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mmcdara

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9 years, 63 days
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@one man try to write the parameter...

mmcdara 7891
July 25 2020

@one man   @vv

Doesn't work in Maple 2015 neither.
This should work (remark the upper bounds of s and t are set to 0.99 to avoid a "division by 0" error).
Their lower bounds are set to 0.01 for convenience, only to display the ellipse since the beginning.
Unfortunately, even in Maple2015, it remains an error: when the values of s and t are changed with the sliders, the ellipse disappears.  This is an error which reminds me one I submitted here a few months ago. From memory I was told (acer ?) that it was a bug now corrected since Maple 2018 (or 2019).
Explore(
    plots:-display(
      plot(T),
      plot([ell[], xi=-infinity..infinity])
    ), 
    parameters=[s=0.1..0.99, t=0.1..0.99]
);

 

@vv  Hi,  Do you think there...

mmcdara 7891
July 25 2020
0 0

@vv 

Hi, 

Do you think there is a more formal method to count this number of singular matrices?
In my initial question I'd written a system of polynomial equations with a[1, 1], ....a[3, 3] (more generally a[N, N]) as indeterminates. Unfortunately solving this system with isolve gave me a result only for N=2 (trivial result).

My problem comes from the construction of particular designs of experiments and has some connections (at least for N=3) with Sudoku matrices. I've read once a paper where a mathematical procedure, using Groebner basis, was developped to find the solution of any sudoku grid. Did you ever heard of that or do you think Groebner basis could be a fruitful tool to tackle this problem?

 

@vv @acer Thanks to both of you fo...

mmcdara 7891
July 20 2020
0 0

@vv @acer

Thanks to both of you for the explanations.
@vv  I saw that `diff/f`' was indeed documented, which enlightens me a few.

I'm going to try to understand more precisely what's really going on based on the diff help page and what you both said.

Maybe I will come bacjk to you for extra explanations.

Thanks again

@vv  Awesome! Could you explain to...

mmcdara 7891
July 19 2020
0 0

@vv 

Awesome!
Could you explain to me how this works?

TIA

@Violet You will find in the attach...

mmcdara 7891
July 19 2020
0 0

@Violet 

You will find in the attached file a "Maple to R parser' (kind of) which (almost) automatically translateyourMaplecode into the correspondaning R code

This could avoid typos. The R code is the blue output at the end of the file
 


 

> 

restart
> 

Maple_params    := [L = 0.5e-1, b = 0.2e-2, ph = 0.1e-1, a = 0.1e-1, m = 0.1e-1, nu = 0.1e-2, th = 0.5e-2, u = .1, v = .1,
                    sg = 0.1e-1, g1 = 0.3e-1, TT = 60];
Maple_functions := {I1(t), P1(t), R1(t), S1(t)};
Maple_start     := {I1(0) = 150, P1(0) = 100, R1(0) = 0, S1(0) = 1000};
Maple_range     := 'range'=0..60;
Maple_system    := {diff(I1(t), t) = (1-u)*b*S1(t)*P1(t)-(nu+sg+v+m+a-ph)*I1(t), diff(P1(t), t) = m*I1(t)-g1*P1(t),
                    diff(R1(t), t) = (a+v)*I1(t)-(nu+th)*R1(t), diff(S1(t), t) = L-(1-u)*b*S1(t)*P1(t)+th*R1(t)-nu*S1(t)};
Maple_colors    := [red, green,blue, black];

[L = 0.5e-1, b = 0.2e-2, ph = 0.1e-1, a = 0.1e-1, m = 0.1e-1, nu = 0.1e-2, th = 0.5e-2, u = .1, v = .1, sg = 0.1e-1, g1 = 0.3e-1, TT = 60]

  

{I1(t), P1(t), R1(t), S1(t)}

  

{I1(0) = 150, P1(0) = 100, R1(0) = 0, S1(0) = 1000}

  

range = 0 .. 60

  

