Kitonum

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11 years, 228 days

MaplePrimes Activity


These are answers submitted by Kitonum

In the figure, the red broken  AEC  is the above border of the first assembly, and the red broken  ABC  is the above border of the second one. The blue line  AC  is a straight line. Using the  geometry  package, we show that the area of the quadrangle  ABCE  is exactly  1 .

restart:
with(plottools): with(plots): with(geometry):  
P1:=polygon([[0,0],[8,0],[8,3]], color="Pink", style=surface):
P2:=polygon([[8,0],[8,1],[10,1],[10,2],[13,2],[13,0]], color=green, style=surface):
P3:=polygon([[8,1],[8,3],[13,3],[13,2],[10,2],[10,1]], color="Yellow", style=surface):
P4:=polygon([[8,3],[13,5],[13,3]], color="Green", style=surface):
L:=plottools:-line([0,0],[13,5], color=blue):
L1:=curve([[0,0],[8,3],[13,5]],color=red,thickness=2):
L2:=curve([[0,0],[5,2],[13,5]],color=red,thickness=2):
A:=[0,0]: B:=[5,2]: C:=[13,5]: E:=[8,3]:
T:=textplot([[A[],"A"],[B[],"B"],[C[],"C"],[E[],"E"]],font=[times,20],align={above,left}):
P:=pointplot([A,B,C,E], symbol=solidcircle, color=red, symbolsize=8):
display(L,L1,L2, P1,P2,P3,P4,T,P, scaling=constrained, size=[1100,450], axis[1] = [gridlines = [13,color=grey,thickness=0]], axis[2] = [gridlines = [5,color=grey,thickness=0]], transparency=0.5);
area(triangle(t1,[point(AA,A),point(BB,B),point(EE,E)]))+area(triangle(t2,[point(CC,C),point(BB,B),point(EE,E)]));

        

I agree that this is a serious bug. It seems that in the second case Maple first rounds each of the operands to 2 digits, and only then performs the calculation. Therefore, we get  1000-1000 = 0 .
Here is a workaround:
restart:  
P1 := 1007:
P3 := 1014.1:
P3 - P1:
evalf(%, 2);
                                
7.1

A useful conclusion: first you need to do all the calculations with maximum accuracy (preferably symbolically), and only at the end, round to the desired number of digits.

In your condition

, instead of  x , there should be a constant. I took  x=b :


 

"restart:Digits :=15: upsilon:=0.3:E(x):=E0*((x)/((b)))^(beta):rho(x):=rho0*((x)/((b)))^(beta):alpha(x):=alpha0*((x)/((b)))^(beta):a:=0.2:b:=1:omega:=100:E0:=390e9:rho0:=3900:T(x):=Ta+(Tb-Ta)/(ln(b/(a)))*(ln(x)-ln(a)):Ta:=373:Tb:=273:upsilon:=0.25:alpha0:=7e-6:  h(x):=(1-n*(x/(b)))^(k):n:=0.415196:k:=3:beta:=1:    dsys5 := {(1/(b))*( diff(u(x),x,x) )+(1/(b*h(x))*(diff(h(x),x))+1/(b*E(x))*(diff(E(x),x))+1/(b*(x)))*(diff(u(x),x))+((upsilon)/((b^(2)*x))*1/(h(x))*(diff(h(x),x))-1/((b*x)^(2))+(upsilon)/(b^(2)*(x))*1/(E(x))*(diff(E(x),x)))*b*u(x)+(1+upsilon)*((rho(x)*x*b*(omega^(2)))/(E(x))*(1-upsilon)-(alpha(x)*Ta)/(b)*(diff(T(x),x))-((diff(alpha(x),x))/(b)+(alpha(x)*diff(E(x),x))/(b*E(x))+(alpha(x)*diff(h(x),x))/(b*h(x)))*Ta*T(x) ),u(a) = 0,(E(b))/((1-upsilon^(2)))*(D^((1))(u)(b)+upsilon/(b)*D^((0))(u)(b))-(E(b)*alpha(b)*T(b)*Ta)/((1-upsilon^())) =-1}:dsol5 := dsolve(dsys5,abserr=1e-1, 'maxmesh'=900, numeric, method=bvp[middefer],output=listprocedure):fy := eval(u(x),dsol5)"

proc (x) local res, data, solnproc, `u(x)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x) else outpoint := evalf(x) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(8, {(1) = .2, (2) = .2973512592166774, (3) = .4046598589973246, (4) = .5253877794811062, (5) = .6502960591623015, (6) = .7736319028878446, (7) = .8952969100357793, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 2, {(1, 1) = .0, (1, 2) = .733488879983426, (2, 1) = 0.6165197085959364e-1, (2, 2) = .5330991714843657, (3, 1) = .1180091558271178, (3, 2) = .5172767551930041, (4, 1) = .18269975228050025, (4, 2) = .554399062532572, (5, 1) = .255347334921374, (5, 2) = .6088157832133286, (6, 1) = .33396482109823816, (6, 2) = .6660364219868107, (7, 1) = .4183769220601095, (7, 2) = .7215786851118666, (8, 1) = .4963025525973446, (8, 2) = .76692811184826}, datatype = float[8], order = C_order); YP := Matrix(8, 2, {(1, 1) = .733488879983426, (1, 2) = -4.437310575901379, (2, 1) = .5330991714843657, (2, 2) = -.6408082738085314, (3, 1) = .5172767551930041, (3, 2) = .16264757217660253, (4, 1) = .554399062532572, (4, 2) = .3928795175533184, (5, 1) = .6088157832133286, (5, 2) = .45496331913237875, (6, 1) = .6660364219868107, (6, 2) = .461339583360867, (7, 1) = .7215786851118666, (7, 2) = .4443915660014327, (8, 1) = .76692811184826, (8, 2) = .41749625147947433}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(8, {(1) = .2, (2) = .2973512592166774, (3) = .4046598589973246, (4) = .5253877794811062, (5) = .6502960591623015, (6) = .7736319028878446, (7) = .8952969100357793, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 2, {(1, 1) = .0, (1, 2) = 0.9052597788842265e-3, (2, 1) = -0.17533040428448915e-2, (2, 2) = 0.11363665769424824e-1, (3, 1) = -0.19873923968831836e-2, (3, 2) = 0.7223177987320639e-2, (4, 1) = -0.17529391294966445e-2, (4, 2) = 0.3957014218449073e-2, (5, 1) = -0.14983216331688753e-2, (5, 2) = 0.21532793401388695e-2, (6, 1) = -0.131401163357453e-2, (6, 2) = 0.11818256841032992e-2, (7, 1) = -0.11878674118888655e-2, (7, 2) = 0.5977854547565276e-3, (8, 1) = -0.1108948738838933e-2, (8, 2) = 0.2772371847096222e-3}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return 0.113636657694248244e-1 elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [2, 8, [u(x), diff(u(x), x)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(2, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(8, 2, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(2, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(8, 2, X, Y, outpoint, yout, L, V) end if; [x = outpoint, seq('[u(x), diff(u(x), x)]'[i] = yout[i], i = 1 .. 2)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return 0.113636657694248244e-1 elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [2, 8, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(2, {(1) = .0, (2) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(8, 2, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(2, {(1) = 0., (2) = 0.}); `dsolve/numeric/hermite`(8, 2, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 2)] end proc, (2) = Array(1..3, {(1) = 18446745813876114814, (2) = 18446745813876115254, (3) = 18446745813876115430}), (3) = [x, u(x), diff(u(x), x)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x) else `u(x)` := pointto(data[2][2]); return ('`u(x)`')(x) end if end if; try res := solnproc(outpoint); res[2] catch: error  end try end proc

(1)

plots:-odeplot(fy, [x, u(x)], x = a .. b, color = red)

 

``


 

Download 2023_new.mw

restart;
pointset := [A, [0,0], B, [0,v_B], C, [u_C, v_C], DD, [x_DD, y_DD], OO, [x_OO, y_OO]];
for i from 1 to nops(pointset) by 2 do
assign(pointset[i],pointset[i+1]);
od:

 A, B, C, DD, OO;  
                [0, 0], [0, v_B], [u_C, v_C], [x_DD, y_DD], [x_OO, y_OO]


Take a look at what your code does:

restart;
pointset := [A, [0,0], B, [0,v_B], C, [u_C, v_C], DD, [x_DD, y_DD], OO, [x_OO, y_OO]]:
for i from 1 to nops(pointset) by 2 do
pointset[i]:=pointset[i+1];
od:
A, B, C, DD, OO;
seq(pointset[i], i=[1,3,5,7,9]);

                                          A, B, C, DD, OO
                    [0, 0], [0, v_B], [u_C, v_C], [x_DD, y_DD], [x_OO, y_OO]

The difference between  X:=Y and assign(X,Y)  is that in the first case  X  is not evaluated.
I replaced the names  D  and  O  with  DD  and  OO  because  D  and  O  are protected.

