23 March 2023 5:03:40.032 PM TRIANGLE_LYNESS_RULE_TEST(): FORTRAN90 version Test 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 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 1.000000000000000 1 1.000000000000000 2 1.000000000000000 3 1.000000000000000 4 1.000000000000000 5 0.9999999999999999 6 0.9999999999999999 7 1.000000000000000 8 1.000000000000000 9 1.000000000000000 10 0.9999999999999959 11 0.9999999999999998 12 0.9999999999999998 13 1.000000000000000 14 0.9999999999999999 15 0.9999999999999999 16 0.9999999999999986 17 1.000000000000000 18 1.000000000000000 19 1.000000000000000 20 1.000000000000001 21 0.9999999999999998 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 1.000000000000000 1 1 1.000000000000000 2 2 1.000000000000000 1.000000000000000 3 2 1.000000000000000 1.000000000000000 4 3 1.000000000000000 1.000000000000000 1.000000000000000 5 2 1.000000000000000 1.000000000000000 6 3 1.000000000000000 1.000000000000000 1.000000000000000 7 3 1.000000000000000 1.000000000000000 1.000000000000000 8 3 1.000000000000000 0.9999999999999999 0.9999999999999999 9 4 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 10 3 1.000000000000000 1.000000000000000 1.000000000000000 11 5 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 12 4 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 13 4 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 14 5 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 15 5 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 16 6 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 17 5 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 18 6 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 19 7 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 20 7 1.000000000000000 1.000000000000000 0.9999999999999999 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 21 8 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 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 0.9713579628279610E-01 0.3333333333333333 0.3333333333333333 2 0.3133470022713983E-01 0.2063496160252593E-01 0.4896825191987370 3 0.3133470022713983E-01 0.4896825191987370 0.4896825191987370 4 0.3133470022713983E-01 0.4896825191987370 0.2063496160252593E-01 5 0.7782754100477543E-01 0.1258208170141290 0.4370895914929355 6 0.7782754100477543E-01 0.4370895914929355 0.4370895914929354 7 0.7782754100477543E-01 0.4370895914929354 0.1258208170141290 8 0.7964773892720910E-01 0.6235929287619356 0.1882035356190322 9 0.7964773892720910E-01 0.1882035356190322 0.1882035356190322 10 0.7964773892720910E-01 0.1882035356190322 0.6235929287619356 11 0.2557767565869810E-01 0.9105409732110941 0.4472951339445297E-01 12 0.2557767565869810E-01 0.4472951339445297E-01 0.4472951339445297E-01 13 0.2557767565869810E-01 0.4472951339445297E-01 0.9105409732110941 14 0.4328353937728940E-01 0.3683841205473626E-01 0.7411985987844980 15 0.4328353937728940E-01 0.7411985987844980 0.2219629891607657 16 0.4328353937728940E-01 0.2219629891607657 0.3683841205473626E-01 17 0.4328353937728940E-01 0.7411985987844980 0.3683841205473626E-01 18 0.4328353937728940E-01 0.2219629891607657 0.7411985987844980 19 0.4328353937728940E-01 0.3683841205473626E-01 0.2219629891607657 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". 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 2.00000 * X ^ 0 * Y ^ 0 Rule QUAD ERROR 0 1.00000 0.0 1 1.00000 0.0 2 1.00000 0.0 3 1.00000 0.0 4 1.00000 0.0 5 1.00000 0.11E-15 6 1.00000 0.11E-15 7 1.00000 0.0 8 1.00000 0.0 9 1.00000 0.0 10 1.00000 0.41E-14 11 1.00000 0.22E-15 12 1.00000 0.22E-15 13 1.00000 0.0 14 1.00000 0.11E-15 15 1.00000 0.11E-15 16 1.00000 0.14E-14 17 1.00000 0.22E-15 18 1.00000 0.0 19 1.00000 0.22E-15 20 1.00000 0.89E-15 21 1.00000 0.22E-15 Integrate 6.00000 * X ^ 0 * Y ^ 1 Rule QUAD ERROR 0 1.00000 0.10E-09 1 1.00000 0.0 2 1.00000 0.75E-10 3 1.00000 0.56E-10 4 1.00000 0.0 5 1.00000 0.0 6 1.00000 0.0 7 1.00000 0.0 8 1.00000 0.11E-15 9 1.00000 0.11E-15 10 1.00000 0.38E-14 11 1.00000 0.0 12 1.00000 0.22E-15 13 1.00000 0.0 14 1.00000 0.0 15 1.00000 0.11E-15 16 1.00000 0.18E-14 17 1.00000 0.22E-15 18 1.00000 0.22E-15 19 1.00000 0.22E-15 20 1.00000 0.89E-15 21 