Mariusz Iwaniuk

1039 Reputation

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4 years, 306 days

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These are answers submitted by Mariusz Iwaniuk


 

restart

with(plots)

FAK := proc (`&vartheta;`, `&vartheta;l`, tau) local fak; if not type(tau, numeric) then return ('procname')(args) end if; fak := 0; if `&vartheta;l` <= `&vartheta;` then fak := 1 end if; return fak end proc

`&vartheta;l` := .7227342478

eq := diff(`&vartheta;`(tau), tau, tau)+6.666666666*sin(`&vartheta;`(tau))+66.66666666*cos(`&vartheta;`(tau))^2*FAK(`&vartheta;`(tau), .7227342478, tau)*(`&vartheta;`(tau)-.7227342478)+66.66666666*sin(`&vartheta;`(tau))^2*FAK(`&vartheta;`(tau), `&vartheta;l`, tau)*(`&vartheta;`(tau)-.7227342478); ic := `&vartheta;`(0) = 0, (D(`&vartheta;`))(0) = 8; ld := dsolve([eq, ic], numeric, range = 0 .. 5, known = [FAK(`&vartheta;`, `&vartheta;l`, tau)])

vartheta(0) = 0, (D(vartheta))(0) = 8

 

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "left" ) = 0., ( "right" ) = 5., ( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 2, (2) = 2, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 1, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = 5.0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.6309573444801932e-3, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..2, {(1) = .0, (2) = 8.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..2, {(1) = .1, (2) = .1}, datatype = float[8], order = C_order), Array(1..2, {(1) = -31.41915781133279, (2) = -8.000025057730129}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = -7.986016163224162, (2) = 1.2169510548763436}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..6, {(1, 1) = -7.986016163224162, (1, 2) = -7.995228782813761, (1, 3) = -7.996021140760665, (1, 4) = -7.990154883815672, (1, 5) = -7.984281628756027, (1, 6) = -7.999528205450552, (2, 1) = 1.2169510548763436, (2, 2) = -1.027531053460354, (2, 3) = -.6534286904019087, (2, 4) = .9829174325813691, (2, 5) = 1.2018980308140104, (2, 6) = -.2752008163676133}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8]), Array(1..2, {(1) = -31.291133397463387, (2) = -7.993546092546788}, datatype = float[8], order = C_order), Array(1..2, {(1) = -31.599498479714843, (2) = -7.986016163224162}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0.16537008207251347e-7, (2) = 0.5431196745675493e-6}, datatype = float[8], order = C_order), Array(1..2, {(1) = -31.148817633256307, (2) = -7.970422593226935}, datatype = float[8], order = C_order), Array(1..2, {(1) = -7.999941735720901, (2) = 0.9672456714659441e-1}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..2, {(1) = .0, (2) = 8.0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = 8.0, (2) = .0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..2, {(1, 1) = .0, (1, 2) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = vartheta(tau), Y[2] = diff(vartheta(tau),tau)]`; YP[2] := -6.666666666*sin(Y[1])-66.66666666*cos(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478)-66.66666666*sin(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478); YP[1] := Y[2]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = vartheta(tau), Y[2] = diff(vartheta(tau),tau)]`; YP[2] := -6.666666666*sin(Y[1])-66.66666666*cos(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478)-66.66666666*sin(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478); YP[1] := Y[2]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] )), ( 3 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 2, (2) = 2, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 1, (9) = 0, (10) = 1, (11) = 437, (12) = 437, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 855, (19) = 30000, (20) = 5, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = 5.0, (2) = 0.10e-5, (3) = 0.6993193822045018e-1, (4) = 0.500001e-14, (5) = .0, (6) = 0.6309573444801932e-3, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..2, {(1) = .0, (2) = 8.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..2, {(1) = .1, (2) = .1}, datatype = float[8], order = C_order), Array(1..2, {(1) = -31.41915781133279, (2) = -8.000025057730129}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = -7.986016163224162, (2) = 1.2169510548763436}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..6, {(1, 1) = -7.986016163224162, (1, 2) = -7.995228782813761, (1, 3) = -7.996021140760665, (1, 4) = -7.990154883815672, (1, 5) = -7.984281628756027, (1, 6) = -7.999528205450552, (2, 1) = 1.2169510548763436, (2, 2) = -1.027531053460354, (2, 3) = -.6534286904019087, (2, 4) = .9829174325813691, (2, 5) = 1.2018980308140104, (2, 6) = -.2752008163676133}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8]), Array(1..2, {(1) = -31.291133397463387, (2) = -7.993546092546788}, datatype = float[8], order = C_order), Array(1..2, {(1) = -31.599498479714843, (2) = -7.986016163224162}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0.16537008207251347e-7, (2) = 0.5431196745675493e-6}, datatype = float[8], order = C_order), Array(1..2, {(1) = -31.148817633256307, (2) = -7.970422593226935}, datatype = float[8], order = C_order), Array(1..2, {(1) = -7.999941735720901, (2) = 0.9672456714659441e-1}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..2, {(1) = -31.148817633256307, (2) = -7.970422593226935}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = -7.986016163224162, (2) = 1.2169510548763436}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..2, {(1, 1) = 4.982173448347681, (1, 2) = -31.148817633256307, (2, 0) = -31.148817633256307, (2, 1) = -7.970422593226935, (2, 2) = 4.996270866195413, (3, 0) = 4.996270866195413, (3, 1) = -31.261330693383552, (3, 2) = -7.990084516686748, (4, 0) = -7.990084516686748, (4, 1) = 5.010368284043146, (4, 2) = -31.374047260481486, (5, 0) = -31.374047260481486, (5, 1) = -7.999298578059383, (5, 2) = 5.024465701890879, (6, 0) = 5.024465701890879, (6, 1) = -31.486819556132005, (6, 2) = -7.997936225285096}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = vartheta(tau), Y[2] = diff(vartheta(tau),tau)]`; YP[2] := -6.666666666*sin(Y[1])-66.66666666*cos(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478)-66.66666666*sin(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478); YP[1] := Y[2]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (Array(1..437, 0..2, {(1, 1) = .0, (1, 2) = .0, (2, 0) = .0, (2, 1) = 8.0, (2, 2) = 0.1577393361200483e-3, (3, 0) = 0.1577393361200483e-3, (3, 1) = 0.12619146540730692e-2, (3, 2) = 7.9999993364881465, (4, 0) = 7.9999993364881465, (4, 1) = 0.3154786722400966e-3, (4, 2) = 0.2523829098822314e-2, (5, 0) = 0.2523829098822314e-2, (5, 1) = 7.999997345953752, (5, 2) = 0.4732180083601449e-3, (6, 0) = 0.4732180083601449e-3, (6, 1) = 0.3785743124924429e-2, (6, 2) = 7.999994028400317, (7, 0) = 7.999994028400317, (7, 1) = 0.6309573444801932e-3, (7, 2) = 0.5047656523056747e-2, (8, 0) = 0.5047656523056747e-2, (8, 1) = 7.999989383833675, (8, 2) = 0.911448743807301e-2, (9, 0) = 0.911448743807301e-2, (9, 1) = 0.7290916691154178e-1, (9, 2) = 7.9977857169021105, (10, 0) = 7.9977857169021105, (10, 1) = 0.17598017531665826e-1, (10, 2) = .14073571986357722, (11, 0) = .14073571986357722, (11, 1) = 7.991756580465714, (11, 2) = 0.26081547625258644e-1, (12, 0) = 0.26081547625258644e-1, (12, 1) = .20849502364262745, (12, 2) = 7.981932567638452, (13, 0) = 7.981932567638452, (13, 1) = 0.34565077718851464e-1, (13, 2) = .27615508454557824, (14, 0) = .27615508454557824, (14, 1) = 7.9683632473475114, (14, 2) = 0.44656062833005626e-1, (15, 0) = 0.44656062833005626e-1, (15, 1) = .35646246683591665, (15, 2) = 7.947441280343913, (16, 0) = 7.947441280343913, (16, 1) = 0.5474704794715979e-1, (16, 2) = .43653305012815946, (17, 0) = .43653305012815946, (17, 1) = 7.921466617147696, (17, 2) = 0.6483803306131394e-1, (18, 0) = 