Of course, it’s most convenient to use a multiple assignment in your problem:

A, B, C, DD, OO :=   [0, 0], [0, v_B], [u_C, v_C], [x_DD, y_DD], [x_OO, y_OO];

restart;
#FIRST STEP: Lets find the recursive formula for 
d:=proc(m)
option remember;
if m=1 then return 1 else
expand(-add(xi[i]*d(m-i+1),i=2..m)) fi;
end proc:
#lets check
for i from 1 to 4 do
d(i);
end do; 


The code for the matrix:

DD:=m->Matrix(m,m, (i,j)->`if`(i>j,0,d[j-i+1])):
DD(4);

 

Just solve these equations together by taking different names for the parameters. If the number of solutions is infinite, then the lines coincide. If Maple returns a unique solution, then the lines intersect. If Maple returns NULL (no solutions), then the lines are parallel:

restart;
L1:=<2-4*t,5+6*t>: L2:=<-6-12*s,17+18*s>: L3:=<20*t,-30*t>:
solve({L1[1]=L2[1],L1[2]=L2[2]}); # The lines are identical
solve({L2[1]=L3[1],L2[2]=L3[2]}); # The lines are parallel

  Output:                                   {s = s, t = 2+3*s}
                                                         NULL


Additionally, in the first example, a relationship is established between the parameters. In 3D, the solution is about the same. The straight lines will be skew if there are no solutions and the direction vectors (coefficients in front of the parameters) are not collinear. Writing a procedure for all of these is trivial.                           

You have a linear system with unknowns  [A,B,C,E,L,F], so you can solve it using  LinearAlgebra:-LinearSolve  command. Maple does not return the whole solution (due to its bulkiness), but you can get the values of individual unknowns (in the file  below the first unknown is returned):

 

Download sys.mw

Should be:

for j to numelems(rkVals) do rk := rkVals[j]; 
p := fsolve({a[1], a[2]}); 
plts := plts, plot(eval(f, p), x = 0 .. 1, color = colors[j]); 
plts := plts; 
ta := eval(eval(diff(f, x$2), p), x = 0); 
print(ta);
 end do:

                          -2.277141067
                          -2.445405258
                          -2.630934764
                          -2.835347980
 

The  color  option should not be used with  plots:-display  command.


 

restart;

restart;

with(plots):

diff(y(x), x) = sqrt(y(x)^(-1-3*w)-k)

diff(y(x), x) = (y(x)^(-1-3*w)-k)^(1/2)

(1)

w:=0;

0

(2)

k:=-1;

-1

(3)

A:=dsolve({diff(y(x), x) = sqrt(y(x)^(-1-3*w)-k),y(0)=1},type=numeric,range=-1..10,output=listprocedure);

Warning, cannot evaluate the solution further left of -.53284009, probably a singularity

 

