02-Jan-2023 19:20:56 triangle_lyness_rule_test(): MATLAB/Octave version 4.2.2 Test triangle_lyness_rule() triangle_lyness_rule_test01(): lyness_rule_num() returns the number of rules; lyness_degree() returns the degree of a rule; lyness_order_num() returns the order of a rule. Number of available rules = 21 Rule Order Precision 0 1 1 1 3 2 2 4 2 3 4 3 4 7 3 5 6 4 6 10 4 7 9 4 8 7 5 9 10 5 10 12 6 11 16 6 12 13 6 13 13 7 14 16 7 15 16 8 16 21 8 17 16 8 18 19 9 19 22 9 20 27 11 21 28 11 triangle_lyness_rule_test02(): lyness_rule() returns the points and weights of a Lyness rule for the triangle. In this test, we simply check that the weights sum to 1. Number of available rules = 21 Rule Sum of weights 0 1.0000000000000000 1 1.0000000000000000 2 1.0000000000000000 3 1.0000000000000000 4 1.0000000000000000 5 0.9999999999999999 6 0.9999999999999999 7 1.0000000000000000 8 1.0000000000000000 9 1.0000000000000000 10 0.9999999999999959 11 0.9999999999999998 12 0.9999999999999998 13 1.0000000000000000 14 0.9999999999999999 15 0.9999999999999999 16 0.9999999999999986 17 1.0000000000000002 18 1.0000000000000000 19 1.0000000000000002 20 1.0000000000000009 21 0.9999999999999998 triangle_lyness_rule_test03(): lyness_rule() returns the points and weights of a Lyness rule for the triangle. In this test, we simply check that, for each quadrature point, the barycentric coordinates sum to 1. Rule Suborder Sum of coordinates 0 1 1.0000000000000000 1 1 1.0000000000000000 2 2 1.0000000000000000 1.0000000000000000 3 2 1.0000000000000000 1.0000000000000000 4 3 1.0000000000000000 1.0000000000000000 1.0000000000000000 5 2 1.0000000000000000 1.0000000000000000 6 3 1.0000000000000000 1.0000000000000000 1.0000000000000000 7 3 1.0000000000000000 1.0000000000000000 1.0000000000000000 8 3 1.0000000000000000 0.9999999999999999 0.9999999999999999 9 4 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 10 3 1.0000000000000000 1.0000000000000000 1.0000000000000000 11 5 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 12 4 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 13 4 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 14 5 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 15 5 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 16 6 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 17 5 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 18 6 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 19 7 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 20 7 1.0000000000000000 1.0000000000000000 0.9999999999999999 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 21 8 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 1.0000000000000000 triangle_lyness_rule_test04(): lyness_rule() returns the points and weights of a Lyness rule for the triangle. In this test, we simply print a rule. Rule = 18 Order = 19 Precision = 9 I W X Y 1 0.0971357962827961 0.3333333333333333 0.3333333333333333 2 0.0313347002271398 0.0206349616025259 0.4896825191987370 3 0.0313347002271398 0.4896825191987370 0.4896825191987370 4 0.0313347002271398 0.4896825191987370 0.0206349616025259 5 0.0778275410047754 0.1258208170141290 0.4370895914929355 6 0.0778275410047754 0.4370895914929355 0.4370895914929354 7 0.0778275410047754 0.4370895914929354 0.1258208170141290 8 0.0796477389272091 0.6235929287619356 0.1882035356190322 9 0.0796477389272091 0.1882035356190322 0.1882035356190322 10 0.0796477389272091 0.1882035356190322 0.6235929287619356 11 0.0255776756586981 0.9105409732110941 0.0447295133944530 12 0.0255776756586981 0.0447295133944530 0.0447295133944530 13 0.0255776756586981 0.0447295133944530 0.9105409732110941 14 0.0432835393772894 0.0368384120547363 0.7411985987844980 15 0.0432835393772894 0.7411985987844980 0.2219629891607657 16 0.0432835393772894 0.2219629891607657 0.0368384120547363 17 0.0432835393772894 0.7411985987844980 0.0368384120547363 18 0.0432835393772894 0.2219629891607657 0.7411985987844980 19 0.0432835393772894 0.0368384120547363 0.2219629891607657 triangle_lyness_rule_test05(): lyness_rule() returns the points and weights of a Lyness rule for the triangle. In this test, we simply print a rule. Rule = 18 Order = 19 Precision = 9 Wrote the region file "lyness_18_r.txt". Wrote the weight file "lyness_18_w.txt". Wrote the point file "lyness_18_x.txt". triangle_lyness_rule_test06(): lyness_rule() returns the points and weights of a Lyness rule for the unit triangle. This routine uses those rules to estimate the integral of monomomials in the unit triangle. Integrate 2.000000 * X^0 * Y*0 Rule QUAD ERROR 0 1.000000 0.00e+00 1 1.000000 0.00e+00 2 1.000000 0.00e+00 3 1.000000 0.00e+00 4 1.000000 0.00e+00 5 1.000000 1.11e-16 6 1.000000 1.11e-16 