0.6483803306131394e-1, (18, 1) = .5163168325496422, (18, 2) = 7.890621819575484, (19, 0) = 7.890621819575484, (19, 1) = 0.7492901817546811e-1, (19, 2) = .595765730569066, (20, 0) = .595765730569066, (20, 1) = 7.855120849280276, (20, 2) = 0.7728821382564362e-1, (21, 0) = 0.7728821382564362e-1, (21, 1) = .6142869922676657, (21, 2) = 7.846175139574565, (22, 0) = 7.846175139574565, (22, 1) = 0.7964740947581911e-1, (22, 2) = .6327868679675704, (23, 0) = .6327868679675704, (23, 1) = 7.836991525560117, (23, 2) = 0.8200660512599461e-1, (24, 0) = 0.8200660512599461e-1, (24, 1) = .6512648004747847, (24, 2) = 7.82757342667227, (25, 0) = 7.82757342667227, (25, 1) = 0.8436580077617012e-1, (25, 2) = .6697202407048742, (26, 0) = .6697202407048742, (26, 1) = 7.8179243376446825, (26, 2) = 0.8519377427087671e-1, (27, 0) = 0.8519377427087671e-1, (27, 1) = .6761918524450153, (27, 2) = 7.8144838351937835, (28, 0) = 7.8144838351937835, (28, 1) = 0.8602174776558329e-1, (28, 2) = .6826606039974968, (29, 0) = .6826606039974968, (29, 1) = 7.811015477066508, (29, 2) = 0.8684972126028986e-1, (30, 0) = 0.8684972126028986e-1, (30, 1) = .6891264723639181, (30, 2) = 7.807519420725296, (31, 0) = 7.807519420725296, (31, 1) = 0.8767769475499645e-1, (31, 2) = .6955894346764621, (32, 0) = .6955894346764621, (32, 1) = 7.803995824691538, (32, 2) = 0.8850566824970305e-1, (33, 0) = 0.8850566824970305e-1, (33, 1) = .7020494681986604, (33, 2) = 7.8004448485393345, (34, 0) = 7.8004448485393345, (34, 1) = 0.8933364174440962e-1, (34, 2) = .708506550326986, (35, 0) = .708506550326986, (35, 1) = 7.7968666528861785, (35, 2) = 0.901616152391162e-1, (36, 0) = 0.901616152391162e-1, (36, 1) = .7149606585914959, (36, 2) = 7.793261399371529, (37, 0) = 7.793261399371529, (37, 1) = 0.9098958873382279e-1, (37, 2) = .7214117706562803, (38, 0) = .7214117706562803, (38, 1) = 7.789629250646504, (38, 2) = 0.9150828443884917e-1, (39, 0) = 0.9150828443884917e-1, (39, 1) = .7254516161517203, (39, 2) = 7.787292346705572, (40, 0) = 7.787292346705572, (40, 1) = 0.9202698014387556e-1, (40, 2) = .7294902167257636, (41, 0) = .7294902167257636, (41, 1) = 7.784828640786988, (41, 2) = 0.9254567584890196e-1, (42, 0) = 0.9254567584890196e-1, (42, 1) = .7335275032902404, (42, 2) = 7.782217976359945, (43, 0) = 7.782217976359945, (43, 1) = 0.9306437155392834e-1, (43, 2) = .7375633975197429, (44, 0) = .7375633975197429, (44, 1) = 7.779454514726426, (44, 2) = 0.9358306725895472e-1, (45, 0) = 0.9358306725895472e-1, (45, 1) = .7415978181228412, (45, 2) = 7.776541372199132, (46, 0) = 7.776541372199132, (46, 1) = 0.9410176296398112e-1, (46, 2) = .7456306888450303, (47, 0) = .7456306888450303, (47, 1) = 7.773478461841443, (47, 2) = 0.946204586690075e-1, (48, 0) = 0.946204586690075e-1, (48, 1) = .7496619320272724, (48, 2) = 7.770265880706045, (49, 0) = 7.770265880706045, (49, 1) = 0.9513915437403389e-1, (49, 2) = .7536914700624112, (50, 0) = .7536914700624112, (50, 1) = 7.766903728845746, (50, 2) = 0.9721393719413944e-1, (51, 0) = 0.9721393719413944e-1, (51, 1) = .7697910208629244, (51, 2) = 7.7519615189000355, (52, 0) = 7.7519615189000355, (52, 1) = 0.9928872001424499e-1, (52, 2) = .7858570947314306, (53, 0) = .7858570947314306, (53, 1) = 7.734634959563075, (53, 2) = .10136350283435054, (54, 0) = .10136350283435054, (54, 1) = .8018847524946877, (54, 2) = 7.714931882007477, (55, 0) = 7.714931882007477, (55, 1) = .10343828565445609, (55, 2) = .8178690727931068, (56, 0) = .8178690727931068, (56, 1) = 7.692860867917549, (56, 2) = .10881670795816578, (57, 0) = .10881670795816578, (57, 1) = .8590683127827715, (57, 2) = 7.624689684524599, (58, 0) = 7.624689684524599, (58, 1) = .11419513026187547, (58, 2) = .8998586584717132, (59, 0) = .8998586584717132, (59, 1) = 7.540856849042105, (59, 2) = .11957355256558518, (60, 0) = .11957355256558518, (60, 1) = .9401564241224466, (60, 2) = 7.441580121353541, (61, 0) = 7.441580121353541, (61, 1) = .12495197486929487, (61, 2) = .9798792736889044, (62, 0) = .9798792736889044, (62, 1) = 7.327108466604511, (62, 2) = .13048308605915332, (63, 0) = .13048308605915332, (63, 1) = 1.0200449961413427, (63, 2) = 7.193833549137809, (64, 0) = 7.193833549137809, (64, 1) = .13601419724901181, (64, 2) = 1.0594306734722212, (65, 0) = 1.0594306734722212, (65, 1) = 7.045121547828793, (65, 2) = .14154530843887025, (66, 0) = .14154530843887025, (66, 1) = 1.0979518938531811, (66, 2) = 6.881340263606544, (67, 0) = 6.881340263606544, (67, 1) = .14707641962872875, (67, 2) = 1.1355264698884855, (68, 0) = 1.1355264698884855, (68, 1) = 6.702887159460921, (68, 2) = .15285659912781446, (69, 0) = .15285659912781446, (69, 1) = 1.1736948539156258, (69, 2) = 6.501183369499769, (70, 0) = 6.501183369499769, (70, 1) = .1586367786269002, (70, 2) = 1.2106536045788865, (71, 0) = 1.2106536045788865, (71, 1) = 6.28444196964498, (71, 2) = .16441695812598592, (72, 0) = .16441695812598592, (72, 1) = 1.2463173320849292, (72, 2) = 6.05321229161356, (73, 0) = 6.05321229161356, (73, 1) = .17019713762507166, (73, 2) = 1.2806040326437478, (74, 0) = 1.2806040326437478, (74, 1) = 5.808072049437234, (74, 2) = .17625628546586772, (75, 0) = .17625628546586772, (75, 1) = 1.3149815186686669, (75, 2) = 5.536827433235842, (76, 0) = 5.536827433235842, (76, 1) = .18231543330666378, (76, 2) = 1.3476730035812117, (77, 0) = 1.3476730035812117, (77, 1) = 5.251691068999393, (77, 2) = .18837458114745986, (78, 0) = .18837458114745986, (78, 1) = 1.3785965353379621, (78, 2) = 4.953419185855179, (79, 0) = 4.953419185855179, (79, 1) = .19443372898825592, (79, 2) = 1.40767496995855, (80, 0) = 1.40767496995855, (80, 1) = 4.642793697612101, (80, 2) = .200025829554618, (81, 0) = .200025829554618, (81, 1) = 1.4328121350112957, (81, 2) = 4.345846900860365, (82, 0) = 4.345846900860365, (82, 1) = .2056179301209801, (82, 2) = 1.4562627472281817, (83, 0) = 1.4562627472281817, (83, 1) = 4.0397168978268265, (83, 2) = .21121003068734218, (84, 0) = .21121003068734218, (84, 1) = 1.4779772748768565, (84, 2) = 3.7250702460875798, (85, 0) = 3.7250702460875798, (85, 1) = .21680213125370426, (85, 2) = 1.4979100327341919, (86, 0) = 1.4979100327341919, (86, 1) = 3.4025865514147045, (86, 2) = .22194966531655907, (87, 0) = .22194966531655907, (87, 1) = 1.5146471538075585, (87, 2) = 3.0994082507898124, (88, 0) = 3.0994082507898124, (88, 1) = .22709719937941386, (88, 2) = 1.5298092443406093, (89, 0) = 1.5298092443406093, (89, 1) = 2.7907249661428626, (89, 2) = .23224473344226865, (90, 0) = .23224473344226865, (90, 1) = 1.5433693748583053, (90, 2) = 2.477092521290772, (91, 0) = 2.477092521290772, (91, 1) = .23739226750512346, (91, 2) = 1.5553035345921162, (92, 0) = 1.5553035345921162, (92, 1) = 2.159072731384831, (92, 2) = .24209330782525815, (93, 0) = .24209330782525815, (93, 1) = 1.564764044091691, (93, 2) = 1.8652862211283494, (94, 0) = 1.8652862211283494, (94, 1) = .2467943481453928, (94, 2) = 1.5728368164695625, (95, 0) = 1.5728368164695625, (95, 1) = 1.5687502334721908, (95, 2) = .2514953884655275, (96, 0) = .2514953884655275, (96, 1) = 1.579509947200802, (96, 2) = 1.2699038156303004, (97, 0) = 1.2699038156303004, (97, 1) = .2561964287856622, (97, 2) = 1.584773619444908, (98, 0) = 1.584773619444908, (98, 1) = .9691881650034271, (98, 2) = .2603621372158916, (99, 0) = .2603621372158916, (99, 1) = 1.588253780170421, (99, 2) = .7015108197781248, (100, 0) = .7015108197781248, (100, 1) = .264527845646121, (100, 2) = 1.5906170808943054, (101, 0) = 1.5906170808943054, (101, 1) = .4330234384243079, (101, 2) = .26869355407635037, (102, 0) = .26869355407635037, (102, 1) = 1.591860789271494, (102, 2) = .1640362230578783, (103, 0) = .1640362230578783, (103, 1) = .27285926250657977, (103, 2) = 1.5919834714977434, (104, 0) = 1.5919834714977434, (104, 1) = -.10514037554435296, (104, 2) = .2762778340314745, (105, 0) = .2762778340314745, (105, 1) = 1.5912465465386945, (105, 