[x = proc (x) 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](x) else _xout := evalf(x) 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( [( "right" ) = 10., ( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 1, (2) = 1, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 1, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = 10.0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.3926157108908329e-1, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..1, {(1) = .1}, datatype = float[8], order = C_order), Array(1..1, {(1) = 12.826875771806842}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.035292985587518}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..6, {(1, 1) = 1.035292985587518, (1, 2) = 1.0412809304802786, (1, 3) = 1.0401451737579508, (1, 4) = 1.0358245885493977, (1, 5) = 1.0352923574827053, (1, 6) = 1.0390689526600414}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8]), Array(1..1, {(1) = 11.998601943394558}, datatype = float[8], order = C_order), Array(1..1, {(1) = 13.921456200836463}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0.9892346373163718e-6}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.038049685203789}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.4142135623730951}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..1, {(1, 1) = .0, (2, 0) = .0, (2, 1) = .0, (3, 0) = .0, (3, 1) = .0, (4, 0) = .0, (4, 1) = .0, (5, 0) = .0, (5, 1) = .0, (6, 0) = .0, (6, 1) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 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] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] )), ( 2 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 1, (2) = 1, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 1, (10) = 1, (11) = 201, (12) = 201, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 641, (19) = 30000, (20) = 1, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = -.5328400969459244, (2) = 0.10e-5, (3) = -0.5439648731453417e-11, (4) = 0.500001e-14, (5) = .0, (6) = 0.3926157108908329e-1, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..1, {(1) = .1}, datatype = float[8], order = C_order), Array(1..1, {(1) = 12.826875771806842}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.035292985587518}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..6, {(1, 1) = 1.035292985587518, (1, 2) = 1.0412809304802786, (1, 3) = 1.0401451737579508, (1, 4) = 1.0358245885493977, (1, 5) = 1.0352923574827053, (1, 6) = 1.0390689526600414}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8]), Array(1..1, {(1) = 11.998601943394558}, datatype = float[8], order = C_order), Array(1..1, {(1) = 13.921456200836463}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0.9892346373163718e-6}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.038049685203789}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = undefined}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..1, {(1, 1) = -.5328400969459244, (2, 0) = -.5328400969459244, (2, 1) = -0.2666605957438441e-8, (3, 0) = -0.2666605957438441e-8, (3, 1) = -.5328400969418446, (4, 0) = -.5328400969418446, (4, 1) = undefined, (5, 0) = undefined, (5, 1) = -.5328400969432046, (6, 0) = -.5328400969432046, (6, 1) = undefined}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (Array(1..201, 0..1, {(1, 1) = .0, (2, 0) = .0, (2, 1) = 1.0, (3, 0) = 1.0, (3, 1) = -0.9815392772270823e-2, (4, 0) = -0.9815392772270823e-2, (4, 1) = .986094626846761, (5, 0) = .986094626846761, (5, 1) = -0.19630785544541646e-1, (6, 0) = -0.19630785544541646e-1, (6, 1) = .9721397099673637, (7, 0) = .9721397099673637, (7, 1) = -0.2944617831681247e-1, (8, 0) = -0.2944617831681247e-1, (8, 1) = .9581338163209241, (9, 0) = .9581338163209241, (9, 1) = -0.3926157108908329e-1, (10, 0) = -0.3926157108908329e-1, (10, 1) = .9440754432989995, (11, 0) = .9440754432989995, (11, 1) = -0.7147072930904094e-1, (12, 0) = -0.7147072930904094e-1, (12, 1) = .8975537289508073, (13, 0) = .8975537289508073, (13, 1) = -.1036798875289986, (14, 0) = -.1036798875289986, (14, 1) = .8503877948917192, (15, 0) = .8503877948917192, (15, 1) = -.13588904574895624, (16, 0) = -.13588904574895624, (16, 1) = .8025038158170855, (17, 0) = .8025038158170855, (17, 1) = -.1680982039689139, (18, 0) = -.1680982039689139, (18, 1) = .7538122386853634, (19, 0) = .7538122386853634, (19, 1) = -.1872646005598393, (20, 0) = -.1872646005598393, (20, 1) = .7244113478627896, (21, 0) = .7244113478627896, (21, 1) = -.20643099715076468, (22, 0) = -.20643099715076468, (22, 1) = .6946602797286142, (23, 0) = .6946602797286142, (23, 1) = -.22559739374169008, (24, 0) = -.22559739374169008, (24, 1) = .6645283021040285, (25, 0) = .6645283021040285, (25, 1) = -.24476379033261547, (26, 0) = -.24476379033261547, (26, 1) = .6339797784930089, (27, 0) = .6339797784930089, (27, 1) = -.26393018692354087, (28, 0) = -.26393018692354087, (28, 1) = .602973249641938, (29, 0) = .602973249641938, (29, 1) = -.28309658351446626, (30, 0) = -.28309658351446626, (30, 1) = .5714612752170005, (31, 0) = .5714612752170005, (31, 1) = -.30226298010539165, (32, 0) = -.30226298010539165, (32, 1) = .5393862635519614, (33, 0) = .5393862635519614, (33, 1) = -.32142937669631705, (34, 0) = -.32142937669631705, (34, 1) = .5066782158979138, (35, 0) = .5066782158979138, (35, 1) = -.3325703288255498, (36, 0) = -.3325703288255498, (36, 1) = .48734236512536, (37, 0) = .48734236512536, (37, 1) = -.34371128095478265, (38, 0) = -.34371128095478265, (38, 1) = .46774508837069423, (39, 0) = .46774508837069423, (39, 1) = -.3548522330840155, (40, 0) = -.3548522330840155, (40, 1) = .4478639508445281, (41, 0) = .4478639508445281, (41, 1) = -.36599318521324825, (42, 0) = -.36599318521324825, (42, 1) = .42767296860849935, (43, 0) = .42767296860849935, (43, 1) = -.377134137342481, (44, 0) = -.377134137342481, (44, 1) = .4071419447289586, (45, 0) = .4071419447289586, (45, 1) = -.38827508947171385, (46, 0) = -.38827508947171385, (46, 1) = .38623634605458096, (47, 0) = .38623634605458096, (47, 1) = -.3994160416009467, (48, 0) = -.3994160416009467, (48, 1) = .36491429807045583, (49, 0) = .36491429807045583, (49, 1) = -.41055699373017945, (50, 0) = -.41055699373017945, (50, 1) = .34312496041060037, (51, 0) = .34312496041060037, (51, 1) = -.417058734678321, (52, 0) = -.417058734678321, (52, 1) = .3301692342567368, (53, 0) = .3301692342567368, (53, 1) = -.4235604756264626, (54, 0) = -.4235604756264626, (54, 1) = .31701952860079113, (55, 0) = .31701952860079113, (55, 1) = -.4300622165746042, (56, 0) = -.4300622165746042, (56, 1) = .3036593650996864, (57, 0) = .3036593650996864, (57, 1) = -.43656395752274574, (58, 0) = -.43656395752274574, (58, 1) = .29006965257403794, (59, 0) = .29006965257403794, (59, 1) = -.4430656984708873, (60, 0) = -.4430656984708873, (60, 1) = .27622819219899586, (61, 0) = .27622819219899586, (61, 1) = -.4495674394190289, (62, 0) = -.4495674394190289, (62, 1) = .26210958840997806, (63, 0) = .26210958840997806, (63, 1) = -.4560691803671705, (64, 0) = -.4560691803671705, (64, 1) = .24768300739714183, (65, 0) = .24768300739714183, (65, 1) = -.462570921315312, (66, 0) = -.462570921315312, (66, 1) = .2329109648258063, (67, 0) = .2329109648258063, (67, 1) = -.466361738283783, (68, 0) = -.466361738283783, (68, 1) = .22412122650091407, (69, 0) = .22412122650091407, (69, 1) = -.4701525552522541, (70, 0) = -.4701525552522541, (70, 1) = .21518837862871668, (71, 0) = .21518837862871668, (71, 1) = -.4739433722207251, (72, 0) = -.4739433722207251, (72, 1) = .20610025308346047, (73, 0) = .20610025308346047, (73, 1) = -.4777341891891961, (74, 