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These are answers submitted by acer

I do not know whether the expression V below is right, because I do not know whether this substitution for 0.6 in your M is right, or even whether M is right. (It may not agree with what Reuben has mentioned.)

I replaced 0.6 (which presumably stands in for a/L) with the parameter name p.

But this may still show you some numeric rootfinding and related plotting methods.

restart;

M := Matrix(8, [[0, 1, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -sin(x), -cos(x), sinh(x), cosh(x)], [0, 0, 0, 0, -cos(x), sin(x), cosh(x), sinh(x)], [sin(p*x), cos(p*x), sinh(p*x), cosh(p*x), 0, 0, 0, 0], [0, 0, 0, 0, sin(p*x), cos(p*x), sinh(p*x), cosh(p*x)], [cos(p*x), -sin(p*x), cosh(p*x), sinh(p*x), -cos(p*x), sin(p*x), -cosh(p*x), -sinh(p*x)], [-sin(p*x), -cos(p*x), sinh(p*x), cosh(p*x), sin(p*x), cos(p*x), -sinh(p*x), -cosh(p*x)]]):

V:=simplify(combine(simplify(LinearAlgebra:-Determinant(M))));

4*cos(p*x)*sinh(p*x)+2*cos(x)*sinh(x)-2*sin(x)*cosh(x)-4*sin(x*(p-1))*cosh(x*(p-1))+4*cos(x*(p-1))*sinh(x*(p-1))-2*sin(x)*cosh(x*(2*p-1))-4*cosh(p*x)*sin(p*x)+2*sinh(x)*cos(x*(2*p-1))

plot(eval(V,p=0.6),x=0..6*Pi,size=[500,250],view=-1..1,xtickmarks=decimalticks);

fsolve(eval(V,p=0.6),x=0..6*Pi,maxsols=20);

0., 3.683036373, 7.222925018, 10.56359616, 12.71834600, 17.23325230

U:=proc(ee) option remember; local x;
  if not ee::numeric then return 'procname'(args); end if;
  [fsolve(eval(V,[:-p=ee,:-x=x]),x=0..6*Pi,maxsols=6)];
end proc:

plot([seq(U(p)[i],i=1..6)],p=0.1..2.0,adaptive=false,numpoints=101,thickness=3);

 

Download par_roots.mw

 

In my Maple 2015 it appears as if the numpoints option of SurfaceOfRevolution is only controlling the values used for the (blue) function curve, whose appearance you have suppressed by passing the showfunction=false option.

And since that detail also appears to be controlled (overridden) by the functionoptions choice, then I don't really see much merit in how it uses the numpoints option.

I do see an effect from the following, however, by temporarily adjusting the "default" for the grid option.

(I suspect that you may find that the grid values get used for the number of points used for the independent parameters in cylindrical coordinates. Hence they may serve the natural purposes.)

Again, this is in Maple 2015.

restart;

with(Student:-Calculus1):

f := 3+surd(abs(sin(x)), 5)*signum(sin(x)):

orig:=plots:-setoptions3d(grid): # [49,49]
plots:-setoptions3d(grid=[490,49]);
SurfaceOfRevolution(f, x=0..10*Pi, output=plot, caption="", showfunction=false);
plots:-setoptions3d(grid=orig);

op([1, 1], %);

Vector(4, {(1) = ` 1..490 x 1..49 x 1..3 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})

 

Download Surface0fRevolution_ac.mw

Member vv's nice method of substitution of the floor call by a name might be modifed, so that isolve finds integer solutions for the dummy name rather than having to pepper the new formula with values from an ad hoc range.

It handles at least these two examples, with only one substitution equation. I'm sure that it could benefit from robustification.

I displayed the intermediate piecewise result, since it helps illustrate how some progress was made (you could also evalf that piecewise, to see it even more clearly).

restart;

P := proc(A,B) local S;
     if A={} then NULL;
     else S:=isolve(A[]);
          if S=NULL then NULL;
          else eval(B,S[]);
          end if;
     end if;
end proc:

Q := proc(k) local i,j,kk;
  kk := PiecewiseTools:-ToList(k):
  seq(`if`(kk[i][2]=[],NULL,
           P({solve({seq(not(kk[j][1]),j=1..i-1),kk[i][1]})},
           kk[i][2])),i=1..nops(kk));
end proc:

 

f := x^2+floor(x)-10;

x^2+floor(x)-10

K := solve({eval(f,[floor(x)=n]),
            n<=x, x<n+1}, x);

K := piecewise(n <= -3/2-3*sqrt(5)*(1/2), [], n <= -1/2-(1/2)*sqrt(41), [{x = -sqrt(-n+10)}], n <= -3/2+3*sqrt(5)*(1/2), [], n <= -1/2+(1/2)*sqrt(41), [{x = sqrt(-n+10)}], -1/2+(1/2)*sqrt(41) < n, [])

Q(K);

[{x = -14^(1/2)}], [{x = 8^(1/2)}]

g := x^2+2*x+floor(x^2+x)-25;

x^2+2*x+floor(x^2+x)-25

K := solve({eval(g,[floor(x^2+x)=n]),
            n<=x^2+x, x^2+x<n+1}, x);

K := piecewise(n <= 99/8-(1/8)*sqrt(217), [], n <= 103/8-(1/8)*sqrt(209), [{x = -1+sqrt(26-n)}], n <= 99/8+(1/8)*sqrt(217), [], n <= 103/8+(1/8)*sqrt(209), [{x = -1-sqrt(26-n)}], 103/8+(1/8)*sqrt(209) < n, [])

Q(K);

[{x = -1+15^(1/2)}]

 

Download solve_uni_floor.mw

Another choice -- if you want to rotate each figure separately -- is to use the viewpoint option.

And, once again, a crude way to slow down the animation (including its gif export) is to repeat frames.

You might want to consider a single color (with glossiness and lighting) instead of shading=zhue, if you plan on exporting to .gif format.

restart

plots:-setoptions3d(scaling = constrained, axes = none, shading = zhue, view = [-1 .. 1, -1 .. 1, -1 .. 1])

with(plots)

with(plottools)

with(geom3d)

p := display(draw(tetrahedron(f, point(o, 0, 0, 0))), title = "Tetrahedron \n 4 Vertices, 6 Edges, 4 Faces")

p1 := display(draw(cube(f, point(o, 0, 0, 0))), title = "Cube (or hexahedron) \n 8 Vertices, 12 Edges, 6 Faces")

p2 := display(draw(octahedron(f, point(o, 0, 0, 0))), title = "Octahedron \n 6 Vertices, 12 Edges, 8 Faces")

p3 := display(draw(dodecahedron(f, point(o, 0, 0, 0), .6)), title = "Dodecahedron \n 20 Vertices, 30 Edges, 12 Faces")

p4 := display(draw(icosahedron(f, point(o, 0, 0, 0))), title = "Icosahedron \n 12 Vertices, 30 Edges, 20 Faces")

plots:-display(p4, viewpoint = [circleleft])

plots:-display(`$`(p1, 6), `$`(p2, 6), `$`(p3, 6), `$`(p4, 6), insequence = true)

``

Download FiguresEspace_ac.mw

The extrusion is done using POLYGONS substructures (rather than GRID or MESH, say), so I don't think that you would be able to get a surface with wireframe grid directly.

You can use overrideoption to get various other styles that are relevant for POLYGONS, though. This affects the CURVES as well as the POLYGONS.

You could use subsindets if you wanted to target just the POLYGONS and leave the CURVES alone (if your choice would be valid for them and otherwise alter them).
 

with(plottools):

p := plot(x^2,x=-5..5, thickness=3, adaptive=false, numpoints=13):

extrude(p, 1..2);
indets(%,specfunc(STYLE));

{STYLE(PATCHNOGRID)}

plots:-display(extrude(p, 1..2), overrideoption, style=polygonoutline);
indets(%,specfunc(STYLE));

{STYLE(PATCH)}

plots:-display(extrude(p, 1..2), overrideoption, style=line);
indets(%,specfunc(STYLE));

{STYLE(LINE)}

plots:-display(extrude(p, 1..2), overrideoption, style=pointline, symbolsize=25);
indets(%,specfunc(STYLE));

{STYLE(_POINTLINE)}

plots:-display(extrude(p, 1..2), overrideoption, style=patchcontour);
indets(%,specfunc(STYLE));

{STYLE(PATCHCONTOUR)}

 

Download extrude_style.mw

Here I've re-used the code from the MathApp itself so as to retain the aspect ratios and relative placement per frame (and a scaling procedure PP to unify the frame view).

One of the few changes I made was to allow the randomize seed to be passed to the Reset procedure, which affects the shuffling randomization of the colors.

restart;

 

Source for FibonacciNum module is based closely on that of the MathApp,
and is in the worksheet's Startup Code.

 

PP := proc(P)
  local data,xmin,xmax,ymin,ymax;
  data := indets(P,specfunc(anything,VIEW))[1];
  (xmin,xmax):=[lhs,rhs](op(1,data))[];
  (ymin,ymax):=[lhs,rhs](op(2,data))[];
  plottools:-transform((x,y)->[(x-xmin)/(xmax-xmin),
                               (y-ymin)/(ymax-ymin)])(P);
end proc:

 

plots:-display(PP(FibonacciNum:-Reset(1234))$5,
               seq(PP(FibonacciNum:-NextStep())$5,i=1..23),insequence=true);

Download fib_anim.mw

I used repeated frames to slow it down. If you have a animated .gif player which allows you to adjust the speed then there's no need to use repeated frames.

Another possibility for your Maple 13 is to transform a result from odeplot using your known procedure FAK.

You could do that in one line (or in two steps, if you want to save the intermediate plot).

In older versions such as yours the odeplot curve renders thinly in places, which you may be able to make up for using the refine=1 option (which Preben also utilized).