7 1.000000 0.00e+00 8 1.000000 0.00e+00 9 1.000000 0.00e+00 10 1.000000 4.11e-15 11 1.000000 2.22e-16 12 1.000000 2.22e-16 13 1.000000 0.00e+00 14 1.000000 1.11e-16 15 1.000000 1.11e-16 16 1.000000 1.44e-15 17 1.000000 2.22e-16 18 1.000000 0.00e+00 19 1.000000 2.22e-16 20 1.000000 8.88e-16 21 1.000000 2.22e-16 Integrate 6.000000 * X^0 * Y*1 Rule QUAD ERROR 0 1.000000 1.00e-10 1 1.000000 0.00e+00 2 1.000000 7.50e-11 3 1.000000 5.63e-11 4 1.000000 0.00e+00 5 1.000000 0.00e+00 6 1.000000 0.00e+00 7 1.000000 0.00e+00 8 1.000000 1.11e-16 9 1.000000 1.11e-16 10 1.000000 3.77e-15 11 1.000000 0.00e+00 12 1.000000 2.22e-16 13 1.000000 0.00e+00 14 1.000000 0.00e+00 15 1.000000 1.11e-16 16 1.000000 1.78e-15 17 1.000000 2.22e-16 18 1.000000 2.22e-16 19 1.000000 2.22e-16 20 1.000000 8.88e-16 21 1.000000 0.00e+00 Integrate 6.000000 * X^1 * Y*0 Rule QUAD ERROR 0 1.000000 1.00e-10 1 1.000000 0.00e+00 2 1.000000 7.50e-11 3 1.000000 5.63e-11 4 1.000000 0.00e+00 5 1.000000 0.00e+00 6 1.000000 0.00e+00 7 1.000000 0.00e+00 8 1.000000 1.11e-16 9 1.000000 1.11e-16 10 1.000000 3.77e-15 11 1.000000 0.00e+00 12 1.000000 2.22e-16 13 1.000000 0.00e+00 14 1.000000 0.00e+00 15 1.000000 2.22e-16 16 1.000000 1.78e-15 17 1.000000 4.44e-16 18 1.000000 2.22e-16 19 1.000000 0.00e+00 20 1.000000 1.11e-15 21 1.000000 0.00e+00 Integrate 12.000000 * X^0 * Y*2 Rule QUAD ERROR 0 0.666667 3.33e-01 1 1.000000 0.00e+00 2 1.000000 1.00e-10 3 1.000000 7.50e-11 4 1.000000 0.00e+00 5 1.000000 2.22e-16 6 1.000000 2.22e-16 7 1.000000 0.00e+00 8 1.000000 3.33e-16 9 1.000000 0.00e+00 10 1.000000 2.55e-15 11 1.000000 1.11e-16 12 1.000000 2.22e-16 13 1.000000 0.00e+00 14 1.000000 2.22e-16 15 1.000000 1.11e-16 16 1.000000 1.33e-15 17 1.000000 2.22e-16 18 1.000000 0.00e+00 19 1.000000 0.00e+00 20 1.000000 4.44e-16 21 1.000000 3.33e-16 Integrate 24.000000 * X^1 * Y*1 Rule QUAD ERROR 0 1.333333 3.33e-01 1 1.000000 0.00e+00 2 1.000000 2.00e-10 3 1.000000 1.50e-10 4 1.000000 0.00e+00 5 1.000000 0.00e+00 6 1.000000 0.00e+00 7 1.000000 2.22e-16 8 1.000000 2.22e-16 9 1.000000 2.22e-16 10 1.000000 5.11e-15 11 1.000000 2.22e-16 12 1.000000 0.00e+00 13 1.000000 0.00e+00 14 1.000000 0.00e+00 15 1.000000 0.00e+00 16 1.000000 2.22e-15 17 1.000000 2.22e-16 18 1.000000 0.00e+00 19 1.000000 2.22e-16 20 1.000000 1.11e-15 21 1.000000 2.22e-16 Integrate 12.000000 * X^2 * Y*0 Rule QUAD ERROR 0 0.666667 3.33e-01 1 1.000000 0.00e+00 2 1.000000 1.00e-10 3 1.000000 7.50e-11 4 1.000000 0.00e+00 5 1.000000 2.22e-16 6 1.000000 2.22e-16 7 1.000000 2.22e-16 8 1.000000 2.22e-16 9 1.000000 0.00e+00 10 1.000000 2.55e-15 11 1.000000 1.11e-16 12 1.000000 1.11e-16 13 1.000000 0.00e+00 14 1.000000 2.22e-16 15 1.000000 1.11e-16 16 1.000000 1.22e-15 17 1.000000 2.22e-16 18 1.000000 1.11e-16 19 1.000000 2.22e-16 20 1.000000 4.44e-16 21 1.000000 3.33e-16 Integrate 20.000000 * X^0 * Y*3 Rule QUAD ERROR 0 0.370370 6.30e-01 1 0.833333 1.67e-01 2 1.111111 1.11e-01 3 1.000000 6.25e-11 4 1.000000 2.22e-16 5 1.000000 1.11e-16 6 1.000000 6.66e-16 7 1.000000 2.22e-16 8 1.000000 2.22e-16 9 1.000000 0.00e+00 10 1.000000 1.55e-15 11 1.000000 1.11e-16 12 1.000000 0.00e+00 13 1.000000 1.11e-16 14 1.000000 2.22e-16 15 1.000000 3.33e-16 16 1.000000 6.66e-16 17 1.000000 0.00e+00 18 1.000000 2.22e-16 19 1.000000 1.11e-16 20 1.000000 4.44e-16 21 1.000000 3.33e-16 Integrate 60.000000 * X^1 * Y*2 Rule QUAD ERROR 0 1.111111 1.11e-01 1 1.250000 2.50e-01 2 0.833333 1.67e-01 3 1.000000 1.88e-10 4 1.000000 0.00e+00 5 1.000000 1.11e-16 6 1.000000 0.00e+00 7 1.000000 2.22e-16 8 1.000000 3.33e-16 9 1.000000 1.11e-16 10 1.000000 4.33e-15 11 1.000000 0.00e+00 12 1.000000 2.22e-16 13 1.000000 2.22e-16 14 1.000000 1.11e-16 15 1.000000 2.22e-16 16 1.000000 1.44e-15 17 1.000000 2.22e-16 18 1.000000 1.11e-16 19 1.000000 0.00e+00 20 1.000000 1.11e-15 21 1.000000 1.11e-16 Integrate 60.000000 * X^2 * Y*1 Rule QUAD ERROR 0 1.111111 1.11e-01 1 1.250000 2.50e-01 2 0.833333 1.67e-01 3 1.000000 1.88e-10 4 1.000000 0.00e+00 5 1.000000 1.11e-16 6 1.000000 0.00e+00 7 1.000000 2.22e-16 8 1.000000 2.22e-16 9 1.000000 2.22e-16 10 1.000000 4.22e-15 11 1.000000 2.22e-16 12 1.000000 0.00e+00 13 1.000000 0.00e+00 14 1.000000 1.11e-16 15 1.000000 0.00e+00 16 1.000000 1.78e-15 17 1.000000 2.22e-16 18 1.000000 0.00e+00 19 1.000000 0.00e+00 20 1.000000 1.11e-15 21 1.000000 0.00e+00 Integrate 20.000000 * X^3 * Y*0 Rule QUAD ERROR 0 0.370370 6.30e-01 1 0.833333 1.67e-01 2 1.111111 1.11e-01 3 1.000000 6.25e-11 4 1.000000 2.22e-16 5 1.000000 2.22e-16 6 1.000000 6.66e-16 7 1.000000 2.22e-16 8 1.000000 3.33e-16 9 1.000000 0.00e+00 10 1.000000 1.55e-15 11 1.000000 1.11e-16 12 1.000000 1.11e-16 13 1.000000 2.22e-16 14 1.000000 0.00e+00 15 1.000000 3.33e-16 16 1.000000 6.66e-16 