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tomleslie

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14 years, 236 days
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I'm going to take a wild guess...

tomleslie 13821
January 30 2023
1 1

that the attached is what the OP was aiming for


 

> 

 

> 

  restart;
  _EnvHorizomtalName='x':
  _EnvVerticalName='y':
  aProc:=proc(t)
              uses geometry, plots:
              local a := 11,
                    b := 7,
                    R := sqrt(a^2 + b^2),
                    lt:= y=m*x+c,
                    sol, l1,l2, ell, xv, yv;
              point( P, [R*sin(t), R*cos(t)]);
              point( OO, [0,0]);
              circle( cir, [OO, R]);
              ellipse(ell, x^2/a^2+y^2/b^2-1=0, [x, y]):
              sol:= [ solve
                      ( subs
                        ( c=VerticalCoord(P)-m*HorizontalCoord(P),
                          discrim
                          ( lhs
                            ( collect
                              ( expand
                                ( subs
                                  ( lt,
                                    Equation(ell)
                                  )
                                ),
                                x
                              )
                            ),
                            x
                          )
                        )=0,
                        m
                      )
                    ];
              line( l1,
                    eval
                    ( y=m*x-m*HorizontalCoord(P)+VerticalCoord(P),
                      m=sol[1]
                    ),
                    [x,y]
                  );
              line( l2,
                    eval
                    ( y=m*x-m*HorizontalCoord(P)+VerticalCoord(P),
                      m=sol[2]
                    ),
                    [x,y]
                  );
              xv:=evalf~
                  ( evalc~
                    ( [ solve
                        ( subs
                          ( isolate(Equation(l1),y),
                            Equation(ell)
                          )
                        )
                      ]
                    )
                  )[1];
              yv:= solve
                   ( eval
                     ( Equation(l1),
                       x=xv
                     )
                   ) ;
              point( S, [xv, yv]);
              xv:=evalf~
                  ( evalc~
                    ( [ solve
                        ( subs
                          ( isolate(Equation(l2),y),
                            Equation(ell)
                          )
                        )
                      ]
                    )
                  )[1];
              yv:= solve
                   ( eval
                     ( Equation(l2),
                       x=xv
                     )
                   );
              point( T, [xv, yv]);
              display
              ( [ textplot
                  ( [ [ coordinates(P)[], "P"],
                      [ coordinates(S)[], "S"],
                      [ coordinates(T)[], "T"]
                    ],
                    font=[times, bold, 16],
                    align=[above, right]
                  ),                        
                  draw
                  ( [ ell(color=blue),
                      cir(color=blue),
                      l1(color=green),
                      l2(color=red),
                       S(color=black, symbol=solidcircle, symbolsize=16),
                       T(color=black, symbol=solidcircle, symbolsize=16),
                       P(color=black, symbol=solidcircle, symbolsize=16)
                    ],
                    scaling=constrained,
                    axes=none,
                    view=[-15..15, -15..15]
                  )
                ]
              );
        end proc:
> 

  nFig := 60:
 plots:-display(seq(aProc(2*Pi*i/nFig), i=0..nFig), insequence = true);

 
> 

 


 

Download Monge.mw

I still...

tomleslie 13821
January 26 2023
1 1

don't really understand what you are trying to achieve, or why, but maybe something in the code below will help

  restart;
  with(GraphTheory):

  L1:=[ [ (0, 1), (1, 2), (1, 10), (2, 3), (3, 4), (4, 5), (4, 9), (5, 6), (6, 7), (7, 8),
          (8, 9), (10, 11), (11, 12), (11, 16), (12, 13), (13, 14), (14, 15), (15, 16)
        ],
        [ (0, 10), (1, 2), (1, 9), (2, 3), (3, 4), (4, 5), (4, 9), (5, 6), (6, 7), (7, 8),
          (8, 9), (10, 11), (11, 12), (11, 16), (12, 13), (13, 14), (14, 15), (15, 16)
        ]
      ]:
  g:= [ seq
        ( Graph
          ( { seq
              ( {L1[j][i-1], L1[j][i]},
                i=2..numelems(L1[j]),2
              )
            }
          ),
          j=1..numelems(L1)
        )
      ]:

  g[1];
  Edges(g[1]);
  g[2];
  Edges(g[2]);
  DrawGraph(g[1]);
  DrawGraph(g[2]);

I would normally upload a worksheet , but someone seems to have broken the big green uparrow. Let's hope it is (very) temporary

Something(?)...

tomleslie 13821
January 25 2023
3 4

The first thing to realise is that pdsolve(...., numeric) does not return any information about the derivatives of the dependent function T(y,t). The only way I can think of to generate this information is to use the pds:-value() method combined with the numeric differentiation command fdiff(), to obtain derivative values at a point.