2) = -.32596231906197765, (106, 0) = -.32596231906197765, (106, 1) = .2796964055563692, (106, 2) = 1.589755110752713, (107, 0) = 1.589755110752713, (107, 1) = -.5465308142275299, (107, 2) = .2831149770812639, (108, 0) = .2831149770812639, (108, 1) = 1.587510323067415, (108, 2) = -.7666742936341794, (109, 0) = -.7666742936341794, (109, 1) = .2865335486061586, (109, 2) = 1.5845139290407153, (110, 0) = 1.5845139290407153, (110, 1) = -.9862214853878717, (110, 2) = .2899555672413805, (111, 0) = .2899555672413805, (111, 1) = 1.5807641057965514, (111, 2) = -1.2052216012058805, (112, 0) = -1.2052216012058805, (112, 1) = .29337758587660245, (112, 2) = 1.5762664203446783, (113, 0) = 1.5762664203446783, (113, 1) = -1.4232817857406486, (113, 2) = .2967996045118244, (114, 0) = .2967996045118244, (114, 1) = 1.57102438072059, (114, 2) = -1.640231464529247, (115, 0) = -1.640231464529247, (115, 1) = .3002216231470463, (115, 2) = 1.5650420769850095, (116, 0) = 1.5650420769850095, (116, 1) = -1.8559007441033182, (116, 2) = .3042864247020922, (117, 0) = .3042864247020922, (117, 1) = 1.55698066246766, (117, 2) = -2.110183500670552, (118, 0) = -2.110183500670552, (118, 1) = .3083512262571381, (118, 2) = 1.5478902767927025, (119, 0) = 1.5478902767927025, (119, 1) = -2.3621387714739184, (119, 2) = .312416027812184, (120, 0) = .312416027812184, (120, 1) = 1.5377809505236644, (120, 2) = -2.611486255303619, (121, 0) = -2.611486255303619, (121, 1) = .31648082936722993, (121, 2) = 1.52666384547716, (122, 0) = 1.52666384547716, (122, 1) = -2.8579478872729096, (122, 2) = .3209655784174644, (123, 0) = .3209655784174644, (123, 1) = 1.513243649419716, (123, 2) = -3.126192905075415, (124, 0) = -3.126192905075415, (124, 1) = .325450327467699, (124, 2) = 1.4986297643593924, (125, 0) = 1.4986297643593924, (125, 1) = -3.3902222814937124, (125, 2) = .32993507651793347, (126, 0) = .32993507651793347, (126, 1) = 1.482841911734064, (126, 2) = -3.649673285534956, (127, 0) = -3.649673285534956, (127, 1) = .33441982556816796, (127, 2) = 1.4659014183003498, (128, 0) = 1.4659014183003498, (128, 1) = -3.9041880366599346, (128, 2) = .3392547142469069, (129, 0) = .3392547142469069, (129, 1) = 1.4463735644824303, (129, 2) = -4.172638809553999, (130, 0) = -4.172638809553999, (130, 1) = .34408960292564583, (130, 2) = 1.4255635318164526, (131, 0) = 1.4255635318164526, (131, 1) = -4.434506747393247, (131, 2) = .34892449160438477, (132, 0) = .34892449160438477, (132, 1) = 1.4035041866655111, (132, 2) = -4.6893643827097256, (133, 0) = -4.6893643827097256, (133, 1) = .3537593802831237, (133, 2) = 1.3802304177870608, (134, 0) = 1.3802304177870608, (134, 1) = -4.936793201208234, (134, 2) = .35890327549951206, (135, 0) = .35890327549951206, (135, 1) = 1.3541772569913462, (135, 2) = -5.191420706487074, (136, 0) = -5.191420706487074, (136, 1) = .36404717071590037, (136, 2) = 1.3268381904635798, (137, 0) = 1.3268381904635798, (137, 1) = -5.436694807954317, (137, 2) = .3691910659322887, (138, 0) = .3691910659322887, (138, 1) = 1.2982625453239334, (138, 2) = -5.672147951155809, (139, 0) = -5.672147951155809, (139, 1) = .37433496114867704, (139, 2) = 1.2685019741953583, (140, 0) = 1.2685019741953583, (140, 1) = -5.897327595187652, (140, 2) = .3797729342675293, (141, 0) = .3797729342675293, (141, 1) = 1.2358113229563144, (141, 2) = -6.123725401422993, (142, 0) = -6.123725401422993, (142, 1) = .38521090738638153, (142, 2) = 1.2019232348822264, (143, 0) = 1.2019232348822264, (143, 1) = -6.337655375367502, (143, 2) = .3906488805052338, (144, 0) = .3906488805052338, (144, 1) = 1.1669068225757708, (144, 2) = -6.538642069462055, (145, 0) = -6.538642069462055, (145, 1) = .396086853624086, (145, 2) = 1.1308336532332235, (146, 0) = 1.1308336532332235, (146, 1) = -6.7262337787760815, (146, 2) = .40183341746671136, (147, 0) = .40183341746671136, (147, 1) = 1.0916469570913554, (147, 2) = -6.909441231290376, (148, 0) = -6.909441231290376, (148, 1) = .4075799813093367, (148, 2) = 1.0514529869085032, (149, 0) = 1.0514529869085032, (149, 1) = -7.076738585854852, (149, 2) = .41332654515196204, (150, 0) = .41332654515196204, (150, 1) = 1.0103444683361704, (150, 2) = -7.227685462677389, (151, 0) = -7.227685462677389, (151, 1) = .4190731089945874, (151, 2) = .9684164520630016, (152, 0) = .9684164520630016, (152, 1) = -7.361877716839585, (152, 2) = .4249662690604356, (153, 0) = .4249662690604356, (153, 1) = .9246696403023807, (153, 2) = -7.4817076363881165, (154, 0) = -7.4817076363881165, (154, 1) = .43085942912628383, (154, 2) = .8802706484121009, (155, 0) = .8802706484121009, (155, 1) = -7.583175746038299, (155, 2) = .43675258919213206, (156, 0) = .43675258919213206, (156, 1) = .8353286419886118, (156, 2) = -7.665971657399472, (157, 0) = -7.665971657399472, (157, 1) = .4426457492579803, (157, 2) = .7899543490559398, (158, 0) = .7899543490559398, (158, 1) = -7.729831827072581, (158, 2) = .44415455541356497, (159, 0) = .44415455541356497, (159, 1) = .778281356079461, (159, 2) = -7.743109832564286, (160, 0) = -7.743109832564286, (160, 1) = .4456633615691496, (160, 2) = .7665892784992561, (161, 0) = .7665892784992561, (161, 1) = -7.7551290270523054, (161, 2) = .4471721677247342, (162, 0) = .4471721677247342, (162, 1) = .7548800178721511, (162, 2) = -7.765886496167805, (163, 0) = -7.765886496167805, (163, 1) = .4486809738803189, (163, 2) = .7431554798348934, (164, 0) = .7431554798348934, (164, 1) = -7.775379538770485, (164, 2) = .4491026095653292, (165, 0) = .4491026095653292, (165, 1) = .739876587341913, (165, 2) = -7.77780598228757, (166, 0) = -7.77780598228757, (166, 1) = .44952424525033946, (166, 2) = .7365966926406777, (167, 0) = .7365966926406777, (167, 1) = -7.780133437063171, (167, 2) = .4499458809353497, (168, 0) = .4499458809353497, (168, 1) = .7333158374790067, (168, 2) = -7.782361853122314, (169, 0) = -7.782361853122314, (169, 1) = .45036751662036, (169, 2) = .7300340636252433, (170, 0) = .7300340636252433, (170, 1) = -7.784491181807153, (170, 2) = .4506418210392642, (171, 0) = .4506418210392642, (171, 1) = .7278985594898288, (171, 2) = -7.785825946041931, (172, 0) = -7.785825946041931, (172, 1) = .45091612545816845, (172, 2) = .7257626956605541, (173, 0) = .7257626956605541, (173, 1) = -7.787115533148494, (173, 2) = .4511904298770727, (174, 0) = .4511904298770727, (174, 1) = .7236264836387117, (174, 2) = -7.788359278699654, (175, 0) = -7.788359278699654, (175, 1) = .4514647342959769, (175, 2) = .7214899344270745, (176, 0) = .7214899344270745, (176, 1) = -7.789572884421334, (176, 2) = .4517390387148811, (177, 0) = .4517390387148811, (177, 1) = .7193530546368538, (177, 2) = -7.790779277798553, (178, 0) = -7.790779277798553, (178, 1) = .45201334313378533, (178, 2) = .7172158443306533, (179, 0) = .7172158443306533, (179, 1) = -7.791982731448791, (179, 2) = .4522876475526896, (180, 0) = .4522876475526896, (180, 1) = .7150783043156684, (180, 2) = -7.793183239420547, (181, 0) = -7.793183239420547, (181, 1) = .45256195197159377, (181, 2) = .7129404354007267, (182, 0) = .7129404354007267, (182, 1) = -7.794380795774368, (182, 2) = .45365916964721065, (183, 0) = .45365916964721065, (183, 1) = .7043856869749219, (183, 2) = -7.799141386652577, (184, 0) = -7.799141386652577, (184, 1) = .4547563873228275, (184, 2) = .6958257412782278, (185, 0) = .6958257412782278, (185, 1) = -7.803854279637731, (185, 2) = .4558536049984444, (186, 0) = .4558536049984444, (186, 1) = .6872606508502357, (186, 2) = -7.808519100481721, (187, 0) = -7.808519100481721, (187, 1) = .4569508226740613, (187, 2) = .6786904686403321, (188, 0) = .6786904686403321, (188, 1) = -7.813135478149267, (188, 2) = .4613396933765288, (189, 0) = .4613396933765288, (189, 1) = .6443598951706142, (189, 2) = -7.831109258499925, (190, 0) = -7.831109258499925, (190, 1) = .4657285640789963, (190, 2) = .6099521935155742, (191, 0) = .6099521935155742, (191, 