17 1.000000 2.22e-16 18 1.000000 2.22e-16 19 1.000000 2.22e-16 20 1.000000 2.22e-16 21 1.000000 3.33e-16 Integrate 30.000000 * X^0 * Y*4 Rule QUAD ERROR 0 0.185185 8.15e-01 1 0.625000 3.75e-01 2 1.388889 3.89e-01 3 0.933333 6.67e-02 4 1.083333 8.33e-02 5 1.000000 3.33e-16 6 1.000000 7.77e-16 7 1.000000 4.44e-16 8 1.000000 4.44e-16 9 1.000000 0.00e+00 10 1.000000 4.44e-16 11 1.000000 1.11e-16 12 1.000000 1.11e-16 13 1.000000 2.22e-16 14 1.000000 0.00e+00 15 1.000000 4.44e-16 16 1.000000 2.22e-16 17 1.000000 0.00e+00 18 1.000000 2.22e-16 19 1.000000 0.00e+00 20 1.000000 2.22e-16 21 1.000000 2.22e-16 Integrate 120.000000 * X^1 * Y*3 Rule QUAD ERROR 0 0.740741 2.59e-01 1 1.250000 2.50e-01 2 0.555556 4.44e-01 3 1.133333 1.33e-01 4 0.833333 1.67e-01 5 1.000000 0.00e+00 6 1.000000 2.22e-16 7 1.000000 4.44e-16 8 1.000000 4.44e-16 9 1.000000 0.00e+00 10 1.000000 3.44e-15 11 1.000000 2.22e-16 12 1.000000 2.22e-16 13 1.000000 0.00e+00 14 1.000000 2.22e-16 15 1.000000 2.22e-16 16 1.000000 9.99e-16 17 1.000000 2.22e-16 18 1.000000 1.11e-16 19 1.000000 0.00e+00 20 1.000000 8.88e-16 21 1.000000 1.11e-16 Integrate 180.000000 * X^2 * Y*2 Rule QUAD ERROR 0 1.111111 1.11e-01 1 1.875000 8.75e-01 2 0.833333 1.67e-01 3 0.800000 2.00e-01 4 1.250000 2.50e-01 5 1.000000 0.00e+00 6 1.000000 0.00e+00 7 1.000000 4.44e-16 8 1.000000 2.22e-16 9 1.000000 0.00e+00 10 1.000000 3.77e-15 11 1.000000 2.22e-16 12 1.000000 2.22e-16 13 1.000000 2.22e-16 14 1.000000 2.22e-16 15 1.000000 0.00e+00 16 1.000000 1.78e-15 17 1.000000 2.22e-16 18 1.000000 0.00e+00 19 1.000000 2.22e-16 20 1.000000 1.55e-15 21 1.000000 3.33e-16 Integrate 120.000000 * X^3 * Y*1 Rule QUAD ERROR 0 0.740741 2.59e-01 1 1.250000 2.50e-01 2 0.555556 4.44e-01 3 1.133333 1.33e-01 4 0.833333 1.67e-01 5 1.000000 0.00e+00 6 1.000000 1.11e-16 7 1.000000 4.44e-16 8 1.000000 5.55e-16 9 1.000000 0.00e+00 10 1.000000 3.22e-15 11 1.000000 2.22e-16 12 1.000000 0.00e+00 13 1.000000 2.22e-16 14 1.000000 0.00e+00 15 1.000000 2.22e-16 16 1.000000 1.33e-15 17 1.000000 2.22e-16 18 1.000000 0.00e+00 19 1.000000 1.11e-16 20 1.000000 8.88e-16 21 1.000000 1.11e-16 Integrate 30.000000 * X^4 * Y*0 Rule QUAD ERROR 0 0.185185 8.15e-01 1 0.625000 3.75e-01 2 1.388889 3.89e-01 3 0.933333 6.67e-02 4 1.083333 8.33e-02 5 1.000000 2.22e-16 6 1.000000 7.77e-16 7 1.000000 4.44e-16 8 1.000000 4.44e-16 9 1.000000 2.22e-16 10 1.000000 4.44e-16 11 1.000000 2.22e-16 12 1.000000 1.11e-16 13 1.000000 3.33e-16 14 1.000000 0.00e+00 15 1.000000 3.33e-16 16 1.000000 2.22e-16 17 1.000000 0.00e+00 18 1.000000 2.22e-16 19 1.000000 1.11e-16 20 1.000000 1.11e-16 21 1.000000 3.33e-16 Integrate 42.000000 * X^0 * Y*5 Rule QUAD ERROR 0 0.086420 9.14e-01 1 0.437500 5.62e-01 2 1.814815 8.15e-01 3 0.808889 1.91e-01 4 1.263889 2.64e-01 5 1.005274 5.27e-03 6 0.972222 2.78e-02 7 1.008891 8.89e-03 8 1.000000 7.77e-16 9 1.000000 0.00e+00 10 1.000000 6.66e-16 11 1.000000 0.00e+00 12 1.000000 2.22e-16 13 1.000000 3.33e-16 14 1.000000 2.22e-16 15 1.000000 3.33e-16 16 1.000000 2.22e-16 17 1.000000 2.22e-16 18 1.000000 4.44e-16 19 1.000000 2.22e-16 20 1.000000 3.33e-16 21 1.000000 1.11e-16 Integrate 210.000000 * X^1 * Y*4 Rule QUAD ERROR 0 0.432099 5.68e-01 1 1.093750 9.38e-02 2 0.324074 6.76e-01 3 1.244444 2.44e-01 4 0.631944 3.68e-01 5 0.986815 1.32e-02 6 1.069444 6.94e-02 7 0.977773 2.22e-02 8 1.000000 4.44e-16 9 1.000000 0.00e+00 10 1.000000 2.89e-15 11 1.000000 0.00e+00 12 1.000000 2.22e-16 13 1.000000 1.11e-16 14 1.000000 1.11e-16 15 1.000000 2.22e-16 16 1.000000 5.55e-16 17 1.000000 2.22e-16 18 1.000000 3.33e-16 19 1.000000 1.11e-16 20 1.000000 2.22e-16 21 1.000000 2.22e-16 Integrate 420.000000 * X^2 * Y*3 Rule QUAD ERROR 0 0.864198 1.36e-01 1 2.187500 1.19e+00 2 0.648148 3.52e-01 3 0.808889 1.91e-01 4 1.263889 2.64e-01 5 1.005274 5.27e-03 6 0.972222 2.78e-02 7 1.008891 8.89e-03 8 1.000000 5.55e-16 9 1.000000 0.00e+00 10 1.000000 2.66e-15 11 1.000000 2.22e-16 12 1.000000 4.44e-16 13 1.000000 2.22e-16 14 1.000000 2.22e-16 15 1.000000 0.00e+00 16 1.000000 1.55e-15 17 1.000000 4.44e-16 18 1.000000 0.00e+00 19 1.000000 2.22e-16 20 1.000000 1.11e-15 21 1.000000 3.33e-16 Integrate 420.000000 * X^3 * Y*2 Rule QUAD ERROR 0 0.864198 1.36e-01 1 2.187500 1.19e+00 2 0.648148 3.52e-01 3 0.808889 1.91e-01 4 1.263889 2.64e-01 5 1.005274 5.27e-03 6 0.972222 2.78e-02 7 1.008891 8.89e-03 8 1.000000 5.55e-16 9 1.000000 0.00e+00 10 1.000000 2.66e-15 11 1.000000 2.22e-16 12 1.000000 2.22e-16 13 1.000000 4.44e-16 14 1.000000 0.00e+00 15 1.000000 1.11e-16 16 1.000000 1.55e-15 17 1.000000 4.44e-16 18 1.000000 0.00e+00 19 1.000000 0.00e+00 20 1.000000 1.11e-15 21 1.000000 3.33e-16 Integrate 210.000000 * X^4 * Y*1 Rule QUAD ERROR 0 0.432099 5.68e-01 1 1.093750 9.38e-02 2 0.324074 