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how to find the homomorphism between prime ideal and space?

how to find the homomorphism between prime ideal and distributive lattice?

 

which homomorphism result in space if given prime ideal?


psif := (0.5731939284e-1*(x-97.79105004))/((x-97.79105004)^2+(y+.3750470777)^2)+(0.2599707238e-1*(y+.3750470777))/((x-97.79105004)^2+(y+.3750470777)^2)+(0.7176288278e-1*x-7.025711349)/((x-97.90174359)^2+(y-.8198365723)^2)+(-0.6648084910e-2*y+0.5450343145e-2)/((x-97.90174359)^2+(y-.8198365723)^2)+(0.6378426459e-1*x-6.295510046)/((x-98.70004908)^2+(y-1.715776493)^2)+(-0.5683341879e-1*y+0.9751344398e-1)/((x-98.70004908)^2+(y-1.715776493)^2)+(0.6500592479e-2*x-.6493949981)/((x-99.89781703)^2+(y-1.788933400)^2)+(-.1064315267*y+.1903989129)/((x-99.89781703)^2+(y-1.788933400)^2)+(-.1026176004*x+10.33830579)/((x-100.7459320)^2+(y-.9399922915)^2)+(-.1025177385*y+0.9636588393e-1)/((x-100.7459320)^2+(y-.9399922915)^2)+(-.1841914880*x+18.41914880)/((x-100.)^2+y^2)+.1461653667*y/((x-100.)^2+y^2)+3.*y-11.93662073*ln((x-100.)^2+y^2):

xf := 98.17642962:

ode := diff(X(t), t) = evalf(subs(x = X(t), y = Y(t), subs(vvx = Vx, vvx))), diff(Y(t), t) = evalf(subs(x = X(t), y = Y(t), subs(vvy = Vy, vvy))), diff(S(t), t) = -Y(t)*evalf(subs(x = X(t), y = Y(t), subs(vvx = Vx, vvx))):

ds := dsolve(odse, type = numeric, method = rkf45, maxfun = 0, output = listprocedure, abserr = .1^10, relerr = .1^10, minstep = .1^10);

