tomleslie

6672 Reputation

17 Badges

10 years, 174 days

MaplePrimes Activity


These are answers submitted by tomleslie

there is no way to (directly) access Sage from Maple. (obviously one could probably do it with system calls, but this generally gets very untidy, very quickly)

A better approach may be just to write the necessary code within Maple.

I don't know anything about "Topological indices in Graph theory" - but the definition of the Wiener index, given here

https://en.wikipedia.org/wiki/Wiener_index

seems pretty trivial to implement, using commands from Maple's Graph Theory package. (Not sure about other topological indices - I didn't check)

The attached (correctly!!) computes the Wiener index for the two examples given in the above Wikipedia article

  restart;

  with(GraphTheory):
  with(SpecialGraphs):
  G1:= Graph( {{1,2},{2,3},{3,4}});
  G2:= StarGraph(3);

GRAPHLN(undirected, unweighted, [1, 2, 3, 4], Array(1..4, {(1) = {2}, (2) = {1, 3}, (3) = {2, 4}, (4) = {3}}), `GRAPHLN/table/1`, 0)

 

GRAPHLN(undirected, unweighted, [0, 1, 2, 3], Array(1..4, {(1) = {2, 3, 4}, (2) = {1}, (3) = {1}, (4) = {1}}), `GRAPHLN/table/6`, 0)

(1)

  DrawGraph(G1);
  DrawGraph(G2);

 

 

  wienerIndex:=proc( g::Graph)
                     uses GraphTheory;
                     local v:=NumberOfVertices(g),
                           dists:=AllPairsDistance(g):
                     return add
                            ( add
                              ( dists[i,j],
                                j=i+1..v
                              ),
                              i=1..v
                            ):
         end proc:
  wienerIndex(G1);
  wienerIndex(G2);

10

 

9

(2)

 


Download wiener.mw

because it isn't obvious from your worksheet

I made a couple of animations in the attachment - maybe one of these is what you intend?


 

NULL

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")

 

display([p, p1,p2,p3,p4], insequence=true);

 

display( [seq( plottools:-rotate(p, 0, 0, j), j=0..evalf(2*Pi), evalf(Pi/16))], insequence=true);

 

NULL


 

Download anim.mw

the use of the SolveTools() package can be useful. It appears to be in this case!

See the attached

restart:
expr:=-1/2*ln(u)-1/4*ln(u^2+2)-ln(x)-C[1]:
SolveTools:-Combine(expr);
solve(%, u);

-C[1]-(1/4)*ln(u^2*x^4*(u^2+2))

 

(-x^2+(x^4+exp(-4*C[1]))^(1/2))^(1/2)/x, -(-x^2+(x^4+exp(-4*C[1]))^(1/2))^(1/2)/x, (-x^2-(x^4+exp(-4*C[1]))^(1/2))^(1/2)/x, -(-x^2-(x^4+exp(-4*C[1]))^(1/2))^(1/2)/x

(1)

 

Download STcom.mw

is just to test both solution for _B1 in {0,1} and a range of integers for _Z1 as in


 

restart;
s:=solve(sin(x^2)=1/2,allsolutions);

(1/6)*(24*Pi*_B1+72*Pi*_Z1+6*Pi)^(1/2), -(1/6)*(24*Pi*_B1+72*Pi*_Z1+6*Pi)^(1/2)

(1)

#
# Convert the above solutions to applicable
# functions
#
  tf:=unapply~(sin~(simplify~([s]^~2)), _B1,_Z1);
#
# Evaluate both of these functions for _B1 in {0,1}
# and _Z1 any value from -10..10
#
  seq
  ( seq
    ( tf(i,j)[],
      i=0..1
    ),
    j=-10..10
  );

[proc (_B1, _Z1) options operator, arrow; sin((1/6)*Pi*(4*_B1+12*_Z1+1)) end proc, proc (_B1, _Z1) options operator, arrow; sin((1/6)*Pi*(4*_B1+12*_Z1+1)) end proc]

 

1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2

(2)

 


 

Download testSol.mw

Well - if I fix the syntax errors, and then remove all references to parameters which are never used anywhere in your ODE system, but you want optimal values for (neat trick if you can do it!?), then allow for the fact that the Optimiser might attempt to use parameter values for whihc the dsolve() operation cannot find a meaningful solution etc, etc, etc, I can eventually come up with the attached - whihc does produce an "optimal" solution. However looking at the size of the residual error, I have doubts about how useful/relevant it is???

Anyhow for what it is worth (not much I suspect) see the attached

restart; with(plots); with(Optimization); with(Statistics)

A := 0.346e-1; mu := 0.491e-1
Parameterizing (with respect to l, m, n, rho, k, q, r, u, v, sigma, iota, nu, phi, upsilon, w, x, delta, g) the numerical solution of the model deq
      #Calculating the sum of the square of the errors between the model predictions and experimental data
     #Minimizing the sum of the square of the errors to find the best fit values of " l, m, n ,rho, k, q, r, u , v , sigma, iota, nu, phi,upsilon, w, x, delta, g."