6.76e-01 3 1.244444 2.44e-01 4 0.631944 3.68e-01 5 0.986815 1.32e-02 6 1.069444 6.94e-02 7 0.977773 2.22e-02 8 1.000000 5.55e-16 9 1.000000 0.00e+00 10 1.000000 2.55e-15 11 1.000000 2.22e-16 12 1.000000 0.00e+00 13 1.000000 3.33e-16 14 1.000000 2.22e-16 15 1.000000 3.33e-16 16 1.000000 8.88e-16 17 1.000000 2.22e-16 18 1.000000 2.22e-16 19 1.000000 0.00e+00 20 1.000000 0.00e+00 21 1.000000 2.22e-16 Integrate 42.000000 * X^5 * Y*0 Rule QUAD ERROR 0 0.086420 9.14e-01 1 0.437500 5.62e-01 2 1.814815 8.15e-01 3 0.808889 1.91e-01 4 1.263889 2.64e-01 5 1.005274 5.27e-03 6 0.972222 2.78e-02 7 1.008891 8.89e-03 8 1.000000 7.77e-16 9 1.000000 2.22e-16 10 1.000000 8.88e-16 11 1.000000 1.11e-16 12 1.000000 2.22e-16 13 1.000000 3.33e-16 14 1.000000 2.22e-16 15 1.000000 4.44e-16 16 1.000000 2.22e-16 17 1.000000 0.00e+00 18 1.000000 4.44e-16 19 1.000000 3.33e-16 20 1.000000 2.22e-16 21 1.000000 1.11e-16 Integrate 56.000000 * X^0 * Y*6 Rule QUAD ERROR 0 0.038409 9.62e-01 1 0.291667 7.08e-01 2 2.362140 1.36e+00 3 0.660662 3.39e-01 4 1.533951 5.34e-01 5 1.012949 1.29e-02 6 0.898765 1.01e-01 7 1.039972 4.00e-02 8 0.995414 4.59e-03 9 1.003175 3.17e-03 10 1.000000 1.11e-15 11 1.000000 3.33e-16 12 1.000000 3.33e-16 13 1.000000 5.55e-16 14 1.000000 4.44e-16 15 1.000000 5.55e-16 16 1.000000 2.22e-16 17 1.000000 2.22e-16 18 1.000000 1.11e-16 19 1.000000 0.00e+00 20 1.000000 4.44e-16 21 1.000000 0.00e+00 Integrate 336.000000 * X^1 * Y*5 Rule QUAD ERROR 0 0.230453 7.70e-01 1 0.875000 1.25e-01 2 0.172840 8.27e-01 3 1.253570 2.54e-01 4 0.453704 5.46e-01 5 0.982247 1.78e-02 6 1.192593 1.93e-01 7 0.915646 8.44e-02 8 1.013757 1.38e-02 9 0.990476 9.52e-03 10 1.000000 6.66e-16 11 1.000000 2.22e-16 12 1.000000 0.00e+00 13 1.000000 0.00e+00 14 1.000000 0.00e+00 15 1.000000 2.22e-16 16 1.000000 1.11e-16 17 1.000000 0.00e+00 18 1.000000 1.11e-16 19 1.000000 1.11e-16 20 1.000000 0.00e+00 21 1.000000 1.11e-16 Integrate 840.000000 * X^2 * Y*4 Rule QUAD ERROR 0 0.576132 4.24e-01 1 2.187500 1.19e+00 2 0.432099 5.68e-01 3 0.949926 5.01e-02 4 1.134259 1.34e-01 5 0.958434 4.16e-02 6 1.037037 3.70e-02 7 1.026908 2.69e-02 8 0.962963 3.70e-02 9 1.000000 1.11e-16 10 1.000000 5.55e-15 11 1.000000 2.22e-16 12 1.000000 4.44e-16 13 1.000000 2.22e-16 14 1.000000 2.22e-16 15 1.000000 6.66e-16 16 1.000000 9.99e-16 17 1.000000 2.22e-16 18 1.000000 1.11e-16 19 1.000000 2.22e-16 20 1.000000 8.88e-16 21 1.000000 4.44e-16 Integrate 1120.000000 * X^3 * Y*3 Rule QUAD ERROR 0 0.768176 2.32e-01 1 2.916667 1.92e+00 2 0.576132 4.24e-01 3 0.594568 4.05e-01 4 1.512346 5.12e-01 5 1.063496 6.35e-02 6 0.864198 1.36e-01 7 1.003794 3.79e-03 8 1.051146 5.11e-02 9 1.015873 1.59e-02 10 1.000000 1.78e-15 11 1.000000 4.44e-16 12 1.000000 4.44e-16 13 1.000000 8.88e-16 14 1.000000 0.00e+00 15 1.000000 2.22e-16 16 1.000000 2.00e-15 17 1.000000 2.22e-16 18 1.000000 0.00e+00 19 1.000000 0.00e+00 20 1.000000 8.88e-16 21 1.000000 3.33e-16 Integrate 840.000000 * X^4 * Y*2 Rule QUAD ERROR 0 0.576132 4.24e-01 1 2.187500 1.19e+00 2 0.432099 5.68e-01 3 0.949926 5.01e-02 4 1.134259 1.34e-01 5 0.958434 4.16e-02 6 1.037037 3.70e-02 7 1.026908 2.69e-02 8 0.962963 3.70e-02 9 1.000000 2.22e-16 10 1.000000 5.33e-15 11 1.000000 2.22e-16 12 1.000000 0.00e+00 13 1.000000 4.44e-16 14 1.000000 2.22e-16 15 1.000000 0.00e+00 16 1.000000 1.44e-15 17 1.000000 2.22e-16 18 1.000000 0.00e+00 19 1.000000 2.22e-16 20 1.000000 4.44e-16 21 1.000000 3.33e-16 Integrate 336.000000 * X^5 * Y*1 Rule QUAD ERROR 0 0.230453 7.70e-01 1 0.875000 1.25e-01 2 0.172840 8.27e-01 3 1.253570 2.54e-01 4 0.453704 5.46e-01 5 0.982247 1.78e-02 6 1.192593 1.93e-01 7 0.915646 8.44e-02 8 1.013757 1.38e-02 9 0.990476 9.52e-03 10 1.000000 4.44e-16 11 1.000000 4.44e-16 12 1.000000 0.00e+00 13 1.000000 4.44e-16 14 1.000000 2.22e-16 15 1.000000 4.44e-16 16 1.000000 3.33e-16 17 1.000000 0.00e+00 18 1.000000 0.00e+00 19 1.000000 2.22e-16 20 1.000000 1.11e-16 21 1.000000 2.22e-16 Integrate 56.000000 * X^6 * Y*0 Rule QUAD ERROR 0 0.038409 9.62e-01 1 0.291667 7.08e-01 2 2.362140 1.36e+00 3 0.660662 3.39e-01 4 1.533951 5.34e-01 5 1.012949 1.29e-02 6 0.898765 1.01e-01 7 1.039972 4.00e-02 8 0.995414 4.59e-03 9 1.003175 3.17e-03 10 1.000000 8.88e-16 11 1.000000 3.33e-16 12 1.000000 2.22e-16 13 1.000000 4.44e-16 14 1.000000 4.44e-16 15 1.000000 5.55e-16 16 1.000000 3.33e-16 17 1.000000 2.22e-16 18 1.000000 1.11e-16 19 1.000000 0.00e+00 20 1.000000 4.44e-16 21 1.000000 2.22e-16 Integrate 72.000000 * X^0 * Y*7 Rule QUAD ERROR 0 0.016461 9.84e-01 1 0.187500 8.12e-01 2 3.012346 2.01e+00 3 0.516101 4.84e-01 4 1.882407 8.82e-01 5 1.016902 1.69e-02 6 0.774074 2.26e-01 7 1.102775 1.03e-01 8 0.981708 1.83e-02 9 1.013605 1.36e-02 10 1.000198 1.98e-04 11 0.995833 4.17e-03 12 0.999320 