(Although, for your given FAK, Preben's solution to utilize piecewise seems much more sensible.)
 

restart; with(plots)

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

eq := diff(`&vartheta;`(tau), tau, tau)+6.666666666*sin(`&vartheta;`(tau))+66.66666666*cos(`&vartheta;`(tau))^2*FAK(`&vartheta;`(tau), .7227342478, tau)*(`&vartheta;`(tau)-.7227342478)+66.66666666*sin(`&vartheta;`(tau))^2*FAK(`&vartheta;`(tau), .7227342478, tau)*(`&vartheta;`(tau)-.7227342478):

`&vartheta;`(0) = 0, (D(`&vartheta;`))(0) = 8

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false, ( "left" ) = 0., ( "right" ) = 5. ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 19, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..53, {(1) = 2, (2) = 2, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 1, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = 5.0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.6309573444801932e-3, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..2, {(1) = .0, (2) = 8.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..2, {(1) = .1, (2) = .1}, datatype = float[8], order = C_order), Array(1..2, {(1) = -31.367281279722167, (2) = -7.999036635422113}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = -7.993181631999045, (2) = .8523118973259195}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..6, {(1, 1) = -7.993181631999045, (1, 2) = -7.987723491460202, (1, 3) = -7.9909107025476915, (1, 4) = -7.995700172919506, (1, 5) = -7.9915071177936206, (1, 6) = -7.9966631348764885, (2, 1) = .8523118973259195, (2, 2) = -1.3469687361243274, (2, 3) = -.9831356859087976, (2, 4) = .621296268837965, (2, 5) = .8382472012664016, (2, 6) = -.6145172162229459}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8]), Array(1..2, {(1) = -31.291095186812182, (2) = -7.99353540904542}, datatype = float[8], order = C_order), Array(1..2, {(1) = -31.544124179000836, (2) = -7.993181631999045}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0.2201682894015495e-6, (2) = 0.31135401469623278e-5}, datatype = float[8], order = C_order), Array(1..2, {(1) = -7.999433750830772, (2) = -.25054944218527625}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = 8.0, (2) = .0}, datatype = float[8], order = C_order)]), ( 11 ) = (Array(1..6, 0..2, {(1, 1) = .0, (1, 2) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = \`&vartheta;\`(tau), Y[2] = diff(\`&vartheta;\`(tau),tau)]`; YP[2] := -6.666666666*sin(Y[1])-66.66666666*cos(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478)-66.66666666*sin(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478); YP[1] := Y[2]; 0 end proc, -1, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = \`&vartheta;\`(tau), Y[2] = diff(\`&vartheta;\`(tau),tau)]`; YP[2] := -6.666666666*sin(Y[1])-66.66666666*cos(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478)-66.66666666*sin(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478); YP[1] := Y[2]; 0 end proc, -1, 0, 0, 0, 0])  ] )), ( 3 ) = (array( 1 .. 19, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..53, {(1) = 2, (2) = 2, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 1, (9) = 0, (10) = 1, (11) = 441, (12) = 441, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 862, (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}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = 5.0, (2) = 0.10e-5, (3) = 0.8118142031911368e-1, (4) = 0.500001e-14, (5) = .0, (6) = 0.6309573444801932e-3, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..2, {(1) = .0, (2) = 8.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..2, {(1) = .1, (2) = .1}, datatype = float[8], order = C_order), Array(1..2, {(1) = -31.367281279722167, (2) = -7.999036635422113}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = -7.993181631999045, (2) = .8523118973259195}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..6, {(1, 1) = -7.993181631999045, (1, 2) = -7.987723491460202, (1, 3) = -7.9909107025476915, (1, 4) = -7.995700172919506, (1, 5) = -7.9915071177936206, (1, 6) = -7.9966631348764885, (2, 1) = .8523118973259195, (2, 2) = -1.3469687361243274, (2, 3) = -.9831356859087976, (2, 4) = .621296268837965, (2, 5) = .8382472012664016, (2, 6) = -.6145172162229459}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8]), Array(1..2, {(1) = -31.291095186812182, (2) = -7.99353540904542}, datatype = float[8], order = C_order), Array(1..2, {(1) = -31.544124179000836, (2) = -7.993181631999045}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0.2201682894015495e-6, (2) = 0.31135401469623278e-5}, datatype = float[8], order = C_order), Array(1..2, {(1) = -7.999433750830772, (2) = -.25054944218527625}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..2, {(1) = .0, (2) = 8.0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = -7.993181631999045, (2) = .8523118973259195}, datatype = float[8], order = C_order)]), ( 11 ) = (Array(1..6, 0..2, {(1, 1) = 4.976362116674161, (1, 2) = -31.10249248642951, (2, 0) = -31.10249248642951, (2, 1) = -7.959318755955807, (2, 2) = 4.9901809118967755, (3, 0) = 4.9901809118967755, (3, 1) = -31.212654494758723, (3, 2) = -7.982846656351056, (4, 0) = -7.982846656351056, (4, 1) = 5.003999707119389, (4, 2) = -31.323072978227856, (5, 0) = -31.323072978227856, (5, 1) = -7.996431837511704, (5, 2) = 5.017818502342004, (6, 0) = 5.017818502342004, (6, 1) = -31.433609657345325, (6, 2) = -7.9998923291572375}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = \`&vartheta;\`(tau), Y[2] = diff(\`&vartheta;\`(tau),tau)]`; YP[2] := -6.666666666*sin(Y[1])-66.66666666*cos(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478)-66.66666666*sin(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478); YP[1] := Y[2]; 0 end proc, -1, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (Array(1..441, 0..2, {(1, 1) = .0, (1, 2) = .0, (2, 0) = .0, (2, 1) = 8.0, (2, 2) = 0.1577393361200483e-3, (3, 0) = 0.1577393361200483e-3, (3, 1) = 0.1261914654073069e-2, (3, 2) = 7.9999993364881465, (4, 0) = 7.9999993364881465, (4, 1) = 0.3154786722400966e-3, (4, 2) = 0.2523829098822314e-2, (5, 0) = 0.2523829098822314e-2, (5, 1) = 7.999997345953752, (5, 2) = 0.4732180083601449e-3, (6, 0) = 0.4732180083601449e-3, (6, 1) = 0.3785743124924429e-2, (6, 2) = 7.999994028400317, (7, 0) = 7.999994028400317, (7, 1) = 0.6309573444801932e-3, (7, 2) = 0.5047656523056748e-2, (8, 0) = 0.5047656523056748e-2, (8, 1) = 7.999989383833675, (8, 2) = 0.910466599549169e-2, (9, 0) = 0.910466599549169e-2, (9, 1) = 0.7283061711886847e-1, (9, 2) = 7.997790484361768, (10, 0) = 7.997790484361768, (10, 1) = 0.17578374646503185e-1, (10, 2) = .14057873869733103, (11, 0) = .14057873869733103, (11, 1) = 7.9917749395975575, (11, 2) = 0.2605208329751468e-1, (12, 0) = 0.2605208329751468e-1, (12, 1) = .2082598409430194, (12, 2) = 7.9819732032097885, (13, 0) = 7.9819732032097885, (13, 1) = 0.3452579194852618e-1, (13, 2) = .27584203987205436, (14, 0) = .27584203987205436, (14, 1) = 7.968434618165476, (14, 2) = 0.4461537725945372e-1, (15, 0) = 0.4461537725945372e-1, (15, 1) = .3561391187071168, (15, 2) = 7.947535890654133, (16, 0) = 7.947535890654133, (16, 1) = 0.5470496257038125e-1, (16, 2) = .4361996697516819, (17, 0) = .4361996697516819, (17, 1) = 7.921585199614493, (17, 2) = 0.6479454788130878e-1, (18, 0) = 0.6479454788130878e-1, (18, 1) = .5159737043750608, (18, 2) = 7.890764894537611, (19, 0) = 7.890764894537611, (19, 1) = 0.7488413319223633e-1, (19, 2) = .5954131498621087, (20, 0) = .5954131498621087, (20, 1) = 7.855288717718425, (20, 2) = 0.7724192945456435e-1, (21, 0) = 0.7724192945456435e-1, (21, 1) = .6139238328981906, (21, 2) = 7.846352941352147, (22, 0) = 7.846352941352147, (22, 1) = 0.7959972571689237e-1, (22, 2) = .6324131662978086, (23, 0) = .6324131662978086, (23, 1) = 7.837179476582829, (23, 2) = 0.819575219792204e-1, (24, 0) = 0.819575219792204e-1, (24, 1) = .6508805936975003, (24, 2) = 7.827771735235569, (25, 0) = 7.827771735235569, (25, 1) = 0.8431531824154842e-1, (25, 2) = .6693255668205345, (26, 0) = .6693255668205345, (26, 1) = 7.81813320429867, (26, 2) = 0.8515831718399572e-1, (27, 0) = 0.8515831718399572e-1, (27, 1) = .6759147710142368, (27, 2) = 7.814631742640519, (28, 0) = 7.814631742640519, (28, 1) = 0.8600131612644302e-1, (28, 2) = .682501011293615, (29, 0) = .682501011293615, (29, 1) = 7.811101398162396, (29, 2) = 0.8684431506889033e-1, (30, 0) = 0.8684431506889033e-1, (30, 1) = .6890842633807064, (30, 2) = 7.807542337017661, (31, 0) = 7.807542337017661, (31, 1) = 0.8768731401133763e-1, (31, 2) = .6956645031378431, (32, 0) = .6956645031378431, (32, 1) = 7.803954726497892, (32, 2) = 0.8853031295378493e-1, (33, 0) = 0.8853031295378493e-1, (33, 1) = .702241706568491, (33, 2) = 7.8003387350260045, (34, 0) = 7.8003387350260045, (34, 1) = 0.8937331189623224e-1, (34, 2) = .7088158498189915, (35, 0) = .7088158498189915, (35, 1) = 7.796694532146091, (35, 2) = 0.9021631083867954e-1, (36, 0) = 0.9021631083867954e-1, (36, 1) = .715386909179264, (36, 2) = 7.793022288499969, (37, 0) = 7.793022288499969, (37, 1) = 0.9105930978112683e-1, (37, 2) = .7219548610832975, (38, 0) = .7219548610832975, (38, 1) = 7.789322175815902, (38, 2) = 0.9222883385974404e-1, (39, 0) = 0.9222883385974404e-1, (39, 1) = .7310615097424107, (39, 2) = 7.783817204004633, (40, 0) = 7.783817204004633, (40, 1) = 0.9339835793836124e-1, (40, 2) = .740161292597822, (41, 0) = .740161292597822, (41, 1) = 7.7775806177881766, (41, 2) = 0.9456788201697845e-1, (42, 0) = 0.9456788201697845e-1, (42, 1) = .7492533446070906, (42, 2) = 7.770586563883372, (43, 0) = 7.770586563883372, (43, 1) = 0.9573740609559565e-1, (43, 