proc (t) local _res, _dat, _solnproc, _xout, _ndsol, _pars, _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](t) else _xout := evalf(t) 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( [( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 20, [( 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..53, {(1) = 3, (2) = 3, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 0, (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}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-9, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.5313975432658623e-3, (7) = .0, (8) = 0.10e-9, (9) = .0, (10) = .0, (11) = 0.10e-9, (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..3, {(1) = .0, (2) = 98.17642962, (3) = -1.578177289}, 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..3, {(1) = 1.0, (2) = 1.0, (3) = 1.0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, 1..3, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0}, datatype = float[8], order = C_order), Array(1..3, 1..3, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0}, datatype = float[8], order = C_order), Array(1..3, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = 0, (2) = 0, (3) = 0}, datatype = integer[8]), Array(1..3, {(1) = .0, (2) = 98.17642962, (3) = -1.578177289}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = 15.054642426145987, (2) = 9.539259328516408, (3) = -7.5367596882075505}, datatype = float[8], order = C_order)]), ( 11 ) = (Array(1..6, 0..3, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = S(t), Y[2] = X(t), Y[3] = Y(t)]`; YP[1] := -Y[3]*(-0.5731939284e-1*(Y[2]-97.79105004)*(2.*Y[3]+.7500941554)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2+0.2599707238e-1/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)-0.2599707238e-1*(Y[3]+.3750470777)*(2.*Y[3]+.7500941554)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2-1.*(0.7176288278e-1*Y[2]-7.025711349)*(2.*Y[3]-1.639673145)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2-0.6648084910e-2/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)-1.*(-0.6648084910e-2*Y[3]+0.5450343145e-2)*(2.*Y[3]-1.639673145)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2-1.*(0.6378426459e-1*Y[2]-6.295510046)*(2.*Y[3]-3.431552986)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2-0.5683341879e-1/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)-1.*(-0.5683341879e-1*Y[3]+0.9751344398e-1)*(2.*Y[3]-3.431552986)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2-1.*(0.6500592479e-2*Y[2]-.6493949981)*(2.*Y[3]-3.577866800)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2-.1064315267/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)-1.*(-.1064315267*Y[3]+.1903989129)*(2.*Y[3]-3.577866800)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2-1.*(-.1026176004*Y[2]+10.33830579)*(2.*Y[3]-1.879984583)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2-.1025177385/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)-1.*(-.1025177385*Y[3]+0.9636588393e-1)*(2.*Y[3]-1.879984583)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2-2.*(-.1841914880*Y[2]+18.41914880)*Y[3]/((Y[2]-100.)^2+Y[3]^2)^2+.1461653667/((Y[2]-100.)^2+Y[3]^2)-.2923307334*Y[3]^2/((Y[2]-100.)^2+Y[3]^2)^2+3.-23.87324146*Y[3]/((Y[2]-100.)^2+Y[3]^2)); YP[2] := -0.5731939284e-1*(Y[2]-97.79105004)*(2.*Y[3]+.7500941554)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2+0.2599707238e-1/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)-0.2599707238e-1*(Y[3]+.3750470777)*(2.*Y[3]+.7500941554)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2-1.*(0.7176288278e-1*Y[2]-7.025711349)*(2.*Y[3]-1.639673145)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2-0.6648084910e-2/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)-1.*(-0.6648084910e-2*Y[3]+0.5450343145e-2)*(2.*Y[3]-1.639673145)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2-1.*(0.6378426459e-1*Y[2]-6.295510046)*(2.*Y[3]-3.431552986)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2-0.5683341879e-1/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)-1.*(-0.5683341879e-1*Y[3]+0.9751344398e-1)*(2.*Y[3]-3.431552986)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2-1.*(0.6500592479e-2*Y[2]-.6493949981)*(2.*Y[3]-3.577866800)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2-.1064315267/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)-1.*(-.1064315267*Y[3]+.1903989129)*(2.*Y[3]-3.577866800)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2-1.*(-.1026176004*Y[2]+10.33830579)*(2.*Y[3]-1.879984583)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2-.1025177385/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)-1.*(-.1025177385*Y[3]+0.9636588393e-1)*(2.*Y[3]-1.879984583)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2-2.*(-.1841914880*Y[2]+18.41914880)*Y[3]/((Y[2]-100.)^2+Y[3]^2)^2+.1461653667/((Y[2]-100.)^2+Y[3]^2)-.2923307334*Y[3]^2/((Y[2]-100.)^2+Y[3]^2)^2+3.-23.87324146*Y[3]/((Y[2]-100.)^2+Y[3]^2); YP[3] := -0.5731939284e-1/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)+0.5731939284e-1*(Y[2]-97.79105004)*(2.