1) = -7.8482791210546345, (191, 2) = .47011743478146384, (192, 0) = .47011743478146384, (192, 1) = .5754709396547975, (192, 2) = -7.864622959260164, (193, 0) = -7.864622959260164, (193, 1) = .47450630548393136, (193, 2) = .5409198056102584, (194, 0) = .5409198056102584, (194, 1) = -7.88011961688783, (194, 2) = .48745532465833297, (195, 0) = .48745532465833297, (195, 1) = .4386087665600395, (195, 2) = -7.920716000244283, (196, 0) = -7.920716000244283, (196, 1) = .5004043438327346, (196, 2) = .33582360188701177, (197, 0) = .33582360188701177, (197, 1) = -7.953302561729213, (197, 2) = .5133533630071361, (198, 0) = .5133533630071361, (198, 1) = .23267022526737316, (198, 2) = -7.977502380974195, (199, 0) = -7.977502380974195, (199, 1) = .5263023821815377, (199, 2) = .1292591437196286, (200, 0) = .1292591437196286, (200, 1) = -7.993033959513704, (200, 2) = .5380253686224814, (201, 0) = .5380253686224814, (201, 1) = 0.3551211754430397e-1, (201, 2) = -7.999463375733951, (202, 0) = -7.999463375733951, (202, 1) = .5497483550634251, (202, 2) = -0.582673032941086e-1, (203, 0) = -0.582673032941086e-1, (203, 1) = -7.998574502548318, (203, 2) = .5614713415043688, (204, 0) = .5614713415043688, (204, 1) = -.15199354182246852, (204, 2) = -7.99037604528351, (205, 0) = -7.99037604528351, (205, 1) = .5731943279453126, (205, 2) = -.24558131889437668, (206, 0) = -.24558131889437668, (206, 1) = -7.974946903607312, (206, 2) = .5836388455080312, (207, 0) = .5836388455080312, (207, 1) = -.3287776415748822, (207, 2) = -7.955228360212225, (208, 0) = -7.955228360212225, (208, 1) = .59408336307075, (208, 2) = -.4117392381450997, (209, 0) = -.4117392381450997, (209, 1) = -7.9300380794813305, (209, 2) = .6045278806334687, (210, 0) = .6045278806334687, (210, 1) = -.49441002957827174, (210, 2) = -7.899566255540083, (211, 0) = -7.899566255540083, (211, 1) = .6149723981961874, (211, 2) = -.5767360157686612, (212, 0) = -.5767360157686612, (212, 1) = -7.864039939689357, (212, 2) = .6270360170970933, (213, 0) = .6270360170970933, (213, 1) = -.671327615565848, (213, 2) = -7.81706021912386, (214, 0) = -7.81706021912386, (214, 1) = .6390996359979992, (214, 2) = -.7653161302256445, (215, 0) = -.7653161302256445, (215, 1) = -7.764147601677043, (215, 2) = .6511632548989051, (216, 0) = .6511632548989051, (216, 1) = -.8586331310911235, (216, 2) = -7.70580729094018, (217, 0) = -7.70580729094018, (217, 1) = .663226873799811, (217, 2) = -.9512163973439858, (218, 0) = -.9512163973439858, (218, 1) = -7.642583157738949, (218, 2) = .6753836018366912, (219, 0) = .6753836018366912, (219, 1) = -1.0437155891920986, (219, 2) = -7.574517340150062, (220, 0) = -7.574517340150062, (220, 1) = .6875403298735714, (220, 2) = -1.1353638670508754, (221, 0) = -1.1353638670508754, (221, 1) = -7.502700466510652, (221, 2) = .6996970579104514, (222, 0) = .6996970579104514, (222, 1) = -1.2261195097974062, (222, 2) = -7.427767607157234, (223, 0) = -7.427767607157234, (223, 1) = .7118537859473316, (223, 2) = -1.3159485437245313, (224, 0) = -1.3159485437245313, (224, 1) = -7.350361177055548, (224, 2) = .7242825739626336, (225, 0) = .7242825739626336, (225, 1) = -1.406802748232662, (225, 2) = -7.269338385844888, (226, 0) = -7.269338385844888, (226, 1) = .7367113619779357, (226, 2) = -1.4966416618084168, (227, 0) = -1.4966416618084168, (227, 1) = -7.187093352335662, (227, 2) = .7491401499932377, (228, 0) = .7491401499932377, (228, 1) = -1.5854542225278627, (228, 2) = -7.104299259352038, (229, 0) = -7.104299259352038, (229, 1) = .7615689380085398, (229, 2) = -1.6732376955103132, (230, 0) = -1.6732376955103132, (230, 1) = -7.021609761178974, (230, 2) = .7752626438655669, (231, 0) = .7752626438655669, (231, 1) = -1.7687703246810103, (231, 2) = -6.931381478873594, (232, 0) = -6.931381478873594, (232, 1) = .788956349722594, (232, 2) = -1.86307822872474, (233, 0) = -1.86307822872474, (233, 1) = -6.8428542337035925, (233, 2) = .8026500555796212, (234, 0) = .8026500555796212, (234, 1) = -1.9561897371739303, (234, 2) = -6.756788104442705, (235, 0) = -6.756788104442705, (235, 1) = .8163437614366483, (235, 2) = -2.048143484357981, (236, 0) = -2.048143484357981, (236, 1) = -6.6738925032205625, (236, 2) = .8337459731870884, (237, 0) = .8337459731870884, (237, 1) = -2.163406432031228, (237, 2) = -6.574151554059861, (238, 0) = -6.574151554059861, (238, 1) = .8511481849375285, (238, 2) = -2.2769966956885095, (239, 0) = -2.2769966956885095, (239, 1) = -6.481811558093251, (239, 2) = .8685503966879686, (240, 0) = .8685503966879686, (240, 1) = -2.389051782877827, (240, 2) = -6.397951651762824, (241, 0) = -6.397951651762824, (241, 1) = .8859526084384087, (241, 2) = -2.4997277411065553, (242, 0) = -2.4997277411065553, (242, 1) = -6.3235091120694555, (242, 2) = .9048754111972125, (243, 0) = .9048754111972125, (243, 1) = -2.618710890321904, (243, 2) = -6.254177954738825, (244, 0) = -6.254177954738825, (244, 1) = .9237982139560164, (244, 2) = -2.736503524176302, (245, 0) = -2.736503524176302, (245, 1) = -6.197765757346317, (245, 2) = .9427210167148201, (246, 0) = .9427210167148201, (246, 1) = -2.853355354729258, (246, 2) = -6.15493640735021, (247, 0) = -6.15493640735021, (247, 1) = .9616438194736239, (247, 2) = -2.969528608351498, (248, 0) = -2.969528608351498, (248, 1) = -6.126180355127086, (248, 2) = .981299518387772, (249, 0) = .981299518387772, (249, 1) = -3.0897740118993338, (249, 2) = -6.111553372672571, (250, 0) = -6.111553372672571, (250, 1) = 1.0009552173019203, (250, 2) = -3.209886511829642, (251, 0) = -3.209886511829642, (251, 1) = -6.112631889534587, (251, 2) = 1.0206109162160684, (252, 0) = 1.0206109162160684, (252, 1) = -3.330173488097483, (252, 2) = -6.12940417891032, (253, 0) = -6.12940417891032, (253, 1) = 1.0402666151302165, (253, 2) = -3.450942155807806, (254, 0) = -3.450942155807806, (254, 1) = -6.161667299799957, (254, 2) = 1.0575257217827037, (255, 0) = 1.0575257217827037, (255, 1) = -3.5576227729073375, (255, 2) = -6.202462744930731, (256, 0) = -6.202462744930731, (256, 1) = 1.0747848284351909, (256, 2) = -3.665105495548625, (257, 0) = -3.665105495548625, (257, 1) = -6.2545158184024485, (257, 2) = 1.092043935087678, (258, 0) = 1.092043935087678, (258, 1) = -3.77357959117573, (258, 2) = -6.317317235521147, (259, 0) = -6.317317235521147, (259, 1) = 1.1093030417401653, (259, 2) = -3.883225448801852, (260, 0) = -3.883225448801852, (260, 1) = -6.3902292806729575, (260, 2) = 1.1242484706035503, (261, 0) = 1.1242484706035503, (261, 1) = -3.9792503119880376, (261, 2) = -6.460947575736682, (262, 0) = -6.460947575736682, (262, 1) = 1.1391938994669353, (262, 2) = -4.076381050609916, (263, 0) = -4.076381050609916, (263, 1) = -6.538098089753096, (263, 2) = 1.1541393283303205, (264, 0) = 1.1541393283303205, (264, 1) = -4.174708601434061, (264, 2) = -6.6210256512390195, (265, 0) = -6.6210256512390195, (265, 1) = 1.1690847571937055, (265, 2) = -4.274313983582447, (266, 0) = -4.274313983582447, (266, 1) = -6.708996154603087, (266, 2) = 1.184855496164897, (267, 0) = 1.184855496164897, (267, 1) = -4.380882380976787, (267, 2) = -6.806396247641125, (268, 0) = -6.806396247641125, (268, 1) = 1.2006262351360881, (268, 2) = -4.489017328840983, (269, 0) = -4.489017328840983, (269, 1) = -6.907460635467638, (269, 2) = 1.2163969741072795, (270, 0) = 1.2163969741072795, (270, 1) = -4.598767369711119, (270, 2) = -7.011054526993981, (271, 0) = -7.011054526993981, (271, 1) = 1.232167713078471, (271, 2) = -4.710162949690482, (272, 0) = -4.710162949690482, (272, 1) = -7.115961676360024, (272, 2) = 1.2479462637646108, (273, 0) = 1.2479462637646108, (273, 1) = -4.8232716135563285, (273, 2) = -7.220945038107288, (274, 0) = -7.220945038107288, (274, 1) = 1.263724814450751, (274, 2) = -4.938028094552053, (275, 0) = -4.938028094552053, (275, 1) = -7.324595010038418, (275, 2) = 1.279503365136891, (276, 0) = 