Unfortunately the fdiff() command is very slow, so in the attached, I have restricted the computation of your desired functions

1+Nr*(T(y, t)+1)^3)*(diff(T(y, t), y)), at t = 1,

 diff(T(y, t), y) at y = 0

 diff(T(y, t), y) at y = 1

to only a few points across the range of the relevant variable. Even with this restriction, the attached worksheet takes several minutes to execute on my machine.

The last plot in the attached, ie diff(T(y, t), y) at y = 1 for Nr=[0, 1, 10] essentially produces zero for all t and any Nr. I am not sure whether this is plausible or not!

> 

   restart;
   with(plots):
  PDE1 := Pr*(diff(T(y, t), t)-Ree*(diff(T(y, t), y))) = (1+Nr*(T(y, t)+1)^3)*(diff(T(y, t), y, y))+3*Nr*(T(y, t)+1)^2*(diff(T(y, t), y))^2;
  ICandBC := {T(1, t) = 1, T(y, 0) = 1, (D[1](T))(0, t) = T(0, t)}:
  Ree := .1:
  Pr := 6.2:
  HA1 := [0, 1, 10]:
  AA := [red, green, blue, cyan, purple, black]:
  for i to nops(HA1) do
     Nr := op(i, HA1);
     print("Nr = ", %);
     PDE[i] := {PDE1};
     pds[i] := pdsolve( PDE[i],
                        ICandBC,
                        numeric,
                        spacestep = 1/200,
                        timestep = 1/100
                      );
     PlotsT[i] := pds[i]:-plot( T(y, t),
                                t = 1,
                                linestyle = "solid",
                                labels = ["y", "u"],
                                color = AA[i],
                                numpoints = 800
                              );
     Tv:=eval( T(y,t),
               pds[i]:-value( t=1,
                              output=listprocedure
                            )
             ):
     f:=yv->(1+Nr*(Tv(yv)+1)^3)*fdiff(Tv(y), y=yv):
     plt1[i]:=plot( 'f(y)',
                   y=0..1,
                   color=AA[i],
                   size = [1000, 600],
                   axes = boxed,
                   axesfont = ["Arial", 14, Bold],
                   thickness = 3
                 ):
     Tv:=tv-> eval(T(y,t), pds[i]:-value( y=0, t=0..1 )(tv));
     f:=tau->fdiff('Tv(t)', t=tau);
     plt2[i]:= plot( 'f(t)',
                     sample=[seq(j, j=0..1, 0.1)],
                     adaptive=false,       
                     color=AA[i],
                     style=point,
                     view=[0..1, default],
                     symbol=solidcircle,
                     symbolsize=16,
                     size = [1000, 600],
                     axes = boxed,
                     axesfont = ["Arial", 14, Bold],
                     thickness = 3
                  );
     Tv:=tv-> eval(T(y,t), pds[i]:-value( y=1, t=0..1 )(tv));
     f:=tau->fdiff('Tv(t)', t=tau);
     plt3[i]:= plot( 'f(t)',
                     sample=[seq(j, j=0..1, 0.1)],
                     adaptive=false,       
                     color=AA[i],
                     style=point,
                     view=[0..1, default],
                     symbol=solidcircle,
                     symbolsize=16,
                     size = [1000, 600],
                     axes = boxed,
                     axesfont = ["Arial", 14, Bold],
                     thickness = 3
                  );
  od:   
  display( [seq(PlotsT[k], k = 1 .. nops(HA1))],
           size = [1000, 600],
           axes = boxed,
           labels = [x, (convert("T", symbol))(x, T)],
           labelfont = ["Times", 14, Bold],
           labeldirections = [horizontal, vertical],
           axesfont = ["Arial", 14, Bold],
           thickness = 3
         );
  display( [seq(plt1[j], j=1..nops(HA1))],
           title=typeset((1+'Nr'*(T(y, t)+1)^3)*(diff(T(y, t), y)), "at t = 1"),
           titlefont=["Arial", 16, Bold]
         );
  display( [seq(plt2[j], j=1..nops(HA1))],
           title=typeset( diff(T(y, t), y), "at y = 0"),
           titlefont=["Arial", 16, Bold]
         );
  display( [seq(plt3[j], j=1..nops(HA1))],
           title=typeset( diff(T(y, t), y), "at y = 1"),
           titlefont=["Arial", 16, Bold]
         );