*Y[2]-195.5821001)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2+0.2599707238e-1*(Y[3]+.3750470777)*(2.*Y[2]-195.5821001)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2-0.7176288278e-1/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)+(0.7176288278e-1*Y[2]-7.025711349)*(2.*Y[2]-195.8034872)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2+(-0.6648084910e-2*Y[3]+0.5450343145e-2)*(2.*Y[2]-195.8034872)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2-0.6378426459e-1/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)+(0.6378426459e-1*Y[2]-6.295510046)*(2.*Y[2]-197.4000982)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2+(-0.5683341879e-1*Y[3]+0.9751344398e-1)*(2.*Y[2]-197.4000982)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2-0.6500592479e-2/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)+(0.6500592479e-2*Y[2]-.6493949981)*(2.*Y[2]-199.7956341)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2+(-.1064315267*Y[3]+.1903989129)*(2.*Y[2]-199.7956341)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2+.1026176004/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)+(-.1026176004*Y[2]+10.33830579)*(2.*Y[2]-201.4918640)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2+(-.1025177385*Y[3]+0.9636588393e-1)*(2.*Y[2]-201.4918640)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2+.1841914880/((Y[2]-100.)^2+Y[3]^2)+(-.1841914880*Y[2]+18.41914880)*(2.*Y[2]-200.)/((Y[2]-100.)^2+Y[3]^2)^2+.1461653667*Y[3]*(2.*Y[2]-200.)/((Y[2]-100.)^2+Y[3]^2)^2+11.93662073*(2.*Y[2]-200.)/((Y[2]-100.)^2+Y[3]^2); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = S(t), Y[2] = X(t), Y[3] = Y(t)]`; YP[1] := -Y[3]*(-0.5731939284e-1*(Y[2]-97.79105004)*(2.*Y[3]+.7500941554)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2+0.2599707238e-1/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)-0.2599707238e-1*(Y[3]+.3750470777)*(2.*Y[3]+.7500941554)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2-1.*(0.7176288278e-1*Y[2]-7.025711349)*(2.*Y[3]-1.639673145)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2-0.6648084910e-2/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)-1.*(-0.6648084910e-2*Y[3]+0.5450343145e-2)*(2.*Y[3]-1.639673145)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2-1.*(0.6378426459e-1*Y[2]-6.295510046)*(2.*Y[3]-3.431552986)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2-0.5683341879e-1/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)-1.*(-0.5683341879e-1*Y[3]+0.9751344398e-1)*(2.*Y[3]-3.431552986)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2-1.*(0.6500592479e-2*Y[2]-.6493949981)*(2.*Y[3]-3.577866800)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2-.1064315267/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)-1.*(-.1064315267*Y[3]+.1903989129)*(2.*Y[3]-3.577866800)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2-1.*(-.1026176004*Y[2]+10.33830579)*(2.*Y[3]-1.879984583)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2-.1025177385/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)-1.*(-.1025177385*Y[3]+0.9636588393e-1)*(2.*Y[3]-1.879984583)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2-2.*(-.1841914880*Y[2]+18.41914880)*Y[3]/((Y[2]-100.)^2+Y[3]^2)^2+.1461653667/((Y[2]-100.)^2+Y[3]^2)-.2923307334*Y[3]^2/((Y[2]-100.)^2+Y[3]^2)^2+3.-23.87324146*Y[3]/((Y[2]-100.)^2+Y[3]^2)); YP[2] := -0.5731939284e-1*(Y[2]-97.79105004)*(2.*Y[3]+.7500941554)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2+0.2599707238e-1/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)-0.2599707238e-1*(Y[3]+.3750470777)*(2.*Y[3]+.7500941554)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2-1.*(0.7176288278e-1*Y[2]-7.025711349)*(2.*Y[3]-1.639673145)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2-0.6648084910e-2/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)-1.*(-0.6648084910e-2*Y[3]+0.5450343145e-2)*(2.*Y[3]-1.639673145)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2-1.*(0.6378426459e-1*Y[2]-6.295510046)*(2.*Y[3]-3.431552986)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2-0.5683341879e-1/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)-1.*(-0.5683341879e-1*Y[3]+0.9751344398e-1)*(2.*Y[3]-3.431552986)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2-1.*(0.6500592479e-2*Y[2]-.6493949981)*(2.*Y[3]-3.577866800)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2-.1064315267/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)-1.*(-.1064315267*Y[3]+.1903989129)*(2.*Y[3]-3.577866800)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2-1.*(-.1026176004*Y[2]+10.33830579)*(2.*Y[3]-1.879984583)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2-.1025177385/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)-1.*(-.1025177385*Y[3]+0.9636588393e-1)*(2.*Y[3]-1.879984583)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2-2.*(-.1841914880*Y[2]+18.41914880)*Y[3]/((Y[2]-100.)^2+Y[3]^2)^2+.1461653667/((Y[2]-100.)^2+Y[3]^2)-.2923307334*Y[3]^2/((Y[2]-100.)^2+Y[3]^2)^2+3.-23.87324146*Y[3]/((Y[2]-100.)