1.279503365136891, (276, 1) = -5.054400323085117, (276, 2) = -7.425520664953999, (277, 0) = -7.425520664953999, (277, 1) = 1.2952819158230309, (277, 2) = -5.172334243345563, (278, 0) = -5.172334243345563, (278, 1) = -7.522316423568937, (278, 2) = 1.3091220658391063, (279, 0) = 1.3091220658391063, (279, 1) = -5.277005996342105, (279, 2) = -7.602709597941774, (280, 0) = -7.602709597941774, (280, 1) = 1.3229622158551817, (280, 2) = -5.3827554284717145, (281, 0) = -5.3827554284717145, (281, 1) = -7.677908004386181, (281, 2) = 1.336802365871257, (282, 0) = 1.336802365871257, (282, 1) = -5.489504602457428, (282, 2) = -7.747017231535218, (283, 0) = -7.747017231535218, (283, 1) = 1.3506425158873323, (283, 2) = -5.597163367290701, (284, 0) = -5.597163367290701, (284, 1) = -7.809196891828507, (284, 2) = 1.3635743248383065, (285, 0) = 1.3635743248383065, (285, 1) = -5.6984886709609315, (285, 2) = -7.860344260744057, (286, 0) = -7.860344260744057, (286, 1) = 1.3765061337892808, (286, 2) = -5.80042862717268, (287, 0) = -5.80042862717268, (287, 1) = -7.904188777296075, (287, 2) = 1.389437942740255, (288, 0) = 1.389437942740255, (288, 1) = -5.902885804324612, (288, 2) = -7.940234047795247, (289, 0) = -7.940234047795247, (289, 1) = 1.4023697516912292, (289, 2) = -6.005756602548836, (290, 0) = -6.005756602548836, (290, 1) = -7.968068024749733, (290, 2) = 1.4163999726467043, (291, 0) = 1.4163999726467043, (291, 1) = -6.117706312137548, (291, 2) = -7.988604488022426, (292, 0) = -7.988604488022426, (292, 1) = 1.430430193602179, (292, 2) = -6.2298716835753805, (293, 0) = -6.2298716835753805, (293, 1) = -7.9988123375796, (293, 2) = 1.4444604145576538, (294, 0) = 1.4444604145576538, (294, 1) = -6.3421072201058735, (294, 2) = -7.998550519533448, (295, 0) = -7.998550519533448, (295, 1) = 1.4584906355131289, (295, 2) = -6.454265924051917, (296, 0) = -6.454265924051917, (296, 1) = -7.987822398065872, (296, 2) = 1.4709569339076776, (297, 0) = 1.4709569339076776, (297, 1) = -6.553739422817985, (297, 2) = -7.969624268832939, (298, 0) = -7.969624268832939, (298, 1) = 1.483423232302226, (298, 2) = -6.6529361326059755, (299, 0) = -6.6529361326059755, (299, 1) = -7.943477671237111, (299, 2) = 1.4958895306967745, (300, 0) = 1.4958895306967745, (300, 1) = -6.751758920249053, (300, 2) = -7.909665076522119, (301, 0) = -7.909665076522119, (301, 1) = 1.5083558290913233, (301, 2) = -6.850114404563916, (302, 0) = -6.850114404563916, (302, 1) = -7.868546097728132, (302, 2) = 1.520822127485872, (303, 0) = 1.520822127485872, (303, 1) = -6.947913779548772, (303, 2) = -7.820553722219722, (304, 0) = -7.820553722219722, (304, 1) = 1.5332884258804205, (304, 2) = -7.04507452492583, (305, 0) = -7.04507452492583, (305, 1) = -7.766190308114345, (305, 2) = 1.545754724274969, (306, 0) = 1.545754724274969, (306, 1) = -7.141520789696923, (306, 2) = -7.7060106304215275, (307, 0) = -7.7060106304215275, (307, 1) = 1.5582210226695177, (307, 2) = -7.237183773012527, (308, 0) = -7.237183773012527, (308, 1) = -7.640613796807662, (308, 2) = 1.5703703621704896, (309, 0) = 1.5703703621704896, (309, 1) = -7.329602317638933, (309, 2) = -7.572469163510009, (310, 0) = -7.572469163510009, (310, 1) = 1.5825197016714618, (310, 2) = -7.421169648388984, (311, 0) = -7.421169648388984, (311, 1) = -7.50059643125255, (311, 2) = 1.5946690411724338, (312, 0) = 1.5946690411724338, (312, 1) = -7.511844343106748, (312, 2) = -7.425629896344123, (313, 0) = -7.425629896344123, (313, 1) = 1.6068183806734058, (313, 2) = -7.601592712300481, (314, 0) = -7.601592712300481, (314, 1) = -7.34821096735671, (314, 2) = 1.619252425197644, (315, 0) = 1.619252425197644, (315, 1) = -7.692458112866918, (315, 2) = -7.267111724235786, (316, 0) = -7.267111724235786, (316, 1) = 1.631686469721882, (316, 2) = -7.7823069515363805, (317, 0) = -7.7823069515363805, (317, 1) = -7.184807817712401, (317, 2) = 1.6441205142461204, (318, 0) = 1.6441205142461204, (318, 1) = -7.871128382431607, (318, 2) = -7.101972861160584, (319, 0) = -7.101972861160584, (319, 1) = 1.6565545587703585, (319, 2) = -7.958919895198879, (320, 0) = -7.958919895198879, (320, 1) = -7.019260758595401, (320, 2) = 1.6702619458516867, (321, 0) = 1.6702619458516867, (321, 1) = -8.054515365665365, (321, 2) = -6.928977254877058, (322, 0) = -6.928977254877058, (322, 1) = 1.6839693329330148, (322, 2) = -8.148884298043036, (323, 0) = -8.148884298043036, (323, 1) = -6.8404193514072995, (323, 2) = 1.6976767200143428, (324, 0) = 1.6976767200143428, (324, 1) = -8.242055392327572, (324, 2) = -6.754348080088835, (325, 0) = -6.754348080088835, (325, 1) = 1.711384107095671, (325, 2) = -8.334067676247736, (326, 0) = -8.334067676247736, (326, 1) = -6.671473518008902, (326, 2) = 1.7288043580888655, (327, 0) = 1.7288043580888655, (327, 1) = -8.449408440416969, (327, 2) = -6.571794067710094, (328, 0) = -6.571794067710094, (328, 1) = 1.74622460908206, (328, 2) = -8.56307623955498, (329, 0) = -8.56307623955498, (329, 1) = -6.479559257870619, (329, 2) = 1.7636448600752543, (330, 0) = 1.7636448600752543, (330, 1) = -8.675209479480351, (330, 2) = -6.395847974771032, (331, 0) = -6.395847974771032, (331, 1) = 1.7810651110684488, (331, 2) = -8.785965121129792, (332, 0) = -8.785965121129792, (332, 1) = -6.321596723621878, (332, 2) = 1.7999555423554905, (333, 0) = 1.7999555423554905, (333, 1) = -8.904712665122746, (333, 2) = -6.2526926639766565, (334, 0) = -6.2526926639766565, (334, 1) = 1.8188459736425322, (334, 2) = -9.0222795598986, (335, 0) = -9.0222795598986, (335, 1) = -6.19668128444948, (335, 2) = 1.837736404929574, (336, 0) = 1.837736404929574, (336, 1) = -9.138914530764868, (336, 2) = -6.154219023516781, (337, 0) = -6.154219023516781, (337, 1) = 1.8566268362166156, (337, 2) = -9.25487865705056, (338, 0) = -9.25487865705056, (338, 1) = -6.125790204862019, (338, 2) = 1.8763158203093704, (339, 0) = 1.8763158203093704, (339, 1) = -9.375322575654149, (339, 2) = -6.111433580495756, (340, 0) = -6.111433580495756, (340, 1) = 1.8960048044021252, (340, 2) = -9.49563923581737, (341, 0) = -9.49563923581737, (341, 1) = -6.112837239820312, (341, 2) = 1.91569378849488, (342, 0) = 1.91569378849488, (342, 1) = -9.616137570112938, (342, 2) = -6.129985549683499, (343, 0) = -6.129985549683499, (343, 1) = 1.9353827725876347, (343, 2) = -9.737126268909316, (344, 0) = -9.737126268909316, (344, 1) = -6.162670288806423, (344, 2) = 1.9526059583948092, (345, 0) = 1.9526059583948092, (345, 1) = -9.84360415662407, (345, 2) = -6.203691623110352, (346, 0) = -6.203691623110352, (346, 1) = 1.9698291442019837, (346, 2) = -9.950885866441196, (347, 0) = -9.950885866441196, (347, 1) = -6.255912114574667, (347, 2) = 1.9870523300091583, (348, 0) = 1.9870523300091583, (348, 1) = -10.059159270908816, (348, 2) = -6.318822582838795, (349, 0) = -6.318822582838795, (349, 1) = 2.0042755158163326, (349, 2) = -10.16860338415028, (350, 0) = -10.16860338415028, (350, 1) = -6.391786376175685, (350, 2) = 2.0192194433082014, (351, 0) = 2.0192194433082014, (351, 1) = -10.264642986379506, (351, 2) = -6.462651655852464, (352, 0) = -6.462651655852464, (352, 1) = 2.03416337080007, (352, 2) = -10.361790436407333, (353, 0) = -10.361790436407333, (353, 1) = -6.539933756956713, (353, 2) = 2.049107298291939, (354, 0) = 2.049107298291939, (354, 1) = -10.460136420265492, (354, 2) = -6.622975929595581, (355, 0) = -6.622975929595581, (355, 1) = 2.0640512257838077, (355, 2) = -10.559761683418074, (356, 0) = -10.559761683418074, (356, 1) = -6.711042519923356, (356, 2) = 2.0798355004108813, (357, 0) = 2.0798355004108813, (357, 1) = -10.666455248366306, (357, 2) = -6.808617659464042, (358, 0) = -6.808617659464042, (358, 1) = 2.095619775037955, (358, 2) = -10.774719335277272, (359, 0) = -10.774719335277272, (359, 1) = -6.909839028001667, (359, 2) = 2.1114040496650284, (360, 0) = 2.1114040496650284, (360, 1) = -10.884602204474835, (360, 