{diff(I1(t), t) = (1-u)*b*S1(t)*P1(t)-(nu+sg+v+m+a-ph)*I1(t), diff(P1(t), t) = m*I1(t)-g1*P1(t), diff(R1(t), t) = (a+v)*I1(t)-(nu+th)*R1(t), diff(S1(t), t) = L-(1-u)*b*S1(t)*P1(t)+th*R1(t)-nu*S1(t)}

  

[red, green, blue, black]

 (1)
> 

with(plots):

Maple_sol := dsolve(Maple_system union Maple_start, numeric, Maple_range, parameters=lhs~(Maple_params));

Maple_sol(parameters=rhs~(Maple_params));
display(
  seq(
    odeplot(Maple_sol, [t, Maple_functions[n]], t=rhs(Maple_range), color=Maple_colors[n], legend=Maple_functions[n]),
    n=1..numelems(Maple_functions)
  )
);

Warning, the unknowns {TT} were specified in 'parameters', but are not present in the input system

  

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, b = b, ph = ph, a = a, m = m, nu = nu, th = th, u = u, v = v, sg = sg, g1 = g1, TT = TT]; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 24, [( 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..54, {(1) = 4, (2) = 4, (3) = 0, (4) = 0, (5) = 12, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 1, (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}, 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..16, {(1) = 150., (2) = 100., (3) = 0., (4) = 1000., (5) = Float(undefined), (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)})), ( 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..4, {(1) = .1, (2) = .1, (3) = .1, (4) = .1}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0}, datatype = float[8], order = C_order), Array(1..4, 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}, datatype = float[8], order = C_order), Array(1..4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0}, datatype = integer[8]), Array(1..16, {(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}, datatype = float[8], order = C_order), Array(1..16, {(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}, datatype = float[8], order = C_order), Array(1..16, {(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}, datatype = float[8], order = C_order), Array(1..16, {(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}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..16, {(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}, datatype = float[8], order = C_order), Array(1..16, {(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}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = I1(t), Y[2] = P1(t), Y[3] = R1(t), Y[4] = S1(t)]`; YP[1] := (1-Y[12])*Y[6]*Y[4]*Y[2]-(Y[10]+Y[14]+Y[13]+Y[9]+Y[8]-Y[7])*Y[1]; YP[2] := Y[1]*Y[9]-Y[2]*Y[15]; YP[3] := (Y[8]+Y[13])*Y[1]-(Y[10]+Y[11])*Y[3]; YP[4] := Y[5]-(1-Y[12])*Y[6]*Y[4]*Y[2]+Y[11]*Y[3]-Y[10]*Y[4]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = I1(t), Y[2] = P1(t), Y[3] = R1(t), Y[4] = S1(t)]`; YP[1] := (1-Y[12])*Y[6]*Y[4]*Y[2]-(Y[10]+Y[14]+Y[13]+Y[9]+Y[8]-Y[7])*Y[1]; YP[2] := Y[1]*Y[9]-Y[2]*Y[15]; YP[3] := (Y[8]+Y[13])*Y[1]-(Y[10]+Y[11])*Y[3]; YP[4] := Y[5]-(1-Y[12])*Y[6]*Y[4]*Y[2]+Y[11]*Y[3]-Y[10]*Y[4]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 24 ) = (0) ] )) ] ); _y0 := Array(0..16, {(1) = 0., (2) = 150., (3) = 100., (4) = 0., (5) = 1000., (6) = undefined, (7) = undefined, (8) = undefined, (9) = undefined, (10) = undefined, (11) = undefined, (12) = undefined, (13) = undefined, (14) = undefined, (15) = undefined, (16) = undefined}); _vmap := array( 1 .. 4, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4) ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch: end try else try procname(procname("right")) catch: end try end if end if end if; return elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch: end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch: end try end if end if end if; return elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error end try; if _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]; _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) = [t, I1(t), P1(t), R1(t), S1(t)], (4) = [L = L, b = b, ph = ph, a = a, m = m, nu = nu, th = th, u = u, v = v, sg = sg, g1 = g1, TT = TT]}); _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

  

[L = 0.5e-1, b = 0.2e-2, ph = 0.1e-1, a = 0.1e-1, m = 0.1e-1, nu = 0.1e-2, th = 0.5e-2, u = .1, v = .1, sg = 0.1e-1, g1 = 0.3e-1, TT = 60.]