^2+Y[3]^2); YP[3] := -0.5731939284e-1/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)+0.5731939284e-1*(Y[2]-97.79105004)*(2.*Y[2]-195.5821001)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2+0.2599707238e-1*(Y[3]+.3750470777)*(2.*Y[2]-195.5821001)/((Y[2]-97.79105004)^2+(Y[3]+.3750470777)^2)^2-0.7176288278e-1/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)+(0.7176288278e-1*Y[2]-7.025711349)*(2.*Y[2]-195.8034872)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2+(-0.6648084910e-2*Y[3]+0.5450343145e-2)*(2.*Y[2]-195.8034872)/((Y[2]-97.90174359)^2+(Y[3]-.8198365723)^2)^2-0.6378426459e-1/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)+(0.6378426459e-1*Y[2]-6.295510046)*(2.*Y[2]-197.4000982)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2+(-0.5683341879e-1*Y[3]+0.9751344398e-1)*(2.*Y[2]-197.4000982)/((Y[2]-98.70004908)^2+(Y[3]-1.715776493)^2)^2-0.6500592479e-2/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)+(0.6500592479e-2*Y[2]-.6493949981)*(2.*Y[2]-199.7956341)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2+(-.1064315267*Y[3]+.1903989129)*(2.*Y[2]-199.7956341)/((Y[2]-99.89781703)^2+(Y[3]-1.788933400)^2)^2+.1026176004/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)+(-.1026176004*Y[2]+10.33830579)*(2.*Y[2]-201.4918640)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2+(-.1025177385*Y[3]+0.9636588393e-1)*(2.*Y[2]-201.4918640)/((Y[2]-100.7459320)^2+(Y[3]-.9399922915)^2)^2+.1841914880/((Y[2]-100.)^2+Y[3]^2)+(-.1841914880*Y[2]+18.41914880)*(2.*Y[2]-200.)/((Y[2]-100.)^2+Y[3]^2)^2+.1461653667*Y[3]*(2.*Y[2]-200.)/((Y[2]-100.)^2+Y[3]^2)^2+11.93662073*(2.*Y[2]-200.)/((Y[2]-100.)^2+Y[3]^2); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 20 ) = ([])  ] ))  ] ); _y0 := Array(0..3, {(1) = 0., (2) = 0., (3) = 98.17642962}); _vmap := array( 1 .. 3, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3)  ] ); _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); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `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; 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] < 10 and 10 <= _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 10 <= _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] < 10 and 10 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 10 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-10 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-10; 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] < 10 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 _src = 0 and 10 < _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 <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> 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 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _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]-10, 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 <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> 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 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _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]-10, 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]; _dat[4][26] := _EnvDSNumericSaveDigits; _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(1..4, {(1) = 18446744074566161350, (2) = 18446744074566161614, (3) = 18446744074566161790, (4) = 18446744074566161966}), (3) = [t, S(t), X(t), Y(t)], (4) = []}); _solnproc := _dat[1]; _pars := map(rhs, _dat[4]); if not type(_xout, 'numeric') then if member(t, ["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(t, '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(t, ["last", 'last', "initial", 'initial', NULL]) then _res := _solnproc(convert(t, 'string')); if type(_res, 'list') then return _res[2] else return NULL end if elif member(t, ["parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(t, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[2], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(t), 'string') = rhs(t); if lhs(_xout) = "initial" then if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else _res := _solnproc("initial" = ["single", 2, rhs(_xout)]) end if elif not type(rhs(_xout), 'list') then error "initial and/or parameter values must be specified in a list" elif lhs(_xout) = "initial_and_parameters" and nops(rhs(_xout)) = nops(_pars)+1 then _res := _solnproc(lhs(_xout) = ["single", 2, op(rhs(_xout))]) else _res := _solnproc(_xout) end if; if lhs(_xout) = "initial" then return _res[2] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[2], 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(t), 'string') = rhs(t)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _dat[3] end if; if procname <> unknown then return ('procname')(t) else _ndsol := `tools/gensym`("S(t)"); eval(FromInert(_Inert_FUNCTION(_Inert_NAME("assign"), _Inert_EXPSEQ(ToInert(_ndsol), _Inert_VERBATIM(pointto(_dat[2][2])))))); return FromInert(_Inert_FUNCTION(ToInert(_ndsol), _Inert_EXPSEQ(ToInert(t)))) end if end if; try _res := _solnproc(_xout); _res[2] catch: error  end try end proc