2) = .7583367742188167, (44, 0) = .7583367742188167, (44, 1) = 7.762828288793826, (44, 2) = 0.9690693017421285e-1, (45, 0) = 0.9690693017421285e-1, (45, 1) = .7674106821991918, (45, 2) = 7.754311011985184, (46, 0) = 7.754311011985184, (46, 1) = 0.9807645425283007e-1, (46, 2) = .7764741856443589, (47, 0) = .7764741856443589, (47, 1) = 7.745035769299268, (47, 2) = 0.9924597833144727e-1, (48, 0) = 0.9924597833144727e-1, (48, 1) = .7855263988698492, (48, 2) = 7.7350039138304725, (49, 0) = 7.7350039138304725, (49, 1) = .10041550241006447, (49, 2) = .7945664378628262, (50, 0) = .7945664378628262, (50, 1) = 7.724216874921755, (50, 2) = .10509359872453329, (51, 0) = .10509359872453329, (51, 1) = .830587256307844, (51, 2) = 7.673548067152378, (52, 0) = 7.673548067152378, (52, 1) = .10977169503900211, (52, 2) = .8663430294386847, (53, 0) = .8663430294386847, (53, 1) = 7.610930371092187, (53, 2) = .11444979135347093, (54, 0) = .11444979135347093, (54, 1) = .9017781390816609, (54, 2) = 7.5364910171980375, (55, 0) = 7.5364910171980375, (55, 1) = .11912788766793975, (55, 2) = .936837651927675, (56, 0) = .936837651927675, (56, 1) = 7.450375583942169, (56, 2) = .1246136984772347, (57, 0) = .1246136984772347, (57, 1) = .977399047182726, (57, 2) = 7.334738920998827, (58, 0) = 7.334738920998827, (58, 1) = .13009950928652966, (58, 2) = 1.0172832948850594, (59, 0) = 1.0172832948850594, (59, 1) = 7.203566810338618, (59, 2) = .1355853200958246, (60, 0) = .1355853200958246, (60, 1) = 1.056406022688301, (60, 2) = 7.0571853808973275, (61, 0) = 7.0571853808973275, (61, 1) = .14107113090511958, (61, 2) = 1.0946848342630966, (62, 0) = 1.0946848342630966, (62, 1) = 6.8959509062200395, (62, 2) = .14678216166975566, (63, 0) = .14678216166975566, (63, 1) = 1.1335520537682477, (63, 2) = 6.7127324559531045, (64, 0) = 6.7127324559531045, (64, 1) = .15249319243439174, (64, 2) = 1.171329209001558, (65, 0) = 1.171329209001558, (65, 1) = 6.514302767327525, (65, 2) = .1582042231990278, (66, 0) = .1582042231990278, (66, 1) = 1.2079307976217073, (66, 2) = 6.301160294706734, (67, 0) = 6.301160294706734, (67, 1) = .16391525396366388, (67, 2) = 1.243274369622535, (68, 0) = 1.243274369622535, (68, 1) = 6.073832355161447, (68, 2) = .1698958884107268, (69, 0) = .1698958884107268, (69, 1) = 1.278851562593288, (69, 2) = 5.821172123895152, (70, 0) = 5.821172123895152, (70, 1) = .1758765228577897, (70, 2) = 1.3128746222391015, (71, 0) = 1.3128746222391015, (71, 1) = 5.5542344716421574, (71, 2) = .18185715730485263, (72, 0) = .18185715730485263, (72, 1) = 1.3452601807300395, (72, 2) = 5.273717459105724, (73, 0) = 5.273717459105724, (73, 1) = .18783779175191556, (73, 2) = 1.3759292676266226, (74, 0) = 1.3759292676266226, (74, 1) = 4.980345685869605, (74, 2) = .19355132835306116, (75, 0) = .19355132835306116, (75, 1) = 1.4035568110301446, (75, 2) = 4.688759800989917, (76, 0) = 4.688759800989917, (76, 1) = .19926486495420678, (76, 2) = 1.42948839526954, (77, 0) = 1.42948839526954, (77, 1) = 4.386801712716325, (77, 2) = .2049784015553524, (78, 0) = .2049784015553524, (78, 1) = 1.4536666879438358, (78, 2) = 4.075163927534554, (79, 0) = 4.075163927534554, (79, 1) = .210691938156498, (79, 2) = 1.4760384559428055, (80, 0) = 1.4760384559428055, (80, 1) = 3.7545547725410398, (80, 2) = .21596109984563922, (81, 0) = .21596109984563922, (81, 1) = 1.4950265118455826, (81, 2) = 3.4515539851328247, (82, 0) = 3.4515539851328247, (82, 1) = .22123026153478043, (82, 2) = 1.5124007892881386, (83, 0) = 1.5124007892881386, (83, 1) = 3.142117159891026, (83, 2) = .22649942322392164, (84, 0) = .22649942322392164, (84, 1) = 1.52812889530071, (84, 2) = 2.826831472391012, (85, 0) = 2.826831472391012, (85, 1) = .23176858491306285, (85, 2) = 1.5421816021497121, (86, 0) = 1.5421816021497121, (86, 1) = 2.5062916603252905, (86, 2) = .23659984161913422, (87, 0) = .23659984161913422, (87, 1) = 1.5535717674526115, (87, 2) = 2.208288033125178, (88, 0) = 2.208288033125178, (88, 1) = .2414310983252056, (88, 2) = 1.5635136956930513, (89, 0) = 1.5635136956930513, (89, 1) = 1.9068426756238754, (89, 2) = .24626235503127697, (90, 0) = .24626235503127697, (90, 1) = 1.5719918873415348, (90, 2) = 1.6024284407751443, (91, 0) = 1.6024284407751443, (91, 1) = .25109361173734834, (91, 2) = 1.5789931586004786, (92, 0) = 1.5789931586004786, (92, 1) = 1.295521181909761, (92, 2) = .25542657016525233, (93, 0) = .25542657016525233, (93, 1) = 1.5840070535309498, (93, 2) = 1.018541073280115, (94, 0) = 1.018541073280115, (94, 1) = .2597595285931564, (94, 2) = 1.5878179220650785, (95, 0) = 1.5878179220650785, (95, 1) = .7402879652217428, (95, 2) = .26409248702106036, (96, 0) = .26409248702106036, (96, 1) = 1.590420997033388, (96, 2) = .46111004438263886, (97, 0) = .46111004438263886, (97, 1) = .2684254454489644, (97, 2) = 1.5918130298602629, (98, 0) = 1.5918130298602629, (98, 1) = .18135612403410417, (98, 2) = .2720410474072668, (99, 0) = .2720410474072668, (99, 1) = 1.592046408857974, (99, 2) = -0.5227046739391352e-1, (100, 0) = -0.5227046739391352e-1, (100, 1) = .2756566493655692, (100, 2) = 1.5914351086156264, (101, 0) = 1.5914351086156264, (101, 1) = -.2858515785049789, (101, 2) = .27927225132387157, (102, 0) = .27927225132387157, (102, 1) = 1.5899796595702271, (102, 2) = -.5191840485851557, (103, 0) = -.5191840485851557, (103, 1) = .282887853282174, (103, 2) = 1.5876813276502564, (104, 0) = 1.5876813276502564, (104, 1) = -.7520649506188066, (104, 2) = .28622219901998947, (105, 0) = .28622219901998947, (105, 1) = 1.5848164147812076, (105, 2) = -.9662549172881296, (106, 0) = -.9662549172881296, (106, 1) = .289556544757805, (106, 2) = 1.5812384673475255, (107, 0) = 1.5812384673475255, (107, 1) = -1.1797297231959167, (107, 2) = .29289089049562056, (108, 0) = .29289089049562056, (108, 1) = 1.5769501335544218, (108, 2) = -1.392331043959241, (109, 0) = -1.392331043959241, (109, 1) = .29622523623343605, (109, 2) = 1.5719545884510844, (110, 0) = 1.5719545884510844, (110, 1) = -1.6039010703295555, (110, 2) = .30014947426295147, (111, 0) = .30014947426295147, (111, 1) = 1.5651743615913893, (111, 2) = -1.851366391016546, (112, 0) = -1.851366391016546, (112, 1) = .3040737122924668, (112, 2) = 1.5574266719966954, (113, 0) = 1.5574266719966954, (113, 1) = -2.0969300293366886, (113, 2) = .30799795032198224, (114, 0) = .30799795032198224, (114, 1) = 1.548719480452293, (114, 2) = -2.3403380510139424, (115, 0) = -2.3403380510139424, (115, 1) = .31192218835149765, (115, 2) = 1.5390617384581458, (116, 0) = 1.5390617384581458, (116, 1) = -2.5813382447343844, (116, 2) = .31630201842764794, (117, 0) = .31630201842764794, (117, 1) = 1.5271724975029926, (117, 2) = -2.8471673845382965, (118, 0) = -2.8471673845382965, (118, 1) = .3206818485037983, (118, 2) = 1.514126857563062, (119, 0) = 1.514126857563062, (119, 1) = -3.1093397335975523, (119, 2) = .3250616785799486, (120, 0) = .3250616785799486, (120, 1) = 1.499941584918137, (120, 2) = -3.3675133336121217, (121, 0) = -3.3675133336121217, (121, 1) = .3294415086560989, (121, 2) = 1.4846349265606742, (122, 0) = 1.4846349265606742, (122, 1) = -3.6213502416711894, (122, 2) = .3341873559052846, (123, 0) = .3341873559052846, (123, 1) = 1.466806154945537, (123, 2) = -3.8911173676871877, (124, 0) = -3.8911173676871877, (124, 1) = .33893320315447034, (124, 2) = 1.4477109617856145, (125, 0) = 1.4477109617856145, (125, 1) = -4.154981645661831, (125, 2) = .3436790504036561, (126, 0) = .3436790504036561, (126, 1) = 1.4273783437127143, (126, 2) = -4.412530874299008, (127, 0) = -4.412530874299008, (127, 1) = .3484248976528418, (127, 2) = 1.405839216494501, (128, 0) = 1.405839216494501, (128, 1) = -4.663360531634131, (128, 2) = .3534880933026569, (129, 0) = .3534880933026569, (129, 1) = 1.3815666019500132, (129, 2) = -4.923107380206349, (130, 0) = -4.923107380206349, (130, 1) = .358551288952472, (130, 2) = 1.3560003571412884, (131, 0) = 1.3560003571412884, (131, 1) = -5.174282894513542, (131, 2) = .3636144846022872, (132, 0) = .3636144846022872, (132, 1) = 1.3291850536745695, (132, 2) = -5.41642750942523, (133, 0) = -5.41642750942523, (133, 1) = .3686776802521023, (133, 2) = 1.3011675213441034, (134, 0) = 1.3011675213441034, (134, 1) = -5.6490948132663155, (134, 2) = .3740364445110345, (135, 0) = .3740364445110345, (135, 1) = 1.270259408556187, (135, 2) = -5.884540469630054, (136, 0) = -5.884540469630054, (136, 1) = .37939520876996674, (136, 2) = 1.2381204807374548, (137, 0) = 1.2381204807374548, (137, 1) = -6.1083885270949265, (137, 2) = .38475397302889897, (138, 0) = .38475397302889897, (138, 1) = 1.2048141823931064, (138, 2) = -6.320161961422066, (139, 0) = -6.320161961422066, (139, 1) = .3901127372878312, (139, 2) = 1.1704063991345115, (140, 0) = 1.1704063991345115, (140, 1) = -6.519404825559516, (140, 2) = .39577256461768484, (141, 0) = .39577256461768484, (141, 1) = 1.1329450576363154, (141, 2) = -6.715755001513947, (142, 0) = -6.715755001513947, (142, 1) = .4014323919475385, (142, 2) = 1.094414526923341, (143, 0) = 1.094414526923341, (143, 1) = -6.897157326147072, (143, 2) = .40709221927739214, (144, 0) = .40709221927739214, (144, 1) = 1.0549007247668531, (144, 2) = -7.063156945994943, (145, 0) = -7.063156945994943, (145, 1) = .4127520466072458, (145, 2) = 1.0144919608275662, (146, 0) = 1.0144919608275662, (146, 1) = -7.21333141903612, (146, 2) = .4187361768032799, (147, 0) = .4187361768032799, (147, 1) = .9708949398250795, (147, 2) = -7.354468476784398, (148, 0) = -7.354468476784398, (148, 1) = .42472030699931407, (148, 2) = .9265086857688131, (149, 0) = .9265086857688131, (149, 1) = -7.477060340407247, (149, 