0) = -.4777341891891961, (74, 1) = .196842729174941, (75, 0) = .196842729174941, (75, 1) = -.4815250061576671, (76, 0) = -.4815250061576671, (76, 1) = .18739935463125304, (77, 0) = .18739935463125304, (77, 1) = -.4853158231261381, (78, 0) = -.4853158231261381, (78, 1) = .17775128594898237, (79, 0) = .17775128594898237, (79, 1) = -.48910664009460914, (80, 0) = -.48910664009460914, (80, 1) = .16787556437347406, (81, 0) = .16787556437347406, (81, 1) = -.49289745706308014, (82, 0) = -.49289745706308014, (82, 1) = .15774418209160898, (83, 0) = .15774418209160898, (83, 1) = -.49509740393720353, (84, 0) = -.49509740393720353, (84, 1) = .15173431101659524, (85, 0) = .15173431101659524, (85, 1) = -.497297350811327, (86, 0) = -.497297350811327, (86, 1) = .14561928572214822, (87, 0) = .14561928572214822, (87, 1) = -.49949729768545037, (88, 0) = -.49949729768545037, (88, 1) = .13939005794779608, (89, 0) = .13939005794779608, (89, 1) = -.5016972445595738, (90, 0) = -.5016972445595738, (90, 1) = .13303609560154586, (91, 0) = .13303609560154586, (91, 1) = -.5038971914336972, (92, 0) = -.5038971914336972, (92, 1) = .12654508351360672, (93, 0) = .12654508351360672, (93, 1) = -.5060971383078205, (94, 0) = -.5060971383078205, (94, 1) = .11990288871042241, (95, 0) = .11990288871042241, (95, 1) = -.5082970851819439, (96, 0) = -.5082970851819439, (96, 1) = .11309218875973061, (97, 0) = .11309218875973061, (97, 1) = -.5104970320560673, (98, 0) = -.5104970320560673, (98, 1) = .1060917268812939, (99, 0) = .1060917268812939, (99, 1) = -.5117620319445919, (100, 0) = -.5117620319445919, (100, 1) = .10197064690419455, (101, 0) = .10197064690419455, (101, 1) = -.5130270318331165, (102, 0) = -.5130270318331165, (102, 1) = 0.977725825094285e-1, (103, 0) = 0.977725825094285e-1, (103, 1) = -.5142920317216412, (104, 0) = -.5142920317216412, (104, 1) = 0.9349075578043026e-1, (105, 0) = 0.9349075578043026e-1, (105, 1) = -.5155570316101658, (106, 0) = -.5155570316101658, (106, 1) = 0.8911724125588247e-1, (107, 0) = 0.8911724125588247e-1, (107, 1) = -.516568296576827, (108, 0) = -.516568296576827, (108, 1) = 0.8554887407148233e-1, (109, 0) = 0.8554887407148233e-1, (109, 1) = -.5175795615434882, (110, 0) = -.5175795615434882, (110, 1) = 0.8191060691607988e-1, (111, 0) = 0.8191060691607988e-1, (111, 1) = -.5185908265101493, (112, 0) = -.5185908265101493, (112, 1) = 0.7819606688876918e-1, (113, 0) = 0.7819606688876918e-1, (113, 1) = -.5196020914768106, (114, 0) = -.5196020914768106, (114, 1) = 0.7439775679972419e-1, (115, 0) = 0.7439775679972419e-1, (115, 1) = -.5203860490669759, (116, 0) = -.5203860490669759, (116, 1) = 0.713900308301898e-1, (117, 0) = 0.713900308301898e-1, (117, 1) = -.5211700066571413, (118, 0) = -.5211700066571413, (118, 1) = 0.6832198138328917e-1, (119, 0) = 0.6832198138328917e-1, (119, 1) = -.5219539642473067, (120, 0) = -.5219539642473067, (120, 1) = 0.6518804623866077e-1, (121, 0) = 0.6518804623866077e-1, (121, 1) = -.522737921837472, (122, 0) = -.522737921837472, (122, 1) = 0.6198166746510999e-1, (123, 0) = 0.6198166746510999e-1, (123, 1) = -.5233476941190687, (124, 0) = -.5233476941190687, (124, 1) = 0.5943273223942325e-1, (125, 0) = 0.5943273223942325e-1, (125, 1) = -.5239574664006654, (126, 0) = -.5239574664006654, (126, 1) = 0.5683113935930595e-1, (127, 0) = 0.5683113935930595e-1, (127, 1) = -.5245672386822621, (128, 0) = -.5245672386822621, (128, 1) = 0.54171936120110814e-1, (129, 0) = 0.54171936120110814e-1, (129, 1) = -.5251770109638587, (130, 0) = -.5251770109638587, (130, 1) = 0.51449261739580934e-1, (131, 0) = 0.51449261739580934e-1, (131, 1) = -.5256485523679193, (132, 0) = -.5256485523679193, (132, 1) = 0.4929594240740358e-1, (133, 0) = 0.4929594240740358e-1, (133, 1) = -.5261200937719798, (134, 0) = -.5261200937719798, (134, 1) = 0.470968515201533e-1, (135, 0) = 0.470968515201533e-1, (135, 1) = -.5265916351760402, (136, 0) = -.5265916351760402, (136, 1) = 0.4484759510814104e-1, (137, 0) = 0.4484759510814104e-1, (137, 1) = -.5270631765801008, (138, 0) = -.5270631765801008, (138, 1) = 0.42542953640465814e-1, (139, 0) = 0.42542953640465814e-1, (139, 1) = -.5274262646468568, (140, 0) = -.5274262646468568, (140, 1) = 0.40726785599143014e-1, (141, 0) = 0.40726785599143014e-1, (141, 1) = -.5277893527136128, (142, 0) = -.5277893527136128, (142, 1) = 0.3887085792031868e-1, (143, 0) = 0.3887085792031868e-1, (143, 1) = -.5281524407803687, (144, 0) = -.5281524407803687, (144, 1) = 0.3697126476317059e-1, (145, 0) = 0.3697126476317059e-1, (145, 1) = -.5285155288471247, (146, 0) = -.5285155288471247, (146, 1) = 0.3502334619248398e-1, (147, 0) = 0.3502334619248398e-1, (147, 1) = -.528793557427472, (148, 0) = -.528793557427472, (148, 1) = 0.3349567646171821e-1, (149, 0) = 0.3349567646171821e-1, (149, 1) = -.5290715860078194, (150, 0) = -.5290715860078194, (150, 1) = 0.3193354161072096e-1, (151, 0) = 0.3193354161072096e-1, (151, 1) = -.5293496145881668, (152, 0) = -.5293496145881668, (152, 1) = 0.3033346987713898e-1, (153, 0) = 0.3033346987713898e-1, (153, 1) = -.5296276431685141, (154, 0) = -.5296276431685141, (154, 1) = 0.28691299203262247e-1, (155, 0) = 0.28691299203262247e-1, (155, 1) = -.5298392287331177, (156, 0) = -.5298392287331177, (156, 1) = 0.27410333338029367e-1, (157, 0) = 0.27410333338029367e-1, (157, 1) = -.5300508142977214, (158, 0) = -.5300508142977214, (158, 1) = 0.26099560317493713e-1, (159, 0) = 0.26099560317493713e-1, (159, 1) = -.530262399862325, (160, 0) = -.530262399862325, (160, 1) = 0.24755894678381078e-1, (161, 0) = 0.24755894678381078e-1, (161, 1) = -.5304739854269287, (162, 0) = -.5304739854269287, (162, 1) = 0.23375617665756757e-1, (163, 0) = 0.23375617665756757e-1, (163, 1) = -.530633876456287, (164, 0) = -.530633876456287, (164, 1) = 0.22305595966041352e-1, (165, 0) = 0.22305595966041352e-1, (165, 1) = -.5307937674856454, (166, 0) = -.5307937674856454, (166, 1) = 0.21209870610690764e-1, (167, 0) = 0.21209870610690764e-1, (167, 1) = -.5309536585150039, (168, 0) = -.5309536585150039, (168, 1) = 0.2008570181357363e-1, (169, 0) = 0.2008570181357363e-1, (169, 1) = -.5311135495443622, (170, 0) = -.5311135495443622, (170, 1) = 0.18929767954651778e-1, (171, 0) = 0.18929767954651778e-1, (171, 1) = -.531233423229223, (172, 0) = -.531233423229223, (172, 1) = 0.1803992548623269e-1, (173, 0) = 0.1803992548623269e-1, (173, 1) = -.5313532969140837, (174, 0) = -.5313532969140837, (174, 1) = 0.17127995447682513e-1, (175, 0) = 0.17127995447682513e-1, (175, 1) = -.5314731705989445, (176, 0) = -.5314731705989445, (176, 1) = 0.16191548641715008e-1, (177, 0) = 0.16191548641715008e-1, (177, 1) = -.5315930442838053, (178, 0) = -.5315930442838053, (178, 1) = 0.1522762088630656e-1, (179, 0) = 0.1522762088630656e-1, (179, 1) = -.5316821225323373, (180, 0) = -.5316821225323373, (180, 1) = 0.14491423953719903e-1, (181, 0) = 0.14491423953719903e-1, (181, 1) = -.5317712007808693, (182, 0) = -.5317712007808693, (182, 1) = 0.13736326067110232e-1, (183, 0) = 0.13736326067110232e-1, (183, 1) = -.5318602790294013, (184, 0) = -.5318602790294013, (184, 1) = 0.12960178253867747e-1, (185, 0) = 0.12960178253867747e-1, (185, 1) = -.5319493572779332, (186, 0) = -.5319493572779332, (186, 1) = 0.1216033962906081e-1, (187, 0) = 0.1216033962906081e-1, (187, 1) = -.5320149006701193, (188, 0) = -.5320149006701193, (188, 1) = 0.11554839241354389e-1, (189, 0) = 0.11554839241354389e-1, (189, 1) = -.5320804440623053, (190, 0) = -.5320804440623053, (190, 1) = 0.10933244186773898e-1, (191, 0) = 0.10933244186773898e-1, (191, 1) = -.5321459874544914, (192, 0) = -.5321459874544914, (192, 