Pr*(diff(T(y, t), t)-Ree*(diff(T(y, t), y))) = (1+Nr*(T(y, t)+1)^3)*(diff(diff(T(y, t), y), y))+3*Nr*(T(y, t)+1)^2*(diff(T(y, t), y))^2

  

"Nr = ", 0

  

"Nr = ", 1

  

"Nr = ", 10

  

 

 

 

 
> 

 

Download PDEfunc.mw

Leaving aside...

tomleslie 13821
January 24 2023
2 0

minor syntax issues, the big problem you have is that your PDE is

  1. second-order in 'x' ,requiring two boundary conditions, and
  2. first-order in 't' requiring one initial condition.

You only have a total of two conditions

Not a "Hard-coded number"...

tomleslie 13821
January 23 2023
2 3

when you write X[`1`], the backquotes convert whatever is between them to a name., so you now have a variable whose name is 1, and whose value can be anything you want. You can tnen set the variable named `1` to be the value 1, as shown in the attached.

By the way this only "works" if you use the long-deprecated (since Maple 8 in 20002) vector() constructor. If you had used the recommended Vector() constructor, then X[`1`] would generate an error.

> 

  restart;
  X := vector([seq(x, x = 1 .. 5)]);
  Y := vector([seq(x, x = 6 .. 10)]);
  X[1];
  Y[1];
  Yfactor := evalf(X[`1`])/Y[`1`];
  eval(Yfactor, `1`=1);
  eval(Yfactor, `1`=2);
  eval(Yfactor, `1`=3);

 

X := Matrix(1, 5, {(1, 1) = 1, (1, 2) = 2, (1, 3) = 3, (1, 4) = 4, (1, 5) = 5})

  

array( 1 .. 5, [( 1 ) = (6), ( 2 ) = (7), ( 3 ) = (8), ( 4 ) = (9), ( 5 ) = (10) ] )

  

1

  

6

  

X[`1`]/Y[`1`]

  

1/6

  

2/7

  

3/8

 (1)
> 

 

Download nameNumb.mw

Use backquotes...

tomleslie 13821
January 23 2023
2 1

See the "toy" example in the attached

> 

plot( x^2,
      x=0..1,
      labels=[ typeset("a-value=", `A__*`),
               typeset("y-value=", `A__*`^2)
             ]
    );

 
> 

 

Download plotLab.mw

I suspect...

tomleslie 13821
January 21 2023
2 6

that your basic problem is that eqn3 contains the parameter 'T' which is defined nowhere. In the attached I have just set this equal to 1.

There are various other "inconsistencies" in the code, eg use of non-commutative multiplication, use of greek symbols together with their "roman" transliteration. Theses latter two are probably(?) not significant, but since I wouln't trust MAple's 2D input parser further than I could throw it, I fixed these up as well

At least the attached now executes!

> 

NULL
> 

restart
> 

with(plots)
> 

with(plottools)
> 

with(DEtools)
> 

eqn1 := diff(s(t), t) = lambda-beta*s(t)*i(t)-mu*s(t)

diff(s(t), t) = lambda-beta*s(t)*i(t)-mu*s(t)

 (1)
> 

eqn2 := diff(i(t), t) = beta*s(t)*i(t)-(mu+y+delta+`μ__1`)*i(t)

diff(i(t), t) = beta*s(t)*i(t)-(mu+y+delta+mu__1)*i(t)