2) = -7.013566937027976, (361, 0) = -7.013566937027976, (361, 1) = 2.127188324292102, (361, 2) = -10.99613392657502, (362, 0) = -10.99613392657502, (362, 1) = -7.118580189329371, (362, 2) = 2.1429538836019804, (363, 0) = 2.1429538836019804, (363, 1) = -11.109189977687338, (363, 2) = -7.223461065962468, (364, 0) = -7.223461065962468, (364, 1) = 2.158719442911859, (364, 2) = -11.223890626923417, (365, 0) = -11.223890626923417, (365, 1) = -7.32697781958626, (365, 2) = 2.1744850022217377, (366, 0) = 2.1744850022217377, (366, 1) = -11.340203369917653, (366, 2) = -7.427742229508007, (367, 0) = -7.427742229508007, (367, 1) = 2.190250561531616, (367, 2) = -11.458073778644044, (368, 0) = -11.458073778644044, (368, 1) = -7.52435201761034, (368, 2) = 2.2040780847710764, (369, 0) = 2.2040780847710764, (369, 1) = -11.562676904119108, (369, 2) = -7.604557825821765, (370, 0) = -7.604557825821765, (370, 1) = 2.217905608010537, (370, 2) = -11.668354046956713, (371, 0) = -11.668354046956713, (371, 1) = -7.679556774308182, (371, 2) = 2.2317331312499973, (372, 0) = 2.2317331312499973, (372, 1) = -11.775027197933248, (372, 2) = -7.748457877861575, (373, 0) = -7.748457877861575, (373, 1) = 2.2455606544894575, (373, 2) = -11.88260619316062, (374, 0) = -11.88260619316062, (374, 1) = -7.810424338980463, (374, 2) = 2.2584926733385737, (375, 0) = 2.2584926733385737, (375, 1) = -11.983948017012528, (375, 2) = -7.861415235520356, (376, 0) = -7.861415235520356, (376, 1) = 2.27142469218769, (376, 2) = -12.085902398956334, (377, 0) = -12.085902398956334, (377, 1) = -7.905091088884665, (377, 2) = 2.2843567110368057, (378, 0) = 2.2843567110368057, (378, 1) = -12.188371759817548, (378, 2) = -7.94095723077565, (379, 0) = -7.94095723077565, (379, 1) = 2.297288729885922, (379, 2) = -12.291252374994361, (380, 0) = -12.291252374994361, (380, 1) = -7.968603534594819, (380, 2) = 2.311333720292115, (381, 0) = 2.311333720292115, (381, 1) = -12.403326115858567, (381, 2) = -7.988944900114736, (382, 0) = -7.988944900114736, (382, 1) = 2.3253787106983084, (382, 2) = -12.515612816459681, (383, 0) = -12.515612816459681, (383, 1) = -7.998931318880445, (383, 2) = 2.3394237011045016, (384, 0) = 2.3394237011045016, (384, 1) = -12.62796647824195, (384, 2) = -7.998424503083994, (385, 0) = -7.998424503083994, (385, 1) = 2.353468691510695, (385, 2) = -12.740239641115064, (386, 0) = -12.740239641115064, (386, 1) = -7.9874312069295055, (386, 2) = 2.36593490106829, (387, 0) = 2.36593490106829, (387, 1) = -12.839706142528371, (387, 2) = -7.969007517092147, (388, 0) = -7.969007517092147, (388, 1) = 2.378401110625885, (388, 2) = -12.938893085811369, (389, 0) = -12.938893085811369, (389, 1) = -7.942642251570056, (389, 2) = 2.3908673201834802, (390, 0) = 2.3908673201834802, (390, 1) = -13.037703438239033, (390, 2) = -7.908620167913998, (391, 0) = -7.908620167913998, (391, 1) = 2.4033335297410754, (391, 2) = -13.136043947023653, (392, 0) = -13.136043947023653, (392, 1) = -7.867302986664748, (392, 2) = 2.4157997392986705, (393, 0) = 2.4157997392986705, (393, 1) = -13.233825960505321, (393, 2) = -7.819125610216599, (394, 0) = -7.819125610216599, (394, 1) = 2.4282659488562657, (394, 2) = -13.330967134252585, (395, 0) = -13.330967134252585, (395, 1) = -7.764592080814277, (395, 2) = 2.440732158413861, (396, 0) = 2.440732158413861, (396, 1) = -13.427391811626926, (396, 2) = -7.704258602420315, (397, 0) = -7.704258602420315, (397, 1) = 2.453198367971456, (397, 2) = -13.523031403127861, (398, 0) = -13.523031403127861, (398, 1) = -7.638725447535343, (398, 2) = 2.4653465181107728, (399, 0) = 2.4653465181107728, (399, 1) = -13.61541728097374, (399, 2) = -7.570472013573171, (400, 0) = -7.570472013573171, (400, 1) = 2.47749466825009, (400, 2) = -13.706950819933528, (401, 0) = -13.706950819933528, (401, 1) = -7.498509139290917, (401, 2) = 2.489642818389407, (402, 0) = 2.489642818389407, (402, 1) = -13.79759082912716, (402, 2) = -7.423471303434782, (403, 0) = -7.423471303434782, (403, 1) = 2.5017909685287236, (403, 2) = -13.887303851218123, (404, 0) = -13.887303851218123, (404, 1) = -7.3459998811822755, (404, 2) = 2.514230150340874, (405, 0) = 2.514230150340874, (405, 1) = -13.978178796763714, (405, 2) = -7.264824307593009, (406, 0) = -7.264824307593009, (406, 1) = 2.5266693321530242, (406, 2) = -14.068035923418016, (407, 0) = -14.068035923418016, (407, 1) = -7.182462192216424, (407, 2) = 2.5391085139651746, (408, 0) = 2.5391085139651746, (408, 1) = -14.156864608158788, (408, 2) = -7.099587543322661, (409, 0) = -7.099587543322661, (409, 1) = 2.551547695777325, (409, 2) = -14.244662571442847, (410, 0) = -14.244662571442847, (410, 1) = -7.016854476110384, (410, 2) = 2.565269221003186, (411, 0) = 2.565269221003186, (411, 1) = -14.340323206671359, (411, 2) = -6.926514264353242, (412, 0) = -6.926514264353242, (412, 1) = 2.5789907462290476, (412, 2) = -14.434755433122174, (413, 0) = -14.434755433122174, (413, 1) = -6.837924913267809, (413, 2) = 2.5927122714549093, (414, 0) = 2.5927122714549093, (414, 1) = -14.527988332686618, (414, 2) = -6.75184844408653, (415, 0) = -6.75184844408653, (415, 1) = 2.6064337966807707, (415, 2) = -14.62006133877994, (416, 0) = -14.62006133877994, (416, 1) = -6.668995625793579, (416, 2) = 2.6238725922598687, (417, 0) = 2.6238725922598687, (417, 1) = -14.735482170223138, (417, 2) = -6.569380123671183, (418, 0) = -6.569380123671183, (418, 1) = 2.641311387838967, (418, 2) = -14.849229763442501, (419, 0) = -14.849229763442501, (419, 1) = -6.47725415913787, (419, 2) = 2.658750183418065, (420, 0) = 2.658750183418065, (420, 1) = -14.961443449006323, (420, 2) = -6.393696353590666, (421, 0) = -6.393696353590666, (421, 1) = 2.676188978997163, (421, 2) = -15.072281128049934, (422, 0) = -15.072281128049934, (422, 1) = -6.319642410921113, (422, 2) = 2.695047076049267, (423, 0) = 2.695047076049267, (423, 1) = -15.190792691708035, (423, 2) = -6.251173112245407, (424, 0) = -6.251173112245407, (424, 1) = 2.7139051731013715, (424, 2) = -15.3081335914815, (425, 0) = -15.3081335914815, (425, 1) = -6.195570609065231, (425, 2) = 2.732763270153476, (426, 0) = 2.732763270153476, (426, 1) = -15.424551575216718, (426, 2) = -6.153483834711129, (427, 0) = -6.153483834711129, (427, 1) = 2.75162136720558, (427, 2) = -15.54030658394461, (428, 0) = -15.54030658394461, (428, 1) = -6.125390924201944, (428, 2) = 2.7713456167560984, (429, 0) = 2.7713456167560984, (429, 1) = -15.660961033125046, (429, 2) = -6.111315272803052, (430, 0) = -6.111315272803052, (430, 1) = 2.791069866306617, (430, 2) = -15.781494118588505, (431, 0) = -15.781494118588505, (431, 1) = -6.113057946240252, (431, 2) = 2.810794115857135, (432, 0) = 2.810794115857135, (432, 1) = -15.902216421967077, (432, 2) = -6.13059920915312, (433, 0) = -6.13059920915312, (433, 1) = 2.8305183654076536, (433, 2) = -16.02343820115754, (434, 0) = -16.02343820115754, (434, 1) = -6.163725273812224, (434, 2) = 2.8477046004090236, (435, 0) = 2.8477046004090236, (435, 1) = -16.1297078859082, (435, 2) = -6.204981750927832, (436, 0) = -6.204981750927832, (436, 1) = 2.8648908354103932, (436, 2) = -16.2367831910682, (437, 0) = -16.2367831910682, (437, 1) = -6.257377179462282, (437, 2) = 2.8820770704117633}, datatype = float[8], order = C_order)), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = vartheta(tau), Y[2] = diff(vartheta(tau),tau)]`; YP[2] := -6.666666666*sin(Y[1])-66.66666666*cos(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478)-66.66666666*sin(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478); YP[1] := Y[2]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] )), ( 4 ) = (3)  ] ); _y0 := Array(0..2, {(1) = 0., (2) = 0.}); _vmap := array( 1 .. 2, [( 1 ) = (1), ( 2 ) = (2)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [tau, vartheta(tau), diff(vartheta(tau), tau)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(1)