1.00000 0.0 Integrate 6.00000 * X ^ 1 * Y ^ 0 Rule QUAD ERROR 0 1.00000 0.10E-09 1 1.00000 0.0 2 1.00000 0.75E-10 3 1.00000 0.56E-10 4 1.00000 0.0 5 1.00000 0.0 6 1.00000 0.0 7 1.00000 0.0 8 1.00000 0.11E-15 9 1.00000 0.11E-15 10 1.00000 0.38E-14 11 1.00000 0.0 12 1.00000 0.22E-15 13 1.00000 0.0 14 1.00000 0.0 15 1.00000 0.22E-15 16 1.00000 0.18E-14 17 1.00000 0.44E-15 18 1.00000 0.22E-15 19 1.00000 0.0 20 1.00000 0.11E-14 21 1.00000 0.0 Integrate 12.0000 * X ^ 0 * Y ^ 2 Rule QUAD ERROR 0 0.666667 0.33 1 1.00000 0.0 2 1.00000 0.10E-09 3 1.00000 0.75E-10 4 1.00000 0.0 5 1.00000 0.22E-15 6 1.00000 0.22E-15 7 1.00000 0.0 8 1.00000 0.33E-15 9 1.00000 0.0 10 1.00000 0.26E-14 11 1.00000 0.11E-15 12 1.00000 0.22E-15 13 1.00000 0.0 14 1.00000 0.22E-15 15 1.00000 0.11E-15 16 1.00000 0.13E-14 17 1.00000 0.22E-15 18 1.00000 0.0 19 1.00000 0.0 20 1.00000 0.44E-15 21 1.00000 0.33E-15 Integrate 24.0000 * X ^ 1 * Y ^ 1 Rule QUAD ERROR 0 1.33333 0.33 1 1.00000 0.0 2 1.00000 0.20E-09 3 1.00000 0.15E-09 4 1.00000 0.0 5 1.00000 0.0 6 1.00000 0.0 7 1.00000 0.22E-15 8 1.00000 0.22E-15 9 1.00000 0.22E-15 10 1.00000 0.51E-14 11 1.00000 0.22E-15 12 1.00000 0.0 13 1.00000 0.0 14 1.00000 0.0 15 1.00000 0.0 16 1.00000 0.22E-14 17 1.00000 0.22E-15 18 1.00000 0.0 19 1.00000 0.22E-15 20 1.00000 0.11E-14 21 1.00000 0.22E-15 Integrate 12.0000 * X ^ 2 * Y ^ 0 Rule QUAD ERROR 0 0.666667 0.33 1 1.00000 0.0 2 1.00000 0.10E-09 3 1.00000 0.75E-10 4 1.00000 0.0 5 1.00000 0.22E-15 6 1.00000 0.22E-15 7 1.00000 0.22E-15 8 1.00000 0.22E-15 9 1.00000 0.0 10 1.00000 0.26E-14 11 1.00000 0.11E-15 12 1.00000 0.11E-15 13 1.00000 0.0 14 1.00000 0.22E-15 15 1.00000 0.11E-15 16 1.00000 0.12E-14 17 1.00000 0.22E-15 18 1.00000 0.11E-15 19 1.00000 0.22E-15 20 1.00000 0.44E-15 21 1.00000 0.33E-15 Integrate 20.0000 * X ^ 0 * Y ^ 3 Rule QUAD ERROR 0 0.370370 0.63 1 0.833333 0.17 2 1.11111 0.11 3 1.00000 0.63E-10 4 1.00000 0.11E-15 5 1.00000 0.11E-15 6 1.00000 0.67E-15 7 1.00000 0.22E-15 8 1.00000 0.22E-15 9 1.00000 0.0 10 1.00000 0.16E-14 11 1.00000 0.22E-15 12 1.00000 0.0 13 1.00000 0.11E-15 14 1.00000 0.22E-15 15 1.00000 0.33E-15 16 1.00000 0.89E-15 17 1.00000 0.0 18 1.00000 0.33E-15 19 1.00000 0.11E-15 20 1.00000 0.22E-15 21 1.00000 0.33E-15 Integrate 60.0000 * X ^ 1 * Y ^ 2 Rule QUAD ERROR 0 1.11111 0.11 1 1.25000 0.25 2 0.833333 0.17 3 1.00000 0.19E-09 4 1.00000 0.0 5 1.00000 0.11E-15 6 1.00000 0.0 7 1.00000 0.22E-15 8 1.00000 0.33E-15 9 1.00000 0.11E-15 10 1.00000 0.43E-14 11 1.00000 0.0 12 1.00000 0.22E-15 13 1.00000 0.22E-15 14 1.00000 0.11E-15 15 1.00000 0.22E-15 16 1.00000 0.14E-14 17 1.00000 0.22E-15 18 1.00000 0.11E-15 19 1.00000 0.0 20 1.00000 0.11E-14 21 1.00000 0.11E-15 Integrate 60.0000 * X ^ 2 * Y ^ 1 Rule QUAD ERROR 0 1.11111 0.11 1 1.25000 0.25 2 0.833333 0.17 3 1.00000 0.19E-09 4 1.00000 0.0 5 1.00000 0.11E-15 6 1.00000 0.0 7 1.00000 0.22E-15 8 1.00000 0.22E-15 9 1.00000 0.22E-15 10 1.00000 0.42E-14 11 1.00000 0.22E-15 12 1.00000 0.0 13 1.00000 0.0 14 1.00000 0.11E-15 15 1.00000 0.0 16 1.00000 0.18E-14 17 1.00000 0.22E-15 18 1.00000 0.0 19 1.00000 0.0 20 1.00000 0.11E-14 21 1.00000 0.0 Integrate 20.0000 * X ^ 3 * Y ^ 0 Rule QUAD ERROR 0 0.370370 0.63 1 0.833333 0.17 2 1.11111 0.11 3 1.00000 0.63E-10 4 1.00000 0.11E-15 5 1.00000 0.22E-15 6 1.00000 0.67E-15 7 1.00000 0.22E-15 8 1.00000 0.22E-15 9 1.00000 0.0 10 1.00000 0.16E-14 11 1.00000 0.22E-15 12 1.00000 0.11E-15 13 1.00000 0.22E-15 14 1.00000 0.22E-15 15 1.00000 0.33E-15 16 1.00000 0.67E-15 17 1.00000 0.22E-15 18 1.00000 0.22E-15 19 1.00000 0.22E-15 20 1.00000 0.22E-15 21 1.00000 0.33E-15 Integrate 30.0000 * X ^ 0 * Y ^ 4 Rule QUAD ERROR 0 0.185185 0.81 1 0.625000 0.38 2 1.38889 0.39 3 0.933333 0.67E-01 4 1.08333 0.83E-01 5 1.00000 0.33E-15 6 1.00000 0.78E-15 7 1.00000 0.44E-15 8 1.00000 0.44E-15 9 1.00000 0.0 10 1.00000 0.67E-15 11 1.00000 0.11E-15 12 1.00000 0.22E-15 13 1.00000 0.22E-15 14 1.00000 0.0 15 1.00000 0.44E-15 16 1.00000 0.22E-15 17 1.00000 0.22E-15 18 1.00000 0.33E-15 19 1.00000 0.11E-15 20 1.00000 0.33E-15 21 1.00000 0.11E-15 Integrate 120.000 * X ^ 1 * Y ^ 3 Rule QUAD ERROR 0 0.740741 0.26 1 1.25000 0.25 2 0.555556 0.44 3 1.13333 0.13 4 0.833333 0.17 5 1.00000 0.0 