2) = .43070443719534823, (150, 0) = .43070443719534823, (150, 1) = .8814453370831891, (150, 2) = -7.580733289533636, (151, 0) = -7.580733289533636, (151, 1) = .43668856739138234, (151, 2) = .8358189896240945, (152, 0) = .8358189896240945, (152, 1) = -7.665161691568966, (152, 2) = .4378929948991111, (153, 0) = .4378929948991111, (153, 1) = .8265779615108086, (153, 2) = -7.679802672304922, (154, 0) = -7.679802672304922, (154, 1) = .43909742240683985, (154, 2) = .8173197767836574, (155, 0) = .8173197767836574, (155, 1) = -7.693650637375634, (155, 2) = .4403018499145686, (156, 0) = .4403018499145686, (156, 1) = .8080453917558491, (156, 2) = -7.7067036522677625, (157, 0) = -7.7067036522677625, (157, 1) = .44150627742229737, (157, 2) = .7987557649695164, (158, 0) = .7987557649695164, (158, 1) = -7.718959866544123, (158, 2) = .4427107049300261, (159, 0) = .4427107049300261, (159, 1) = .7894518571583069, (159, 2) = -7.730417514046595, (160, 0) = -7.730417514046595, (160, 1) = .4439151324377549, (160, 2) = .7801346312172007, (161, 0) = .7801346312172007, (161, 1) = -7.741074913130029, (161, 2) = .44511955994548363, (162, 0) = .44511955994548363, (162, 1) = .7708050519670215, (162, 2) = -7.750930467619745, (163, 0) = -7.750930467619745, (163, 1) = .4463239874532124, (163, 2) = .7614640860485955, (164, 0) = .7614640860485955, (164, 1) = -7.759982667255651, (164, 2) = .4470384105507191, (165, 0) = .4470384105507191, (165, 1) = .7559183761030625, (165, 2) = -7.764971933122205, (166, 0) = -7.764971933122205, (166, 1) = .4477528336482258, (166, 2) = .750369202944065, (167, 0) = .750369202944065, (167, 1) = -7.769677758095763, (167, 2) = .4484672567457325, (168, 0) = .4484672567457325, (168, 1) = .7448167691668857, (168, 2) = -7.774099870064164, (169, 0) = -7.774099870064164, (169, 1) = .4491816798432392, (169, 2) = .7392612775536026, (170, 0) = .7392612775536026, (170, 1) = -7.778238007706159, (170, 2) = .44962253961467835, (171, 0) = .44962253961467835, (171, 1) = .7358316297158923, (171, 2) = -7.78064979485627, (172, 0) = -7.78064979485627, (172, 1) = .45006339938611745, (172, 2) = .7324009424862602, (173, 0) = .7324009424862602, (173, 1) = -7.782953293896213, (173, 2) = .45050425915755654, (174, 0) = .45050425915755654, (174, 1) = .7289692636168755, (174, 2) = -7.78514844958939, (175, 0) = -7.78514844958939, (175, 1) = .4509451189289957, (175, 2) = .7255366408835744, (176, 0) = .7255366408835744, (176, 1) = -7.7872352082765675, (176, 2) = .45138597870043484, (177, 0) = .45138597870043484, (177, 1) = .7221031200934152, (177, 2) = -7.78922437099814, (178, 0) = -7.78922437099814, (178, 1) = .45182683847187394, (178, 2) = .7186687334589243, (179, 0) = .7186687334589243, (179, 1) = -7.791163952188871, (179, 2) = .45226769824331303, (180, 0) = .45226769824331303, (180, 1) = .7152334977331236, (180, 2) = -7.793090383245708, (181, 0) = -7.793090383245708, (181, 1) = .4527085580147522, (181, 2) = .7117974154706747, (182, 0) = .7117974154706747, (182, 1) = -7.7950143139411106, (182, 2) = .4530651624140873, (183, 0) = .4530651624140873, (183, 1) = .7090174024885219, (183, 2) = -7.796564693183492, (184, 0) = -7.796564693183492, (184, 1) = .4534217668134224, (184, 2) = .7062368375284361, (185, 0) = .7062368375284361, (185, 1) = -7.798110055610804, (185, 2) = .45377837121275755, (186, 0) = .45377837121275755, (186, 1) = .7034557223817415, (186, 2) = -7.799650388279463, (187, 0) = -7.799650388279463, (187, 1) = .45413497561209265, (187, 2) = .7006740588443741, (188, 0) = .7006740588443741, (188, 1) = -7.8011856782809845, (188, 2) = .4555613932094331, (189, 0) = .4555613932094331, (189, 1) = .6895419568678633, (189, 2) = -7.807276154711581, (190, 0) = -7.807276154711581, (190, 1) = .4569878108067736, (190, 2) = .6784012255071429, (191, 0) = .6784012255071429, (191, 1) = -7.813284924989592, (191, 2) = .45841422840411405, (192, 0) = .45841422840411405, (192, 1) = .6672519818835787, (192, 2) = -7.819211180180442, (193, 0) = -7.819211180180442, (193, 1) = .4598406460014545, (193, 2) = .6560943442692185, (194, 0) = .6560943442692185, (194, 1) = -7.825054120815269, (194, 2) = .4655463163908164, (195, 0) = .4655463163908164, (195, 1) = .6113822590742646, (195, 2) = -7.847577114372417, (196, 0) = -7.847577114372417, (196, 1) = .47125198678017827, (196, 2) = .5665456226344675, (197, 0) = .5665456226344675, (197, 1) = -7.868705654677926, (197, 2) = .47695765716954014, (198, 0) = .47695765716954014, (198, 1) = .5215925199823714, (198, 2) = -7.88839347521671, (199, 0) = -7.88839347521671, (199, 1) = .482663327558902, (199, 2) = .4765312962729426, (200, 0) = .4765312962729426, (200, 1) = -7.90659719378094, (200, 2) = .49581177269506715, (201, 0) = .49581177269506715, (201, 1) = .37232552479327874, (201, 2) = -7.942681840672743, (202, 0) = -7.942681840672743, (202, 1) = .5089602178312324, (202, 2) = .26770106323214893, (203, 0) = .26770106323214893, (203, 1) = -7.970246691395995, (203, 2) = .5221086629673974, (204, 0) = .5221086629673974, (204, 1) = .16277183282967028, (204, 2) = -7.98896087901469, (205, 0) = -7.98896087901469, (205, 1) = .5352571081035626, (205, 2) = 0.5765578172180408e-1, (206, 0) = 0.5765578172180408e-1, (206, 1) = -7.998598891515165, (206, 2) = .5464727618701309, (207, 0) = .5464727618701309, (207, 1) = -0.3206534864317351e-1, (207, 2) = -7.999555099498284, (208, 0) = -7.999555099498284, (208, 1) = .5576884156366994, (208, 2) = -.12175952675692299, (209, 0) = -.12175952675692299, (209, 1) = -7.993811506290754, (209, 2) = .5689040694032677, (210, 0) = .5689040694032677, (210, 1) = -.21135202580364515, (210, 2) = -7.981419094776882, (211, 0) = -7.981419094776882, (211, 1) = .5801197231698361, (211, 2) = -.30076884603594245, (212, 0) = -.30076884603594245, (212, 1) = -7.962486883815777, (212, 2) = .59051447442476, (213, 0) = .59051447442476, (213, 1) = -.383420782660408, (213, 2) = -7.939244773785794, (214, 0) = -7.939244773785794, (214, 1) = .600909225679684, (214, 2) = -.4658033607360733, (215, 0) = -.4658033607360733, (215, 1) = -7.910702649197814, (215, 2) = .611303976934608, (216, 0) = .611303976934608, (216, 1) = -.5478626623774588, (216, 2) = -7.87707266769194, (217, 0) = -7.87707266769194, (217, 1) = .621698728189532, (217, 2) = -.6295470606691361, (218, 0) = -.6295470606691361, (218, 1) = -7.8386012699370164, (218, 2) = .6341257571281204, (219, 0) = .6341257571281204, (219, 1) = -.7266412320451858, (219, 2) = -7.786645918289973, (220, 0) = -7.786645918289973, (220, 1) = .6465527860667089, (220, 2) = -.8230519111283794, (221, 0) = -.8230519111283794, (221, 1) = -7.728704632500372, (221, 2) = .6589798150052972, (222, 0) = .6589798150052972, (222, 1) = -.9187084131411163, (222, 2) = -7.665357566824385, (223, 0) = -7.665357566824385, (223, 1) = .6714068439438856, (223, 2) = -1.0135473777473216, (224, 0) = -1.0135473777473216, (224, 1) = -7.597222744700552, (224, 2) = .6835417272073966, (225, 0) = .6835417272073966, (225, 1) = -1.1053145262312571, (225, 2) = -7.526693041083931, (226, 0) = -7.526693041083931, (226, 1) = .6956766104709076, (226, 2) = -1.1962050424465236, (227, 0) = -1.1962050424465236, (227, 1) = -7.4528490264629745, (227, 2) = .7078114937344187, (228, 0) = .7078114937344187, (228, 1) = -1.2861825895649694, (228, 2) = -7.376329434938738, (229, 0) = -7.376329434938738, (229, 1) = .7199463769979296, (229, 2) = -1.3752185955919924, (230, 0) = -1.3752185955919924, (230, 1) = -7.297775410644999, (230, 2) = .7325073492133464, (231, 0) = .7325073492133464, (231, 1) = -1.4663671036164827, (231, 2) = -7.215002614317857, (232, 0) = -7.215002614317857, (232, 1) = .7450683214287631, (232, 2) = -1.5564702402300534, (233, 0) = -1.5564702402300534, (233, 1) = -7.131438228572601, (233, 2) = .7576292936441799, (234, 0) = .7576292936441799, (234, 1) = -1.6455222838522743, (234, 2) = -7.047765248052426, (235, 0) = -7.047765248052426, (235, 1) = .7701902658595966, (235, 2) = -1.7335260423787509, (236, 0) = -1.7335260423787509, (236, 1) = -6.964642769087884, (236, 2) = .7842420514110421, (237, 0) = .7842420514110421, (237, 1) = -1.8307462541150652, (237, 2) = -6.873086161783311, (238, 0) = -6.873086161783311, (238, 1) = .7982938369624877, (238, 2) = -1.9266953879200652, (239, 0) = -1.9266953879200652, (239, 1) = -6.783851043629574, (239, 2) = .8123456225139332, (240, 0) = .8123456225139332, (240, 1) = -2.0214113827405247, (240, 2) = -6.697722972076699, (241, 0) = -6.697722972076699, (241, 1) = .8263974080653786, (241, 2) = -2.114943099058882, (242, 0) = -2.114943099058882, (242, 1) = -6.615429330198988, (242, 2) = .8442528554195505, (243, 0) = .8442528554195505, (243, 1) = -2.23217816906993, (243, 2) = -6.517437205537282, (244, 0) = -6.517437205537282, (244, 1) = .8621083027737224, (244, 2) = -2.3477380106807897, (245, 0) = -2.3477380106807897, (245, 1) = -6.427939687672447, (245, 2) = .8799637501278942, (246, 0) = .8799637501278942, (246, 1) = -2.461783081544498, (246, 2) = -6.348007332698202, (247, 0) = -6.348007332698202, (247, 1) = .8978191974820661, (247, 2) = -2.5744927191735902, (248, 0) = -2.5744927191735902, (248, 1) = -6.2785556656082155, (248, 2) = .9161529747521646, (249, 0) = .9161529747521646, (249, 1) = -2.689037608306874, (249, 2) = -6.21894953434366, (250, 0) = -6.21894953434366, (250, 1) = .9344867520222632, (250, 2) = -2.8026038702873888, (251, 0) = -2.8026038702873888, (251, 1) = -6.171862755686531, (251, 2) = .9528205292923617, (252, 0) = .9528205292923617, (252, 1) = -2.9154248421016256, (252, 2) = -6.137806572876266, (253, 0) = -6.137806572876266, (253, 1) = .9711543065624603, (253, 