6.80e-04 13 1.000000 5.55e-16 14 1.000000 2.22e-16 15 1.000000 5.55e-16 16 1.000000 3.33e-16 17 1.000000 0.00e+00 18 1.000000 3.33e-16 19 1.000000 0.00e+00 20 1.000000 2.22e-16 21 1.000000 2.22e-16 Integrate 504.000000 * X^1 * Y*6 Rule QUAD ERROR 0 0.115226 8.85e-01 1 0.656250 3.44e-01 2 0.086420 9.14e-01 3 1.166625 1.67e-01 4 0.314352 6.86e-01 5 0.999117 8.83e-04 6 1.335185 3.35e-01 7 0.820163 1.80e-01 8 1.043386 4.34e-02 9 0.966667 3.33e-02 10 0.999307 6.93e-04 11 1.014583 1.46e-02 12 1.002381 2.38e-03 13 1.000000 8.88e-16 14 1.000000 0.00e+00 15 1.000000 2.22e-16 16 1.000000 1.11e-16 17 1.000000 2.22e-16 18 1.000000 2.22e-16 19 1.000000 0.00e+00 20 1.000000 2.22e-16 21 1.000000 2.22e-16 Integrate 1512.000000 * X^2 * Y*5 Rule QUAD ERROR 0 0.345679 6.54e-01 1 1.968750 9.69e-01 2 0.259259 7.41e-01 3 1.080676 8.07e-02 4 0.943056 5.69e-02 5 0.881502 1.18e-01 6 1.205556 2.06e-01 7 1.017246 1.72e-02 8 0.909751 9.02e-02 9 0.989796 1.02e-02 10 1.000891 8.91e-04 11 0.981250 1.87e-02 12 0.996939 3.06e-03 13 1.000000 9.99e-16 14 1.000000 2.22e-16 15 1.000000 4.44e-16 16 1.000000 0.00e+00 17 1.000000 2.22e-16 18 1.000000 4.44e-16 19 1.000000 2.22e-16 20 1.000000 1.33e-15 21 1.000000 5.55e-16 Integrate 2520.000000 * X^3 * Y*4 Rule QUAD ERROR 0 0.576132 4.24e-01 1 3.281250 2.28e+00 2 0.432099 5.68e-01 3 0.591526 4.08e-01 4 1.571759 5.72e-01 5 1.057370 5.74e-02 6 0.842593 1.57e-01 7 1.028272 2.83e-02 8 1.053666 5.37e-02 9 1.037415 3.74e-02 10 0.999505 4.95e-04 11 1.010417 1.04e-02 12 1.001700 1.70e-03 13 1.000000 6.66e-16 14 1.000000 0.00e+00 15 1.000000 4.44e-16 16 1.000000 1.22e-15 17 1.000000 2.22e-16 18 1.000000 1.11e-16 19 1.000000 2.22e-16 20 1.000000 2.22e-16 21 1.000000 3.33e-16 Integrate 2520.000000 * X^4 * Y*3 Rule QUAD ERROR 0 0.576132 4.24e-01 1 3.281250 2.28e+00 2 0.432099 5.68e-01 3 0.591526 4.08e-01 4 1.571759 5.72e-01 5 1.057370 5.74e-02 6 0.842593 1.57e-01 7 1.028272 2.83e-02 8 1.053666 5.37e-02 9 1.037415 3.74e-02 10 0.999505 4.95e-04 11 1.010417 1.04e-02 12 1.001700 1.70e-03 13 1.000000 6.66e-16 14 1.000000 0.00e+00 15 1.000000 1.11e-16 16 1.000000 1.22e-15 17 1.000000 6.66e-16 18 1.000000 1.11e-16 19 1.000000 1.11e-16 20 1.000000 2.22e-16 21 1.000000 1.11e-16 Integrate 1512.000000 * X^5 * Y*2 Rule QUAD ERROR 0 0.345679 6.54e-01 1 1.968750 9.69e-01 2 0.259259 7.41e-01 3 1.080676 8.07e-02 4 0.943056 5.69e-02 5 0.881502 1.18e-01 6 1.205556 2.06e-01 7 1.017246 1.72e-02 8 0.909751 9.02e-02 9 0.989796 1.02e-02 10 1.000891 8.91e-04 11 0.981250 1.87e-02 12 0.996939 3.06e-03 13 1.000000 1.33e-15 14 1.000000 0.00e+00 15 1.000000 1.11e-16 16 1.000000 1.11e-15 17 1.000000 4.44e-16 18 1.000000 2.22e-16 19 1.000000 2.22e-16 20 1.000000 8.88e-16 21 1.000000 4.44e-16 Integrate 504.000000 * X^6 * Y*1 Rule QUAD ERROR 0 0.115226 8.85e-01 1 0.656250 3.44e-01 2 0.086420 9.14e-01 3 1.166625 1.67e-01 4 0.314352 6.86e-01 5 0.999117 8.83e-04 6 1.335185 3.35e-01 7 0.820163 1.80e-01 8 1.043386 4.34e-02 9 0.966667 3.33e-02 10 0.999307 6.93e-04 11 1.014583 1.46e-02 12 1.002381 2.38e-03 13 1.000000 2.22e-16 14 1.000000 0.00e+00 15 1.000000 3.33e-16 16 1.000000 5.55e-16 17 1.000000 0.00e+00 18 1.000000 2.22e-16 19 1.000000 1.11e-16 20 1.000000 6.66e-16 21 1.000000 2.22e-16 Integrate 72.000000 * X^7 * Y*0 Rule QUAD ERROR 0 0.016461 9.84e-01 1 0.187500 8.12e-01 2 3.012346 2.01e+00 3 0.516101 4.84e-01 4 1.882407 8.82e-01 5 1.016902 1.69e-02 6 0.774074 2.26e-01 7 1.102775 1.03e-01 8 0.981708 1.83e-02 9 1.013605 1.36e-02 10 1.000198 1.98e-04 11 0.995833 4.17e-03 12 0.999320 6.80e-04 13 1.000000 6.66e-16 14 1.000000 2.22e-16 15 1.000000 5.55e-16 16 1.000000 4.44e-16 17 1.000000 2.22e-16 18 1.000000 3.33e-16 19 1.000000 2.22e-16 20 1.000000 0.00e+00 21 1.000000 2.22e-16 Integrate 90.000000 * X^0 * Y*8 Rule QUAD ERROR 0 0.006859 9.93e-01 1 0.117188 8.83e-01 2 3.755144 2.76e+00 3 0.389922 6.10e-01 4 2.299961 1.30e+00 5 1.012161 1.22e-02 6 0.600309 4.00e-01 7 1.201740 2.02e-01 8 0.956602 4.34e-02 9 1.035153 3.52e-02 10 1.000439 4.39e-04 11 0.980221 1.98e-02 12 0.996936 3.06e-03 13 0.999572 4.28e-04 14 1.000325 3.25e-04 15 1.000000 1.11e-15 16 1.000000 3.33e-16 17 1.000000 1.11e-16 18 1.000000 9.99e-16 19 1.000000 1.11e-16 20 1.000000 4.44e-16 21 1.000000 1.11e-16 Integrate 720.000000 * X^1 * Y*7 Rule QUAD ERROR 0 0.054870 9.45e-01 1 0.468750 5.31e-01 2 0.041152 9.59e-01 3 1.020816 2.08e-02 4 0.212191 7.88e-01 5 1.035863 3.59e-02 6 1.469136 4.69e-01 7 0.706913 2.93e-01 8 1.082131 8.21e-02 9 0.927415 7.26e-02 10 0.999233 7.67e-04 11 1.058284 5.83e-02 12 1.008854 8.85e-03 13 1.001712 1.71e-03 14 0.998702 1.30e-03 15 1.000000 0.00e+00 16 1.000000 2.22e-16 17 1.000000 2.22e-16 18 1.000000 4.44e-16 19 1.000000 0.00e+00 20 1.000000 2.00e-15 21 1.000000 2.22e-16 