6 1.00000 0.22E-15 7 1.00000 0.44E-15 8 1.00000 0.44E-15 9 1.00000 0.0 10 1.00000 0.34E-14 11 1.00000 0.22E-15 12 1.00000 0.22E-15 13 1.00000 0.0 14 1.00000 0.0 15 1.00000 0.22E-15 16 1.00000 0.10E-14 17 1.00000 0.22E-15 18 1.00000 0.11E-15 19 1.00000 0.0 20 1.00000 0.89E-15 21 1.00000 0.11E-15 Integrate 180.000 * X ^ 2 * Y ^ 2 Rule QUAD ERROR 0 1.11111 0.11 1 1.87500 0.88 2 0.833333 0.17 3 0.800000 0.20 4 1.25000 0.25 5 1.00000 0.0 6 1.00000 0.0 7 1.00000 0.44E-15 8 1.00000 0.22E-15 9 1.00000 0.0 10 1.00000 0.38E-14 11 1.00000 0.22E-15 12 1.00000 0.22E-15 13 1.00000 0.22E-15 14 1.00000 0.22E-15 15 1.00000 0.0 16 1.00000 0.18E-14 17 1.00000 0.22E-15 18 1.00000 0.0 19 1.00000 0.22E-15 20 1.00000 0.16E-14 21 1.00000 0.33E-15 Integrate 120.000 * X ^ 3 * Y ^ 1 Rule QUAD ERROR 0 0.740741 0.26 1 1.25000 0.25 2 0.555556 0.44 3 1.13333 0.13 4 0.833333 0.17 5 1.00000 0.0 6 1.00000 0.11E-15 7 1.00000 0.44E-15 8 1.00000 0.56E-15 9 1.00000 0.0 10 1.00000 0.32E-14 11 1.00000 0.0 12 1.00000 0.0 13 1.00000 0.22E-15 14 1.00000 0.0 15 1.00000 0.22E-15 16 1.00000 0.13E-14 17 1.00000 0.22E-15 18 1.00000 0.0 19 1.00000 0.11E-15 20 1.00000 0.89E-15 21 1.00000 0.11E-15 Integrate 30.0000 * X ^ 4 * Y ^ 0 Rule QUAD ERROR 0 0.185185 0.81 1 0.625000 0.38 2 1.38889 0.39 3 0.933333 0.67E-01 4 1.08333 0.83E-01 5 1.00000 0.22E-15 6 1.00000 0.78E-15 7 1.00000 0.44E-15 8 1.00000 0.44E-15 9 1.00000 0.22E-15 10 1.00000 0.67E-15 11 1.00000 0.22E-15 12 1.00000 0.11E-15 13 1.00000 0.33E-15 14 1.00000 0.0 15 1.00000 0.44E-15 16 1.00000 0.22E-15 17 1.00000 0.0 18 1.00000 0.44E-15 19 1.00000 0.22E-15 20 1.00000 0.22E-15 21 1.00000 0.44E-15 Integrate 42.0000 * X ^ 0 * Y ^ 5 Rule QUAD ERROR 0 0.864198E-01 0.91 1 0.437500 0.56 2 1.81481 0.81 3 0.808889 0.19 4 1.26389 0.26 5 1.00527 0.53E-02 6 0.972222 0.28E-01 7 1.00889 0.89E-02 8 1.00000 0.44E-15 9 1.00000 0.0 10 1.00000 0.67E-15 11 1.00000 0.22E-15 12 1.00000 0.33E-15 13 1.00000 0.22E-15 14 1.00000 0.22E-15 15 1.00000 0.44E-15 16 1.00000 0.33E-15 17 1.00000 0.22E-15 18 1.00000 0.44E-15 19 1.00000 0.22E-15 20 1.00000 0.33E-15 21 1.00000 0.11E-15 Integrate 210.000 * X ^ 1 * Y ^ 4 Rule QUAD ERROR 0 0.432099 0.57 1 1.09375 0.94E-01 2 0.324074 0.68 3 1.24444 0.24 4 0.631944 0.37 5 0.986815 0.13E-01 6 1.06944 0.69E-01 7 0.977773 0.22E-01 8 1.00000 0.44E-15 9 1.00000 0.0 10 1.00000 0.29E-14 11 1.00000 0.0 12 1.00000 0.0 13 1.00000 0.11E-15 14 1.00000 0.22E-15 15 1.00000 0.22E-15 16 1.00000 0.33E-15 17 1.00000 0.22E-15 18 1.00000 0.22E-15 19 1.00000 0.11E-15 20 1.00000 0.22E-15 21 1.00000 0.33E-15 Integrate 420.000 * X ^ 2 * Y ^ 3 Rule QUAD ERROR 0 0.864198 0.14 1 2.18750 1.2 2 0.648148 0.35 3 0.808889 0.19 4 1.26389 0.26 5 1.00527 0.53E-02 6 0.972222 0.28E-01 7 1.00889 0.89E-02 8 1.00000 0.56E-15 9 1.00000 0.0 10 1.00000 0.27E-14 11 1.00000 0.22E-15 12 1.00000 0.44E-15 13 1.00000 0.22E-15 14 1.00000 0.22E-15 15 1.00000 0.0 16 1.00000 0.16E-14 17 1.00000 0.44E-15 18 1.00000 0.0 19 1.00000 0.22E-15 20 1.00000 0.89E-15 21 1.00000 0.33E-15 Integrate 420.000 * X ^ 3 * Y ^ 2 Rule QUAD ERROR 0 0.864198 0.14 1 2.18750 1.2 2 0.648148 0.35 3 0.808889 0.19 4 1.26389 0.26 5 1.00527 0.53E-02 6 0.972222 0.28E-01 7 1.00889 0.89E-02 8 1.00000 0.56E-15 9 1.00000 0.0 10 1.00000 0.27E-14 11 1.00000 0.22E-15 12 1.00000 0.22E-15 13 1.00000 0.44E-15 14 1.00000 0.0 15 1.00000 0.0 16 1.00000 0.16E-14 17 1.00000 0.44E-15 18 1.00000 0.0 19 1.00000 0.0 20 1.00000 0.11E-14 21 1.00000 0.33E-15 Integrate 210.000 * X ^ 4 * Y ^ 1 Rule QUAD ERROR 0 0.432099 0.57 1 1.09375 0.94E-01 2 0.324074 0.68 3 1.24444 0.24 4 0.631944 0.37 5 0.986815 0.13E-01 6 1.06944 0.69E-01 7 0.977773 0.22E-01 8 1.00000 0.56E-15 9 1.00000 0.0 10 1.00000 0.27E-14 11 1.00000 0.22E-15 12 1.00000 0.0 13 1.00000 0.33E-15 14 1.00000 0.0 15 1.00000 0.33E-15 16 1.00000 0.67E-15 17 1.00000 0.22E-15 18 1.00000 0.22E-15 19 1.00000 0.11E-15 20 1.00000 0.0 21 1.00000 0.33E-15 Integrate 42.0000 * X ^ 5 * Y ^ 0 Rule QUAD ERROR 0 0.864198E-01 0.91 1 0.437500 0.56 2 1.81481 0.81 3 0.808889 0.19 4 1.26389 0.26 5 1.00527 0.53E-02 6 0.972222 0.28E-01 7 1.00889 0.89E-02 8 1.00000 0.44E-15 9 1.00000 0.22E-15 10 1.00000 0.44E-15 11 1.00000 0.33E-15 12 1.00000 0.22E-15 13 