(1)

``

NULL

with(plots):

animate(plot, [[XX(t), YY(t), t = 0 .. (1/10)*a]], a = 1 .. 260);

 

plot([XX(t), YY(t), t = 0 .. 22.7])

with(DEtools)

solve([XX(t) = xf, t > 22, t < 23], [t], allsolutions = true)

[]

(2)

min(allvalues(abs(RootOf(50000000*X(_Z)-4908821481))))

min(abs(RootOf(50000000*X(_Z)-4908821481)))

(3)

remove_RootOf(t = RootOf(50000000*X(_Z)-4908821481))

50000000*X(t)-4908821481 = 0

(4)

allvalues(RootOf(50000000*X(_Z)-4908821481))

RootOf(50000000*X(_Z)-4908821481)

(5)

solve(50000000*X(t)-4908821481 = 0)

RootOf(50000000*X(_Z)-4908821481)

(6)

tyu := RootOf(50000000*XX(t)-4908821481, t)

allvalues(tyu)

NULL


Download for_clever_guys.mw


i m calculating space of this elipse,i need to find point t1 wherein [XX(t1), YY(t1)] creates full circle and get S(t1). here its between 22.6-22.7. but i need to find it with ~0.1^3  accuracy.

for_clever_guys.mw

Hello Hello everybody 
   I have to solve the following differential equation numerically 


``

 

restart:with(plots):

mb:=765 : mp:=587 : Ib:=76.3*10^3 : Ip:=7.3*10^3 : l:=0.92 : d:=10: F:=490: omega:=0.43 :

eq1:=(mp+mb)*diff(x(t),t$2)+mp*(d*cos(theta(t))+l*cos(alpha(t)+theta(t)))*diff(theta(t),t$2)+mp*l*cos(alpha(t)+theta(t))*diff(alpha(t),t$2)+mp*(d*diff(theta(t),t)^2*sin(theta(t))+l*(diff(theta(t),t)+diff(alpha(t),t))^2*sin(alpha(t)+theta(t)))-F*sin(omega*t)=0;

1352*(diff(diff(x(t), t), t))+587*(10*cos(theta(t))+.92*cos(alpha(t)+theta(t)))*(diff(diff(theta(t), t), t))+540.04*cos(alpha(t)+theta(t))*(diff(diff(alpha(t), t), t))+5870*(diff(theta(t), t))^2*sin(theta(t))+540.04*(diff(theta(t), t)+diff(alpha(t), t))^2*sin(alpha(t)+theta(t))-490*sin(.43*t) = 0

(1)

eq2:=(mp+mb)*diff(z(t),t$2)-mp*d*(sin(theta(t)+alpha(t))+sin(theta(t)))*diff(theta(t),t$2)-mp*l*sin(alpha(t)+theta(t))*diff(alpha(t),t$2)+mp*(d*diff(theta(t),t)^2*cos(theta(t))+l*(diff(theta(t),t)+diff(alpha(t),t))^2*cos(alpha(t)+theta(t)))+9.81*(mp+mb)-F*sin(omega*t)=0;

1352*(diff(diff(z(t), t), t))-5870*(sin(alpha(t)+theta(t))+sin(theta(t)))*(diff(diff(theta(t), t), t))-540.04*sin(alpha(t)+theta(t))*(diff(diff(alpha(t), t), t))+5870*(diff(theta(t), t))^2*cos(theta(t))+540.04*(diff(theta(t), t)+diff(alpha(t), t))^2*cos(alpha(t)+theta(t))+13263.12-490*sin(.43*t) = 0