Integrate 2520.000000 * X^2 * Y*6 Rule QUAD ERROR 0 0.192044 8.08e-01 1 1.640625 6.41e-01 2 0.144033 8.56e-01 3 1.133495 1.33e-01 4 0.742670 2.57e-01 5 0.811392 1.89e-01 6 1.447531 4.48e-01 7 0.967166 3.28e-02 8 0.866501 1.33e-01 9 0.968983 3.10e-02 10 0.996224 3.78e-03 11 0.948785 5.12e-02 12 0.996620 3.38e-03 13 0.994117 5.88e-03 14 1.006217 6.22e-03 15 1.000000 6.66e-16 16 1.000000 4.44e-16 17 1.000000 2.22e-16 18 1.000000 3.33e-16 19 1.000000 4.44e-16 20 1.000000 2.44e-15 21 1.000000 8.88e-16 Integrate 5040.000000 * X^3 * Y*5 Rule QUAD ERROR 0 0.384088 6.16e-01 1 3.281250 2.28e+00 2 0.288066 7.12e-01 3 0.694511 3.05e-01 4 1.485340 4.85e-01 5 0.972131 2.79e-02 6 0.950617 4.94e-02 7 1.044813 4.48e-02 8 0.992477 7.52e-03 9 1.034176 3.42e-02 10 1.011537 1.15e-02 11 1.001736 1.74e-03 12 0.987653 1.23e-02 13 1.011658 1.17e-02 14 0.985894 1.41e-02 15 1.000000 4.44e-16 16 1.000000 8.88e-16 17 1.000000 0.00e+00 18 1.000000 3.33e-16 19 1.000000 2.22e-16 20 1.000000 4.44e-16 21 1.000000 1.11e-16 Integrate 6300.000000 * X^4 * Y*4 Rule QUAD ERROR 0 0.480110 5.20e-01 1 4.101562 3.10e+00 2 0.360082 6.40e-01 3 0.414538 5.85e-01 4 1.856674 8.57e-01 5 1.129907 1.30e-01 6 0.702160 2.98e-01 7 1.064591 6.46e-02 8 1.137746 1.38e-01 9 1.110504 1.11e-01 10 0.983592 1.64e-02 11 1.043837 4.38e-02 12 1.023611 2.36e-02 13 0.985455 1.45e-02 14 1.018051 1.81e-02 15 1.000000 6.66e-16 16 1.000000 1.78e-15 17 1.000000 0.00e+00 18 1.000000 0.00e+00 19 1.000000 2.22e-16 20 1.000000 2.22e-16 21 1.000000 3.33e-16 Integrate 5040.000000 * X^5 * Y*3 Rule QUAD ERROR 0 0.384088 6.16e-01 1 3.281250 2.28e+00 2 0.288066 7.12e-01 3 0.694511 3.05e-01 4 1.485340 4.85e-01 5 0.972131 2.79e-02 6 0.950617 4.94e-02 7 1.044813 4.48e-02 8 0.992477 7.52e-03 9 1.034176 3.42e-02 10 1.011537 1.15e-02 11 1.001736 1.74e-03 12 0.987653 1.23e-02 13 1.011658 1.17e-02 14 0.985894 1.41e-02 15 1.000000 0.00e+00 16 1.000000 1.22e-15 17 1.000000 2.22e-16 18 1.000000 3.33e-16 19 1.000000 2.22e-16 20 1.000000 5.55e-16 21 1.000000 2.22e-16 Integrate 2520.000000 * X^6 * Y*2 Rule QUAD ERROR 0 0.192044 8.08e-01 1 1.640625 6.41e-01 2 0.144033 8.56e-01 3 1.133495 1.33e-01 4 0.742670 2.57e-01 5 0.811392 1.89e-01 6 1.447531 4.48e-01 7 0.967166 3.28e-02 8 0.866501 1.33e-01 9 0.968983 3.10e-02 10 0.996224 3.78e-03 11 0.948785 5.12e-02 12 0.996620 3.38e-03 13 0.994117 5.88e-03 14 1.006217 6.22e-03 15 1.000000 2.22e-16 16 1.000000 5.55e-16 17 1.000000 4.44e-16 18 1.000000 2.22e-16 19 1.000000 2.22e-16 20 1.000000 2.44e-15 21 1.000000 7.77e-16 Integrate 720.000000 * X^7 * Y*1 Rule QUAD ERROR 0 0.054870 9.45e-01 1 0.468750 5.31e-01 2 0.041152 9.59e-01 3 1.020816 2.08e-02 4 0.212191 7.88e-01 5 1.035863 3.59e-02 6 1.469136 4.69e-01 7 0.706913 2.93e-01 8 1.082131 8.21e-02 9 0.927415 7.26e-02 10 0.999233 7.67e-04 11 1.058284 5.83e-02 12 1.008854 8.85e-03 13 1.001712 1.71e-03 14 0.998702 1.30e-03 15 1.000000 7.77e-16 16 1.000000 1.11e-16 17 1.000000 2.22e-16 18 1.000000 8.88e-16 19 1.000000 1.11e-16 20 1.000000 2.66e-15 21 1.000000 2.22e-16 Integrate 90.000000 * X^8 * Y*0 Rule QUAD ERROR 0 0.006859 9.93e-01 1 0.117188 8.83e-01 2 3.755144 2.76e+00 3 0.389922 6.10e-01 4 2.299961 1.30e+00 5 1.012161 1.22e-02 6 0.600309 4.00e-01 7 1.201740 2.02e-01 8 0.956602 4.34e-02 9 1.035153 3.52e-02 10 1.000439 4.39e-04 11 0.980221 1.98e-02 12 0.996936 3.06e-03 13 0.999572 4.28e-04 14 1.000325 3.25e-04 15 1.000000 9.99e-16 16 1.000000 3.33e-16 17 1.000000 2.22e-16 18 1.000000 9.99e-16 19 1.000000 1.11e-16 20 1.000000 4.44e-16 21 1.000000 4.44e-16 Integrate 110.000000 * X^0 * Y*9 Rule QUAD ERROR 0 0.002794 9.97e-01 1 0.071615 9.28e-01 2 4.585429 3.59e+00 3 0.287142 7.13e-01 4 2.779903 1.78e+00 5 0.996255 3.74e-03 6 0.383202 6.17e-01 7 1.337613 3.38e-01 8 0.920084 7.99e-02 9 1.070951 7.10e-02 10 1.000086 8.58e-05 11 0.945230 5.48e-02 12 0.991867 8.13e-03 13 0.997886 2.11e-03 14 1.001643 1.64e-03 15 0.999942 5.79e-05 16 1.000197 1.97e-04 17 1.000127 1.27e-04 18 1.000000 1.33e-15 19 1.000000 0.00e+00 20 1.000000 1.55e-15 21 1.000000 4.44e-16 Integrate 990.000000 * X^1 * Y*8 Rule QUAD ERROR 0 0.025149 9.75e-01 1 0.322266 6.78e-01 2 0.018861 9.81e-01 3 0.852434 1.48e-01 4 0.140223 8.60e-01 5 1.083738 8.37e-02 6 1.577289 5.77e-01 7 0.590312 4.10e-01 8 1.120935 1.21e-01 9 0.874065 1.26e-01 10 1.002030 2.03e-03 11 1.137677 1.38e-01 12 1.019749 1.97e-02 13 1.007157 7.16e-03 14 0.994392 5.61e-03 15 1.000260 2.60e-04 16 0.999113 8.87e-04 17 0.999431 5.69e-04 18 1.000000 1.11e-15 19 1.000000 0.00e+00 20 1.000000 5.00e-15 21 1.000000 6.66e-16 Integrate 3960.000000 * X^2 * Y*7 Rule QUAD ERROR 0 0.100594 8.99e-01 1 1.289062 2.89e-01 2 0.075446 9.25e-01 3 1.103432 1.03e-01 4 0.560892 4.39e-01 5 0.769683 2.30e-01 6 1.725823 7.26e-01 7 0.883621 