1.00000 0.22E-15 14 1.00000 0.22E-15 15 1.00000 0.67E-15 16 1.00000 0.22E-15 17 1.00000 0.0 18 1.00000 0.56E-15 19 1.00000 0.33E-15 20 1.00000 0.22E-15 21 1.00000 0.11E-15 Integrate 56.0000 * X ^ 0 * Y ^ 6 Rule QUAD ERROR 0 0.384088E-01 0.96 1 0.291667 0.71 2 2.36214 1.4 3 0.660662 0.34 4 1.53395 0.53 5 1.01295 0.13E-01 6 0.898765 0.10 7 1.03997 0.40E-01 8 0.995414 0.46E-02 9 1.00317 0.32E-02 10 1.00000 0.89E-15 11 1.00000 0.33E-15 12 1.00000 0.11E-15 13 1.00000 0.44E-15 14 1.00000 0.44E-15 15 1.00000 0.44E-15 16 1.00000 0.22E-15 17 1.00000 0.11E-15 18 1.00000 0.22E-15 19 1.00000 0.0 20 1.00000 0.11E-15 21 1.00000 0.11E-15 Integrate 336.000 * X ^ 1 * Y ^ 5 Rule QUAD ERROR 0 0.230453 0.77 1 0.875000 0.12 2 0.172840 0.83 3 1.25357 0.25 4 0.453704 0.55 5 0.982247 0.18E-01 6 1.19259 0.19 7 0.915646 0.84E-01 8 1.01376 0.14E-01 9 0.990476 0.95E-02 10 1.00000 0.78E-15 11 1.00000 0.22E-15 12 1.00000 0.0 13 1.00000 0.22E-15 14 1.00000 0.22E-15 15 1.00000 0.22E-15 16 1.00000 0.11E-15 17 1.00000 0.0 18 1.00000 0.11E-15 19 1.00000 0.11E-15 20 1.00000 0.22E-15 21 1.00000 0.33E-15 Integrate 840.000 * X ^ 2 * Y ^ 4 Rule QUAD ERROR 0 0.576132 0.42 1 2.18750 1.2 2 0.432099 0.57 3 0.949926 0.50E-01 4 1.13426 0.13 5 0.958434 0.42E-01 6 1.03704 0.37E-01 7 1.02691 0.27E-01 8 0.962963 0.37E-01 9 1.00000 0.0 10 1.00000 0.56E-14 11 1.00000 0.22E-15 12 1.00000 0.44E-15 13 1.00000 0.22E-15 14 1.00000 0.22E-15 15 1.00000 0.67E-15 16 1.00000 0.56E-15 17 1.00000 0.22E-15 18 1.00000 0.22E-15 19 1.00000 0.0 20 1.00000 0.89E-15 21 1.00000 0.33E-15 Integrate 1120.00 * X ^ 3 * Y ^ 3 Rule QUAD ERROR 0 0.768176 0.23 1 2.91667 1.9 2 0.576132 0.42 3 0.594568 0.41 4 1.51235 0.51 5 1.06350 0.63E-01 6 0.864198 0.14 7 1.00379 0.38E-02 8 1.05115 0.51E-01 9 1.01587 0.16E-01 10 1.00000 0.18E-14 11 1.00000 0.22E-15 12 1.00000 0.44E-15 13 1.00000 0.89E-15 14 1.00000 0.44E-15 15 1.00000 0.44E-15 16 1.00000 0.20E-14 17 1.00000 0.22E-15 18 1.00000 0.0 19 1.00000 0.0 20 1.00000 0.89E-15 21 1.00000 0.33E-15 Integrate 840.000 * X ^ 4 * Y ^ 2 Rule QUAD ERROR 0 0.576132 0.42 1 2.18750 1.2 2 0.432099 0.57 3 0.949926 0.50E-01 4 1.13426 0.13 5 0.958434 0.42E-01 6 1.03704 0.37E-01 7 1.02691 0.27E-01 8 0.962963 0.37E-01 9 1.00000 0.0 10 1.00000 0.56E-14 11 1.00000 0.22E-15 12 1.00000 0.22E-15 13 1.00000 0.33E-15 14 1.00000 0.22E-15 15 1.00000 0.0 16 1.00000 0.10E-14 17 1.00000 0.44E-15 18 1.00000 0.22E-15 19 1.00000 0.0 20 1.00000 0.67E-15 21 1.00000 0.33E-15 Integrate 336.000 * X ^ 5 * Y ^ 1 Rule QUAD ERROR 0 0.230453 0.77 1 0.875000 0.12 2 0.172840 0.83 3 1.25357 0.25 4 0.453704 0.55 5 0.982247 0.18E-01 6 1.19259 0.19 7 0.915646 0.84E-01 8 1.01376 0.14E-01 9 0.990476 0.95E-02 10 1.00000 0.67E-15 11 1.00000 0.22E-15 12 1.00000 0.0 13 1.00000 0.33E-15 14 1.00000 0.11E-15 15 1.00000 0.44E-15 16 1.00000 0.44E-15 17 1.00000 0.0 18 1.00000 0.0 19 1.00000 0.22E-15 20 1.00000 0.11E-15 21 1.00000 0.22E-15 Integrate 56.0000 * X ^ 6 * Y ^ 0 Rule QUAD ERROR 0 0.384088E-01 0.96 1 0.291667 0.71 2 2.36214 1.4 3 0.660662 0.34 4 1.53395 0.53 5 1.01295 0.13E-01 6 0.898765 0.10 7 1.03997 0.40E-01 8 0.995414 0.46E-02 9 1.00317 0.32E-02 10 1.00000 0.89E-15 11 1.00000 0.33E-15 12 1.00000 0.11E-15 13 1.00000 0.33E-15 14 1.00000 0.44E-15 15 1.00000 0.44E-15 16 1.00000 0.22E-15 17 1.00000 0.11E-15 18 1.00000 0.22E-15 19 1.00000 0.0 20 1.00000 0.22E-15 21 1.00000 0.11E-15 Integrate 72.0000 * X ^ 0 * Y ^ 7 Rule QUAD ERROR 0 0.164609E-01 0.98 1 0.187500 0.81 2 3.01235 2.0 3 0.516101 0.48 4 1.88241 0.88 5 1.01690 0.17E-01 6 0.774074 0.23 7 1.10277 0.10 8 0.981708 0.18E-01 9 1.01361 0.14E-01 10 1.00020 0.20E-03 11 0.995833 0.42E-02 12 0.999320 0.68E-03 13 1.00000 0.44E-15 14 1.00000 0.22E-15 15 1.00000 0.44E-15 16 1.00000 0.44E-15 17 1.00000 0.0 18 1.00000 0.78E-15 19 1.00000 0.0 20 1.00000 0.11E-15 21 1.00000 0.0 Integrate 504.000 * X ^ 1 * Y ^ 6 Rule QUAD ERROR 0 0.115226 0.88 1 0.656250 0.34 2 0.864198E-01 0.91 3 1.16663 0.17 4 0.314352 0.69 5 0.999117 0.88E-03 6 1.33519 0.34 7 0.820163 0.18 8 1.04339 0.43E-01 9 0.966667 0.33E-01 10 0.999307 0.69E-03 11 1.01458 0.15E-01 12 1.00238 0.24E-02 13 1.00000 0.89E-15 14 1.00000 0.22E-15 15 1.00000 0.22E-15 16 1.00000 0.11E-15 17 1.00000 