0.0417 -0.8333 5.0000 -10.0000 5.0000

14   Pass
n = 5; a = 1; P_correct = [-1 30 -300 1200 -1800 720]/120; assert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));

a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -3.0000 3.0000 a = 0 0 0 0 0 0 a = 0 0 -0.1667 2.0000 -6.0000 4.0000 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -3.0000 3.0000 a = 0 0.0417 -0.8333 5.0000 -10.0000 5.0000 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -3.0000 3.0000 a = 0 0 0 0 0 0 a = 0 0 -0.1667 2.0000 -6.0000 4.0000 a = -0.0083 0.2500 -2.5000 10.0000 -15.0000 6.0000

15   Pass
n = 6; a = 1; P_correct = [1 -42 630 -4200 12600 -15120 5040]/720; assert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));

a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -3.0000 3.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 2.0000 -6.0000 4.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -3.0000 3.0000 a = 0 0 0.0417 -0.8333 5.0000 -10.0000 5.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -3.0000 3.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 2.0000 -6.0000 4.0000 a = 0 -0.0083 0.2500 -2.5000 10.0000 -15.0000 6.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -3.0000 3.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 2.0000 -6.0000 4.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -3.0000 3.0000 a = 0 0 0.0417 -0.8333 5.0000 -10.0000 5.0000 a = 0.0014 -0.0583 0.8750 -5.8333 17.5000 -21.0000 7.0000

16   Pass
n = 0; a = 2; P_correct = [1]/1; assert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));

a = 0

17   Pass
n = 1; a = 2; P_correct = [-1 3]/1; assert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));

a = 0 0

18   Pass
n = 2; a = 2; P_correct = [1 -8 12]/2; assert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));

a = 0 0 0 a = 0 0 0 a = 0 0 0 a = 0.5000 -4.0000 6.0000

19   Pass
n = 3; a = 2; P_correct = [-1 15 -60 60]/6; assert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));

a = 0 0 0 0 a = 0 0 0 0 a = 0 0 0 0 a = 0 0 0 0 a = 0 0.5000 -4.0000 6.0000 a = 0 0 0 0 a = -0.1667 2.5000 -10.0000 10.0000

20   Pass
n = 4; a = 2; P_correct = [1 -24 180 -480 360]/24; assert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));

a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0.5000 -4.0000 6.0000 a = 0 0 0 0 0 a = 0 -0.1667 2.5000 -10.0000 10.0000 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0.5000 -4.0000 6.0000 a = 0.0417 -1.0000 7.5000 -20.0000 15.0000

21   Pass
n = 5; a = 2; P_correct = [-1 35 -420 2100 -4200 2520]/120; assert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));

a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -4.0000 6.0000 a = 0 0 0 0 0 0 a = 0 0 -0.1667 2.5000 -10.0000 10.0000 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -4.0000 6.0000 a = 0 0.0417 -1.0000 7.5000 -20.0000 15.0000 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -4.0000 6.0000 a = 0 0 0 0 0 0 a = 0 0 -0.1667 2.5000 -10.0000 10.0000 a = -0.0083 0.2917 -3.5000 17.5000 -35.0000 21.0000

22   Pass
n = 6; a = 2; P_correct = [1 -48 840 -6720 25200 -40320 20160]/720; assert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));

a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -4.0000 6.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 2.5000 -10.0000 10.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -4.0000 6.0000 a = 0 0 0.0417 -1.0000 7.5000 -20.0000 15.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -4.0000 6.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 2.5000 -10.0000 10.0000 a = 0 -0.0083 0.2917 -3.5000 17.5000 -35.0000 21.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -4.0000 6.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 2.5000 -10.0000 10.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -4.0000 6.0000 a = 0 0 0.0417 -1.0000 7.5000 -20.0000 15.0000 a = 0.0014 -0.0667 1.1667 -9.3333 35.0000 -56.0000 28.0000

23   Pass
n = 0; a = 3; P_correct = [1]/1; assert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));

a = 0

24   Pass
n = 1; a = 3; P_correct = [-1 4]/1; assert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));

a = 0 0

25   Pass
n = 2; a = 3; P_correct = [1 -10 20]/2; assert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));

a = 0 0 0 a = 0 0 0 a = 0 0 0 a = 0.5000 -5.0000 10.0000

26   Pass
n = 3; a = 3; P_correct = [-1 18 -90 120]/6; assert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));

a = 0 0 0 0 a = 0 0 0 0 a = 0 0 0 0 a = 0 0 0 0 a = 0 0.5000 -5.0000 10.0000 a = 0 0 0 0 a = -0.1667 3.0000 -15.0000 20.0000