  

 
> 

# R declaration commands

R_params    := cat(
                    "params <- c(",
                    substring(sprintf("%a", Maple_params), 2..-2),
                    ")"
               );
R_functions := cat(
                    substring(sprintf("%a", op~(0, Maple_functions)), 2..-2)
               );
R_diffs     := substring(
                 cat(
                    op( map(u -> cat("d", u, ","), op~(0, Maple_functions)) )
                 ),
                 1..-2
               );
R_start     := cat(
                    "start <- c(",
                    StringTools:-SubstituteAll( substring(sprintf("%a", Maple_start), 2..-2), "(0)","" ),
                    ")"
               );
R_range     := cat(
                    "time <- ",
                    sprintf(%a, op(1, rhs(Maple_range))), ":", sprintf(%a, op(2, rhs(Maple_range)))
               );

"params <- c(L = .5e-1, b = .2e-2, ph = .1e-1, a = .1e-1, m = .1e-1, nu = .1e-2, th = .5e-2, u = .1, v = .1, sg = .1e-1, g1 = .3e-1, TT = 60)"

  

"I1, P1, R1, S1"

  

"dI1,dP1,dR1,dS1"

  

"start <- c(I1 = 150, P1 = 100, R1 = 0, S1 = 1000)"

  

"time <- 0:60"

 (2)
> 

# R system declaration and solution commands

R_system := "spirs <- function(t, x, params) {",
            "with(as.list(c(params, x)), {":

for eq in convert~(Maple_system, string) do
  StringTools:-SubstituteAll(eq, "(t)", ""):
  StringTools:-SubstituteAll(%, ",t)", ""):
  StringTools:-SubstituteAll(%, "diff(", "d");
  R_system   := R_system, %
end do:

R_system := R_system,
            cat("list(c(", R_diffs, "))"),
            "})}":

R_ode := cat("run_d <- ode(start, time, spirs, params)"):
 
> 

# R plotting commands

R_matplot := cat("matplot(run_d[,2:", numelems(Maple_functions)+1, "], type=""l"")"):

R_plot_1 := cat(
                 "plot(run_d[,2], lwd=3, col=""",
                  Maple_colors[1],
                 """, ylim=c(0,1000), type=""l"", main=""SIR Model"", ylab=""Population"")"
            ):
for n from 2 to numelems(Maple_functions) do
  R_plot_||n := cat( "lines(run_d[,", n+1, "], lwd=3, col=""", Maple_colors[n], """)" );
end do:

R_legend := cat(
                  "legend(""topright"", legend=c(",
                   substring( cat( op( map(u -> cat("""", u, ""","), StringTools:-Split( R_functions, ",")) ) ), 1..-2),
                  ")" ,
                  ", col=c(",
                   substring( cat( seq(cat("""", Maple_colors[n], ""","), n=1..numelems(Maple_functions)) ), 1..-2),
                  "),",
                  "lty=c(", seq("1,", n=1..numelems(Maple_functions)-1), "1))"
                  
            )

"legend("topright", legend=c("I1"," P1"," R1"," S1"), col=c("red","green","blue","black"),lty=c(1,1,1,1))"

 (3)
> 

# Here is, in R syntax, the declaration of the problem to solve

# writeto(My_R_source_file)
# or copy-paste the result in the upper left window of RStudio (if you do ise it) or within the Rcommander command window
#
# think to add library(...) to attach the deSolve package

map(u -> printf("%s\n", u), [R_system]):
printf("%s\n", R_params):
printf("%s\n", R_start):
printf("%s\n", R_range):
printf("%s\n", R_ode):
printf("%s\n", R_matplot):
for n from 1 to numelems(Maple_functions) do
  printf("%s\n", R_plot_||n):
end do:
printf("%s\n", R_legend):