odeplot(ld, [tau, FAK(`&vartheta;`(tau), `&vartheta;l`, tau)])

 

NULL


 

Download odeplot_test_ver2.mw


 

restart

with(PDEtools)

U := diff_table(u(x, y))

pde := 18*U[]^2*U[x, x]+36*U[]*U[x]^2-x*U[x, x]-2*y*U[y, x]-2*U[x]+3*U[y, y]+3*U[x, x, x, x] = 0

18*u(x, y)^2*(diff(diff(u(x, y), x), x))+36*u(x, y)*(diff(u(x, y), x))^2-x*(diff(diff(u(x, y), x), x))-2*y*(diff(diff(u(x, y), x), y))-2*(diff(u(x, y), x))+3*(diff(diff(u(x, y), y), y))+3*(diff(diff(diff(diff(u(x, y), x), x), x), x)) = 0

(1)

pdsolve(pde)

``

NULL

PDEtools:-PolynomialSolutions(pde)

{u(x, y) = _C2*y+_C1}

(2)

NULL

pdetest({u(x, y) = _C2*y+_C1}[1], pde)

0

(3)

NULL

``


 

Download pde_ver2.mw

I don't know why Maple 2020.1 can't give a solution,probably a weakness in here.

All computer algebra systems, including Maple, are limited in their capabilities.

The delta function can be defined as the following :

DIRAC := proc (x, `&epsilon;`) options operator, arrow; `&epsilon;`/(Pi*(1+`&epsilon;`^2*x^2)) end proc

proc (x, epsilon) options operator, arrow; epsilon/(Pi*(1+epsilon^2*x^2)) end proc

(1)

sol := int(DIRAC(sin(x), `&epsilon;`), x = -(3/2)*Pi .. (3/2)*Pi)

3*epsilon/(epsilon^2+1)^(1/2)

(2)

limit(sol, `&epsilon;` = infinity)

3

(3)

NULL

Int(Dirac(sin(x)), x = -(3/2)*Pi .. (3/2)*Pi) = 3

Int(Dirac(sin(x)), x = -(3/2)*Pi .. (3/2)*Pi) = 3

(4)

``


I tried with Mathematica 12.1.1 and works fine,give me 3.