27   Pass
n = 4; a = 3; P_correct = [1 -28 252 -840 840]/24; assert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));

a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0.5000 -5.0000 10.0000 a = 0 0 0 0 0 a = 0 -0.1667 3.0000 -15.0000 20.0000 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0.5000 -5.0000 10.0000 a = 0.0417 -1.1667 10.5000 -35.0000 35.0000

28   Pass
n = 5; a = 3; P_correct = [-1 40 -560 3360 -8400 6720]/120; assert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));

a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -5.0000 10.0000 a = 0 0 0 0 0 0 a = 0 0 -0.1667 3.0000 -15.0000 20.0000 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -5.0000 10.0000 a = 0 0.0417 -1.1667 10.5000 -35.0000 35.0000 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -5.0000 10.0000 a = 0 0 0 0 0 0 a = 0 0 -0.1667 3.0000 -15.0000 20.0000 a = -0.0083 0.3333 -4.6667 28.0000 -70.0000 56.0000

29   Pass
n = 6; a = 3; P_correct = [1 -54 1080 -10080 45360 -90720 60480]/720; assert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));

a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -5.0000 10.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 3.0000 -15.0000 20.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -5.0000 10.0000 a = 0 0 0.0417 -1.1667 10.5000 -35.0000 35.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -5.0000 10.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 3.0000 -15.0000 20.0000 a = 0 -0.0083 0.3333 -4.6667 28.0000 -70.0000 56.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -5.0000 10.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 3.0000 -15.0000 20.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -5.0000 10.0000 a = 0 0 0.0417 -1.1667 10.5000 -35.0000 35.0000 a = 0.0014 -0.0750 1.5000 -14.0000 63.0000 -126.0000 84.0000

30   Pass
n = 0; a = 4; P_correct = [1]/1; assert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));

a = 0

31   Pass
n = 1; a = 4; P_correct = [-1 5]/1; assert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));

a = 0 0

32   Pass
n = 2; a = 4; P_correct = [1 -12 30]/2; assert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));

a = 0 0 0 a = 0 0 0 a = 0 0 0 a = 0.5000 -6.0000 15.0000

33   Pass
n = 3; a = 4; P_correct = [-1 21 -126 210]/6; assert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));

a = 0 0 0 0 a = 0 0 0 0 a = 0 0 0 0 a = 0 0 0 0 a = 0 0.5000 -6.0000 15.0000 a = 0 0 0 0 a = -0.1667 3.5000 -21.0000 35.0000

34   Pass
n = 4; a = 4; P_correct = [1 -32 336 -1344 1680]/24; assert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));

a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0.5000 -6.0000 15.0000 a = 0 0 0 0 0 a = 0 -0.1667 3.5000 -21.0000 35.0000 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0 0 0 a = 0 0 0.5000 -6.0000 15.0000 a = 0.0417 -1.3333 14.0000 -56.0000 70.0000

35   Pass
n = 5; a = 4; P_correct = [-1 45 -720 5040 -15120 15120]/120; assert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));

a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -6.0000 15.0000 a = 0 0 0 0 0 0 a = 0 0 -0.1667 3.5000 -21.0000 35.0000 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -6.0000 15.0000 a = 0 0.0417 -1.3333 14.0000 -56.0000 70.0000 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0 0 0 a = 0 0 0 0.5000 -6.0000 15.0000 a = 0 0 0 0 0 0 a = 0 0 -0.1667 3.5000 -21.0000 35.0000 a = -0.0083 0.3750 -6.0000 42.0000 -126.0000 126.0000

36   Pass
n = 6; a = 4; P_correct = [1 -60 1350 -14400 75600 -181440 151200]/720; assert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));

a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -6.0000 15.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 3.5000 -21.0000 35.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -6.0000 15.0000 a = 0 0 0.0417 -1.3333 14.0000 -56.0000 70.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -6.0000 15.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 3.5000 -21.0000 35.0000 a = 0 -0.0083 0.3750 -6.0000 42.0000 -126.0000 126.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -6.0000 15.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 -0.1667 3.5000 -21.0000 35.0000 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0 0 0 a = 0 0 0 0 0.5000 -6.0000 15.0000 a = 0 0 0.0417 -1.3333 14.0000 -56.0000 70.0000 a = 0.0014 -0.0833 1.8750 -20.0000 105.0000 -252.0000 210.0000

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