spirs <- function(t, x, params) {

with(as.list(c(params, x)), {
dP1 = m*I1-g1*P1
dR1 = (a+v)*I1-(nu+th)*R1
dS1 = L-(1-u)*b*S1*P1+th*R1-nu*S1
dI1 = (1-u)*b*S1*P1-(nu+sg+v+m+a-ph)*I1
list(c(dI1,dP1,dR1,dS1))
})}
params <- c(L = .5e-1, b = .2e-2, ph = .1e-1, a = .1e-1, m = .1e-1, nu = .1e-2, th = .5e-2, u = .1, v = .1, sg = .1e-1, g1 = .3e-1, TT = 60)
start <- c(I1 = 150, P1 = 100, R1 = 0, S1 = 1000)
time <- 0:60
run_d <- ode(start, time, spirs, params)
matplot(run_d[,2:5], type="l")
plot(run_d[,2], lwd=3, col="red", ylim=c(0,1000), type="l", main="SIR Model", ylab="Population")
lines(run_d[,3], lwd=3, col="green")
lines(run_d[,4], lwd=3, col="blue")
lines(run_d[,5], lwd=3, col="black")
legend("topright", legend=c("I1"," P1"," R1"," S1"), col=c("red","green","blue","black"),lty=c(1,1,1,1))

  
> 

 


 

Download Maple2R.mw

can you upload your code by using the ni...

mmcdara 7891
July 18 2020
0 0

Can you upload your R and Maple codes by using the big green arrow?

@vv  Thanks again vv. I understand...

mmcdara 7891
July 16 2020
0 0

@vv 

Thanks again vv.
I understand that deriving in general can be quite lengthy.
I'm going to start from this your last answer and see how far I can go.

@vv Thanks vv.So the key was in the...

mmcdara 7891
July 16 2020
0 0

@vv 

Thanks vv.
So the key was in the 'explicit' option of the solve command.

As I'm mainly interested in the equations of the intersection curves the display doesn't really matter to me, so your reply suits me perfectly well.
Happily, for I met some issues with Maple 2015  Download Little_inconveniences.mw


I did a few test, for instance this one
cylx := y^2 + z^2 - 1;
cylz := x^2 + (y+1)^2 - 1/2;

Here there is a single intersection curve but it's parametric representation contains several radicals that must be real valued.
How can we determine the ranges of z (if any) for the parametric curve be "real" ?


 

> 

restart
> 

interface(version)

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

 (1)
> 

with(plots):
> 

cylx := y^2 + z^2 - 1;
> 

cylz := x^2 + (y+1)^2 - 1/2;
> 

cyl:=implicitplot3d([cylx,cylz], x=-2..2, y=-2..2, z=-2..2,
scaling=constrained, style=wireframeopaque, grid=[40, 40, 40], labels=[x, y, z]):
display(cyl);
> 

s:=solve([cylx,cylz],[x,y,z], explicit):

print~(s):

y^2+z^2-1

  

x^2+(y+1)^2-1/2

  

 

[x = (1/2)*(-6+4*z^2-8*(-z^2+1)^(1/2))^(1/2), y = (-z^2+1)^(1/2), z = z]

  

[x = -(1/2)*(-6+4*z^2-8*(-z^2+1)^(1/2))^(1/2), y = (-z^2+1)^(1/2), z = z]

  

[x = (1/2)*(-6+4*z^2+8*(-z^2+1)^(1/2))^(1/2), y = -(-z^2+1)^(1/2), z = z]

  

[x = -(1/2)*(-6+4*z^2+8*(-z^2+1)^(1/2))^(1/2), y = -(-z^2+1)^(1/2), z = z]

 (2)
> 

Zy0 := solve(op(1, eval(y,s[1])) >= 0);

T := NULL:
R := NULL:
for t in s do
  U := op([2, 1], eval(x, t));
  S := solve(U >=0);
  if S <> NULL then
    T := T, t:
    # what follows assumesthat S contains only a single range
    if verify(op(1, S), op(1, Zy0)..op(2, Zy0), interval) then r:=op(1, S)    else r:=op(1, Zy0)    end if:
    if verify(op(2, S), op(1, Zy0)..op(2, Zy0), interval) then r:=r..op(2, S) else r:=r..op(2, Zy0) end if:
    R := R, r:
  end if:
end do:
T;R;