0.22E-15 18 1.00000 0.22E-15 19 1.00000 0.11E-15 20 1.00000 0.44E-15 21 1.00000 0.33E-15 Integrate 1512.00 * X ^ 2 * Y ^ 5 Rule QUAD ERROR 0 0.345679 0.65 1 1.96875 0.97 2 0.259259 0.74 3 1.08068 0.81E-01 4 0.943056 0.57E-01 5 0.881502 0.12 6 1.20556 0.21 7 1.01725 0.17E-01 8 0.909751 0.90E-01 9 0.989796 0.10E-01 10 1.00089 0.89E-03 11 0.981250 0.19E-01 12 0.996939 0.31E-02 13 1.00000 0.10E-14 14 1.00000 0.44E-15 15 1.00000 0.44E-15 16 1.00000 0.11E-15 17 1.00000 0.22E-15 18 1.00000 0.44E-15 19 1.00000 0.22E-15 20 1.00000 0.13E-14 21 1.00000 0.56E-15 Integrate 2520.00 * X ^ 3 * Y ^ 4 Rule QUAD ERROR 0 0.576132 0.42 1 3.28125 2.3 2 0.432099 0.57 3 0.591526 0.41 4 1.57176 0.57 5 1.05737 0.57E-01 6 0.842593 0.16 7 1.02827 0.28E-01 8 1.05367 0.54E-01 9 1.03741 0.37E-01 10 0.999505 0.50E-03 11 1.01042 0.10E-01 12 1.00170 0.17E-02 13 1.00000 0.67E-15 14 1.00000 0.44E-15 15 1.00000 0.44E-15 16 1.00000 0.78E-15 17 1.00000 0.44E-15 18 1.00000 0.11E-15 19 1.00000 0.0 20 1.00000 0.22E-15 21 1.00000 0.33E-15 Integrate 2520.00 * X ^ 4 * Y ^ 3 Rule QUAD ERROR 0 0.576132 0.42 1 3.28125 2.3 2 0.432099 0.57 3 0.591526 0.41 4 1.57176 0.57 5 1.05737 0.57E-01 6 0.842593 0.16 7 1.02827 0.28E-01 8 1.05367 0.54E-01 9 1.03741 0.37E-01 10 0.999505 0.50E-03 11 1.01042 0.10E-01 12 1.00170 0.17E-02 13 1.00000 0.67E-15 14 1.00000 0.22E-15 15 1.00000 0.22E-15 16 1.00000 0.13E-14 17 1.00000 0.67E-15 18 1.00000 0.11E-15 19 1.00000 0.0 20 1.00000 0.22E-15 21 1.00000 0.11E-15 Integrate 1512.00 * X ^ 5 * Y ^ 2 Rule QUAD ERROR 0 0.345679 0.65 1 1.96875 0.97 2 0.259259 0.74 3 1.08068 0.81E-01 4 0.943056 0.57E-01 5 0.881502 0.12 6 1.20556 0.21 7 1.01725 0.17E-01 8 0.909751 0.90E-01 9 0.989796 0.10E-01 10 1.00089 0.89E-03 11 0.981250 0.19E-01 12 0.996939 0.31E-02 13 1.00000 0.13E-14 14 1.00000 0.22E-15 15 1.00000 0.11E-15 16 1.00000 0.67E-15 17 1.00000 0.44E-15 18 1.00000 0.33E-15 19 1.00000 0.0 20 1.00000 0.89E-15 21 1.00000 0.67E-15 Integrate 504.000 * X ^ 6 * Y ^ 1 Rule QUAD ERROR 0 0.115226 0.88 1 0.656250 0.34 2 0.864198E-01 0.91 3 1.16663 0.17 4 0.314352 0.69 5 0.999117 0.88E-03 6 1.33519 0.34 7 0.820163 0.18 8 1.04339 0.43E-01 9 0.966667 0.33E-01 10 0.999307 0.69E-03 11 1.01458 0.15E-01 12 1.00238 0.24E-02 13 1.00000 0.44E-15 14 1.00000 0.0 15 1.00000 0.22E-15 16 1.00000 0.44E-15 17 1.00000 0.22E-15 18 1.00000 0.22E-15 19 1.00000 0.22E-15 20 1.00000 0.78E-15 21 1.00000 0.44E-15 Integrate 72.0000 * X ^ 7 * Y ^ 0 Rule QUAD ERROR 0 0.164609E-01 0.98 1 0.187500 0.81 2 3.01235 2.0 3 0.516101 0.48 4 1.88241 0.88 5 1.01690 0.17E-01 6 0.774074 0.23 7 1.10277 0.10 8 0.981708 0.18E-01 9 1.01361 0.14E-01 10 1.00020 0.20E-03 11 0.995833 0.42E-02 12 0.999320 0.68E-03 13 1.00000 0.44E-15 14 1.00000 0.22E-15 15 1.00000 0.44E-15 16 1.00000 0.56E-15 17 1.00000 0.22E-15 18 1.00000 0.67E-15 19 1.00000 0.0 20 1.00000 0.11E-15 21 1.00000 0.22E-15 Integrate 90.0000 * X ^ 0 * Y ^ 8 Rule QUAD ERROR 0 0.685871E-02 0.99 1 0.117188 0.88 2 3.75514 2.8 3 0.389922 0.61 4 2.29996 1.3 5 1.01216 0.12E-01 6 0.600309 0.40 7 1.20174 0.20 8 0.956602 0.43E-01 9 1.03515 0.35E-01 10 1.00044 0.44E-03 11 0.980221 0.20E-01 12 0.996936 0.31E-02 13 0.999572 0.43E-03 14 1.00032 0.32E-03 15 1.00000 0.12E-14 16 1.00000 0.44E-15 17 1.00000 0.11E-15 18 1.00000 0.12E-14 19 1.00000 0.11E-15 20 1.00000 0.0 21 1.00000 0.22E-15 Integrate 720.000 * X ^ 1 * Y ^ 7 Rule QUAD ERROR 0 0.548697E-01 0.95 1 0.468750 0.53 2 0.411523E-01 0.96 3 1.02082 0.21E-01 4 0.212191 0.79 5 1.03586 0.36E-01 6 1.46914 0.47 7 0.706913 0.29 8 1.08213 0.82E-01 9 0.927415 0.73E-01 10 0.999233 0.77E-03 11 1.05828 0.58E-01 12 1.00885 0.89E-02 13 1.00171 0.17E-02 14 0.998702 0.13E-02 15 1.00000 0.22E-15 16 1.00000 0.0 17 1.00000 0.22E-15 18 1.00000 0.22E-15 19 1.00000 0.22E-15 20 1.00000 0.21E-14 21 1.00000 0.0 Integrate 2520.00 * X ^ 2 * Y ^ 6 Rule QUAD ERROR 0 0.192044 0.81 1 1.64062 0.64 2 0.144033 0.86 3 1.13350 0.13 4 0.742670 0.26 5 0.811392 0.19 6 1.44753 0.45 7 0.967166 0.33E-01 8 0.866501 0.13 9 0.968983 0.31E-01 10 0.996224 0.38E-02 11 0.948785 0.51E-01 12 0.996620 0.34E-02 13 0.994117 0.59E-02 14 1.00622 0.62E-02 15 1.00000 0.67E-15 16 1.00000 0.22E-15 17 1.00000 0.22E-15 18 1.00000 0.33E-15 19 