2) = -3.0277432229520356, (254, 0) = -3.0277432229520356, (254, 1) = -6.11714236539504, (254, 2) = .9912876046199857, (255, 0) = .9912876046199857, (255, 1) = -3.150803680381802, (255, 2) = -6.110127716732306, (256, 0) = -6.110127716732306, (256, 1) = 1.011420902677511, (256, 2) = -3.2738894141853416, (257, 0) = -3.2738894141853416, (257, 1) = -6.119608336718841, (257, 2) = 1.0315542007350362, (258, 0) = 1.0315542007350362, (258, 1) = -3.3973299914208965, (258, 2) = -6.145467166049122, (259, 0) = -6.145467166049122, (259, 1) = 1.0516874987925617, (259, 2) = -3.5214526768512933, (260, 0) = -3.5214526768512933, (260, 1) = -6.18737436123529, (260, 2) = 1.068212518269731, (261, 0) = 1.068212518269731, (261, 1) = -3.6240653709457127, (261, 2) = -6.233388843487111, (262, 0) = -6.233388843487111, (262, 1) = 1.0847375377469002, (262, 2) = -3.72752226661241, (263, 0) = -3.72752226661241, (263, 1) = -6.2894481999677305, (263, 2) = 1.1012625572240695, (264, 0) = 1.1012625572240695, (264, 1) = -3.831984611194717, (264, 2) = -6.35504011580025, (265, 0) = -6.35504011580025, (265, 1) = 1.1177875767012386, (265, 2) = -3.937605094399068, (266, 0) = -3.937605094399068, (266, 1) = -6.429542175230008, (266, 2) = 1.1327121854674953, (267, 0) = 1.1327121854674953, (267, 1) = -4.034110365515379, (267, 2) = -6.50387957464193, (268, 0) = -6.50387957464193, (268, 1) = 1.1476367942337518, (268, 2) = -4.131771211438475, (269, 0) = -4.131771211438475, (269, 1) = -6.584270563291763, (269, 2) = 1.1625614030000082, (270, 0) = 1.1625614030000082, (270, 1) = -4.230672490602925, (270, 2) = -6.670018790922218, (271, 0) = -6.670018790922218, (271, 1) = 1.1774860117662649, (271, 2) = -4.330888534828567, (272, 0) = -4.330888534828567, (272, 1) = -6.7603495646703795, (272, 2) = 1.1936477269716326, (273, 0) = 1.1936477269716326, (273, 1) = -4.440966559558433, (273, 2) = -6.862348826165057, (274, 0) = -6.862348826165057, (274, 1) = 1.2098094421770005, (274, 2) = -4.552720690150453, (275, 0) = -4.552720690150453, (275, 1) = -6.967541985967905, (275, 2) = 1.2259711573823684, (276, 0) = 1.2259711573823684, (276, 1) = -4.666191950100036, (276, 2) = -7.074655934156521, (277, 0) = -7.074655934156521, (277, 1) = 1.242132872587736, (277, 2) = -4.781400570679881, (278, 0) = -4.781400570679881, (278, 1) = -7.18233461744902, (278, 2) = 1.2575996660278732, (279, 0) = 1.2575996660278732, (279, 1) = -4.893280926883987, (279, 2) = -7.2845944262420055, (280, 0) = -7.2845944262420055, (280, 1) = 1.2730664594680103, (280, 2) = -5.006728416544206, (281, 0) = -5.006728416544206, (281, 1) = -7.384758262859309, (281, 2) = 1.2885332529081472, (282, 0) = 1.2885332529081472, (282, 1) = -5.12170037529636, (282, 2) = -7.481502210435845, (283, 0) = -7.481502210435845, (283, 1) = 1.3040000463482844, (283, 2) = -5.23813366707745, (284, 0) = -5.23813366707745, (284, 1) = -7.573502256294422, (284, 2) = 1.3175524614853278, (285, 0) = 1.3175524614853278, (285, 1) = -5.341291453742679, (285, 2) = -7.64918138824489, (286, 0) = -7.64918138824489, (286, 1) = 1.3311048766223712, (286, 2) = -5.445438404246043, (287, 0) = -5.445438404246043, (287, 1) = -7.719351896932769, (287, 2) = 1.3446572917594146, (288, 0) = 1.3446572917594146, (288, 1) = -5.550494509640031, (288, 2) = -7.783200514597136, (289, 0) = -7.783200514597136, (289, 1) = 1.358209706896458, (289, 2) = -5.656368914890545, (290, 0) = -5.656368914890545, (290, 1) = -7.839972253753254, (290, 2) = 1.3711656927897296, (291, 0) = 1.3711656927897296, (291, 1) = -5.758256022236683, (291, 2) = -7.886992926710785, (292, 0) = -7.886992926710785, (292, 1) = 1.3841216786830013, (292, 2) = -5.860703276872757, (293, 0) = -5.860703276872757, (293, 1) = -7.926381353451221, (293, 2) = 1.397077664576273, (294, 0) = 1.397077664576273, (294, 1) = -5.963609102945517, (294, 2) = -7.95768614546526, (295, 0) = -7.95768614546526, (295, 1) = 1.4100336504695445, (295, 2) = -6.066866345242355, (296, 0) = -6.066866345242355, (296, 1) = -7.98054567337271, (296, 2) = 1.4245137516977953, (297, 0) = 1.4245137516977953, (297, 1) = -6.182548945165972, (297, 2) = -7.9957733199665215, (298, 0) = -7.9957733199665215, (298, 1) = 1.438993852926046, (298, 2) = -6.29837149714626, (299, 0) = -6.29837149714626, (299, 1) = -7.99989482190583, (299, 2) = 1.4534739541542967, (300, 0) = 1.4534739541542967, (300, 1) = -6.414173219862737, (300, 2) = -7.992849646868704, (301, 0) = -7.992849646868704, (301, 1) = 1.4679540553825474, (301, 2) = -6.529793015653621, (302, 0) = -6.529793015653621, (302, 1) = -7.9747407978662626, (302, 2) = 1.4803678144102401, (303, 0) = 1.4803678144102401, (303, 1) = -6.62864778418909, (303, 2) = -7.950604357708325, (304, 0) = -7.950604357708325, (304, 1) = 1.4927815734379328, (304, 2) = -6.727154843605928, (305, 0) = -6.727154843605928, (305, 1) = -7.918790344363261, (305, 2) = 1.5051953324656255, (306, 0) = 1.5051953324656255, (306, 1) = -6.82522116397168, (306, 2) = -7.879637001163829, (307, 0) = -7.879637001163829, (307, 1) = 1.5176090914933182, (307, 2) = -6.922758125531021, (308, 0) = -6.922758125531021, (308, 1) = -7.8335534438071175, (308, 2) = 1.530022850521011, (309, 0) = 1.530022850521011, (309, 1) = -7.0196822695594365, (309, 2) = -7.781015644907291, (310, 0) = -7.781015644907291, (310, 1) = 1.5424366095487037, (310, 2) = -7.115916851509591, (311, 0) = -7.115916851509591, (311, 1) = -7.722561553038059, (311, 2) = 1.5548503685763964, (312, 0) = 1.5548503685763964, (312, 1) = -7.211392140334896, (312, 2) = -7.658773980661597, (313, 0) = -7.658773980661597, (313, 1) = 1.567264127604089, (313, 2) = -7.306045751402252, (314, 0) = -7.306045751402252, (314, 1) = -7.590272511643448, (314, 2) = 1.5793990333053147, (315, 0) = 1.5793990333053147, (315, 1) = -7.3977264569089165, (315, 2) = -7.519378848009207, (316, 0) = -7.519378848009207, (316, 1) = 1.5915339390065406, (316, 2) = -7.488526501061866, (317, 0) = -7.488526501061866, (317, 1) = -7.445235011410901, (317, 2) = 1.6036688447077663, (318, 0) = 1.6036688447077663, (318, 1) = -7.578410328102267, (318, 2) = -7.3684805084705625, (319, 0) = -7.3684805084705625, (319, 1) = 1.615803750408992, (319, 2) = -7.667350154625343, (320, 0) = -7.667350154625343, (320, 1) = -7.289756541665078, (320, 2) = 1.6283868929550145, (321, 0) = 1.6283868929550145, (321, 1) = -7.7585569657134545, (321, 2) = -7.206728618668496, (322, 0) = -7.206728618668496, (322, 1) = 1.640970035501037, (322, 2) = -7.848713765597275, (323, 0) = -7.848713765597275, (323, 1) = -7.1229753096230075, (323, 2) = 1.6535531780470594, (324, 0) = 1.6535531780470594, (324, 1) = -7.937815663561867, (324, 2) = -7.039181191688683, (325, 0) = -7.039181191688683, (325, 1) = 1.666136320593082, (325, 2) = -8.025866331941751, (326, 0) = -8.025866331941751, (326, 1) = -6.956006271189805, (326, 2) = 1.6802477380384768, (327, 0) = 1.6802477380384768, (327, 1) = -8.123375716747969, (327, 2) = -6.864248882082933, (328, 0) = -6.864248882082933, (328, 1) = 1.694359155483872, (328, 2) = -8.219606496017516, (329, 0) = -8.219606496017516, (329, 1) = -6.7749126850359636, (329, 2) = 1.7084705729292669, (330, 0) = 1.7084705729292669, (330, 1) = -8.314598202463435, (330, 2) = -6.688787588929423, (331, 0) = -6.688787588929423, (331, 1) = 1.7225819903746618, (331, 2) = -8.408401396398846, (332, 0) = -8.408401396398846, (332, 1) = -6.606604076354404, (332, 2) = 1.7405093232744457, (333, 0) = 1.7405093232744457, (333, 1) = -8.525952832208548, (333, 2) = -6.50892964475631, (334, 0) = -6.50892964475631, (334, 1) = 1.7584366561742297, (334, 2) = -8.641829549232147, (335, 0) = -8.641829549232147, (335, 1) = -6.419923091108786, (335, 2) = 1.776363989074014, (336, 0) = 1.776363989074014, (336, 1) = -8.756195727499158, (336, 2) = -6.3406531347445405, (337, 0) = -6.3406531347445405, (337, 1) = 1.794291321973798, (337, 2) = -8.869234472100645, (338, 0) = -8.869234472100645, (338, 1) = -6.272031355306602, (338, 2) = 1.812565665292329, (339, 0) = 1.812565665292329, (339, 1) = -8.98330160929397, (339, 2) = -6.213824541264584, (340, 0) = -6.213824541264584, (340, 1) = 1.8308400086108603, (340, 2) = -9.096418661689693, (341, 0) = -9.096418661689693, (341, 1) = -6.168112192316887, (341, 2) = 1.8491143519293913, (342, 0) = 1.8491143519293913, (342, 1) = -9.208817590029327, (342, 2) = -6.135386173441055, (343, 0) = -6.135386173441055, (343, 1) = 1.8673886952479224, (343, 2) = -9.320739337245728, (344, 0) = -9.320739337245728, (344, 1) = -6.1159908493259785, (344, 2) = 1.8836139127714733, (345, 0) = 1.8836139127714733, (345, 1) = -9.419910571849261, (345, 2) = -6.110106575550155, (346, 0) = -6.110106575550155, (346, 1) = 1.8998391302950242, (346, 2) = -9.519073412923351, (347, 0) = -9.519073412923351, (347, 1) = -6.114938890634537, (347, 2) = 1.916064347818575, (348, 0) = 1.916064347818575, (348, 1) = -9.618400961543509, (348, 2) = -6.130449035567309, (349, 0) = -6.130449035567309, (349, 1) = 1.932289565342126, (349, 2) = -9.718065718082821, (350, 0) = -9.718065718082821, (350, 1) = -6.156509785008993, (350, 2) = 1.9485147828656768, (351, 0) = 1.9485147828656768, (351, 1) = -9.818238046858305, (351, 2) = -6.192905134590962, (352, 0) = -6.192905134590962, (352, 1) = 1.9647400003892277, (352, 2) = -9.919082914447614, (353, 0) = -9.919082914447614, (353, 1) = -6.23933190180948, (353, 2) = 1.9809652179127786, (354, 0) = 1.9809652179127786, (354, 1) = -10.02075938213676, (354, 2) = -6.295391434560397, (355, 0) = -6.295391434560397, (355, 1) = 1.9971904354363295, (355, 2) = -10.123419988610138, (356, 0) = -10.123419988610138, (356, 1) = -6.3605860009845445, (356, 2) = 2.0122547546811353, (357, 0) = 2.0122547546811353, (357, 