1) = 0.10293659215767886e-1, (193, 0) = 0.10293659215767886e-1, (193, 1) = -.5322115308466774, (194, 0) = -.5322115308466774, (194, 1) = 0.963373715444971e-2, (195, 0) = 0.963373715444971e-2, (195, 1) = -.5322592319564932, (196, 0) = -.5322592319564932, (196, 1) = 0.9139045562712942e-2, (197, 0) = 0.9139045562712942e-2, (197, 1) = -.532306933066309, (198, 0) = -.532306933066309, (198, 1) = 0.863072721697693e-2, (199, 0) = 0.863072721697693e-2, (199, 1) = -.5323546341761248, (200, 0) = -.5323546341761248, (200, 1) = 0.8107117251877476e-2, (201, 0) = 0.8107117251877476e-2, (201, 1) = -.5324023352859406}, datatype = float[8], order = C_order)), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] )), ( 3 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 1, (2) = 1, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 1, (9) = 0, (10) = 1, (11) = 61, (12) = 61, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 106, (19) = 30000, (20) = 5, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = 10.0, (2) = 0.10e-5, (3) = 3.44329543943776, (4) = 0.500001e-14, (5) = .0, (6) = 0.3926157108908329e-1, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..1, {(1) = .1}, datatype = float[8], order = C_order), Array(1..1, {(1) = 12.826875771806842}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.035292985587518}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..6, {(1, 1) = 1.035292985587518, (1, 2) = 1.0412809304802786, (1, 3) = 1.0401451737579508, (1, 4) = 1.0358245885493977, (1, 5) = 1.0352923574827053, (1, 6) = 1.0390689526600414}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8]), Array(1..1, {(1) = 11.998601943394558}, datatype = float[8], order = C_order), Array(1..1, {(1) = 13.921456200836463}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0.9892346373163718e-6}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.038049685203789}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.035292985587518}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..1, {(1, 1) = 9.21308871471217, (2, 0) = 9.21308871471217, (2, 1) = 11.178427083734542, (3, 0) = 11.178427083734542, (3, 1) = 9.87296403698277, (4, 0) = 9.87296403698277, (4, 1) = 11.866349781230939, (5, 0) = 11.866349781230939, (5, 1) = 10.532839359253373, (6, 0) = 10.532839359253373, (6, 1) = 12.55272269672412}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (Array(1..61, 0..1, {(1, 1) = .0, (2, 0) = .0, (2, 1) = 1.0, (3, 0) = 1.0, (3, 1) = 0.9815392772270823e-2, (4, 0) = 0.9815392772270823e-2, (4, 1) = 1.0138571969847456, (5, 0) = 1.0138571969847456, (5, 1) = 0.19630785544541646e-1, (6, 0) = 0.19630785544541646e-1, (6, 1) = 1.0276675255180219, (7, 0) = 1.0276675255180219, (7, 1) = 0.2944617831681247e-1, (8, 0) = 0.2944617831681247e-1, (8, 1) = 1.0414322371439455, (9, 0) = 1.0414322371439455, (9, 1) = 0.3926157108908329e-1, (10, 0) = 0.3926157108908329e-1, (10, 1) = 1.0551525306597858, (11, 0) = 1.0551525306597858, (11, 1) = 0.7421913776606083e-1, (12, 0) = 0.7421913776606083e-1, (12, 1) = 1.1036735952135004, (13, 0) = 1.1036735952135004, (13, 1) = .10917670444303837, (14, 0) = .10917670444303837, (14, 1) = 1.151692360560062, (15, 0) = 1.151692360560062, (15, 1) = .14413427112001592, (16, 0) = .14413427112001592, (16, 1) = 1.1992499355706485, (17, 0) = 1.1992499355706485, (17, 1) = .17909183779699345, (18, 0) = .17909183779699345, (18, 1) = 1.2463824285263596, (19, 0) = 1.2463824285263596, (19, 1) = .22003700154818584, (20, 0) = .22003700154818584, (20, 1) = 1.3010895396182998, (21, 0) = 1.3010895396182998, (21, 1) = .26098216529937823, (22, 0) = .26098216529937823, (22, 1) = 1.3553008653546121, (23, 0) = 1.3553008653546121, (23, 1) = .3019273290505706, (24, 0) = .3019273290505706, (24, 1) = 1.4090553566587913, (25, 0) = 1.4090553566587913, (25, 1) = .342872492801763, (26, 0) = .342872492801763, (26, 1) = 1.4623874261273146, (27, 0) = 1.4623874261273146, (27, 1) = .39374825011930903, (28, 0) = .39374825011930903, (28, 1) = 1.528111104676646, (29, 0) = 1.528111104676646, (29, 1) = .4446240074368551, (30, 0) = .4446240074368551, (30, 1) = 1.593279853547814, (31, 0) = 1.593279853547814, (31, 1) = .49549976475440116, (32, 0) = .49549976475440116, (32, 1) = 1.657938235238753, (33, 0) = 1.657938235238753, (33, 1) = .5463755220719472, (34, 0) = .5463755220719472, (34, 1) = 1.7221255423380761, (35, 0) = 1.7221255423380761, (35, 1) = .609425471855682, (36, 0) = .609425471855682, (36, 1) = 1.801070088732534, (37, 0) = 1.801070088732534, (37, 1) = .6724754216394168, (38, 0) = .6724754216394168, (38, 1) = 1.8794010795807021, (39, 0) = 1.8794010795807021, (39, 1) = .7355253714231516, (40, 0) = .7355253714231516, (40, 1) = 1.9571687015105361, (41, 0) = 1.9571687015105361, (41, 1) = .7985753212068863, (42, 0) = .7985753212068863, (42, 1) = 2.0344171361907124, (43, 0) = 2.0344171361907124, (43, 1) = .876929535653806, (44, 0) = .876929535653806, (44, 1) = 2.129750676830733, (45, 0) = 2.129750676830733, (45, 1) = .9552837501007257, (46, 0) = .9552837501007257, (46, 1) = 2.224406519957709, (47, 0) = 2.224406519957709, (47, 1) = 1.0336379645476454, (48, 0) = 1.0336379645476454, (48, 1) = 2.3184412382231283, (49, 0) = 2.3184412382231283, (49, 1) = 1.1119921789945653, (50, 0) = 1.1119921789945653, (50, 1) = 2.4119045424915186, (51, 0) = 2.4119045424915186, (51, 1) = 1.2096287918757802, (52, 0) = 1.2096287918757802, (52, 1) = 2.527634203497312, (53, 0) = 2.527634203497312, (53, 1) = 1.3072654047569954, (54, 0) = 1.3072654047569954, (54, 1) = 2.6426167417245696, (55, 0) = 2.6426167417245696, (55, 1) = 1.4049020176382103, (56, 0) = 1.4049020176382103, (56, 1) = 2.7569158996625, (57, 0) = 2.7569158996625, (57, 1) = 1.5025386305194255, (58, 0) = 1.5025386305194255, (58, 1) = 2.87058757063309, (59, 0) = 2.87058757063309, (59, 1) = 1.6245811380592985, (60, 0) = 1.6245811380592985, (60, 1) = 3.0118647534640655, (61, 0) = 3.0118647534640655, (61, 1) = 1.7466236455991715}, datatype = float[8], order = C_order)), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] )), ( 4 ) = (3)  ] ); _y0 := Array(0..1, {(1) = 0.}); _vmap := array( 1 .. 1, [( 1 ) = (1)  ] ); _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] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(1..2, {(1) = 18446745506974851510, (2) = 18446745506974851686}), (3) = [x, y(x)], (4) = []}); _solnproc := _dat[1]; _pars := map(rhs, _dat[4]); if not type(_xout, 'numeric') then if member(x, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x, ["last", 'last', "initial", 'initial', NULL]) then _res := _solnproc(convert(x, 'string')); if type(_res, 'list') then return _res[1] else return NULL end if elif member(x, ["parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[1], 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(x), 'string') = rhs(x); if lhs(_xout) = "initial" then if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else _res := _solnproc("initial" = ["single", 1, 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", 1, op(rhs(_xout))]) else _res := _solnproc(_xout) end if; if lhs(_xout) = "initial" then return _res[1] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[1], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x), 'string') = rhs(x)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _dat[3] end if; if procname <> unknown then return ('procname')(x) else _ndsol := 1; _ndsol := `tools/gensym`("x"); eval(FromInert(_Inert_FUNCTION(_Inert_NAME("assign"), _Inert_EXPSEQ(ToInert(_ndsol), _Inert_VERBATIM(pointto(_dat[2][1])))))); return FromInert(_Inert_FUNCTION(ToInert(_ndsol), _Inert_EXPSEQ(ToInert(x)))) end