1.16e-01 8 0.846090 1.54e-01 9 0.939825 6.02e-02 10 0.981678 1.83e-02 11 0.922919 7.71e-02 12 1.006074 6.07e-03 13 0.979223 2.08e-02 14 1.022978 2.30e-02 15 0.999209 7.91e-04 16 1.001319 1.32e-03 17 1.001210 1.21e-03 18 1.000000 4.44e-16 19 1.000000 2.22e-16 20 1.000000 4.66e-15 21 1.000000 1.44e-15 Integrate 9240.000000 * X^3 * Y*6 Rule QUAD ERROR 0 0.234720 7.65e-01 1 3.007812 2.01e+00 2 0.176040 8.24e-01 3 0.800594 1.99e-01 4 1.308749 3.09e-01 5 0.846318 1.54e-01 6 1.175069 1.75e-01 7 1.025849 2.58e-02 8 0.896388 1.04e-01 9 1.001755 1.76e-03 10 1.030392 3.04e-02 11 0.959901 4.01e-02 12 0.959792 4.02e-02 13 1.028932 2.89e-02 14 0.963277 3.67e-02 15 1.001552 1.55e-03 16 0.999523 4.77e-04 17 0.998423 1.58e-03 18 1.000000 8.88e-16 19 1.000000 4.44e-16 20 1.000000 3.33e-16 21 1.000000 6.66e-16 Integrate 13860.000000 * X^4 * Y*5 Rule QUAD ERROR 0 0.352080 6.48e-01 1 4.511719 3.51e+00 2 0.264060 7.36e-01 3 0.402555 5.97e-01 4 1.963124 9.63e-01 5 1.106105 1.06e-01 6 0.693158 3.07e-01 7 1.107800 1.08e-01 8 1.142490 1.42e-01 9 1.159026 1.59e-01 10 0.982741 1.73e-02 11 1.067455 6.75e-02 12 1.028439 2.84e-02 13 0.985505 1.45e-02 14 1.018673 1.87e-02 15 0.999065 9.35e-04 16 0.999750 2.50e-04 17 1.000747 7.47e-04 18 1.000000 3.33e-16 19 1.000000 0.00e+00 20 1.000000 7.77e-16 21 1.000000 0.00e+00 Integrate 13860.000000 * X^5 * Y*4 Rule QUAD ERROR 0 0.352080 6.48e-01 1 4.511719 3.51e+00 2 0.264060 7.36e-01 3 0.402555 5.97e-01 4 1.963124 9.63e-01 5 1.106105 1.06e-01 6 0.693158 3.07e-01 7 1.107800 1.08e-01 8 1.142490 1.42e-01 9 1.159026 1.59e-01 10 0.982741 1.73e-02 11 1.067455 6.75e-02 12 1.028439 2.84e-02 13 0.985505 1.45e-02 14 1.018673 1.87e-02 15 0.999065 9.35e-04 16 0.999750 2.50e-04 17 1.000747 7.47e-04 18 1.000000 2.22e-16 19 1.000000 1.11e-16 20 1.000000 7.77e-16 21 1.000000 0.00e+00 Integrate 9240.000000 * X^6 * Y*3 Rule QUAD ERROR 0 0.234720 7.65e-01 1 3.007812 2.01e+00 2 0.176040 8.24e-01 3 0.800594 1.99e-01 4 1.308749 3.09e-01 5 0.846318 1.54e-01 6 1.175069 1.75e-01 7 1.025849 2.58e-02 8 0.896388 1.04e-01 9 1.001755 1.76e-03 10 1.030392 3.04e-02 11 0.959901 4.01e-02 12 0.959792 4.02e-02 13 1.028932 2.89e-02 14 0.963277 3.67e-02 15 1.001552 1.55e-03 16 0.999523 4.77e-04 17 0.998423 1.58e-03 18 1.000000 7.77e-16 19 1.000000 4.44e-16 20 1.000000 6.66e-16 21 1.000000 4.44e-16 Integrate 3960.000000 * X^7 * Y*2 Rule QUAD ERROR 0 0.100594 8.99e-01 1 1.289062 2.89e-01 2 0.075446 9.25e-01 3 1.103432 1.03e-01 4 0.560892 4.39e-01 5 0.769683 2.30e-01 6 1.725823 7.26e-01 7 0.883621 1.16e-01 8 0.846090 1.54e-01 9 0.939825 6.02e-02 10 0.981678 1.83e-02 11 0.922919 7.71e-02 12 1.006074 6.07e-03 13 0.979223 2.08e-02 14 1.022978 2.30e-02 15 0.999209 7.91e-04 16 1.001319 1.32e-03 17 1.001210 1.21e-03 18 1.000000 2.22e-16 19 1.000000 0.00e+00 20 1.000000 4.22e-15 21 1.000000 1.44e-15 Integrate 990.000000 * X^8 * Y*1 Rule QUAD ERROR 0 0.025149 9.75e-01 1 0.322266 6.78e-01 2 0.018861 9.81e-01 3 0.852434 1.48e-01 4 0.140223 8.60e-01 5 1.083738 8.37e-02 6 1.577289 5.77e-01 7 0.590312 4.10e-01 8 1.120935 1.21e-01 9 0.874065 1.26e-01 10 1.002030 2.03e-03 11 1.137677 1.38e-01 12 1.019749 1.97e-02 13 1.007157 7.16e-03 14 0.994392 5.61e-03 15 1.000260 2.60e-04 16 0.999113 8.87e-04 17 0.999431 5.69e-04 18 1.000000 8.88e-16 19 1.000000 1.11e-16 20 1.000000 5.44e-15 21 1.000000 8.88e-16 Integrate 110.000000 * X^9 * Y*0 Rule QUAD ERROR 0 0.002794 9.97e-01 1 0.071615 9.28e-01 2 4.585429 3.59e+00 3 0.287142 7.13e-01 4 2.779903 1.78e+00 5 0.996255 3.74e-03 6 0.383202 6.17e-01 7 1.337613 3.38e-01 8 0.920084 7.99e-02 9 1.070951 7.10e-02 10 1.000086 8.58e-05 11 0.945230 5.48e-02 12 0.991867 8.13e-03 13 0.997886 2.11e-03 14 1.001643 1.64e-03 15 0.999942 5.79e-05 16 1.000197 1.97e-04 17 1.000127 1.27e-04 18 1.000000 1.22e-15 19 1.000000 2.22e-16 20 1.000000 1.55e-15 21 1.000000 4.44e-16 Integrate 132.000000 * X^0 * Y*10 Rule QUAD ERROR 0 0.001118 9.99e-01 1 0.042969 9.57e-01 2 5.500838 4.50e+00 3 0.207231 7.93e-01 4 3.317690 2.32e+00 5 0.968918 3.11e-02 6 0.129515 8.70e-01 7 1.509072 5.09e-01 8 0.873671 1.26e-01 9 1.123229 1.23e-01 10 0.998219 1.78e-03 11 0.883970 1.16e-01 12 0.983360 1.66e-02 13 0.993975 6.03e-03 14 1.004811 4.81e-03 15 0.999662 3.38e-04 16 1.001093 1.09e-03 17 1.000659 6.59e-04 18 0.999970 3.03e-05 19 0.999979 2.05e-05 20 1.000000 4.00e-15 21 1.000000 7.77e-16 Integrate 1320.000000 * X^1 * Y*9 Rule QUAD ERROR 0 0.011177 9.89e-01 1 0.214844 7.85e-01 2 0.008383 9.92e-01 3 0.686695 3.13e-01 4 0.090967 9.09e-01 5 1.132942 1.33e-01 6 1.651635 6.52e-01 7 0.480319 5.20e-01 8 1.152148 1.52e-01 9 0.809557 1.90e-01 10 1.009418 9.42e-03 11 1.251534 2.52e-01 12 1.034398 3.44e-02 13 1.017444 1.74e-02 14 0.985803 1.42e-02 15 1.001344 1.34e-03 16 0.995717 