As you can see here Mathematica(Rubi) is a leader for solving a indefine integrals probably also for define integrals.

Download dirac_integral.mwDownload dirac_integral.mw

Try:

restart;

f:=x->x^5+2*x^3+3;

[f(x), f(1), f(-1)];

Output: [x^5 + 2*x^3 + 3, 6, 0]

 

pdsolve give you a correct solution see here.

pdetest for some reason(is not smart  enough) to check if is true,this does't mean that pdetest gave you the wrong solution.

IBVP_ver2.mw

Maybe so:

plot(-0.25*t^2 + 16.9*t - 50, t = 5 .. 29, tickmarks = [[5 = "1995", 10 = "2001", 15 = "2007", 20 = "2013", 25 = "2019", 29 = "2024"], default]);

or:

plot(-0.25*t^2 + 16.9*t - 50, t = 5 .. 29, tickmarks = [[seq(n = convert(1988.9583333333333333 + 1.2083333333333333333*n, rational, 4), n = 5 .. 29, 4)], default]);


 

kernelopts("version")

`Maple 2020.0, X86 64 WINDOWS, Mar 4 2020, Build ID 1455132`

(1)

eq1 := diff(c(x, t), t)-3*(diff(c(x, t), x, x))*(1/2)+1/(20*(x+1/1000)) = 0

diff(c(x, t), t)-(3/2)*(diff(diff(c(x, t), x), x))+1/(20*x+1/50) = 0

(2)

ics := c(x, 0) = 0, c(0, t) = 10, (D[1](c))(20, t) = 0

c(x, 0) = 0, c(0, t) = 10, (D[1](c))(20, t) = 0

(3)

sol := pdsolve([eq1, ics])

c(x, t) = Sum(-(1/300000)*exp(-(3/3200)*Pi^2*(1+2*n)^2*t)*sin((1/40)*(1+2*n)*Pi*x)*(Int(-1000*sin((1/40)*(1+2*n)*Pi*x)*((-x-1/1000)*ln(1000*x+1)+x*ln(3)+x*ln(59)+x*ln(113)+x-300), x = 0 .. 20)), n = 0 .. infinity)+(1/30000)*ln(1000*x+1)*(1000*x+1)-(1/30)*x+10-(1/30)*ln(20001)*x

(4)

SOL := value(eval(op(1, rhs(c(x, t) = Sum(-(1/300000)*exp(-(3/3200)*Pi^2*(1+2*n)^2*t)*sin((1/40)*(1+2*n)*Pi*x)*(Int(-1000*sin((1/40)*(1+2*n)*Pi*x)*((-x-1/1000)*ln(1000*x+1)+x*ln(3)+x*ln(59)+x*ln(113)+x-300), x = 0 .. 20)), n = 0 .. infinity)+(1/30000)*ln(1000*x+1)*(1000*x+1)-(1/30)*x+10-(1/30)*ln(20001)*x)), infinity = 50))

plot3d(SOL, x = 0 .. 20, t = 0 .. 100, labels = [x, t, c])

 

``


 

Download solution.mw

 

Select for Palletes -> Common Symbols -> imaginaryunit:  I (uppercase), or (lowercase).


 

Example 2: Multiplying Complex Numbers

 

``

(2-I)*(4+3*I)

(3+2*I)*(3-2*I)

(4*I)*(-1+5*I)

(3+2*I)^2

11+2*I

 

13

 

-20-4*I

 

5+12*I

(1.1)

-1

(1)

(2-I)*(4+3*I)

11+2*I

(2)

(3+2*I)*(3-2*I)

13

(3)

(4*I)*(-1+5*I)

-20-4*I

(4)

(3+2*I)^2

5+12*I

(5)

``


 

Download Multiplying_Complex_num_ver2.mw

I think that your integral  does not have finite closed-form expression in terms of very large class of special functions.

 Most integrals don't have one. I have only approximation by infinite Sum.


 

Int(x*sqrt(x^2-1)*exp(-x), x = 1 .. y) = BesselK(2, 1)+(1/2)*sqrt(Pi)*(Sum((-1)^(1+m)*GAMMA(3-2*m, y)/(GAMMA(3/2-m)*GAMMA(1+m)), m = 0 .. infinity))

Int(x*(x^2-1)^(1/2)*exp(-x), x = 1 .. y) = BesselK(2, 1)+(1/2)*Pi^(1/2)*(Sum((-1)^(1+m)*GAMMA(3-2*m, y)/(GAMMA(3/2-m)*GAMMA(1+m)), m = 0 .. infinity))

(1)

evalf(eval(lhs(Int(x*(x^2-1)^(1/2)*exp(-x), x = 1 .. y) = BesselK(2, 1)+(1/2)*Pi^(1/2)*(Sum((-1)^(1+m)*GAMMA(3-2*m, y)/(GAMMA(3/2-m)*GAMMA(1+m)), m = 0 .. infinity))), y = 3))

.8038144469

(2)

evalf(eval(rhs(Int(x*(x^2-1)^(1/2)*exp(-x), x = 1 .. y) = BesselK(2, 1)+(1/2)*Pi^(1/2)*(Sum((-1)^(1+m)*GAMMA(3-2*m, y)/(GAMMA(3/2-m)*GAMMA(1+m)), m = 0 .. infinity))), y = 3))

.8038144470

(3)

f := proc (y) options operator, arrow; evalf(Int(x*sqrt(x^2-1)*exp(-x), x = 1 .. y)) end proc

proc (y) options operator, arrow; evalf(Int(x*sqrt(x^2-1)*exp(-x), x = 1 .. y)) end proc

(4)

g := proc (y, N) options operator, arrow; BesselK(2, 1)+(1/2)*sqrt(Pi)*add((-1)^(1+m)*GAMMA(3-2*m, y)/(GAMMA(3/2-m)*GAMMA(1+m)), m = 0 .. N) end proc

proc (y, N) local m; options operator, arrow; BesselK(2, 1)+(1/2)*sqrt(Pi)*add((-1)^(m+1)*GAMMA(3-2*m, y)/(GAMMA(3/2-m)*GAMMA(m+1)), m = 0 .. N) end proc

(5)

plot([f(y), g(y, 10)], y = 1 .. 8, linestyle = [dash, dot], color = ["Red", "Black"], thickness = 3)

 

``


 

Download integral.mw

From comment by user:vv 7062 

IntegrationTools:-Parts(int(arccos(x)*arcsin(x), x), arcsin(x));

#(x*arccos(x) - sqrt(-x^2 + 1))*arcsin(x) + 2*x + arccos(x)*sqrt(-x^2 + 1)

From Wikipedia see example:

See attached file:

Download integral.mw

 

I found the analytical solution of the double integral,difficult calculations to get solution I will not describe it here.

Numeric integration works ,but is very slow.

See attached file:

Download Maple_question_v1.mw

 

 

 

 

I found a workaround. See attached file.

DIFF_eq.mw


 

restart

with(NumberTheory)

n := 10^13; N := 346065536839

10000000000000

 

346065536839

(1)

evalf(trunc(add(Ei(ln(n)/j)*Moebius(j)/j, j = 1 .. 20)))-N

-5774.

(2)

evalf(trunc(add(Moebius(j)*Li(n^(1/j))/j, j = 1 .. 20)))-N

-5774.

(3)

evalf(trunc(-4*add((-1)^j*j*(ln(n)/(2*Pi))^(2*j-1)/((2*j-1)*bernoulli(2*j)), j = 1 .. 200)/Pi))-N

-5774.

(4)

evalf(trunc(1+add(ln(n)^j/(factorial(j)*j*Zeta(j+1)), j = 1 .. 300)))-N

-5774.

(5)

trunc(evalf(Li(n)))-N

108971

(6)

trunc(evalf(sqrt(exp(1)*n*Li(n/exp(1))/ln(n))))-N

452312

(7)

``


 

Download PrimePi_-approximation.mw

I have analitycal solution only with conditions:

[f3(0,t)=-exp(-2*t),f4(x,0)=exp(-3*x)*cos(2*Pi*x),f1(x,3)=0,f1(3,t)=0,f2(3,0)=0].

last condition You may change in the code from :f2(3,0)=0 to f2(0,3)=0

from eval(rhs(sol[2]), x = 3) = 0 to eval(rhs(sol[2]), t = 3) = 0 in SOL.

See attached file.

EQ_diff.mw

 

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