if end if; try _res := _solnproc(_xout); _res[1] catch: error  end try end proc, y(x) = proc (x) 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](x) else _xout := evalf(x) 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( [( "right" ) = 10., ( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 1, (2) = 1, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 1, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = 10.0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.3926157108908329e-1, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..1, {(1) = .1}, datatype = float[8], order = C_order), Array(1..1, {(1) = 12.826875771806842}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.035292985587518}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..6, {(1, 1) = 1.035292985587518, (1, 2) = 1.0412809304802786, (1, 3) = 1.0401451737579508, (1, 4) = 1.0358245885493977, (1, 5) = 1.0352923574827053, (1, 6) = 1.0390689526600414}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8]), Array(1..1, {(1) = 11.998601943394558}, datatype = float[8], order = C_order), Array(1..1, {(1) = 13.921456200836463}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0.9892346373163718e-6}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.038049685203789}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.4142135623730951}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..1, {(1, 1) = .0, (2, 0) = .0, (2, 1) = .0, (3, 0) = .0, (3, 1) = .0, (4, 0) = .0, (4, 1) = .0, (5, 0) = .0, (5, 1) = .0, (6, 0) = .0, (6, 1) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 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] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] )), ( 2 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 1, (2) = 1, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 1, (10) = 1, (11) = 201, (12) = 201, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 641, (19) = 30000, (20) = 1, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = -.5328400969459244, (2) = 0.10e-5, (3) = -0.5439648731453417e-11, (4) = 0.500001e-14, (5) = .0, (6) = 0.3926157108908329e-1, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..1, {(1) = .1}, datatype = float[8], order = C_order), Array(1..1, {(1) = 12.826875771806842}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.035292985587518}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..6, {(1, 1) = 1.035292985587518, (1, 2) = 1.0412809304802786, (1, 3) = 1.0401451737579508, (1, 4) = 1.0358245885493977, (1, 5) = 1.0352923574827053, (1, 6) = 1.0390689526600414}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8]), Array(1..1, {(1) = 11.998601943394558}, datatype = float[8], order = C_order), Array(1..1, {(1) = 13.921456200836463}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0.9892346373163718e-6}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.038049685203789}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = undefined}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..1, {(1, 1) = -.5328400969459244, (2, 0) = -.5328400969459244, (2, 1) = -0.2666605957438441e-8, (3, 0) = -0.2666605957438441e-8, (3, 1) = -.5328400969418446, (4, 0) = -.5328400969418446, (4, 1) = undefined, (5, 0) = undefined, (5, 1) = -.5328400969432046, (6, 0) = -.5328400969432046, (6, 1) = undefined}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (Array(1..201, 0..1, {(1, 1) = .0, (2, 0) = .0, (2, 1) = 1.0, (3, 0) = 1.0, (3, 1) = -0.9815392772270823e-2, (4, 0) = -0.9815392772270823e-2, (4, 1) = .986094626846761, (5, 0) = .986094626846761, (5, 1) = -0.19630785544541646e-1, (6, 0) = -0.19630785544541646e-1, (6, 1) = .9721397099673637, (7, 0) = .9721397099673637, (7, 1) = -0.2944617831681247e-1, (8, 0) = -0.2944617831681247e-1, (8, 1) = .9581338163209241, (9, 0) = .9581338163209241, (9, 1) = -0.3926157108908329e-1, (10, 0) = -0.3926157108908329e-1, (10, 1) = .9440754432989995, (11, 0) = .9440754432989995, (11, 1) = -0.7147072930904094e-1, (12, 0) = -0.7147072930904094e-1, (12, 1) = .8975537289508073, (13, 0) = .8975537289508073, (13, 1) = -.1036798875289986, (14, 0) = -.1036798875289986, (14, 1) = .8503877948917192, (15, 0) = .8503877948917192, (15, 1) = -.13588904574895624, (16, 0) = -.13588904574895624, (16, 1) = .8025038158170855, (17, 0) = .8025038158170855, (17, 1) = -.1680982039689139, (18, 0) = -.1680982039689139, (18, 1) = .7538122386853634, (19, 0) = .7538122386853634, (19, 1) = -.1872646005598393, (20, 0) = -.1872646005598393, (20, 1) = .7244113478627896, (21, 0) = .7244113478627896, (21, 1) = -.20643099715076468, (22, 0) = -.20643099715076468, (22, 1) = .6946602797286142, (23, 0) = .6946602797286142, (23, 1) = -.22559739374169008, (24, 0) = -.22559739374169008, (24, 1) = .6645283021040285, (25, 0) = .6645283021040285, (25, 1) = -.24476379033261547, (26, 0) = -.24476379033261547, (26, 1) = .6339797784930089, (27, 0) = .6339797784930089, (27, 1) = -.26393018692354087, (28, 0) = -.26393018692354087, (28, 1) = .602973249641938, (29, 0) = .602973249641938, (29, 1) = -.28309658351446626, (30, 0) = -.28309658351446626, (30, 1) = .5714612752170005, (31, 0) = .5714612752170005, (31, 1) = -.30226298010539165, (32, 0) = -.30226298010539165, (32, 1) = .5393862635519614, (33, 0) = .5393862635519614, (33, 1) = -.32142937669631705, (34, 0) = -.32142937669631705, (34, 1) = .5066782158979138, (35, 0) = .5066782158979138, (35, 1) = -.3325703288255498, (36, 0) = -.3325703288255498, (36, 1) = .48734236512536, (37, 0) = .48734236512536, (37, 1) = -.34371128095478265, (38, 0) = -.34371128095478265, (38, 1) = .46774508837069423, (39, 0) = .46774508837069423, (39, 1) = -.3548522330840155, (40, 0) = -.3548522330840155, (40, 1) = .4478639508445281, (41, 0) = .4478639508445281, (41, 1) = -.36599318521324825, (42, 0) = -.36599318521324825, (42, 1) = .42767296860849935, (43, 0) = .42767296860849935, (43, 1) = -.377134137342481, (44, 0) = -.377134137342481, (44, 1) = .4071419447289586, (45, 0) = .4071419447289586, (45, 1) = -.38827508947171385, (46, 0) = -.38827508947171385, (46, 1) = .38623634605458096, (47, 0) = .38623634605458096, (47, 1) = -.3994160416009467, (48, 0) = -.3994160416009467, (48, 1) = .36491429807045583, (49, 0) = .36491429807045583, (49, 1) = -.41055699373017945, (50, 0) = -.41055699373017945, (50, 1) = .34312496041060037, (51, 0) = .34312496041060037, (51, 1) = -.417058734678321, (52, 0) = -.417058734678321, (52, 1) = .3301692342567368, (53, 0) = .3301692342567368, (53, 1) = -.4235604756264626, (54, 0) = -.4235604756264626, (54, 1) = .31701952860079113, (55, 0) = .31701952860079113, (55, 1) = -.4300622165746042, (56, 0) = -.4300622165746042, (56, 1) = .3036593650996864, (57, 0) = .3036593650996864, (57, 1) = -.43656395752274574, (58, 0) = -.43656395752274574, (58, 1) = .29006965257403794, (59, 0) = .29006965257403794, (59, 1) = -.4430656984708873, (60, 0) = -.4430656984708873, (60, 1) = .27622819219899586, (61, 0) = .27622819219899586, (61, 1) = -.4495674394190289, (62, 0) = -.4495674394190289, (62, 1) = .26210958840997806, (63, 0) = .26210958840997806, (63, 1) = -.4560691803671705, (64, 0) = -.4560691803671705, (64, 1) = .24768300739714183, (65, 0) = .24768300739714183, (65, 1) = -.462570921315312, (66, 0) = -.462570921315312, (66, 1) = .2329109648258063, (67, 0) = .2329109648258063, (67, 1) = -.466361738283783, (68, 0) = -.466361738283783, (68, 1) = .22412122650091407, (69, 0) = .22412122650091407, (69, 1) = -.4701525552522541, (70, 0) = -.4701525552522541, (70, 1) = .21518837862871668, (71, 0) = .21518837862871668, (71, 1) = -.4739433722207251, (72, 