1.00000 0.22E-15 20 1.00000 0.24E-14 21 1.00000 0.78E-15 Integrate 5040.00 * X ^ 3 * Y ^ 5 Rule QUAD ERROR 0 0.384088 0.62 1 3.28125 2.3 2 0.288066 0.71 3 0.694511 0.31 4 1.48534 0.49 5 0.972131 0.28E-01 6 0.950617 0.49E-01 7 1.04481 0.45E-01 8 0.992477 0.75E-02 9 1.03418 0.34E-01 10 1.01154 0.12E-01 11 1.00174 0.17E-02 12 0.987653 0.12E-01 13 1.01166 0.12E-01 14 0.985894 0.14E-01 15 1.00000 0.67E-15 16 1.00000 0.44E-15 17 1.00000 0.22E-15 18 1.00000 0.56E-15 19 1.00000 0.22E-15 20 1.00000 0.56E-15 21 1.00000 0.22E-15 Integrate 6300.00 * X ^ 4 * Y ^ 4 Rule QUAD ERROR 0 0.480110 0.52 1 4.10156 3.1 2 0.360082 0.64 3 0.414538 0.59 4 1.85667 0.86 5 1.12991 0.13 6 0.702160 0.30 7 1.06459 0.65E-01 8 1.13775 0.14 9 1.11050 0.11 10 0.983592 0.16E-01 11 1.04384 0.44E-01 12 1.02361 0.24E-01 13 0.985455 0.15E-01 14 1.01805 0.18E-01 15 1.00000 0.44E-15 16 1.00000 0.44E-15 17 1.00000 0.44E-15 18 1.00000 0.0 19 1.00000 0.22E-15 20 1.00000 0.11E-15 21 1.00000 0.11E-15 Integrate 5040.00 * X ^ 5 * Y ^ 3 Rule QUAD ERROR 0 0.384088 0.62 1 3.28125 2.3 2 0.288066 0.71 3 0.694511 0.31 4 1.48534 0.49 5 0.972131 0.28E-01 6 0.950617 0.49E-01 7 1.04481 0.45E-01 8 0.992477 0.75E-02 9 1.03418 0.34E-01 10 1.01154 0.12E-01 11 1.00174 0.17E-02 12 0.987653 0.12E-01 13 1.01166 0.12E-01 14 0.985894 0.14E-01 15 1.00000 0.0 16 1.00000 0.12E-14 17 1.00000 0.22E-15 18 1.00000 0.33E-15 19 1.00000 0.22E-15 20 1.00000 0.56E-15 21 1.00000 0.22E-15 Integrate 2520.00 * X ^ 6 * Y ^ 2 Rule QUAD ERROR 0 0.192044 0.81 1 1.64062 0.64 2 0.144033 0.86 3 1.13350 0.13 4 0.742670 0.26 5 0.811392 0.19 6 1.44753 0.45 7 0.967166 0.33E-01 8 0.866501 0.13 9 0.968983 0.31E-01 10 0.996224 0.38E-02 11 0.948785 0.51E-01 12 0.996620 0.34E-02 13 0.994117 0.59E-02 14 1.00622 0.62E-02 15 1.00000 0.22E-15 16 1.00000 0.33E-15 17 1.00000 0.44E-15 18 1.00000 0.44E-15 19 1.00000 0.0 20 1.00000 0.22E-14 21 1.00000 0.78E-15 Integrate 720.000 * X ^ 7 * Y ^ 1 Rule QUAD ERROR 0 0.548697E-01 0.95 1 0.468750 0.53 2 0.411523E-01 0.96 3 1.02082 0.21E-01 4 0.212191 0.79 5 1.03586 0.36E-01 6 1.46914 0.47 7 0.706913 0.29 8 1.08213 0.82E-01 9 0.927415 0.73E-01 10 0.999233 0.77E-03 11 1.05828 0.58E-01 12 1.00885 0.89E-02 13 1.00171 0.17E-02 14 0.998702 0.13E-02 15 1.00000 0.67E-15 16 1.00000 0.33E-15 17 1.00000 0.0 18 1.00000 0.67E-15 19 1.00000 0.33E-15 20 1.00000 0.27E-14 21 1.00000 0.22E-15 Integrate 90.0000 * X ^ 8 * Y ^ 0 Rule QUAD ERROR 0 0.685871E-02 0.99 1 0.117188 0.88 2 3.75514 2.8 3 0.389922 0.61 4 2.29996 1.3 5 1.01216 0.12E-01 6 0.600309 0.40 7 1.20174 0.20 8 0.956602 0.43E-01 9 1.03515 0.35E-01 10 1.00044 0.44E-03 11 0.980221 0.20E-01 12 0.996936 0.31E-02 13 0.999572 0.43E-03 14 1.00032 0.32E-03 15 1.00000 0.11E-14 16 1.00000 0.44E-15 17 1.00000 0.22E-15 18 1.00000 0.12E-14 19 1.00000 0.11E-15 20 1.00000 0.22E-15 21 1.00000 0.33E-15 Integrate 110.000 * X ^ 0 * Y ^ 9 Rule QUAD ERROR 0 0.279429E-02 1.0 1 0.716146E-01 0.93 2 4.58543 3.6 3 0.287142 0.71 4 2.77990 1.8 5 0.996255 0.37E-02 6 0.383202 0.62 7 1.33761 0.34 8 0.920084 0.80E-01 9 1.07095 0.71E-01 10 1.00009 0.86E-04 11 0.945230 0.55E-01 12 0.991867 0.81E-02 13 0.997886 0.21E-02 14 1.00164 0.16E-02 15 0.999942 0.58E-04 16 1.00020 0.20E-03 17 1.00013 0.13E-03 18 1.00000 0.17E-14 19 1.00000 0.11E-15 20 1.00000 0.13E-14 21 1.00000 0.56E-15 Integrate 990.000 * X ^ 1 * Y ^ 8 Rule QUAD ERROR 0 0.251486E-01 0.97 1 0.322266 0.68 2 0.188615E-01 0.98 3 0.852434 0.15 4 0.140223 0.86 5 1.08374 0.84E-01 6 1.57729 0.58 7 0.590312 0.41 8 1.12094 0.12 9 0.874065 0.13 10 1.00203 0.20E-02 11 1.13768 0.14 12 1.01975 0.20E-01 13 1.00716 0.72E-02 14 0.994392 0.56E-02 15 1.00026 0.26E-03 16 0.999113 0.89E-03 17 0.999431 0.57E-03 18 1.00000 0.89E-15 19 1.00000 0.22E-15 20 1.00000 0.51E-14 21 1.00000 0.89E-15 Integrate 3960.00 * X ^ 2 * Y ^ 7 Rule QUAD ERROR 0 0.100594 0.90 1 1.28906 0.29 2 0.754458E-01 0.92 3 1.10343 0.10 4 0.560892 0.44 5 0.769683 0.23 6 1.72582 0.73 7 0.883621 0.12 8 0.846090 0.15 9 0.939825 0.60E-01 10 0.981678 0.18E-01 11 0.922919 0.77E-01 12 1.00607 0.61E-02 13 0.979223 0.21E-01 14 1.02298 0.23E-01 15 0.999209 0.79E-03 16 1.00132 0.13E-02 17 1.00121 0.12E-02 18 1.00000 0.56E-15 19 1.00000 0.11E-15 20 1.00000 