0.346e-1

 

0.491e-1

(1)

times := [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]

[5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]

(2)

C__f := [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 8, 12, 12, 22, 30, 40, 44, 51, 65, 70, 97, 111, 131, 135, 174, 184, 210, 214, 232, 238, 254, 276, 285, 305, 318, 323, 343, 373, 407, 442, 493, 542, 627, 665, 782, 873, 981, 1095, 1182, 1273, 1337, 1532, 1728, 1932, 2170, 2388, 2558, 2802, 2950, 3145, 3526, 3912, 4151, 4399, 4641, 4787, 4971, 5162, 5445, 5621, 5959, 6175, 6401, 6677, 7016, 7261, 7526, 7839, 8068, 8344, 8733, 8915, 9302, 9855, 10162, 10819, 11166, 11516, 11844, 12233, 12486, 12801, 13464, 13873, 14554, 15181, 15682, 16085, 16658, 17148, 17735]

DE1 := diff(B(T), T) = A-l*B(T)*C(T)/(1+sigma*C(T))-nu*m*B(T)*P(T)/(1+iota*P(T))-mu*B(T)-n*B(T)*E(T)/(E(T)+g); DE2 := diff(C(T), T) = l*B(T)*C(T)/(1+sigma*C(T))-q*C(T)-r*C(T)-phi; DE3 := diff(P(T), T) = nu*m*B(T)*P(T)/(1+iota*P(T))-u*P(T)-v*P(T)-upsilon; DE4 := diff(E(T), T) = phi*C(T)+upsilon*P(T)-delta*E(T); DE5 := diff(F(T), T) = q*C(T)+u*P(T)-mu*F(T); ics := B(0) = 19000, C(0) = 160000, P(0) = 17000, E(0) = 10000, F(0) = 15500

res := dsolve({DE1, DE2, DE3, DE4, DE5, ics}, parameters = [l, m, n, q, r, u, v, sigma, iota, nu, phi, upsilon, delta, g], numeric)

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 ] ) _xout := _xin; _pars := [l = l, m = m, n = n, q = q, r = r, u = u, v = v, sigma = sigma, iota = iota, nu = nu, phi = phi, upsilon = upsilon, delta = delta, g = g]; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 5, (2) = 5, (3) = 0, (4) = 0, (5) = 14, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 0, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = .0, (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..19, {(1) = 19000., (2) = 160000., (3) = 10000., (4) = 15500., (5) = 17000., (6) = Float(undefined), (7) = Float(undefined), (8) = Float(undefined), (9) = Float(undefined), (10) = Float(undefined), (11) = Float(undefined), (12) = Float(undefined), (13) = Float(undefined), (14) = Float(undefined), (15) = Float(undefined), (16) = Float(undefined), (17) = Float(undefined), (18) = Float(undefined), (19) = Float(undefined)})), ( 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..5, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0}, datatype = float[8], order = C_order), Array(1..5, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0}, datatype = float[8], order = C_order), Array(1..5, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0}, datatype = integer[8]), Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = B(T), Y[2] = C(T), Y[3] = E(T), Y[4] = F(T), Y[5] = P(T)]`; YP[1] := 0.346e-1-Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-0.491e-1*Y[1]-Y[8]*Y[1]*Y[3]/(Y[3]+Y[19]); YP[2] := Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[9]*Y[2]-Y[10]*Y[2]-Y[16]; YP[3] := Y[2]*Y[16]-Y[3]*Y[18]+Y[5]*Y[17]; YP[4] := Y[9]*Y[2]+Y[11]*Y[5]-0.491e-1*Y[4]; YP[5] := Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-Y[11]*Y[5]-Y[12]*Y[5]-Y[17]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = B(T), Y[2] = C(T), Y[3] = E(T), Y[4] = F(T), Y[5] = P(T)]`; YP[1] := 0.346e-1-Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-0.491e-1*Y[1]-Y[8]*Y[1]*Y[3]/(Y[3]+Y[19]); YP[2] := Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[9]*Y[2]-Y[10]*Y[2]-Y[16]; YP[3] := Y[2]*Y[16]-Y[3]*Y[18]+Y[5]*Y[17]; YP[4] := Y[9]*Y[2]+Y[11]*Y[5]-0.491e-1*Y[4]; YP[5] := Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-Y[11]*Y[5]-Y[12]*Y[5]-Y[17]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] ))  ] ); _y0 := Array(0..19, {(1) = 0., (2) = 19000., (3) = 160000., (4) = 10000., (5) = 15500., (6) = 17000., (7) = undefined, (8) = undefined, (9) = undefined, (10) = undefined, (11) = undefined, (12) = undefined, (13) = undefined, (14) = undefined, (15) = undefined, (16) = undefined, (17) = undefined, (18) = undefined, (19) = undefined}); _vmap := array( 1 .. 5, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4), ( 5 ) = (5)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [T, B(T), C(T), E(T), F(T), P(T)], (4) = [l = l, m = m, n = n, q = q, r = r, u = u, v = v, sigma = sigma, iota = iota, nu = nu, phi = phi, upsilon = upsilon, delta = delta, g = g]}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(3)

sse:=proc( l, m, n , q, r, u , v , sigma, iota, nu, phi,upsilon, delta, g);
     local testRes:

    res(parameters=[ l, m, n ,q, r, u , v , sigma, iota, nu, phi,upsilon, delta, g]);

    try   testRes:=add( (C__f[i]-rhs(res(times[1])[3]))^2, i=1..numelems(times))
    catch "cannot evaluate the solution":
          testRes:=10^12;
    end try;
    return testRes;
  end proc:

optPars:=Minimize( 'sse'( l, m, n, q, r, u, v, sigma, iota, nu, phi,upsilon, delta, g),
                   initialpoint={ l=0.05, m=0.02, n=0.017, q=0.004,
                                  r=0.098710, u=0.0100, v=0.08543,
                                  sigma=0.0349, iota=0.0032, nu=0.0014,
                                  phi=0.931, upsilon=0.0019, delta=0.01,
                                  g= 0.3
                                },
                   assume=nonnegative,
                   optimalitytolerance=0.00001
                 );

[78067722.2126978040, [delta = HFloat(0.0), g = HFloat(0.3000006496784401), iota = HFloat(0.0), l = HFloat(0.05574983967997584), m = HFloat(0.027015695985550744), n = HFloat(0.029159283217039977), nu = HFloat(3.9010512253698812), phi = HFloat(0.9316734694230215), q = HFloat(4.244163520259199e-4), r = HFloat(0.8781371378666069), sigma = HFloat(0.11661527098829708), u = HFloat(5.712096063240794e-7), upsilon = HFloat(1.1044840588712213e-4), v = HFloat(0.0854299992060102)]]

(4)

 

Download cvodeOpt.mw

 

and I ended up having to do a "manual" installation.

The details of this process are given in this thread

https://www.mapleprimes.com/questions/229832-Phyysics-Updates-Installation

You will have to read quite a lot of the thread to get to the part which makes everything "work"

  1. It really ought to be "easier" to do this
  2. the 'help' pages for the 'events' option definiely could be clearer

BTW I admire Rouben's response - but iti took me a while to figure out how it was being done!

Anyhow, I get the same answers, in a less subtle (but more understandable?) way in the attached

  restart;
  ode2 := diff(varphi(t), t, t) + omega^2*sin(varphi(t));
#
# Return solution module for ODE
#
  ld2 := dsolve( [ eval(ode2, omega = 2*Pi),
                   varphi(0) = evalf(10/180*Pi),
                   D(varphi)(0) = 0
                 ],
                 events=[[diff(varphi(t), t), halt]],
                 numeric,
                 abserr=1e-12,
                 relerr=1e-9
               ):
#
# Find the points where diff(varphi(t), t) = 0,
# up to the end point specified by endPoint.
#
  endPoint:=6:
  ans:=Array():
#
# Turn warnings off becuase they are just boring
#
  interface(warnlevel=0):
  for j from 1 do
        sol:=ld2(endPoint);
        if   rhs(sol[1])=endPoint
        then break;
        else ans(j):=sol[1];
             ld2(eventclear);
        fi;
  od:
#
# Turn warnings back on
#
  interface(warnlevel=3):
#
# Change default tablesize so all results will display
#
  interface(rtablesize=j):
  V:=convert(ans, Vector[column]);
  interface(rtablesize=10):

ode2 := diff(`&varphi;`(t), t, t)+omega^2*sin(`&varphi;`(t))

 

Vector[column](%id = 18446744074390079118)

(1)

 

Download events.mw

No-one is going to actually run this code for debug purposes, since it usses numerous system calls to external software, and

  1. Users (such as me) may not have the required external software installed
  2. Security issue: I  generally don't run MAple code with from this site which contains system calls - one never knows what might happen to my OS!

This means that any debug which I do is just based on reading your code - not executing/debugging it. So here goes

#################################################################################################

The region of code in https://gricad-gitlab.univ-grenoble-alpes.fr/magronv/RealCertify/-/blob/master/multivsos/multivsos.mm which is causing the problem, is shown below. These are lines 256-272 approximately, where I have highlighted line 206 - the one referenced in your Error message Error, (in sos2sdp) invalid arguments for searchtext |multivsos/multivsos.mm:260

  fd := fopen("multivsos/out.dat-s",READ,TEXT):
  nl := "":  yMatText := "yMat := ":  
  while true do     
    nl := readline(fd):
    if SearchText("objValPrimal",nl) = 1 then objValPrimalText := StringTools[RegSubs]("objValPrimal = (.*)" = "\\1",nl): break: fi:
  od:
  while true do     
    nl := readline(fd):
    if SearchText("yMat",nl) = 1 then break: fi:
  od:
  while true do
    nl := readline(fd):
    if SearchText("main loop",nl) > 0 then break: fi:
    yMatText := cat(yMatText,nl):
  od:
  fclose(fd):
 yMatText := StringTools[SubstituteAll](yMatText, "{", "["): yMatText := StringTools[SubstituteAll](yMatText, "}", "]"): yMatText := StringTools[SubstituteAll](yMatText, "][", "],["):

Just from reading the above code is seems odd that some of the commands from the StringTools package, eg

StringTools[SubstituteAll], StringTools[RegSubs]

are given in long form, ie prepended with the package name. On the other hand the case-sensitive 'search' command, ie SearchText(), is not prepended with the package name.