0) = -.4739433722207251, (72, 1) = .20610025308346047, (73, 0) = .20610025308346047, (73, 1) = -.4777341891891961, (74, 0) = -.4777341891891961, (74, 1) = .196842729174941, (75, 0) = .196842729174941, (75, 1) = -.4815250061576671, (76, 0) = -.4815250061576671, (76, 1) = .18739935463125304, (77, 0) = .18739935463125304, (77, 1) = -.4853158231261381, (78, 0) = -.4853158231261381, (78, 1) = .17775128594898237, (79, 0) = .17775128594898237, (79, 1) = -.48910664009460914, (80, 0) = -.48910664009460914, (80, 1) = .16787556437347406, (81, 0) = .16787556437347406, (81, 1) = -.49289745706308014, (82, 0) = -.49289745706308014, (82, 1) = .15774418209160898, (83, 0) = .15774418209160898, (83, 1) = -.49509740393720353, (84, 0) = -.49509740393720353, (84, 1) = .15173431101659524, (85, 0) = .15173431101659524, (85, 1) = -.497297350811327, (86, 0) = -.497297350811327, (86, 1) = .14561928572214822, (87, 0) = .14561928572214822, (87, 1) = -.49949729768545037, (88, 0) = -.49949729768545037, (88, 1) = .13939005794779608, (89, 0) = .13939005794779608, (89, 1) = -.5016972445595738, (90, 0) = -.5016972445595738, (90, 1) = .13303609560154586, (91, 0) = .13303609560154586, (91, 1) = -.5038971914336972, (92, 0) = -.5038971914336972, (92, 1) = .12654508351360672, (93, 0) = .12654508351360672, (93, 1) = -.5060971383078205, (94, 0) = -.5060971383078205, (94, 1) = .11990288871042241, (95, 0) = .11990288871042241, (95, 1) = -.5082970851819439, (96, 0) = -.5082970851819439, (96, 1) = .11309218875973061, (97, 0) = .11309218875973061, (97, 1) = -.5104970320560673, (98, 0) = -.5104970320560673, (98, 1) = .1060917268812939, (99, 0) = .1060917268812939, (99, 1) = -.5117620319445919, (100, 0) = -.5117620319445919, (100, 1) = .10197064690419455, (101, 0) = .10197064690419455, (101, 1) = -.5130270318331165, (102, 0) = -.5130270318331165, (102, 1) = 0.977725825094285e-1, (103, 0) = 0.977725825094285e-1, (103, 1) = -.5142920317216412, (104, 0) = -.5142920317216412, (104, 1) = 0.9349075578043026e-1, (105, 0) = 0.9349075578043026e-1, (105, 1) = -.5155570316101658, (106, 0) = -.5155570316101658, (106, 1) = 0.8911724125588247e-1, (107, 0) = 0.8911724125588247e-1, (107, 1) = -.516568296576827, (108, 0) = -.516568296576827, (108, 1) = 0.8554887407148233e-1, (109, 0) = 0.8554887407148233e-1, (109, 1) = -.5175795615434882, (110, 0) = -.5175795615434882, (110, 1) = 0.8191060691607988e-1, (111, 0) = 0.8191060691607988e-1, (111, 1) = -.5185908265101493, (112, 0) = -.5185908265101493, (112, 1) = 0.7819606688876918e-1, (113, 0) = 0.7819606688876918e-1, (113, 1) = -.5196020914768106, (114, 0) = -.5196020914768106, (114, 1) = 0.7439775679972419e-1, (115, 0) = 0.7439775679972419e-1, (115, 1) = -.5203860490669759, (116, 0) = -.5203860490669759, (116, 1) = 0.713900308301898e-1, (117, 0) = 0.713900308301898e-1, (117, 1) = -.5211700066571413, (118, 0) = -.5211700066571413, (118, 1) = 0.6832198138328917e-1, (119, 0) = 0.6832198138328917e-1, (119, 1) = -.5219539642473067, (120, 0) = -.5219539642473067, (120, 1) = 0.6518804623866077e-1, (121, 0) = 0.6518804623866077e-1, (121, 1) = -.522737921837472, (122, 0) = -.522737921837472, (122, 1) = 0.6198166746510999e-1, (123, 0) = 0.6198166746510999e-1, (123, 1) = -.5233476941190687, (124, 0) = -.5233476941190687, (124, 1) = 0.5943273223942325e-1, (125, 0) = 0.5943273223942325e-1, (125, 1) = -.5239574664006654, (126, 0) = -.5239574664006654, (126, 1) = 0.5683113935930595e-1, (127, 0) = 0.5683113935930595e-1, (127, 1) = -.5245672386822621, (128, 0) = -.5245672386822621, (128, 1) = 0.54171936120110814e-1, (129, 0) = 0.54171936120110814e-1, (129, 1) = -.5251770109638587, (130, 0) = -.5251770109638587, (130, 1) = 0.51449261739580934e-1, (131, 0) = 0.51449261739580934e-1, (131, 1) = -.5256485523679193, (132, 0) = -.5256485523679193, (132, 1) = 0.4929594240740358e-1, (133, 0) = 0.4929594240740358e-1, (133, 1) = -.5261200937719798, (134, 0) = -.5261200937719798, (134, 1) = 0.470968515201533e-1, (135, 0) = 0.470968515201533e-1, (135, 1) = -.5265916351760402, (136, 0) = -.5265916351760402, (136, 1) = 0.4484759510814104e-1, (137, 0) = 0.4484759510814104e-1, (137, 1) = -.5270631765801008, (138, 0) = -.5270631765801008, (138, 1) = 0.42542953640465814e-1, (139, 0) = 0.42542953640465814e-1, (139, 1) = -.5274262646468568, (140, 0) = -.5274262646468568, (140, 1) = 0.40726785599143014e-1, (141, 0) = 0.40726785599143014e-1, (141, 1) = -.5277893527136128, (142, 0) = -.5277893527136128, (142, 1) = 0.3887085792031868e-1, (143, 0) = 0.3887085792031868e-1, (143, 1) = -.5281524407803687, (144, 0) = -.5281524407803687, (144, 1) = 0.3697126476317059e-1, (145, 0) = 0.3697126476317059e-1, (145, 1) = -.5285155288471247, (146, 0) = -.5285155288471247, (146, 1) = 0.3502334619248398e-1, (147, 0) = 0.3502334619248398e-1, (147, 1) = -.528793557427472, (148, 0) = -.528793557427472, (148, 1) = 0.3349567646171821e-1, (149, 0) = 0.3349567646171821e-1, (149, 1) = -.5290715860078194, (150, 0) = -.5290715860078194, (150, 1) = 0.3193354161072096e-1, (151, 0) = 0.3193354161072096e-1, (151, 1) = -.5293496145881668, (152, 0) = -.5293496145881668, (152, 1) = 0.3033346987713898e-1, (153, 0) = 0.3033346987713898e-1, (153, 1) = -.5296276431685141, (154, 0) = -.5296276431685141, (154, 1) = 0.28691299203262247e-1, (155, 0) = 0.28691299203262247e-1, (155, 1) = -.5298392287331177, (156, 0) = -.5298392287331177, (156, 1) = 0.27410333338029367e-1, (157, 0) = 0.27410333338029367e-1, (157, 1) = -.5300508142977214, (158, 0) = -.5300508142977214, (158, 1) = 0.26099560317493713e-1, (159, 0) = 0.26099560317493713e-1, (159, 1) = -.530262399862325, (160, 0) = -.530262399862325, (160, 1) = 0.24755894678381078e-1, (161, 0) = 0.24755894678381078e-1, (161, 1) = -.5304739854269287, (162, 0) = -.5304739854269287, (162, 1) = 0.23375617665756757e-1, (163, 0) = 0.23375617665756757e-1, (163, 1) = -.530633876456287, (164, 0) = -.530633876456287, (164, 1) = 0.22305595966041352e-1, (165, 0) = 0.22305595966041352e-1, (165, 1) = -.5307937674856454, (166, 0) = -.5307937674856454, (166, 1) = 0.21209870610690764e-1, (167, 0) = 0.21209870610690764e-1, (167, 1) = -.5309536585150039, (168, 0) = -.5309536585150039, (168, 1) = 0.2008570181357363e-1, (169, 0) = 0.2008570181357363e-1, (169, 1) = -.5311135495443622, (170, 0) = -.5311135495443622, (170, 1) = 0.18929767954651778e-1, (171, 0) = 0.18929767954651778e-1, (171, 1) = -.531233423229223, (172, 0) = -.531233423229223, (172, 1) = 0.1803992548623269e-1, (173, 0) = 0.1803992548623269e-1, (173, 1) = -.5313532969140837, (174, 0) = -.5313532969140837, (174, 1) = 0.17127995447682513e-1, (175, 0) = 0.17127995447682513e-1, (175, 1) = -.5314731705989445, (176, 0) = -.5314731705989445, (176, 1) = 0.16191548641715008e-1, (177, 0) = 0.16191548641715008e-1, (177, 1) = -.5315930442838053, (178, 0) = -.5315930442838053, (178, 1) = 0.1522762088630656e-1, (179, 0) = 0.1522762088630656e-1, (179, 1) = -.5316821225323373, (180, 0) = -.5316821225323373, (180, 1) = 0.14491423953719903e-1, (181, 0) = 0.14491423953719903e-1, (181, 1) = -.5317712007808693, (182, 0) = -.5317712007808693, (182, 1) = 0.13736326067110232e-1, (183, 0) = 0.13736326067110232e-1, (183, 1) = -.5318602790294013, (184, 0) = -.5318602790294013, (184, 1) = 0.12960178253867747e-1, (185, 0) = 0.12960178253867747e-1, (185, 1) = -.5319493572779332, (186, 0) = -.5319493572779332, (186, 1) = 0.1216033962906081e-1, (187, 0) = 0.1216033962906081e-1, (187, 1) = -.5320149006701193, (188, 0) = -.5320149006701193, (188, 1) = 0.11554839241354389e-1, (189, 0) = 0.11554839241354389e-1, (189, 1) = -.5320804440623053, (190, 0) = -.5320804440623053, (190, 1) = 