1) = -10.219742660369977, (357, 2) = -6.428773792019609, (358, 0) = -6.428773792019609, (358, 1) = 2.0273190739259412, (358, 2) = -10.317144669404417, (359, 0) = -10.317144669404417, (359, 1) = -6.503766534351719, (359, 2) = 2.042383393170747, (360, 0) = 2.042383393170747, (360, 1) = -10.415723422185673, (360, 2) = -6.584928186752666, (361, 0) = -6.584928186752666, (361, 1) = 2.057447712415553, (361, 2) = -10.51556662056094, (362, 0) = -10.51556662056094, (362, 1) = -6.671541364189472, (362, 2) = 2.0729836943538493, (363, 0) = 2.0729836943538493, (363, 1) = -10.6199414980461, (363, 2) = -6.765732491350011, (364, 0) = -6.765732491350011, (364, 1) = 2.0885196762921456, (364, 2) = -10.72581213640605, (365, 0) = -10.72581213640605, (365, 1) = -6.863909298632995, (365, 2) = 2.104055658230442, (366, 0) = 2.104055658230442, (366, 1) = -10.83323201301611, (366, 2) = -6.965022314131712, (367, 0) = -6.965022314131712, (367, 1) = 2.1195916401687382, (367, 2) = -10.942238112071177, (368, 0) = -10.942238112071177, (368, 1) = -7.067941729306011, (368, 2) = 2.1356200918793893, (369, 0) = 2.1356200918793893, (369, 1) = -11.056382280193466, (369, 2) = -7.174742802070845, (370, 0) = -7.174742802070845, (370, 1) = 2.1516485435900403, (370, 2) = -11.17223421621874, (371, 0) = -11.17223421621874, (371, 1) = -7.28078892152774, (371, 2) = 2.167676995300692, (372, 0) = 2.167676995300692, (372, 1) = -11.289770165930324, (372, 2) = -7.3846381291334335, (373, 0) = -7.3846381291334335, (373, 1) = 2.183705447011343, (373, 2) = -11.408943188698236, (374, 0) = -11.408943188698236, (374, 1) = -7.484822488274335, (374, 2) = 2.1977994595206063, (375, 0) = 2.1977994595206063, (375, 1) = -11.515030798353806, (375, 2) = -7.5687140069909145, (376, 0) = -7.5687140069909145, (376, 1) = 2.2118934720298697, (376, 2) = -11.622266785736564, (377, 0) = -11.622266785736564, (377, 1) = -7.6476296303697175, (377, 2) = 2.225987484539133, (378, 0) = 2.225987484539133, (378, 1) = -11.73057438494886, (378, 2) = -7.720607499434741, (379, 0) = -7.720607499434741, (379, 1) = 2.2400814970483967, (379, 2) = -11.839863431613342, (380, 0) = -11.839863431613342, (380, 1) = -7.786736807993239, (380, 2) = 2.2530191770508368, (381, 0) = 2.2530191770508368, (381, 1) = -11.940962008463423, (381, 2) = -7.840681887557638, (382, 0) = -7.840681887557638, (382, 1) = 2.2659568570532773, (382, 2) = -12.042713133802357, (383, 0) = -12.042713133802357, (383, 1) = -7.887537945013254, (383, 2) = 2.2788945370557174, (384, 0) = 2.2788945370557174, (384, 1) = -12.145021887466292, (384, 2) = -7.926777339723823, (385, 0) = -7.926777339723823, (385, 1) = 2.2918322170581575, (385, 2) = -12.247786763155405, (386, 0) = -12.247786763155405, (386, 1) = -7.957953413208937, (386, 2) = 2.3056234842427945, (387, 0) = 2.3056234842427945, (387, 1) = -12.357713331592155, (387, 2) = -7.981902222022512, (388, 0) = -7.981902222022512, (388, 1) = 2.3194147514274315, (388, 2) = -12.467902034211054, (389, 0) = -12.467902034211054, (389, 1) = -7.995960111327916, (389, 2) = 2.3332060186120684, (390, 0) = 2.3332060186120684, (390, 1) = -12.578215539807132, (390, 2) = -7.999939560775096, (391, 0) = -7.999939560775096, (391, 1) = 2.3469972857967054, (391, 2) = -12.688514367227016, (392, 0) = -12.688514367227016, (392, 1) = -7.993787347525169, (392, 2) = 2.359402959372401, (393, 0) = 2.359402959372401, (393, 1) = -12.787603382739077, (393, 2) = -7.979661303038077, (394, 0) = -7.979661303038077, (394, 1) = 2.3718086329480963, (394, 2) = -12.886467324694442, (395, 0) = -12.886467324694442, (395, 1) = -7.957555674812111, (395, 2) = 2.3842143065237917, (396, 0) = 2.3842143065237917, (396, 1) = -12.985008870520248, (396, 2) = -7.927707958003737, (397, 0) = -7.927707958003737, (397, 1) = 2.396619980099487, (397, 2) = -13.083133877507114, (398, 0) = -13.083133877507114, (398, 1) = -7.890434246304209, (398, 2) = 2.4090256536751826, (399, 0) = 2.4090256536751826, (399, 1) = -13.180752219256489, (399, 2) = -7.84612581424277, (400, 0) = -7.84612581424277, (400, 1) = 2.421431327250878, (400, 2) = -13.277779528433381, (401, 0) = -13.277779528433381, (401, 1) = -7.795245906248259, (401, 2) = 2.4338370008265735, (402, 0) = 2.4338370008265735, (402, 1) = -13.374137625114399, (402, 2) = -7.738313708286215, (403, 0) = -7.738313708286215, (403, 1) = 2.446242674402269, (403, 2) = -13.469754915100173, (404, 0) = -13.469754915100173, (404, 1) = -7.675896657687216, (404, 2) = 2.458424448962848, (405, 0) = 2.458424448962848, (405, 1) = -13.562863195226848, (405, 2) = -7.609859896422831, (406, 0) = -7.609859896422831, (406, 1) = 2.4706062235234274, (406, 2) = -13.655141481313487, (407, 0) = -13.655141481313487, (407, 1) = -7.539736498209838, (407, 2) = 2.482787998084006, (408, 0) = 2.482787998084006, (408, 1) = -13.746543864670938, (408, 2) = -7.46615761249862, (409, 0) = -7.46615761249862, (409, 1) = 2.4949697726445854, (409, 2) = -13.837032163074287, (410, 0) = -13.837032163074287, (410, 1) = -7.389765726363671, (410, 2) = 2.507315014983515, (411, 0) = 2.507315014983515, (411, 1) = -13.927771088840956, (411, 2) = -7.31014521561439, (412, 0) = -7.31014521561439, (412, 1) = 2.519660257322445, (412, 2) = -14.017516879432481, (413, 0) = -14.017516879432481, (413, 1) = -7.228981078665224, (413, 2) = 2.5320054996613752, (414, 0) = 2.5320054996613752, (414, 1) = -14.106254547979141, (414, 2) = -7.146939835082072, (415, 0) = -7.146939835082072, (415, 1) = 2.544350742000305, (415, 2) = -14.193977303655693, (416, 0) = -14.193977303655693, (416, 1) = -7.064671737482669, (416, 2) = 2.5578087367873072, (417, 0) = 2.5578087367873072, (417, 1) = -14.288452430288125, (417, 2) = -6.975470467055684, (418, 0) = -6.975470467055684, (418, 1) = 2.571266731574309, (418, 2) = -14.381734824065543, (419, 0) = -14.381734824065543, (419, 1) = -6.88753582106981, (419, 2) = 2.5847247263613116, (420, 0) = 2.5847247263613116, (420, 1) = -14.473846389253655, (420, 2) = -6.801611628681625, (421, 0) = -6.801611628681625, (421, 1) = 2.598182721148314, (421, 2) = -14.564818946385815, (422, 0) = -14.564818946385815, (422, 1) = -6.718396049823892, (422, 2) = 2.6148866347095954, (423, 0) = 2.6148866347095954, (423, 1) = -14.67621154732944, (423, 2) = -6.619851755145491, (424, 0) = -6.619851755145491, (424, 1) = 2.631590548270877, (424, 2) = -14.7860095280653, (425, 0) = -14.7860095280653, (425, 1) = -6.527618198022343, (425, 2) = 2.6482944618321587, (426, 0) = 2.6482944618321587, (426, 1) = -14.894326245028939, (426, 2) = -6.442711495228625, (427, 0) = -6.442711495228625, (427, 1) = 2.66499837539344, (427, 2) = -15.001291813213154, (428, 0) = -15.001291813213154, (428, 1) = -6.366026422966669, (428, 2) = 2.6846892987856865, (429, 0) = 2.6846892987856865, (429, 1) = -15.125848009826301, (429, 2) = -6.287234881637901, (430, 0) = -6.287234881637901, (430, 1) = 2.7043802221779334, (430, 2) = -15.248985111085993, (431, 0) = -15.248985111085993, (431, 1) = -6.221999380743594, (431, 2) = 2.7240711455701803, (432, 0) = 2.7240711455701803, (432, 1) = -15.370977101643156, (432, 2) = -6.171164749166398, (433, 0) = -6.171164749166398, (433, 1) = 2.7437620689624267, (433, 2) = -15.492114501745428, (434, 0) = -15.492114501745428, (434, 1) = -6.13536889306736, (434, 2) = 2.7628796281606642, (435, 0) = 2.7628796281606642, (435, 1) = -15.609193979426642, (435, 2) = -6.115417185639256, (436, 0) = -6.115417185639256, (436, 1) = 2.781997187358902, (436, 2) = -15.726033746752263, (437, 0) = -15.726033746752263, (437, 1) = -6.110279993313302, (437, 2) = 2.8011147465571393, (438, 0) = 2.8011147465571393, (438, 1) = -15.842916528434358, (438, 2) = -6.120015951469447, (439, 0) = -6.120015951469447, (439, 1) = 2.820232305755377, (439, 2) = -15.960126234838878, (440, 0) = -15.960126234838878, (440, 1) = -6.144513572562797, (440, 2) = 2.838283196951421, (441, 0) = 2.838283196951421, (441, 1) = -16.07135003736716, (441, 2) = -6.180942318337621}, 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] = \`&vartheta;\`(tau), Y[2] = diff(\`&vartheta;\`(tau),tau)]`; YP[2] := -6.666666666*sin(Y[1])-66.66666666*cos(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478)-66.66666666*sin(Y[1])^2*FAK(Y[1], .7227342478, X)*(Y[1]-.7227342478); YP[1] := Y[2]; 0 end proc, -1, 0, 0, 0, 0])  ] )), ( 4 ) = (3)  ] ); _y0 := Array(0..2, {(1) = 0., (2) = 0.}); _vmap := array( 1 .. 2, [( 1 ) = (1), ( 2 ) = (2)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 10 and 10 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 10 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 10 and 10 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 10 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-10 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-10; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 10 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _src = 0 and 10 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?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 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-10, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?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 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-10, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; _dat[4][26] := _EnvDSNumericSaveDigits; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [tau, `&vartheta;`(tau), diff(`&vartheta;`(tau), tau)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(plottools:-transform(proc (x, y) options operator, arrow; [x, FAK(y, `&vartheta;l`, x)] end proc))(plots:-odeplot(ld, [tau, `&vartheta;`(tau)], refine = 1));