I can find no evidence that the StringTools package has been loaded elsewhere in the original worksheet - so I'd be tempted to replace all occurrences of 'SearchText()' in the above section of code with 'StringTools[SearchgText]()'  just to see if itt makes any difference.

,

 

 

 

although you should b ware that the if you are accustomed to "serious industry-standard" simulators (eg Spectre, nanoSim, Hspice, whatever) then the capabilites of Syrup are very very limited.

The attached shows an 'ac' and a 'transient' step response for a simple low pass filter

  restart;
  with(Syrup):
#
# A simple low pass circuit
#
  LPckt:= "
            V 1 0 1
            R1 1 2 1000
            C 2 0 1e-06
          .end":

#
# Compute and plot the 'ac' response
#
  p1:=plots:-semilogplot( 20*log10(rhs(Solve(LPckt, 'ac')[2])),
                          s=1..1e3,
                          axes=boxed
                        ):
  p2:=plot(-3, s=1..1e3, color=blue):
  plots:-display([p1,p2]);

 

#
# Compute and plot the transient (ie step) response
#
  plot( rhs(dsolve(Solve(LPckt, 'tran'))), t=0..1e-02);;

 

 

Download syrTest.mw

but if you just want an "alternative", how about the attached

  restart;
  expr         := A*B*C;
  first_part   := op(1,expr);
  second_part  := `*`(op([2..-1], expr));

A*B*C

 

A

 

B*C

(1)

 


 

Download parts.mw

Please ignore my earlier answer - it is incorrect.

I must have been dreaming about this problem, because I woke up this morning determined to have another look

In fact it should always be possible to take the VectorCalculus:-DotProduct() of a free vector expressed in cartesian coordinates and a rootedVector expressed in spherical coordinates.

However it seems that if the polar angle of the rooted vector is anything other than Pi/4, Pi/2, 3*Pi/4, then the command fails, with the somewhat(?) puzzling error message

Error, (in VectorCalculus:-DotProduct) cannot combine two rooted vectors with different points of origin

even when one of the vectors is definitely "free".

Either I'm missing something or this is a bug. See the attached

  restart;
  alias(VC=VectorCalculus):

#
# Define free vector
#
  v1:=VC:-Vector( [0,2,1],
                              cartesian[x,y,z]
                            ):
#
# Define rooted vector in spherical polars. Remember that
# in the VC package, the definitions of polar
# and azimuthal angles are reversed from those which apply
# elsewhere in Maple
#
  v2:=VC:-RootedVector( root=[1,Pi/4,0],
                                    [0,0,1],
                                    spherical[r,theta,phi]
                                  ):
#
# Confirm the types of both vectors, and compute dot product
#
  VC:-IsRootedVector(v1);
  VC:-IsRootedVector(v2);
  VC:-DotProduct(v1,v2);

false

 

true

 

2

(1)

#
# Redefine rooted vector in spherical polars, with a different
# (but equally valid?) polar angle
#
  v2:=VC:-RootedVector( root=[1,3*Pi/2,0],
                                    [0,0,1],
                                    spherical[r,theta,phi]
                                  ):
#
# Confirm the types of both vectors, and compute dot product
#
  VC:-IsRootedVector(v1);
  VC:-IsRootedVector(v2);
  VC:-DotProduct(v1,v2);

false

 

true

 

Error, (in VectorCalculus:-DotProduct) cannot combine two rooted vectors with different points of origin

 

#
# Check which polar angles "work" and which "don't work"
#
# 6*Pi/24, 12*Pi/24, and 18*Pi/24, ie Pi/4, Pi/2, 3*Pi,4
#
# all "work"
#
# All other polar angles checked produce the error message
#
  restart;
  alias(VC=VectorCalculus):
  v1:= VC:-Vector([0,2,1],cartesian[x,y,z]):
  working:=[]:
  nonWorking:=[]:
  for j from 1 to 23 do
      try
            v2:=VC:-RootedVector( root=[1, j*Pi/24, 0],
                                  [0,0,1],
                                  spherical[r,theta,phi]
                                );
            VC:-DotProduct(v1,v2);
            working:=[working[], j];
      catch "cannot combine two rooted vectors":
            nonWorking:=[nonWorking[],j];
      end try;
  od:
  working;
  nonWorking;

[6, 12, 18]

 

[1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23]

(2)

 

Download VCProb.mw

 

 

suggest you consult the help page VectorCalculus:DotProduct(). In particulatr the table on that page whose bullet point heading is

The behavior of the dot product of two Vectors is described by the following table:

This lists the output of the DotProduct() command for all combinations of free vectors, rooted vectors, vector fields and position vectors

 

 

 

 