 (2)
> 

eqn3 := diff(t(t), t) = y*i(t)-(alpha+mu)*T

diff(t(t), t) = y*i(t)-(alpha+mu)*T

 (3)
> 

eqn4 := diff(r(t), t) = alpha*t(t)+delta*i(t)-mu*r(t)

diff(r(t), t) = alpha*t(t)+delta*i(t)-mu*r(t)

 (4)
> 

beta := 0.5e-3

0.5e-3

 (5)
> 

y := .1

.1

 (6)
> 

mu := 0.4e-1

0.4e-1

 (7)
> 

alpha := 0.3e-2

0.3e-2

 (8)
> 

lambda := 15

15

 (9)
> 

delta := 0.6e-2

0.6e-2

 (10)
> 

`μ__1` := 0.42e-1

0.42e-1

 (11)
> 

N := 1783601

1783601

 (12)
> 

T := 1
> 

dsn := dsolve(eval({eqn1, eqn2, eqn3, eqn4, i(0) = 11437, r(0) = 1077, s(0) = 1770000, t(0) = 1087}), {i(t), r(t), s(t), t(t)}, 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 := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 28, [( 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..65, {(1) = 4, (2) = 4, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 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, (64) = -1, (65) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.570483095878728e-4, (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..4, {(1) = 11437.0, (2) = 1077.0, (3) = 1770000.0, (4) = 1087.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..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) = .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..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..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) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..4, {(1) = 11437.0, (2) = 1077.0, (3) = 1770000.0, (4) = 1087.0}, 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) = 10119594.844, (2) = 28.802999999999997, (3) = -0.1019253e8, (4) = 1143.6570000000002}, 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] = i(t), Y[2] = r(t), Y[3] = s(t), Y[4] = t(t)]`; YP[1] := 0.5e-3*Y[3]*Y[1]-.188*Y[1]; YP[2] := 0.3e-2*Y[4]+0.6e-2*Y[1]-0.4e-1*Y[2]; YP[3] := 15-0.5e-3*Y[3]*Y[1]-0.4e-1*Y[3]; YP[4] := .1*Y[1]-0.43e-1; 0 end proc, -1, 0, 0, 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] = i(t), Y[2] = r(t), Y[3] = s(t), Y[4] = t(t)]`; YP[1] := 0.5e-3*Y[3]*Y[1]-.188*Y[1]; YP[2] := 0.3e-2*Y[4]+0.6e-2*Y[1]-0.4e-1*Y[2]; YP[3] := 15-0.5e-3*Y[3]*Y[1]-0.4e-1*Y[3]; YP[4] := .1*Y[1]-0.43e-1; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 27 ) = (""), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0), ( 28 ) = (0) ] )) ] ); _y0 := Array(0..4, {(1) = 0., (2) = 11437., (3) = 1077., (4) = 1770000.}); _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); _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 elif type(_xin, `=`) and lhs(_xin) = "setdatacallback" then if not type(rhs(_xin), 'nonegint') then error "data callback must be a nonnegative integer (address)" end if; _dtbl[1][28] := rhs(_xin) 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, i(t), r(t), s(t), t(t)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 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

 (13)
> 

P1 := plots[odeplot](dsn, [t, s(t)], t = 0 .. 10, color = green); px1 := %

 
> 

P2 := plots[odeplot](dsn, [t, i(t)], t = 0 .. 10, color = blue); px1 := %

 
> 

P3 := plots[odeplot](dsn, [t, t(t)], t = 0 .. 10, color = red); px1 := %

 
> 

P4 := plots[odeplot](dsn, [t, r(t)], t = 0 .. 10, color = orange); px1 := %

 
> 

``
> 

NULL

Download odeIssue.mw

Have you considered...

tomleslie 13821
January 20 2023
0 0

the Maple command ssystem(command) which passes command to the host operating system which, in turn, performs the appropriate function?