0.47E-14 21 1.00000 0.16E-14 Integrate 9240.00 * X ^ 3 * Y ^ 6 Rule QUAD ERROR 0 0.234720 0.77 1 3.00781 2.0 2 0.176040 0.82 3 0.800594 0.20 4 1.30875 0.31 5 0.846318 0.15 6 1.17507 0.18 7 1.02585 0.26E-01 8 0.896388 0.10 9 1.00176 0.18E-02 10 1.03039 0.30E-01 11 0.959901 0.40E-01 12 0.959792 0.40E-01 13 1.02893 0.29E-01 14 0.963277 0.37E-01 15 1.00155 0.16E-02 16 0.999523 0.48E-03 17 0.998423 0.16E-02 18 1.00000 0.89E-15 19 1.00000 0.22E-15 20 1.00000 0.44E-15 21 1.00000 0.67E-15 Integrate 13860.0 * X ^ 4 * Y ^ 5 Rule QUAD ERROR 0 0.352080 0.65 1 4.51172 3.5 2 0.264060 0.74 3 0.402555 0.60 4 1.96312 0.96 5 1.10610 0.11 6 0.693158 0.31 7 1.10780 0.11 8 1.14249 0.14 9 1.15903 0.16 10 0.982741 0.17E-01 11 1.06746 0.67E-01 12 1.02844 0.28E-01 13 0.985505 0.14E-01 14 1.01867 0.19E-01 15 0.999065 0.93E-03 16 0.999750 0.25E-03 17 1.00075 0.75E-03 18 1.00000 0.44E-15 19 1.00000 0.11E-15 20 1.00000 0.78E-15 21 1.00000 0.22E-15 Integrate 13860.0 * X ^ 5 * Y ^ 4 Rule QUAD ERROR 0 0.352080 0.65 1 4.51172 3.5 2 0.264060 0.74 3 0.402555 0.60 4 1.96312 0.96 5 1.10610 0.11 6 0.693158 0.31 7 1.10780 0.11 8 1.14249 0.14 9 1.15903 0.16 10 0.982741 0.17E-01 11 1.06746 0.67E-01 12 1.02844 0.28E-01 13 0.985505 0.14E-01 14 1.01867 0.19E-01 15 0.999065 0.93E-03 16 0.999750 0.25E-03 17 1.00075 0.75E-03 18 1.00000 0.22E-15 19 1.00000 0.11E-15 20 1.00000 0.67E-15 21 1.00000 0.22E-15 Integrate 9240.00 * X ^ 6 * Y ^ 3 Rule QUAD ERROR 0 0.234720 0.77 1 3.00781 2.0 2 0.176040 0.82 3 0.800594 0.20 4 1.30875 0.31 5 0.846318 0.15 6 1.17507 0.18 7 1.02585 0.26E-01 8 0.896388 0.10 9 1.00176 0.18E-02 10 1.03039 0.30E-01 11 0.959901 0.40E-01 12 0.959792 0.40E-01 13 1.02893 0.29E-01 14 0.963277 0.37E-01 15 1.00155 0.16E-02 16 0.999523 0.48E-03 17 0.998423 0.16E-02 18 1.00000 0.78E-15 19 1.00000 0.22E-15 20 1.00000 0.67E-15 21 1.00000 0.44E-15 Integrate 3960.00 * X ^ 7 * Y ^ 2 Rule QUAD ERROR 0 0.100594 0.90 1 1.28906 0.29 2 0.754458E-01 0.92 3 1.10343 0.10 4 0.560892 0.44 5 0.769683 0.23 6 1.72582 0.73 7 0.883621 0.12 8 0.846090 0.15 9 0.939825 0.60E-01 10 0.981678 0.18E-01 11 0.922919 0.77E-01 12 1.00607 0.61E-02 13 0.979223 0.21E-01 14 1.02298 0.23E-01 15 0.999209 0.79E-03 16 1.00132 0.13E-02 17 1.00121 0.12E-02 18 1.00000 0.44E-15 19 1.00000 0.22E-15 20 1.00000 0.42E-14 21 1.00000 0.14E-14 Integrate 990.000 * X ^ 8 * Y ^ 1 Rule QUAD ERROR 0 0.251486E-01 0.97 1 0.322266 0.68 2 0.188615E-01 0.98 3 0.852434 0.15 4 0.140223 0.86 5 1.08374 0.84E-01 6 1.57729 0.58 7 0.590312 0.41 8 1.12094 0.12 9 0.874065 0.13 10 1.00203 0.20E-02 11 1.13768 0.14 12 1.01975 0.20E-01 13 1.00716 0.72E-02 14 0.994392 0.56E-02 15 1.00026 0.26E-03 16 0.999113 0.89E-03 17 0.999431 0.57E-03 18 1.00000 0.67E-15 19 1.00000 0.33E-15 20 1.00000 0.57E-14 21 1.00000 0.67E-15 Integrate 110.000 * X ^ 9 * Y ^ 0 Rule QUAD ERROR 0 0.279429E-02 1.0 1 0.716146E-01 0.93 2 4.58543 3.6 3 0.287142 0.71 4 2.77990 1.8 5 0.996255 0.37E-02 6 0.383202 0.62 7 1.33761 0.34 8 0.920084 0.80E-01 9 1.07095 0.71E-01 10 1.00009 0.86E-04 11 0.945230 0.55E-01 12 0.991867 0.81E-02 13 0.997886 0.21E-02 14 1.00164 0.16E-02 15 0.999942 0.58E-04 16 1.00020 0.20E-03 17 1.00013 0.13E-03 18 1.00000 0.16E-14 19 1.00000 0.0 20 1.00000 0.13E-14 21 1.00000 0.56E-15 Integrate 132.000 * X ^ 0 * Y ^ 10 Rule QUAD ERROR 0 0.111772E-02 1.0 1 0.429688E-01 0.96 2 5.50084 4.5 3 0.207231 0.79 4 3.31769 2.3 5 0.968918 0.31E-01 6 0.129515 0.87 7 1.50907 0.51 8 0.873671 0.13 9 1.12323 0.12 10 0.998219 0.18E-02 11 0.883970 0.12 12 0.983360 0.17E-01 13 0.993975 0.60E-02 14 1.00481 0.48E-02 15 0.999662 0.34E-03 16 1.00109 0.11E-02 17 1.00066 0.66E-03 18 0.999970 0.30E-04 19 0.999979 0.21E-04 20 1.00000 0.38E-14 21 1.00000 0.89E-15 Integrate 1320.00 * X ^ 1 * Y ^ 9 Rule QUAD ERROR 0 0.111772E-01 0.99 1 0.214844 0.79 2 0.838287E-02 0.99 3 0.686695 0.31 4 0.909672E-01 0.91 5 1.13294 0.13 6 1.65163 0.65 7 0.480319 0.52 8 1.15215 0.15 9 0.809557 0.19 10 1.00942 0.94E-02 11 1.25153 0.25 12 1.03440 0.34E-01 13 1.01744 0.17E-01 14 0.985803 0.14E-01 15 1.00134 0.13E-02 16 0.995717 0.43E-02 17 0.997466 0.25E-02 18 1.00015 0.15E-03 19 1.00010 0.10E-03 20 1.00000 0.94E-14 21 1.00000 0.18E-14 Integrate 5940.00 * X ^ 2 * Y ^ 8 Rule QUAD