 

RealRange(-1, 1)

  

[x = (1/2)*(-6+4*z^2+8*(-z^2+1)^(1/2))^(1/2), y = -(-z^2+1)^(1/2), z = z], [x = -(1/2)*(-6+4*z^2+8*(-z^2+1)^(1/2))^(1/2), y = -(-z^2+1)^(1/2), z = z]

  

-(1/2)*(-2+4*2^(1/2))^(1/2) .. (1/2)*(-2+4*2^(1/2))^(1/2), -(1/2)*(-2+4*2^(1/2))^(1/2) .. (1/2)*(-2+4*2^(1/2))^(1/2)

 (3)
> 

a   := 1.05:
ell := seq( plot3d(a*rhs~(T[i]), z=R[i], color=red, thickness=8), i=1..numelems([T]) ):
display(cyl, ell, scaling=constrained);

 
> 

 


 

Download A_more_complex_case.mw

@Rouben Rostamian     "T...

mmcdara 7891
July 15 2020
0 0

@Rouben Rostamian  
 

"The intersection curve lies  on both cylinders, therefore when we are on the curve,

we may replace z in the first equation by the corresponding value in the second
equation, that is "sin(t).""
Great idea !

I'm going to check it on several other examples.

Thank you Rouben


 

Nice. If the third plot can be called&n...

mmcdara 7891
July 13 2020

Nice.

If the third plot can be called "Excel style" for obvious reasons, the second could be called "ggplot2 style" (ggplot2 being a R package) for obvious reasons too ;-).
... Which doesn't take anything away from the interest of your work

About ggplot2, look here Graphs

@mathnoob345  Open a terminal ...

mmcdara 7891
July 12 2020
0 0

@mathnoob345 

 

Open a terminal window (from the Launchpad or from the Applications folder) and type these Linux commands (I guess you have Maple installed in the Applications folder?)

  • Go to the Applications folder
    > cd /Applications
  • Verify Maple 2020 is here
    > ls Maple*
  • Change directory
    cd Maple*2020
  • Search the executable file named maple
    > ls -l
    this should be a link of the form maple -> /Library/Frameworks/Maple.framework/Versions/2020/bin/maple
  • Run this link
    > /Library/Frameworks/Maple.framework/Versions/2020/bin/maple
    This should put you in the old fashioned Maple

Type some commands to verify if Maple works correctly

PS: all this stuff can be simplified by defining environment variables

This is only a hint, so don't take i...

mmcdara 7891
July 12 2020
0 0

This is only a hint, so don't take it as an authoritative or definitive answer.

Catalina only support 64 bytes app (this is why I'm still running Mojave on my Mac)
So, even if Maple 2020 is a 64 bytes app, maybe your JRE (Java Runtime Environment) is not. Verify all the version compatibilities, look here for instance
360019488772-Swapping-the-version-of-the-JRE-used-by-Maple-on-Windows-and-Linux

Another hint: run maple from a terminal window in online mode to verify if Maple executes correctly (the online  maple command avoids running Java)
See here view.aspx

... and wait for a better reply

@acer  I'd already seen it... ...

mmcdara 7891
July 07 2020
0 0

@acer 

I'd already seen it... and forgotten in some remote corner of my mind.
Thanks for the reminder

@acer Thank you very much.With over...

mmcdara 7891
July 07 2020
0 0

@acer 

Thank you very much.
With overrideoption and setoptions3d you taught me a lot today.

See you next

@acer  overrideoption gives me ......

mmcdara 7891
July 06 2020
0 0

@acer 

overrideoption gives me ...partial satisfaction.
It seems that this works correctly only for some kind of "shapes" (watchout: I'm now at home and I'm using Maple 2015, no longer Maple 2019)

For instance
p := plots:-display(circle(1, color = blue)):
or
p := plots:-display(disk(1, color = blue)):
with 
extrude(q, 0..10, overrideoption, style=line);

generate the error 
Error, (in plottools:-extrude) unexpected option: overrideoption

 

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