P := plots:-odeplot(ld, [tau, `&vartheta;`(tau)], refine = 1):

 

 

Download odeplot_actest.mw

You can find older Posts and Questions on this topic.

For example,

   Gridlines in 3d space

   gridlines

Here are various versions, with the rest in black (rather than just default blue for output), or background effects as in the original question, etc.

Mix and match as wanted.

note: In the actual Maple GUI the 2nd and 3rd versions below render properly with the 5's having white foreground as well as the red background. Mapleprimes' backend doesn't render them properly.

a:=[1,3,4,5,3,4,9,4,5,3,9,2,3,4,2,5,21,32,22,12,15,3,2,5,4]:

 

map(x->Typesetting:-mn(sprintf("%a",x),mathcolor=`if`(x=5,"red",black)),a);

[Typesetting:-mn("1", mathcolor = black), Typesetting:-mn("3", mathcolor = black), Typesetting:-mn("4", mathcolor = black), Typesetting:-mn("5", mathcolor = "red"), Typesetting:-mn("3", mathcolor = black), Typesetting:-mn("4", mathcolor = black), Typesetting:-mn("9", mathcolor = black), Typesetting:-mn("4", mathcolor = black), Typesetting:-mn("5", mathcolor = "red"), Typesetting:-mn("3", mathcolor = black), Typesetting:-mn("9", mathcolor = black), Typesetting:-mn("2", mathcolor = black), Typesetting:-mn("3", mathcolor = black), Typesetting:-mn("4", mathcolor = black), Typesetting:-mn("2", mathcolor = black), Typesetting:-mn("5", mathcolor = "red"), Typesetting:-mn("21", mathcolor = black), Typesetting:-mn("32", mathcolor = black), Typesetting:-mn("22", mathcolor = black), Typesetting:-mn("12", mathcolor = black), Typesetting:-mn("15", mathcolor = black), Typesetting:-mn("3", mathcolor = black), Typesetting:-mn("2", mathcolor = black), Typesetting:-mn("5", mathcolor = "red"), Typesetting:-mn("4", mathcolor = black)]

 

 

map(x->Typesetting:-mn(sprintf("%a", x),
                       `if`(x = 5,[mathbackground="red",mathcolor="white"][],
                            NULL)), a);

[Typesetting:-mn("1"), Typesetting:-mn("3"), Typesetting:-mn("4"), Typesetting:-mn("5", mathbackground = "red", mathcolor = "white"), Typesetting:-mn("3"), Typesetting:-mn("4"), Typesetting:-mn("9"), Typesetting:-mn("4"), Typesetting:-mn("5", mathbackground = "red", mathcolor = "white"), Typesetting:-mn("3"), Typesetting:-mn("9"), Typesetting:-mn("2"), Typesetting:-mn("3"), Typesetting:-mn("4"), Typesetting:-mn("2"), Typesetting:-mn("5", mathbackground = "red", mathcolor = "white"), Typesetting:-mn("21"), Typesetting:-mn("32"), Typesetting:-mn("22"), Typesetting:-mn("12"), Typesetting:-mn("15"), Typesetting:-mn("3"), Typesetting:-mn("2"), Typesetting:-mn("5", mathbackground = "red", mathcolor = "white"), Typesetting:-mn("4")]