ERROR 0 0.502972E-01 0.95 1 0.966797 0.33E-01 2 0.377229E-01 0.96 3 1.01255 0.13E-01 4 0.409352 0.59 5 0.761318 0.24 6 2.00874 1.0 7 0.780207 0.22 8 0.849523 0.15 9 0.903830 0.96E-01 10 0.957945 0.42E-01 11 0.924013 0.76E-01 12 1.02938 0.29E-01 13 0.956754 0.43E-01 14 1.05042 0.50E-01 15 0.996306 0.37E-02 16 1.00487 0.49E-02 17 1.00396 0.40E-02 18 0.999303 0.70E-03 19 0.999414 0.59E-03 20 1.00000 0.60E-14 21 1.00000 0.13E-14 Integrate 15840.0 * X ^ 3 * Y ^ 7 Rule QUAD ERROR 0 0.134126 0.87 1 2.57812 1.6 2 0.100594 0.90 3 0.860170 0.14 4 1.09161 0.92E-01 5 0.720497 0.28 6 1.48628 0.49 7 0.967926 0.32E-01 8 0.797080 0.20 9 0.949768 0.50E-01 10 1.04271 0.43E-01 11 0.893970 0.11 12 0.931119 0.69E-01 13 1.03934 0.39E-01 14 0.945921 0.54E-01 15 1.00613 0.61E-02 16 0.999956 0.44E-04 17 0.997525 0.25E-02 18 1.00188 0.19E-02 19 1.00173 0.17E-02 20 1.00000 0.89E-15 21 1.00000 0.11E-14 Integrate 27720.0 * X ^ 4 * Y ^ 6 Rule QUAD ERROR 0 0.234720 0.77 1 4.51172 3.5 2 0.176040 0.82 3 0.467461 0.53 4 1.91031 0.91 5 0.998828 0.12E-02 6 0.818587 0.18 7 1.11924 0.12 8 1.06917 0.69E-01 9 1.15486 0.15 10 1.00786 0.79E-02 11 1.05360 0.54E-01 12 0.999566 0.43E-03 13 1.01024 0.10E-01 14 0.989214 0.11E-01 15 0.997890 0.21E-02 16 0.999336 0.66E-03 17 0.996401 0.36E-02 18 0.996691 0.33E-02 19 0.996853 0.31E-02 20 1.00000 0.23E-14 21 1.00000 0.0 Integrate 33264.0 * X ^ 5 * Y ^ 5 Rule QUAD ERROR 0 0.281664 0.72 1 5.41406 4.4 2 0.211248 0.79 3 0.273552 0.73 4 2.29237 1.3 5 1.16618 0.17 6 0.554527 0.45 7 1.19336 0.19 8 1.23958 0.24 9 1.28766 0.29 10 0.950326 0.50E-01 11 1.13827 0.14 12 1.07273 0.73E-01 13 0.955574 0.44E-01 14 1.05418 0.54E-01 15 0.997684 0.23E-02 16 0.996791 0.32E-02 17 1.00713 0.71E-02 18 1.00398 0.40E-02 19 1.00383 0.38E-02 20 1.00000 0.89E-15 21 1.00000 0.44E-15 Integrate 27720.0 * X ^ 6 * Y ^ 4 Rule QUAD ERROR 0 0.234720 0.77 1 4.51172 3.5 2 0.176040 0.82 3 0.467461 0.53 4 1.91031 0.91 5 0.998828 0.12E-02 6 0.818587 0.18 7 1.11924 0.12 8 1.06917 0.69E-01 9 1.15486 0.15 10 1.00786 0.79E-02 11 1.05360 0.54E-01 12 0.999566 0.43E-03 13 1.01024 0.10E-01 14 0.989214 0.11E-01 15 0.997890 0.21E-02 16 0.999336 0.66E-03 17 0.996401 0.36E-02 18 0.996691 0.33E-02 19 0.996853 0.31E-02 20 1.00000 0.23E-14 21 1.00000 0.0 Integrate 15840.0 * X ^ 7 * Y ^ 3 Rule QUAD ERROR 0 0.134126 0.87 1 2.57812 1.6 2 0.100594 0.90 3 0.860170 0.14 4 1.09161 0.92E-01 5 0.720497 0.28 6 1.48628 0.49 7 0.967926 0.32E-01 8 0.797080 0.20 9 0.949768 0.50E-01 10 1.04271 0.43E-01 11 0.893970 0.11 12 0.931119 0.69E-01 13 1.03934 0.39E-01 14 0.945921 0.54E-01 15 1.00613 0.61E-02 16 0.999956 0.44E-04 17 0.997525 0.25E-02 18 1.00188 0.19E-02 19 1.00173 0.17E-02 20 1.00000 0.44E-15 21 1.00000 0.89E-15 Integrate 5940.00 * X ^ 8 * Y ^ 2 Rule QUAD ERROR 0 0.502972E-01 0.95 1 0.966797 0.33E-01 2 0.377229E-01 0.96 3 1.01255 0.13E-01 4 0.409352 0.59 5 0.761318 0.24 6 2.00874 1.0 7 0.780207 0.22 8 0.849523 0.15 9 0.903830 0.96E-01 10 0.957945 0.42E-01 11 0.924013 0.76E-01 12 1.02938 0.29E-01 13 0.956754 0.43E-01 14 1.05042 0.50E-01 15 0.996306 0.37E-02 16 1.00487 0.49E-02 17 1.00396 0.40E-02 18 0.999303 0.70E-03 19 0.999414 0.59E-03 20 1.00000 0.58E-14 21 1.00000 0.12E-14 Integrate 1320.00 * X ^ 9 * Y ^ 1 Rule QUAD ERROR 0 0.111772E-01 0.99 1 0.214844 0.79 2 0.838287E-02 0.99 3 0.686695 0.31 4 0.909672E-01 0.91 5 1.13294 0.13 6 1.65163 0.65 7 0.480319 0.52 8 1.15215 0.15 9 0.809557 0.19 10 1.00942 0.94E-02 11 1.25153 0.25 12 1.03440 0.34E-01 13 1.01744 0.17E-01 14 0.985803 0.14E-01 15 1.00134 0.13E-02 16 0.995717 0.43E-02 17 0.997466 0.25E-02 18 1.00015 0.15E-03 19 1.00010 0.10E-03 20 1.00000 0.10E-13 21 1.00000 0.16E-14 Integrate 132.000 * X ^ 10 * Y ^ 0 Rule QUAD ERROR 0 0.111772E-02 1.0 1 0.429688E-01 0.96 2 5.50084 4.5 3 0.207231 0.79 4 3.31769 2.3 5 0.968918 0.31E-01 6 0.129515 0.87 7 1.50907 0.51 8 0.873671 0.13 9 1.12323 0.12 10 0.998219 0.18E-02 11 0.883970 0.12 12 0.983360 0.17E-01 13 0.993975 0.60E-02 14 1.00481 0.48E-02 15 0.999662 0.34E-03 16 1.00109 0.11E-02 17 1.00066 0.66E-03 18 0.999970 0.30E-04 19 0.999979 0.21E-04 20 1.00000 0.38E-14 21 1.00000 0.10E-14 TRIANGLE_LYNESS_RULE_TEST(): Normal end of execution. 23 March 2023 5:03:40.036 PM