issue related to gauss-lobatto quadrature rule generated from maxima script

Summary

Resolves a bug in gausslobatto.mac script where coefficients are generated only with double precision instead of high-precision.

Closes #18 (closed)

The order of the quadrature points in many of the rules got permutated. But I don't think that is a problem.

The sum-of-weights situation shows a clear improvement. Without this patch:

./checkrules gausslobatto_imp.hh |BC_LINE_LENGTH=0 bc -l
0,1: 0
2,3: -.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002
4,5: -.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000014
6,7: -.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
8,9: -.00000000000000043039279832576497676072429897133756396453224639205991810904023733228087185531744811414
10,11: -.0000000000000002615951439332842503654645765728576120706113207344912126677582459079064579237405301724
12,13: -.00000000000000051223885812053453370881254544926376186627560186905765599956284970679763371993327683010
14,15: .00000000000000045460184730435088890800439566457997208452981211831685046306088508968948229052636456656
16,17: -.00000000000000055551254818698568714674046192403762225731542691684070735854371337895975983406571991314
18,19: .00000000000000069301973815257730969999664267568020928954978604048873092201175651191198069949791910969
20,21: -.000000000000000428575382092567507888392189093688540490968705685992477378808917670386851672201403877820
22,23: -.00000000000000003092100898345020076286304878750450116771577380015842376444290596128543736094864041737
24,25: -.000000000000000044693975118514868174065619883879337232793322771627153394644013250818552599163567598452
26,27: -.000000000000000053447179395983335523063501450639748508883669702480051499223682765070538561343804000058
28,29: .000000000000000512240843492211628457306685855334167663668751498521897003082567552093731288701832300672
30,31: .000000000000000016553104671905016483195472107403940911802557943928985617007903354778258078017143429992

With the patch:

./checkrules gausslobatto_imp.hh |BC_LINE_LENGTH=0 bc -l
0,1: 0
2,3: -.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002
4,5: -.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000014
6,7: -.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
8,9: -.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000034
10,11: -.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002
12,13: -.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000030
14,15: -.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000020
16,17: -.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000034
18,19: -.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000020
20,21: -.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000090
22,23: -.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000028
24,25: -.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000292
26,27: -.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000218
28,29: -.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000128
30,31: -.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000078

(checkrules)

GaussLobatto is tested in test-quadrature.

mentioned in commit 5e6c08ec

merged