(2)

eq3:=mp*(d*cos(theta(t))+l*cos(alpha(t)+theta(t)))*diff(x(t),t$2)-mp*(l*sin(theta(t)+alpha(t))+d*sin(theta(t)))*diff(z(t),t$2)+(Ip+Ib+mp*(d^2+l^2)+2*mp*d*l*cos(alpha(t)))*diff(theta(t),t$2)+[Ip+mp*l^2+mp*d*l*cos(alpha(t))]*diff(alpha(t),t$2)-mp*sin(alpha(t))*(l*d*diff(alpha(t),t)^2-l*d*(diff(alpha(t),t)+diff(theta(t),t))^2)+mp*9.81*l*sin(alpha(t)+theta(t))+mp*9.81*d*sin(theta(t))=0;

587*(10*cos(theta(t))+.92*cos(alpha(t)+theta(t)))*(diff(diff(x(t), t), t))-587*(.92*sin(alpha(t)+theta(t))+10*sin(theta(t)))*(diff(diff(z(t), t), t))+(142796.8368+10800.80*cos(alpha(t)))*(diff(diff(theta(t), t), t))+[7796.8368+5400.40*cos(alpha(t))]*(diff(diff(alpha(t), t), t))-587*sin(alpha(t))*(9.20*(diff(alpha(t), t))^2-9.20*(diff(theta(t), t)+diff(alpha(t), t))^2)+5297.7924*sin(alpha(t)+theta(t))+57584.70*sin(theta(t)) = 0

(3)

eq4:=mp*l*cos(alpha(t)+theta(t))*diff(x(t),t$2)-mp*l*sin(alpha(t)+theta(t))*diff(z(t),t$2)+(Ip+mp*l^2+mp*d*l*cos(alpha(t)))*diff(theta(t),t$2)+(Ip+mp*l^2)*diff(alpha(t),t$2)-mp*9.81*l*sin(alpha(t)+theta(t))+l*d*mp*diff(theta(t),t$1)^2*sin(alpha(t))=0;

540.04*cos(alpha(t)+theta(t))*(diff(diff(x(t), t), t))-540.04*sin(alpha(t)+theta(t))*(diff(diff(z(t), t), t))+(7796.8368+5400.40*cos(alpha(t)))*(diff(diff(theta(t), t), t))+7796.8368*(diff(diff(alpha(t), t), t))-5297.7924*sin(alpha(t)+theta(t))+5400.40*(diff(theta(t), t))^2*sin(alpha(t)) = 0

(4)

CI:= x(0)=0,z(0)=0,theta(0)=0,alpha(0)=0,D(x)(0)=0,D(alpha)(0)=0,D(z)(0)=0,D(theta)(0)=0;

x(0) = 0, z(0) = 0, theta(0) = 0, alpha(0) = 0, (D(x))(0) = 0, (D(alpha))(0) = 0, (D(z))(0) = 0, (D(theta))(0) = 0

(5)

solution:=dsolve([eq1,eq2,eq3,eq4, CI],numeric);

Error, (in f) unable to store '[0.]/(0.17571268341557e16+[-0.25659510610770e15])' when datatype=float[8]

 

 

 

I don't know why it says : Error, (in f) unable to store '[0.]/(0.17571268341557e16+[-0.25659510610770e15])' when datatype=float[8]

 

Help pleaase!

thank you !!!

Download systéme_complet.mw

 

Dear all;

 

I need a help in this question.

u(x,y,t) my solution of PDE. x,y space, and t=time.

In the case without t. .i.e. u(x,y). Here is a visualization of the lattice u(x_i,y_j). i=1..3, anf j=1..3.  Please try this example, it's working. 

my question, if i would like to add a third variable t, i.e.  and get u(x_i,y_j,t_k)  on each points. I would like to show the lattice in (x,y) plan for each t_k. I Think I will get many parallel lattice. 