4.28e-03 17 0.997466 2.53e-03 18 1.000151 1.51e-04 19 1.000103 1.03e-04 20 1.000000 9.10e-15 21 1.000000 1.78e-15 Integrate 5940.000000 * X^2 * Y*8 Rule QUAD ERROR 0 0.050297 9.50e-01 1 0.966797 3.32e-02 2 0.037723 9.62e-01 3 1.012554 1.26e-02 4 0.409352 5.91e-01 5 0.761318 2.39e-01 6 2.008745 1.01e+00 7 0.780207 2.20e-01 8 0.849523 1.50e-01 9 0.903830 9.62e-02 10 0.957945 4.21e-02 11 0.924013 7.60e-02 12 1.029384 2.94e-02 13 0.956754 4.32e-02 14 1.050421 5.04e-02 15 0.996306 3.69e-03 16 1.004867 4.87e-03 17 1.003957 3.96e-03 18 0.999303 6.97e-04 19 0.999414 5.86e-04 20 1.000000 6.00e-15 21 1.000000 1.22e-15 Integrate 15840.000000 * X^3 * Y*7 Rule QUAD ERROR 0 0.134126 8.66e-01 1 2.578125 1.58e+00 2 0.100594 8.99e-01 3 0.860170 1.40e-01 4 1.091607 9.16e-02 5 0.720497 2.80e-01 6 1.486283 4.86e-01 7 0.967926 3.21e-02 8 0.797080 2.03e-01 9 0.949768 5.02e-02 10 1.042706 4.27e-02 11 0.893970 1.06e-01 12 0.931119 6.89e-02 13 1.039343 3.93e-02 14 0.945921 5.41e-02 15 1.006134 6.13e-03 16 0.999956 4.45e-05 17 0.997525 2.47e-03 18 1.001881 1.88e-03 19 1.001728 1.73e-03 20 1.000000 8.88e-16 21 1.000000 9.99e-16 Integrate 27720.000000 * X^4 * Y*6 Rule QUAD ERROR 0 0.234720 7.65e-01 1 4.511719 3.51e+00 2 0.176040 8.24e-01 3 0.467461 5.33e-01 4 1.910312 9.10e-01 5 0.998828 1.17e-03 6 0.818587 1.81e-01 7 1.119238 1.19e-01 8 1.069173 6.92e-02 9 1.154865 1.55e-01 10 1.007858 7.86e-03 11 1.053596 5.36e-02 12 0.999566 4.34e-04 13 1.010243 1.02e-02 14 0.989214 1.08e-02 15 0.997890 2.11e-03 16 0.999336 6.64e-04 17 0.996401 3.60e-03 18 0.996691 3.31e-03 19 0.996853 3.15e-03 20 1.000000 2.33e-15 21 1.000000 1.11e-16 Integrate 33264.000000 * X^5 * Y*5 Rule QUAD ERROR 0 0.281664 7.18e-01 1 5.414062 4.41e+00 2 0.211248 7.89e-01 3 0.273552 7.26e-01 4 2.292374 1.29e+00 5 1.166185 1.66e-01 6 0.554527 4.45e-01 7 1.193362 1.93e-01 8 1.239579 2.40e-01 9 1.287664 2.88e-01 10 0.950326 4.97e-02 11 1.138274 1.38e-01 12 1.072735 7.27e-02 13 0.955574 4.44e-02 14 1.054177 5.42e-02 15 0.997684 2.32e-03 16 0.996791 3.21e-03 17 1.007125 7.13e-03 18 1.003977 3.98e-03 19 1.003827 3.83e-03 20 1.000000 7.77e-16 21 1.000000 0.00e+00 Integrate 27720.000000 * X^6 * Y*4 Rule QUAD ERROR 0 0.234720 7.65e-01 1 4.511719 3.51e+00 2 0.176040 8.24e-01 3 0.467461 5.33e-01 4 1.910312 9.10e-01 5 0.998828 1.17e-03 6 0.818587 1.81e-01 7 1.119238 1.19e-01 8 1.069173 6.92e-02 9 1.154865 1.55e-01 10 1.007858 7.86e-03 11 1.053596 5.36e-02 12 0.999566 4.34e-04 13 1.010243 1.02e-02 14 0.989214 1.08e-02 15 0.997890 2.11e-03 16 0.999336 6.64e-04 17 0.996401 3.60e-03 18 0.996691 3.31e-03 19 0.996853 3.15e-03 20 1.000000 2.44e-15 21 1.000000 0.00e+00 Integrate 15840.000000 * X^7 * Y*3 Rule QUAD ERROR 0 0.134126 8.66e-01 1 2.578125 1.58e+00 2 0.100594 8.99e-01 3 0.860170 1.40e-01 4 1.091607 9.16e-02 5 0.720497 2.80e-01 6 1.486283 4.86e-01 7 0.967926 3.21e-02 8 0.797080 2.03e-01 9 0.949768 5.02e-02 10 1.042706 4.27e-02 11 0.893970 1.06e-01 12 0.931119 6.89e-02 13 1.039343 3.93e-02 14 0.945921 5.41e-02 15 1.006134 6.13e-03 16 0.999956 4.45e-05 17 0.997525 2.47e-03 18 1.001881 1.88e-03 19 1.001728 1.73e-03 20 1.000000 4.44e-16 21 1.000000 7.77e-16 Integrate 5940.000000 * X^8 * Y*2 Rule QUAD ERROR 0 0.050297 9.50e-01 1 0.966797 3.32e-02 2 0.037723 9.62e-01 3 1.012554 1.26e-02 4 0.409352 5.91e-01 5 0.761318 2.39e-01 6 2.008745 1.01e+00 7 0.780207 2.20e-01 8 0.849523 1.50e-01 9 0.903830 9.62e-02 10 0.957945 4.21e-02 11 0.924013 7.60e-02 12 1.029384 2.94e-02 13 0.956754 4.32e-02 14 1.050421 5.04e-02 15 0.996306 3.69e-03 16 1.004867 4.87e-03 17 1.003957 3.96e-03 18 0.999303 6.97e-04 19 0.999414 5.86e-04 20 1.000000 5.77e-15 21 1.000000 1.22e-15 Integrate 1320.000000 * X^9 * Y*1 Rule QUAD ERROR 0 0.011177 9.89e-01 1 0.214844 7.85e-01 2 0.008383 9.92e-01 3 0.686695 3.13e-01 4 0.090967 9.09e-01 5 1.132942 1.33e-01 6 1.651635 6.52e-01 7 0.480319 5.20e-01 8 1.152148 1.52e-01 9 0.809557 1.90e-01 10 1.009418 9.42e-03 11 1.251534 2.52e-01 12 1.034398 3.44e-02 13 1.017444 1.74e-02 14 0.985803 1.42e-02 15 1.001344 1.34e-03 16 0.995717 4.28e-03 17 0.997466 2.53e-03 18 1.000151 1.51e-04 19 1.000103 1.03e-04 20 1.000000 9.66e-15 21 1.000000 1.78e-15 Integrate 132.000000 * X^10 * Y*0 Rule QUAD ERROR 0 0.001118 9.99e-01 1 0.042969 9.57e-01 2 5.500838 4.50e+00 3 0.207231 7.93e-01 4 3.317690 2.32e+00 5 0.968918 3.11e-02 6 0.129515 8.70e-01 7 1.509072 5.09e-01 8 0.873671 1.26e-01 9 1.123229 1.23e-01 10 0.998219 1.78e-03 11 0.883970 1.16e-01 12 0.983360 1.66e-02 13 0.993975 6.03e-03 14 1.004811 4.81e-03 15 0.999662 3.38e-04 16 1.001093 1.09e-03 17 1.000659 6.59e-04 18 0.999970 3.03e-05 19 0.999979 2.05e-05 20 1.000000 4.00e-15 21 1.000000 7.77e-16 triangle_lyness_rule_test(): Normal end of execution. 02-Jan-2023 19:20:57