 

the attached

  restart;

  c1 := 2.2:c2 := 2.3: c3 := 2.4:A := 1.6:
  EQ1:=diff(f(x),x$4)-c1*diff(g(x),x$2)+R*(diff(f(x),x)*diff(f(x),x$2)-f(x)*diff(f(x),x$3))=0;
  EQ2:=diff(g(x),x$2)+c2*(diff(f(x),x$2)-2*g(x))+c3*(-f(x)*diff(g(x),x)+diff(f(x),x)*g(x))=0;
  BC:=D(f)(-1)=0, D(f)(1)=0,f(-1)=1-A,f(1)=1,g(-1)=0,  g(1)=0;

diff(diff(diff(diff(f(x), x), x), x), x)-2.2*(diff(diff(g(x), x), x))+R*((diff(f(x), x))*(diff(diff(f(x), x), x))-f(x)*(diff(diff(diff(f(x), x), x), x))) = 0

 

diff(diff(g(x), x), x)+2.3*(diff(diff(f(x), x), x))-4.6*g(x)-2.4*f(x)*(diff(g(x), x))+2.4*(diff(f(x), x))*g(x) = 0

 

(D(f))(-1) = 0, (D(f))(1) = 0, f(-1) = -.6, f(1) = 1, g(-1) = 0, g(1) = 0

(1)

  interface(rtablesize=25):
  Rvals:= [0, -1, -5, -7,-50]:
  for j from 1 by 1 to numelems(Rvals) do
      sol:= dsolve
            ( [ eval(EQ1, R=Rvals[j]), EQ2, BC],
               numeric,
               output=listprocedure
            );
      p[j]:= plots:-odeplot
                    ( sol,
                      [ [ x, eval( f(x), sol)(x) ],
                        [ x, eval( diff(f(x),x), sol)(x)],
                        [ x, eval( g(x), sol)(x) ]
                      ],
                      x=-1..1,
                      color=[red, blue, green],
                      title=typeset(" R is ", Rvals[j]),
                      titlefont=[times, bold, 20],
                      legend=[ "f(x", "diff(f(x)", "g(x)"],
                      legendstyle=[font=[times, bold, 16]]
                    );
       M[j]:= Matrix( [ lhs~([sol[1], sol[2], sol[3], sol[6]]),
                      seq( [ eval(x, sol)(k),
                             eval(f(x), sol)(k),
                             eval(diff(f(x),x), sol)(k),
                             eval(g(x), sol)(k)
                           ],
                           k=-1..1, 0.1
                         )
            ]
          );
  od;
  interface(rtablesize=10):

"sol:=[x=proc(x) ... end proc,f(x)=proc(x) ... end proc,(&DifferentialD;)/(&DifferentialD;x) f(x)=proc(x) ... end proc,((&DifferentialD;)^2)/(&DifferentialD;x^2) f(x)=proc(x) ... end proc,((&DifferentialD;)^3)/(&DifferentialD;x^3) f(x)=proc(x) ... end proc,g(x)=proc(x) ... end proc,(&DifferentialD;)/(&DifferentialD;x) g(x)=proc(x) ... end proc]"

 

 

Matrix(22, 4, {(1, 1) = x, (1, 2) = f(x), (1, 3) = diff(f(x), x), (1, 4) = g(x), (2, 1) = -1, (2, 2) = -.5999999999999999, (2, 3) = 0., (2, 4) = 0., (3, 1) = -.9, (3, 2) = -.5921019363135331, (3, 3) = .16117644246579177, (3, 4) = .16278785222711661, (4, 1) = -.8, (4, 2) = -.5673179392294507, (4, 3) = .3358281006942344, (4, 4) = .27398222754004026, (5, 1) = -.7, (5, 2) = -.5248336859114118, (5, 3) = .5136175101475529, (5, 4) = .34249328997691325, (6, 1) = -.6, (6, 2) = -.46477687437327975, (6, 3) = .6859820206881927, (6, 4) = .37560385885019504, (7, 1) = -.5, (7, 2) = -.388056335140733, (7, 3) = .8458151726881442, (7, 4) = .379329359084838, (8, 1) = -.4, (8, 2) = -.29622905813442174, (8, 3) = .9872264166250676, (8, 4) = .3587619863302707, (9, 1) = -.3, (9, 2) = -.19138762111309063, (9, 3) = 1.1053715832210735, (9, 4) = .31836669317513355, (10, 1) = -.2, (10, 2) = -0.7606152260806107e-1, (10, 3) = 1.1963422280782419, (10, 4) = .2622203658496911, (11, 1) = -.1, (11, 2) = 0.4687285133905644e-1, (11, 3) = 1.257101695941537, (11, 4) = .19419882920716647, (12, 1) = 0., (12, 2) = .17427776167518302, (12, 3) = 1.285457587832346, (12, 4) = .11812298579942797, (13, 1) = .1, (13, 2) = .30283839441242316, (13, 3) = 1.2800631860819935, (13, 4) = 0.3787854100769596e-1, (14, 1) = .2, (14, 2) = .42914854495292715, (14, 3) = 1.2404437922191818, (14, 4) = -0.4247440931298191e-1, (15, 1) = .3, (15, 2) = .5498001552169361, (15, 3) = 1.1670477189686659, (15, 4) = -.11858357706073142, (16, 1) = .4, (16, 2) = .6614793307230553, (16, 3) = 1.0613260266593003, (16, 4) = -.1856569908506866, (17, 1) = .5, (17, 2) = .7610721351270342, (17, 3) = .9258503351415268, (17, 4) = -.23825953806119313, (18, 1) = .6, (18, 2) = .8457846937322854, (18, 3) = .7644844667704894, (18, 4) = -.2700210440598001, (19, 1) = .7, (19, 2) = .9132841022735299, (19, 3) = .5826335690125677, (19, 4) = -.2732168506711414, (20, 1) = .8, (20, 2) = .9618694469154144, (20, 3) = .38760346032463744, (20, 4) = -.23817813455209258, (21, 1) = .9, (21, 2) = .9906859783236445, (21, 3) = .18911198892620892, (21, 4) = -.1524947837179067, (22, 1) = 1.0, (22, 2) = 1.0000000000000002, (22, 3) = 0., (22, 4) = 0.})

