08-Jan-2022 10:39:13 triangle_lyness_rule_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 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 2.22e-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 2.22e-16 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 1.11e-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 2.22e-16 8 1.000000 4.44e-16 9 1.000000 0.00e+00 10 1.000000 4.44e-16 11 1.000000 0.00e+00 12 1.000000 3.33e-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 1.11e-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 0.00e+00 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 0.00e+00 12 1.000000 3.33e-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 2.22e-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 3.33e-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 2.22e-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 2.22e-16 12 1.000000 0.00e+00 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 2.22e-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 2.22e-16 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 2.22e-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 1.11e-16 12 1.000000 2.22e-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 3.33e-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 2.22e-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 5.55e-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 3.33e-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 1.11e-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 1.11e-16 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 1.11e-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 1.33e-15 17 1.000000 6.66e-16 18 1.000000 1.11e-16 19 1.000000 0.00e+00 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 0.00e+00 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 2.22e-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 4.44e-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 1.11e-16 21 1.000000 2.22e-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 4.44e-16 20 1.000000 5.55e-16 21 1.000000 3.33e-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 2.22e-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 5.55e-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 8.88e-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 1.44e-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 2.44e-15 21 1.000000 0.00e+00 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 8.88e-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. 08-Jan-2022 10:39:13