 

map(x->Typesetting:-mn(sprintf("%a", x),
                       `if`(x = 5,[mathbackground="red",mathcolor="white"][],
                            mathcolor="black")), a);

[Typesetting:-mn("1", mathcolor = "black"), Typesetting:-mn("3", mathcolor = "black"), Typesetting:-mn("4", mathcolor = "black"), Typesetting:-mn("5", mathbackground = "red", mathcolor = "white"), Typesetting:-mn("3", mathcolor = "black"), Typesetting:-mn("4", mathcolor = "black"), Typesetting:-mn("9", mathcolor = "black"), Typesetting:-mn("4", mathcolor = "black"), Typesetting:-mn("5", mathbackground = "red", mathcolor = "white"), Typesetting:-mn("3", mathcolor = "black"), Typesetting:-mn("9", mathcolor = "black"), Typesetting:-mn("2", mathcolor = "black"), Typesetting:-mn("3", mathcolor = "black"), Typesetting:-mn("4", mathcolor = "black"), Typesetting:-mn("2", mathcolor = "black"), Typesetting:-mn("5", mathbackground = "red", mathcolor = "white"), Typesetting:-mn("21", mathcolor = "black"), Typesetting:-mn("32", mathcolor = "black"), Typesetting:-mn("22", mathcolor = "black"), Typesetting:-mn("12", mathcolor = "black"), Typesetting:-mn("15", mathcolor = "black"), Typesetting:-mn("3", mathcolor = "black"), Typesetting:-mn("2", mathcolor = "black"), Typesetting:-mn("5", mathbackground = "red", mathcolor = "white"), Typesetting:-mn("4", mathcolor = "black")]

 

Download mathcoloring.mw

You can scale the frames to a common x-y range, so that the conventional  animation (from plots:-animate, or collection displayed with the insequence option) renders them more like the Explore frames.

FractalesAnim_ac.mw

For example, using procedure PP to scale all the frames to [0..1]x[0..1],

PP := proc(P)
  local data,xmin,xmax,ymin,ymax;
  data := indets(P, Array)[1];
  xmin,xmax := [min,max](data[..,1])[];
  ymin,ymax := [min,max](data[..,2])[];
  plottools:-transform((x,y)->[(x-xmin)/(xmax-xmin),
                               (y-ymin)/(ymax-ymin)])(P);
end proc:

plots:-display(
  seq(PP(Fractals:-LSystem:-LSystemExamples:-PlotExample(
           Fractals:-LSystem:-LSystemExamples:-KochCurve,a))$5,
      a=1..5),insequence);

plots:-display(
  seq(PP(Fractals:-LSystem:-LSystemExamples:-PlotExample(
           Fractals:-LSystem:-LSystemExamples:-Carpet,a))$5,
      a=1..4),insequence);

plots:-display(
  seq(PP(Fractals:-LSystem:-LSystemExamples:-PlotExample(
           Fractals:-LSystem:-LSystemExamples:-Rings,a))$5,
      a=1..4),insequence);

plots:-display(
  seq(PP(Fractals:-LSystem:-LSystemExamples:-PlotExample(
           Fractals:-LSystem:-LSystemExamples:-Seaweed,a))$5,
      a=1..4),insequence);

plots:-display(
  seq(PP(Fractals:-LSystem:-LSystemExamples:-PlotExample(
           Fractals:-LSystem:-LSystemExamples:-GosperCurve,a))$4,
      a=1..5),insequence);

The most likely scenario is that procedure X called searchtext with invalid arguments by mistake -- in other words, a buggy situation overlooked by whoever wrote procedure X.

There are some other variations on the theme (eg. rethrowing errors of a similar sort, but made at a deeper level).

But it's difficult to say for sure, because you have, unhelpfully, omitted the example in which this arose.

It is not clear from you description what you are trying to do. Is it something like either of these?

restart

with(Statistics):

The Vectors X and Y are the same. so plotting Y against X produces a straight line.

plot(`<|>`(X, Y));

Each Vector could be plotted as a separate curve.

I use a different style for each, since they overlap (because the points are the same).

plots:-display(plots:-listplot(Y, color = blue, style = point, symbol = solidcircle), plots:-listplot(X, color = red));

 

Download fitting_ac.mw

The problem is a lack of simplification, such that a verification fails.

As one of some preliminary steps, the free Vector v2 in cartesian coordinates is used to generate a new rooted Vector, and then a coordinate transformation is done. Unfortunately the coordinates of the ensuing extracted root-point of that new rooted Vector is not in simplified form. A later call to verify produces a spurious false result when comparing against the root-point of the rooted Vector v1, and a somewhat unhelpful error message is emitted.

The following commands are some of these internal steps, done under VectorCalculus:-DotProduct for the example at hand. The following rooted Vector vv2 is generated by MapToBasis, executed under PrepareBinaryVectorOp. The verify call is done under ValidateVectorSpaces.

restart;

with(VectorCalculus):

v1:=RootedVector(root=[1,Pi/6,0],[0,0,1],spherical[r,theta,phi]);

Vector(3, {(1) = 0, (2) = 0, (3) = 1})

GetSpace(v1):-GetRootPoint();

Vector(3, {(1) = 1, (2) = (1/6)*Pi, (3) = 0})

v2:=Vector(3, [0,2,1], attributes = [coordinates = cartesian[x,y,z]]);

Vector(3, {(1) = 0, (2) = 2, (3) = 1})

c1:=spherical[r,theta,phi];

spherical[r, theta, phi]

inorigin:=Vector(3, [1,1/6*Pi,0], attributes = [coordinates = spherical[r,theta,phi]]);

Vector(3, {(1) = 1, (2) = (1/6)*Pi, (3) = 0})

vv2 := VectorCalculus:-MapToBasis(v2,c1,inorigin);

Vector(3, {(1) = (1/2)*sqrt(3), (2) = -(1/4)*sqrt(4), (3) = sqrt(4)})

#
# Hmm. This will cause the problem.
#
GetSpace(vv2):-GetRootPoint();

Vector(3, {(1) = 1, (2) = arctan((1/6)*sqrt(4)*sqrt(3)), (3) = 0})

#
# This will do better.
#
simplify(GetSpace(vv2):-GetRootPoint());

Vector(3, {(1) = 1, (2) = (1/6)*Pi, (3) = 0})

#
# Oops.
#
verify(GetSpace(vv2):-GetRootPoint(),
       GetSpace(v1):-GetRootPoint(),
       ':-Vector');

false

#
# OK
#
verify(simplify(GetSpace(vv2):-GetRootPoint()),
       GetSpace(v1):-GetRootPoint(),
       ':-Vector');

true

 

Download VC_dot_simp.mw

I could probably construct a hot-fix patch. I'm trying to figure out whether it would be best to strengthen the call to verify, or simplify the stored root-point when constructed by MapToBasis.

In the other example, the simplified coordinates happen to be produced directly, and the straight verification succeeds.

restart;

with(VectorCalculus):

v1:=RootedVector(root=[1,Pi/4,0],[0,0,1],spherical[r,theta,phi]):

GetSpace(v1):-GetRootPoint();

Vector(3, {(1) = 1, (2) = (1/4)*Pi, (3) = 0})

v2:=Vector(3, [0,2,1], attributes = [coordinates = cartesian[x,y,z]]):

c1:=spherical[r,theta,phi]:

inorigin:=Vector(3, [1,1/4*Pi,0], attributes = [coordinates = spherical[r,theta,phi]]):

vv2 := VectorCalculus:-MapToBasis(v2,c1,inorigin):

GetSpace(vv2):-GetRootPoint();

Vector(3, {(1) = 1, (2) = (1/4)*Pi, (3) = 0})

verify(GetSpace(vv2):-GetRootPoint(),
       GetSpace(v1):-GetRootPoint(),
       ':-Vector');

true

 

Download VC_dot_simp2.mw

It should be clear to you from the error message that the problem is that T is not assigned and doesn't provide a numeric value. It looks like you inadvertantly omitted it.

There are other efficiency problems, but you need to fix the T issue first. You should know the formula to do one iteration by Newton's method. See below.

I am leaving most of the rest as it was, and not addressing the inefficiency of augmenting a set with each new plot, or cleaning up the role of A, and so on.

I also made a change to allow the initial point to be passed (xinit).

restart;

NewtonM:= proc(f, a, b, xinit, N, e)
               local n, tps, x0, E, A, x1, ps, x, j,  pf, pic, T;
               uses plots:  
   n:=0: tps:={}:
   T := unapply(x-'f'(x)/D(f)(x),x);
   x0:=xinit: E:=evalf(abs(f(x0))):
   while ( E>e and n<N ) do
     A[n,1]:=x0;
     A[n,2]:=E;
     x1:=evalf(T(x0));
     E:=abs(f(x1));
     ps:={plot([[x0,0],[x0,f(x0)],[x1,0]],color=black,
                 thickness=2)}:   
     tps:=tps union ps:
     n:=n+1;
     x0:=x1;
   end do:
 
 for j from 0 to n-1 do x[j]=A[j,1],'E'=A[j,2]end do;

 pf:=plot(f,a..b, color=blue):
 print(display(pf, op(tps)));
 return x0;
end proc:

NewtonM(x->x^2-2,1,40,38.0,10,1e-9);

1.414213562

evalf(2^(1/2));

1.414213562

 


 

Download exc_set_3_task_6_ac.mw

If you are using 2D Input mode then the open context-panel (right panel) may be trying to call ifactor on your 123!+1 (after evaluating it). There is a timeout of a few seconds, but for some inputs it might still seem sluggish.

Try closing (collapsing) the right-panel, using the double chevron that looks like << at the right side of the menubar.

note. I will submit a bug report -- at the very least there ought to be a more sensible check on whether to try ifactor, or a way to disable it while keeping the context-panel open.

[edit] The following command will disable the subexpression menu parts that appear at the top of the context-panel, but it will allow the lower context-menu portion to work as usual.
    _EnvSubexpressionMenu := false:

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