 

"sol:=[x=proc(x) ... end proc,f(x)=proc(x) ... end proc,(&DifferentialD;)/(&DifferentialD;x) f(x)=proc(x) ... end proc,((&DifferentialD;)^2)/(&DifferentialD;x^2) f(x)=proc(x) ... end proc,((&DifferentialD;)^3)/(&DifferentialD;x^3) f(x)=proc(x) ... end proc,g(x)=proc(x) ... end proc,(&DifferentialD;)/(&DifferentialD;x) g(x)=proc(x) ... end proc]"

 

 

Matrix(22, 4, {(1, 1) = x, (1, 2) = f(x), (1, 3) = diff(f(x), x), (1, 4) = g(x), (2, 1) = -1, (2, 2) = -.6000000000000004, (2, 3) = 0., (2, 4) = 0., (3, 1) = -.9, (3, 2) = -.5910567233470129, (3, 3) = .18122537717864878, (3, 4) = .16396504088125943, (4, 1) = -.8, (4, 2) = -.5634797368629983, (4, 3) = .3707794844269797, (4, 4) = .27242971039204567, (5, 1) = -.7, (5, 2) = -.516969715671122, (5, 3) = .5583291678670692, (5, 4) = .3357102861727665, (6, 1) = -.6, (6, 2) = -.45216444180391374, (6, 3) = .7354160507956333, (6, 4) = .36217576157094034, (7, 1) = -.5, (7, 2) = -.3704651748474773, (7, 3) = .8951891646617371, (7, 4) = .35871202401791136, (8, 1) = -.4, (8, 2) = -.27388695993638196, (8, 3) = 1.032192599436718, (8, 4) = .33112662990623104, (9, 1) = -.3, (9, 2) = -.16492772308724132, (9, 3) = 1.1422006814980625, (9, 4) = .2844747844035093, (10, 1) = -.2, (10, 2) = -0.4645182729199544e-1, (10, 3) = 1.2220922378023178, (10, 4) = .22330926940407242, (11, 1) = -.1, (11, 2) = 0.784154458137712e-1, (11, 3) = 1.269756795732628, (11, 4) = .15186760332056226, (12, 1) = 0., (12, 2) = .20638541043083533, (12, 3) = 1.2840276312063286, (12, 4) = 0.7421358259764317e-1, (13, 1) = .1, (13, 2) = .33409800434183184, (13, 3) = 1.2646386645322474, (13, 4) = -0.5648866884394064e-2, (14, 1) = .2, (14, 2) = .4582106456522417, (14, 3) = 1.2122040908812248, (14, 4) = -0.836715744946918e-1, (15, 1) = .3, (15, 2) = .5754862092294035, (15, 3) = 1.128221393564483, (15, 4) = -.1556489493917709, (16, 1) = .4, (16, 2) = .6828825716240221, (16, 3) = 1.0151003650073218, (16, 4) = -.21707454720818847, (17, 1) = .5, (17, 2) = .7776465657105786, (17, 3) = .8762233928986827, (17, 4) = -.26294167827837045, (18, 1) = .6, (18, 2) = .8574158806153623, (18, 3) = .7160459677791091, (18, 4) = -.287455837843665, (19, 1) = .7, (19, 2) = .9203335847329029, (19, 3) = .5402514892963132, (19, 4) = -.28361907679236387, (20, 1) = .8, (20, 2) = .9651816746104471, (20, 3) = .35598103108785795, (20, 4) = -.24263993404105924, (21, 1) = .9, (21, 2) = .9915424895108919, (21, 3) = .17216620285365075, (21, 4) = -.15312216756590794, (22, 1) = 1.0, (22, 2) = .9999999999999999, (22, 3) = 0., (22, 4) = 0.})

 

"sol:=[x=proc(x) ... end proc,f(x)=proc(x) ... end proc,(&DifferentialD;)/(&DifferentialD;x) f(x)=proc(x) ... end proc,((&DifferentialD;)^2)/(&DifferentialD;x^2) f(x)=proc(x) ... end proc,((&DifferentialD;)^3)/(&DifferentialD;x^3) f(x)=proc(x) ... end proc,g(x)=proc(x) ... end proc,(&DifferentialD;)/(&DifferentialD;x) g(x)=proc(x) ... end proc]"

 

 