Please can some one, modify this code to get the parallel lattice. Thanks.


with(LinearAlgebra):
with(plots):
with(PDEtools):
interface(rtablesize=20):

Here,


L := 'L':
N := 'N':
g := 'g':
Z := i -> -L+2*L/(N+1)*i;
x[0] = Z(0),x[N+1] = Z(N+1),y[0] = Z(0),y[N+1] = Z(N+1);

 

N := 4;
L := 1;
r := L/(N+1)/4;
ngon := (n,x,y,r,phi) -> [seq([x+r*cos(2*Pi*i/n+phi), y+r*sin(2*Pi*i/n+phi)], i = 1 .. n)]:
p[1] := display([seq(polygonplot(ngon(4,Z(0),Z(j),r,Pi/2),color=magenta),j=0..N+1),

seq(polygonplot(ngon(4,Z(N+1),Z(j),r,Pi/2),color=magenta),j=0..N+1),

seq(polygonplot(ngon(4,Z(i),Z(0),r,0),color=magenta),i=1..N),

seq(polygonplot(ngon(4,Z(i),Z(N+1),r,0),color=magenta),i=1..N),

seq(seq(polygonplot(ngon(20,Z(i),Z(j),r,0),color=white),i=1..N),j=1..N),

textplot([seq(seq([Z(i+0.1),Z(j),typeset(u[i,j])],i=0..N+1),j=0..N+1)],align={above,right})],view=[Z(-1)..Z(N+2),Z(-1)..Z(N+2)],tickmarks=[[seq(Z(i)=typeset(x[i]=evalf[2](Z(i))),i=0..N+1)],[seq(Z(i)=typeset(y[i]=evalf[2](Z(i))),i=0..N+1)]],

axes=boxed,scaling=constrained,labels=[``,``]):
p[1];

 

 

 

 

 

 

Hello Maple users friends,

I have two lines in the space (x,y,z) described by the equations in L1 and L2:

 

L1:= {4*x + 3*y + z = 0, x + y - z - 15 = 0}:

L2:={12*x + 5*y + 7*z -13 = 0, 9*x + y -3*z - 5 = 0}:

I would like the get the parametric (with z=t) equations P1 and P2 of the two lines..

I see the "form" of such parametric equations P1 and P2 using "solve"

solve(L1, {x, y}); solve(L2, {x,y});

 

but I do not know how to use those values to get my parametric equations P1 and P2 to continue with additional computation (area, volume etc).

Thanks for your attention and help.

JJ

hello guys , i have a 3D dynamical system , what can i do to have its phase space in poincare coordinates ? thanks so muchmaple.mw

Hi all,

There is a state space system as follows:

X_dot = A.X + B.U

Y = C. X

The transfer function of this system is

H(s) = C. (sI-A)-1.B                 (1)

H(s), that is calculated in Maple by using the formula (1), is very complex (please see the attached file).

Would you please show me how to find the transfer function of the system? 

In addition, how to plot its bode plot?

Hello all,

I have the state-space form of a dynamics sytem:

X_dot = AX+B.U

Y= C X,

The initial conditions of the outputs (Y0) are also given.

A is 7x7 known matrix,

C is 14x7 known matrix,

B = 0;

The problem is that it's too long to write down every equations (14+7 eqns) and variables in "dsolve" function

Would you please show me the shorter way to solve a very large state-space system?

I really appreciate your help.

Why does Maple put space after a new string?

How to prevent Maple from doing that?

Screenshot

Dear Markiyan Hirnyk 

From  Phase-space trajectories i mean below photo which the asterisk arecritical points. but how can i compute the critical points and their nature ( stable , unstable , saddle) with maple ?

Thank for your time

 

Jacobe

How to extract affine terms from a differential equation after linearization?

Vanderpol Eqn:

diff(x[1](t),t)=x[2](t)

diff(x[2](t),t)=(1-x[1](t)^2)*x[2](t)-x[1](t)

 

To be precise, I linearized...

On Monday, August 6 at 1:31 a.m. EDT, NASA will attempt the landing of a new planetary rover, named Curiosity, on the surface of Mars.  The Mars Science Laboratory project is managed by the NASA Jet Propulsion Laboratory (JPL) in Pasadena, California, a world-renowned center for robotic space exploration and advanced science and engineering.  JPL recently began a widespread adoption of Maplesoft technology, and Maplesoft’s products are expected to help JPL save...

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