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I have a nonlinear system with 4 equations and 4 unknowns. I am using fsolve. I know that there are multiple solutions for each variable but am only getting one. I need the others. what do I do??

This is my code:

R__1 := Matrix([[1, 0] , [0, 1] ]);

R__2 := Matrix([[1/2, sqrt(3)/2] , [-sqrt(3)/2, 1/2] ]);

R__3 := Matrix([[-1/2, sqrt(3)/2] , [-sqrt(3)/2, -1/2] ]);

R__4 := Matrix([[-1, 0] , [0, -1] ]);

R__5 := Matrix([[-1/2, -sqrt(3)/2] , [sqrt(3)/2, -1/2] ]);

 

d__1 := Vector( [ 0, 5.4] );

d__2 := Vector( [ 6.4, 4.539] );

d__3 := Vector( [ 11, 4.078] );

d__4 := Vector( [ 15.5, 2.079] );

d__5 := Vector( [ 19, 1.039] );

 

a := Vector( [ a__x, a__y] );

 

A__1:=R__1.a+d__1;

A__2:=R__2.a+d__2;

A__3:=R__3.a+d__3;

A__4:=R__4.a+d__4;

A__5:=R__5.a+d__5;

 

OO:=Vector([O__x,O__y]);

 

DA1:=A__2.A__2-A__1.A__1-2*(A__2-A__1).OO;

DA2:=A__3.A__3-A__1.A__1-2*(A__3-A__1).OO;

DA3:=A__4.A__4-A__1.A__1-2*(A__4-A__1).OO;

DA4:=A__5.A__5-A__1.A__1-2*(A__5-A__1).OO;

 

fsolve({DA1,DA2,DA3,DA4},{a__x,a__y,O__x,O__y});

Thanks for any tips you may be able to offer

 

Is it possible in Maple 15 to solve an equation with a parameter for a given set of parameters? How can this be passed to the solve function, should I use some kind of list?  After obtaining the solution how can I assign the solutions to variables such as x1 for the first value of the parameter, x2 for the second value of the parameters and so on. Furthermore, is this possible with the fsolve command?

 

Thanks

Presented at the National University of Trujillo - CUICITI 2014.

IT Solutions for the Next Generation of Engineers

 

 

 

Descarga aqui los Slides de la presentación/mw CUICITI-2014

CUICITI_09102014.pdf

Soluciones_Informáticas_para_la_siguiente_generación_de_Ingenieros.mw

Lenin Araujo Castillo

Physics Pure

Computer Science

 

OK. Perfect. It runs.

Now, I would like to remove all the set of solutions where for two variables (for example a and b) are negative.

For example, if I have this :

{a=1,b=-1,c=1}, {a=1,b=1,c=1}, {a=-2,b=-1,c=1}

After filtering, I would like to have only :

{a=1,b=1,c=1}

Thanks a lot for your help.

 

Hello,

After a solve on a system composed with trigonometric functions, i obtain several group of solutions.

Here a picture of my solutions :



How can I do to extract from thses solutions only the group composed with real components.

Thanks a lot for your help


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

Hi MaplePrimers,

I'm trying to solve a system of algebraic equations using 'solve' [float].  I'd prefer to use 'solve' over 'fsolve', as 'solve' solves my system in about 0.05s, whereas fsolve takes about 5 seconds.  I need to solve the system repeatedly at a different points, so time is important.  I don't know why there is such a large difference in time ... 

I have a few piecewise functions of order 3 to 5.  It solves fine with the other (piecewise) equations, but adding one piecewise function which gives me an error while trying to solve:

Error, (in RootOf) _Z occurs but is not the dependent variable.

I think this is due to solve finding multiple solutions.  Is there a way to limit solve to only real solutions?

Thanks in advance!

Hi,

I have a linear problem A*X = B, with dimensions of A approximately 500*1300, and B is a vector with only one nonzero coordinate.

I feed it to LinearSolve, and there are a *lot* of solutions - presented as one vector with linear polynomial coordinates.

How can I get only one (hopefully with as many zeros as possible) ?

Thank you in advance.

NoThik

Dear all,

I'm a new user of Maple. The pdsolve in Maple is quite an important function for me.

I can see how it works for PDES in the help:

http://www.maplesoft.com/support/help/Maple/view.aspx?path=pdsolve/numeric

However, I'm wondering if I could get the euqations of the discreted PDES forms (equations) rather than just the results, please?

Thanks in advance!

hello guys , i have an autonomous system , maple give me this warning when i want to compute its fixed points !

 

thank you for your time

 

mm.mw

Hi, I have read the help files, and many posts in MaplePrime. However, I am struggling to understand how to properly extract a number from a list. I would like to extract only the positive, or the maximum solution of a quadratic expression.I have uploaded the .mw file. (1) (2) (3) (4) With no brackets around A it does no work, Error, incorrect number of extra arguments in select If I extract the positive value I get a list, (5...

Hi!

I need to assign a name to a result calculated from a system of equations. In this case, i've got 2 equations and 2 solutions. I want to assign a name to the each of the solutions.

solve({-a+4*b = 0, 2*a+7*b = 2}, {a, b})

{a = 8/15, b = 2/15}

How do i assign a name for a and another for b?

Hi!

In the program below, all solutions are found for the equation S.R=T subject to 

the constraints given by eq1 and eq2. I've tried it for a 

few different choices of T and there's usually 80+ solutions.

I want to try more complicated choices of T (for example,

I want the matrix T to have every entry a distinct prime number). 

But then the program crashes. I assume the equations get complicated

or there...

Hi! Any help would be greatly appreciated :)

I have two matrices S and R, where 

S :=

Matrix([[a_1, a_2, a_3, a_4], [b_1, b_2, b_3, b_4], [c_1, c_2, c_3, c_4], [d_1, d_2, d_3, d_4]]);

such that 

a_1*d_1 = b_1*c_1
a_2*d_2 = b_2*c_2
a_3*d_3 = b_3*c_3
a_4*d_4 = b_4*c_4;
and 
R :=
Matrix([[s_1, t_1, r_1, l_1], [s_2, t_2, r_2, l_2], [s_3, t_3, r_3, l_3], [s_4, t_4, r_4, l_4]]);

Anybody has a hint on how to solve a non-linear system with trigonometrics. I want to solve x, y and z.

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