Matrix(22, 4, {(1, 1) = x, (1, 2) = f(x), (1, 3) = diff(f(x), x), (1, 4) = g(x), (2, 1) = -1, (2, 2) = -.6, (2, 3) = 0., (2, 4) = 0., (3, 1) = -.9, (3, 2) = -.5890460844879107, (3, 3) = .2198386517649569, (3, 4) = .16530323348490086, (4, 1) = -.8, (4, 2) = -.5560849074382147, (4, 3) = .43816895209915196, (4, 4) = .26764796070103164, (5, 1) = -.7, (5, 2) = -.501824746995504, (5, 3) = .6441967577731817, (5, 4) = .32004582147804334, (6, 1) = -.6, (6, 2) = -.4279468048318385, (6, 3) = .8292577622345304, (6, 4) = .3330538680096117, (7, 1) = -.5, (7, 2) = -.3368927457898107, (7, 3) = .9868006993649518, (7, 4) = .3154069928968666, (8, 1) = -.4, (8, 2) = -.23165630116353528, (8, 3) = 1.112318306576843, (8, 4) = .2744870694769592, (9, 1) = -.3, (9, 2) = -.11558534417415368, (9, 3) = 1.203204419426625, (9, 4) = .21664697219190648, (10, 1) = -.2, (10, 2) = 0.77977336536539064e-2, (10, 3) = 1.2585316312429464, (10, 4) = .14742694982025012, (11, 1) = -.1, (11, 2) = .13494998754599274, (11, 3) = 1.2787648296225842, (11, 4) = 0.71704794890426e-1, (12, 1) = 0., (12, 2) = .26243142352580456, (12, 3) = 1.2654452961155502, (12, 4) = -0.6183800085005834e-2, (13, 1) = .1, (13, 2) = .386997290300288, (13, 3) = 1.2208903045330994, (13, 4) = -0.8232737042872075e-1, (14, 1) = .2, (14, 2) = .5056628908234575, (14, 3) = 1.1479493670985939, (14, 4) = -.15310505557254883, (15, 1) = .3, (15, 2) = .6157479708522582, (15, 3) = 1.0498420667838475, (15, 4) = -.2150243987585282, (16, 1) = .4, (16, 2) = .7149092180250505, (16, 3) = .9300816061622831, (16, 4) = -.26451781233451827, (17, 1) = .5, (17, 2) = .8011689330506191, (17, 3) = .7924715996791256, (17, 4) = -.29767900145546017, (18, 1) = .6, (18, 2) = .8729462572046487, (18, 3) = .6411574655922088, (18, 4) = -.3099095345489387, (19, 1) = .7, (19, 2) = .9290956309406369, (19, 3) = .4807180162778606, (19, 4) = -.2954313672351693, (20, 1) = .8, (20, 2) = .9689562366716992, (20, 3) = .3162941876999236, (20, 4) = -.24660535105130912, (21, 1) = .9, (21, 2) = .9924165644781593, (21, 3) = .15376572531561677, (21, 4) = -.1529816079274428, (22, 1) = 1.0, (22, 2) = .9999999999999999, (22, 3) = 0., (22, 4) = 0.})

 

"sol:=[x=proc(x) ... end proc,f(x)=proc(x) ... end proc,(&DifferentialD;)/(&DifferentialD;x) f(x)=proc(x) ... end proc,((&DifferentialD;)^2)/(&DifferentialD;x^2) f(x)=proc(x) ... end proc,((&DifferentialD;)^3)/(&DifferentialD;x^3) f(x)=proc(x) ... end proc,g(x)=proc(x) ... end proc,(&DifferentialD;)/(&DifferentialD;x) g(x)=proc(x) ... end proc]"

 

 