0.10933244186773898e-1, (191, 0) = 0.10933244186773898e-1, (191, 1) = -.5321459874544914, (192, 0) = -.5321459874544914, (192, 1) = 0.10293659215767886e-1, (193, 0) = 0.10293659215767886e-1, (193, 1) = -.5322115308466774, (194, 0) = -.5322115308466774, (194, 1) = 0.963373715444971e-2, (195, 0) = 0.963373715444971e-2, (195, 1) = -.5322592319564932, (196, 0) = -.5322592319564932, (196, 1) = 0.9139045562712942e-2, (197, 0) = 0.9139045562712942e-2, (197, 1) = -.532306933066309, (198, 0) = -.532306933066309, (198, 1) = 0.863072721697693e-2, (199, 0) = 0.863072721697693e-2, (199, 1) = -.5323546341761248, (200, 0) = -.5323546341761248, (200, 1) = 0.8107117251877476e-2, (201, 0) = 0.8107117251877476e-2, (201, 1) = -.5324023352859406}, datatype = float[8], order = C_order)), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] )), ( 3 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 1, (2) = 1, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 1, (9) = 0, (10) = 1, (11) = 61, (12) = 61, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 106, (19) = 30000, (20) = 5, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = 10.0, (2) = 0.10e-5, (3) = 3.44329543943776, (4) = 0.500001e-14, (5) = .0, (6) = 0.3926157108908329e-1, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..1, {(1) = .1}, datatype = float[8], order = C_order), Array(1..1, {(1) = 12.826875771806842}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.035292985587518}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..6, {(1, 1) = 1.035292985587518, (1, 2) = 1.0412809304802786, (1, 3) = 1.0401451737579508, (1, 4) = 1.0358245885493977, (1, 5) = 1.0352923574827053, (1, 6) = 1.0390689526600414}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8]), Array(1..1, {(1) = 11.998601943394558}, datatype = float[8], order = C_order), Array(1..1, {(1) = 13.921456200836463}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0.9892346373163718e-6}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.038049685203789}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.035292985587518}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..1, {(1, 1) = 9.21308871471217, (2, 0) = 9.21308871471217, (2, 1) = 11.178427083734542, (3, 0) = 11.178427083734542, (3, 1) = 9.87296403698277, (4, 0) = 9.87296403698277, (4, 1) = 11.866349781230939, (5, 0) = 11.866349781230939, (5, 1) = 10.532839359253373, (6, 0) = 10.532839359253373, (6, 1) = 12.55272269672412}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (Array(1..61, 0..1, {(1, 1) = .0, (2, 0) = .0, (2, 1) = 1.0, (3, 0) = 1.0, (3, 1) = 0.9815392772270823e-2, (4, 0) = 0.9815392772270823e-2, (4, 1) = 1.0138571969847456, (5, 0) = 1.0138571969847456, (5, 1) = 0.19630785544541646e-1, (6, 0) = 0.19630785544541646e-1, (6, 1) = 1.0276675255180219, (7, 0) = 1.0276675255180219, (7, 1) = 0.2944617831681247e-1, (8, 0) = 0.2944617831681247e-1, (8, 1) = 1.0414322371439455, (9, 0) = 1.0414322371439455, (9, 1) = 0.3926157108908329e-1, (10, 0) = 0.3926157108908329e-1, (10, 1) = 1.0551525306597858, (11, 0) = 1.0551525306597858, (11, 1) = 0.7421913776606083e-1, (12, 0) = 0.7421913776606083e-1, (12, 1) = 1.1036735952135004, (13, 0) = 1.1036735952135004, (13, 1) = .10917670444303837, (14, 0) = .10917670444303837, (14, 1) = 1.151692360560062, (15, 0) = 1.151692360560062, (15, 1) = .14413427112001592, (16, 0) = .14413427112001592, (16, 1) = 1.1992499355706485, (17, 0) = 1.1992499355706485, (17, 1) = .17909183779699345, (18, 0) = .17909183779699345, (18, 1) = 1.2463824285263596, (19, 0) = 1.2463824285263596, (19, 1) = .22003700154818584, (20, 0) = .22003700154818584, (20, 1) = 1.3010895396182998, (21, 0) = 1.3010895396182998, (21, 1) = .26098216529937823, (22, 0) = .26098216529937823, (22, 1) = 1.3553008653546121, (23, 0) = 1.3553008653546121, (23, 1) = .3019273290505706, (24, 0) = .3019273290505706, (24, 1) = 1.4090553566587913, (25, 0) = 1.4090553566587913, (25, 1) = .342872492801763, (26, 0) = .342872492801763, (26, 1) = 1.4623874261273146, (27, 0) = 1.4623874261273146, (27, 1) = .39374825011930903, (28, 0) = .39374825011930903, (28, 1) = 1.528111104676646, (29, 0) = 1.528111104676646, (29, 1) = .4446240074368551, (30, 0) = .4446240074368551, (30, 1) = 1.593279853547814, (31, 0) = 1.593279853547814, (31, 1) = .49549976475440116, (32, 0) = .49549976475440116, (32, 1) = 1.657938235238753, (33, 0) = 1.657938235238753, (33, 1) = .5463755220719472, (34, 0) = .5463755220719472, (34, 1) = 1.7221255423380761, (35, 0) = 1.7221255423380761, (35, 1) = .609425471855682, (36, 0) = .609425471855682, (36, 1) = 1.801070088732534, (37, 0) = 1.801070088732534, (37, 1) = .6724754216394168, (38, 0) = .6724754216394168, (38, 1) = 1.8794010795807021, (39, 0) = 1.8794010795807021, (39, 1) = .7355253714231516, (40, 0) = .7355253714231516, (40, 1) = 1.9571687015105361, (41, 0) = 1.9571687015105361, (41, 1) = .7985753212068863, (42, 0) = .7985753212068863, (42, 1) = 2.0344171361907124, (43, 0) = 2.0344171361907124, (43, 1) = .876929535653806, (44, 0) = .876929535653806, (44, 1) = 2.129750676830733, (45, 0) = 2.129750676830733, (45, 1) = .9552837501007257, (46, 0) = .9552837501007257, (46, 1) = 2.224406519957709, (47, 0) = 2.224406519957709, (47, 1) = 1.0336379645476454, (48, 0) = 1.0336379645476454, (48, 1) = 2.3184412382231283, (49, 0) = 2.3184412382231283, (49, 1) = 1.1119921789945653, (50, 0) = 1.1119921789945653, (50, 1) = 2.4119045424915186, (51, 0) = 2.4119045424915186, (51, 1) = 1.2096287918757802, (52, 0) = 1.2096287918757802, (52, 1) = 2.527634203497312, (53, 0) = 2.527634203497312, (53, 1) = 1.3072654047569954, (54, 0) = 1.3072654047569954, (54, 1) = 2.6426167417245696, (55, 0) = 2.6426167417245696, (55, 1) = 1.4049020176382103, (56, 0) = 1.4049020176382103, (56, 1) = 2.7569158996625, (57, 0) = 2.7569158996625, (57, 1) = 1.5025386305194255, (58, 0) = 1.5025386305194255, (58, 1) = 2.87058757063309, (59, 0) = 2.87058757063309, (59, 1) = 1.6245811380592985, (60, 0) = 1.6245811380592985, (60, 1) = 3.0118647534640655, (61, 0) = 3.0118647534640655, (61, 1) = 1.7466236455991715}, datatype = float[8], order = C_order)), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = y(x)]`; if 1/Y[1] < -1 then YP[1] := undefined; return 0 end if; YP[1] := evalf((1/Y[1]+1)^(1/2)); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] )), ( 4 ) = (3)  ] ); _y0 := Array(0..1, {(1) = 0.}); _vmap := array( 1 .. 1, [( 1 ) = (1)  ] ); _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] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(1..2, {(1) = 18446745506974851510, (2) = 18446745506974851686}), (3) = [x, y(x)], (4) = []}); _solnproc := _dat[1]; _pars := map(rhs, _dat[4]); if not type(_xout, 'numeric') then if member(x, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x, ["last", 'last', "initial", 'initial', NULL]) then _res := _solnproc(convert(x, 'string')); if type(_res, 'list') then return _res[2] else return NULL end if elif member(x, ["parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x, '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(x), 'string') = rhs(x); 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(x), 'string') = rhs(x)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _dat[3] end if; if procname <> unknown then return ('procname')(x) else _ndsol := 1; _ndsol := `tools/gensym`("y(x)"); 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(x)))) end if end if; try _res := _solnproc(_xout); _res[2] catch: error  end try end proc]

(4)

k:=1;

1

(5)

B:=dsolve({diff(y(x), x) = sqrt(y(x)^(-1-3*w)-k),y(0)=0.9999},type=numeric,range=-1..10,output=listprocedure);