Matrix(22, 4, {(1, 1) = x, (1, 2) = f(x), (1, 3) = diff(f(x), x), (1, 4) = g(x), (2, 1) = -1, (2, 2) = -.5999999999999999, (2, 3) = 0., (2, 4) = 0., (3, 1) = -.9, (3, 2) = -.5885947382746329, (3, 3) = .22852431650651223, (3, 4) = .16534633634381243, (4, 1) = -.8, (4, 2) = -.5544189692150393, (4, 3) = .4534004612340051, (4, 4) = .26607037116078464, (5, 1) = -.7, (5, 2) = -.4984062412869411, (5, 3) = .6636006972241313, (5, 4) = .31577530763651607, (6, 1) = -.6, (6, 2) = -.42248634612463787, (6, 3) = .8502514742975177, (6, 4) = .32553203705865047, (7, 1) = -.5, (7, 2) = -.3293636263128513, (7, 3) = 1.0067491067162901, (7, 4) = .3045467975331385, (8, 1) = -.4, (8, 2) = -.2222875527101816, (8, 3) = 1.1287898465496373, (8, 4) = .2606288613379166, (9, 1) = -.3, (9, 2) = -.10482663479017114, (9, 3) = 1.2142664538412669, (9, 4) = .2004888707748643, (10, 1) = -.2, (10, 2) = 0.19339481440825857e-1, (10, 3) = 1.2630068824565952, (10, 4) = .12992062935643178, (11, 1) = -.1, (11, 2) = .1465944440231568, (11, 3) = 1.2763736197655813, (11, 4) = 0.5392364168942554e-1, (12, 1) = 0., (12, 2) = .27351521671490775, (12, 3) = 1.2567904467527107, (12, 4) = -0.23185142823880983e-1, (13, 1) = .1, (13, 2) = .3969550901628668, (13, 3) = 1.20729208284578, (13, 4) = -0.9763876092339403e-1, (14, 1) = .2, (14, 2) = .5140865520874546, (14, 3) = 1.131183212788941, (14, 4) = -.16605314300138765, (15, 1) = .3, (15, 2) = .6224175618994571, (15, 3) = 1.031849974160649, (15, 4) = -.2252230606412318, (16, 1) = .4, (16, 2) = .7197963959791739, (16, 3) = .91271505526074, (16, 4) = -.2718789569092242, (17, 1) = .5, (17, 2) = .8044174392211924, (17, 3) = .777292644204684, (17, 4) = -.3023924171455772, (18, 1) = .6, (18, 2) = .8748353664675236, (18, 3) = .6292941394600428, (18, 4) = -.3124010160557897, (19, 1) = .7, (19, 2) = .929990976635027, (19, 3) = .4727519716440513, (19, 4) = -.29630392257166593, (20, 1) = .8, (20, 2) = .969249872312222, (20, 3) = .3121533153501387, (20, 4) = -.2465605862461447, (21, 1) = .9, (21, 2) = .992455479290909, (21, 3) = .15259678595166132, (21, 4) = -.15270793902808713, (22, 1) = 1.0, (22, 2) = .9999999999999999, (22, 3) = 0., (22, 4) = 0.})

 

"sol:=[x=proc(x) ... end proc,f(x)=proc(x) ... end proc,(&DifferentialD;)/(&DifferentialD;x) f(x)=proc(x) ... end proc,((&DifferentialD;)^2)/(&DifferentialD;x^2) f(x)=proc(x) ... end proc,((&DifferentialD;)^3)/(&DifferentialD;x^3) f(x)=proc(x) ... end proc,g(x)=proc(x) ... end proc,(&DifferentialD;)/(&DifferentialD;x) g(x)=proc(x) ... end proc]"

 

 

Matrix(%id = 18446744074593872102)

(2)

 

``

Download plotODEs.mw


 

the simple coeff() command. As in the attached

restart;
eq:=p*(diff(F1(zeta), zeta, zeta))-b^2*p*F1(zeta)+2*G0(zeta)*p*G1(zeta)+p^2*G1(zeta)^2-p*H0(zeta)*(diff(F0(zeta), zeta))-H0(zeta)*p^2*(diff(F1(zeta), zeta))-p^2*H1(zeta)*(diff(F0(zeta), zeta))-p^3*H1(zeta)*(diff(F1(zeta), zeta))-p*F0(zeta)^2-2*F0(zeta)*p^2*F1(zeta)-p^3*F1(zeta)^2+p*b^2*F0(zeta)+b^2*p^2*F1(zeta);

p*(diff(diff(F1(zeta), zeta), zeta))-b^2*p*F1(zeta)+2*G0(zeta)*p*G1(zeta)+p^2*G1(zeta)^2-p*H0(zeta)*(diff(F0(zeta), zeta))-H0(zeta)*p^2*(diff(F1(zeta), zeta))-p^2*H1(zeta)*(diff(F0(zeta), zeta))-p^3*H1(zeta)*(diff(F1(zeta), zeta))-p*F0(zeta)^2-2*F0(zeta)*p^2*F1(zeta)-p^3*F1(zeta)^2+p*b^2*F0(zeta)+b^2*p^2*F1(zeta)

(1)

coeff(eq, p, 1);

diff(diff(F1(zeta), zeta), zeta)-b^2*F1(zeta)+2*G0(zeta)*G1(zeta)-H0(zeta)*(diff(F0(zeta), zeta))-F0(zeta)^2+b^2*F0(zeta)

(2)

 

Download getC.mw

 

the attached.

For reasons I do not understand the "solidcircles" at the vertices do not appear when the animation is "rendered" on this site - however they do exist when this worksheet is executed within Maple - honest!!

restart; r, theta := (abs, argument)(1+I); Explore(plot(`~`[`~`[`*`](r^(1/a), [cos, sin])](([seq])((2*Pi*k+theta)/a, k = 0 .. a)), style = pointline, symbol = solidcircle, symbolsize = 25, gridlines, thickness = 3, scaling = constrained, color = blue, labels = [Re, Im], labelfont = [Helvetica, bolditalic, 20]), parameters = [[a = 1 .. 20, shown = false, animate]])

plots:-animate(plot, ['`~`[`~`[`*`](r^(1/a), [cos, sin])](([seq])((2*Pi*k+theta)/a, k = 0 .. a))', style = pointline, symbol = solidcircle, symbolsize = 25, gridlines, thickness = 3, scaling = constrained, color = blue, labels = [Re, Im], labelfont = [Helvetica, bolditalic, 20]], a = 1 .. 20, frames = 20)

 

``

 

NULL


 

Download pltAnim.mw

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