See the help at ?ssystem

Physics:-Diff()...

tomleslie 13821
January 20 2023
1 0

is *probably* the best way, but you could aslo jut "cheat" a little. Substitute theta(t)=theta in you expression, differentiate with respect to theta, and the (if necessary/desired) substitute theta=thta(t) in the result

As in the attached

> 

  restart;
  p := (m1*a1 + m2*(a123 + z(t)))*sin(theta(t))*g + m3*(sin(theta(t))*(a1234 + z(t)) + cos(theta(t))*a5)*g:
#
# Either
#
  diff
  ( eval
    ( p,
      theta(t)=theta
    ),
    theta
  );
#
# or,
#
  eval
  ( diff
    ( eval
      ( p,
        theta(t)=theta
      ),
      theta
    ),
    theta=theta(t)
  );

(m1*a1+m2*(a123+z(t)))*cos(theta)*g+m3*(cos(theta)*(a1234+z(t))-sin(theta)*a5)*g

  

(m1*a1+m2*(a123+z(t)))*cos(theta(t))*g+m3*(cos(theta(t))*(a1234+z(t))-sin(theta(t))*a5)*g

 (1)
> 

 

Download chain.mw

Well, some simple typos...

tomleslie 13821
January 19 2023
1 0

for example, in the draw() command , you want to draw

seg1,seg2,seg3,seq4,

there is a difference between seg4 and seq4". Also there is no command

Triangle()

although there is a command

triangle()

Still on the subject of simple typos, you might want to consider the spelling of

_EnvHorizont:lName = 'x';

I fixed all of these in the attached, and probably a few more things. I also deleted several lines of completely redundant coded

> 

  restart:
  with(geometry):
  with(plots):
  _EnvHorizontalName = 'x':
  _EnvVerticalName = 'y':
   R := 5:
   ang := [3/4*Pi, -(3*Pi)/4, -Pi/6,4*Pi/9]:
   seq
   ( point
     ( `||`(P, i),
       [ R*cos(ang[i]), R*sin(ang[i])]
     ),
     i = 1 .. 4
   ):
   seq
   ( dsegment
     ( `||`(seg, i),
       [ `||`(P, i),
         `||`(P, irem(i, 4) + 1)
       ]
     ),
     i = 1 .. 4
   ):
   triangle(Tr1,[P1,P2,P4]):
   EulerCircle(Elc1,Tr1,'centername'=o):
   circle(cir, [point(OO, [0, 0]), R]):
   display
   ( [ draw
       ( [ P1(color = black, symbol = solidcircle, symbolsize = 12),
           P2(color = black, symbol = solidcircle, symbolsize = 12),
           P3(color = black, symbol = solidcircle, symbolsize = 12),
           P4(color = black, symbol = solidcircle, symbolsize = 12),
           seg1,
           seg2,
           seg3,
           seg4,
           Tr1(color=green),
           Elc1,
           cir(color = blue)
         ]
       ),
       textplot
       ( [ seq
           ( [ coordinates(`||`(P, i))[],
               convert(`||`(P, i), string)
             ],
             i=1..4
           )
         ],
         align=[above, right]
       )
     ],
     axes=none
   );
 

 
> 

 

Download euCir.mw

Mugged by 2D input...

tomleslie 13821
January 18 2023
2 0

Although you do not post a worksheet (again), I can tell that you are using Maple's 2-D input mode. You have to be careful when doing this, because whitespace is *sometimes* interpreted as an implicit multiplication. However you managed to post code here (some kind of cut-and-paste, I guess) actually illustrates the problem

display*([draw*[P1(color = black, symbol = solidcircle, symbolsize = 12), 
P2(color = black, symbol = solidcircle, symbolsize = 12), 
P3(color = black, symbol = solidcircle, symbolsize = 12), 
cir(color = blue)], 
textplot*([[coordinates(P1)[], "P1"], 
[coordinates(P2)[], "P2"], 
[coordinates(P3)[], "P3"]], align = [above, right])], axes = none);

Notice that instead of display(, you have display*( And the same with the 'draw and 'textplot' commands.

This problem is fixed in the attached which uses Maple's 1D-input mode where whitespace is whitespace and thus the user can use as much indentation (ie spaces) as desired, in order to make code easily readable. I also deleted some code whihc you don't seem to be using.

> 

  restart;
  with(geometry):
  with(plots):
  _EnvHorizontalName = 'x':
  _EnvVerticalName = 'y':
  R := 5:
  ang := [2/3*Pi, -3*Pi*1/4, -Pi*1/6]:
  seq
  ( point
    ( `||`(P, i),
      [ R*cos(ang[i]), R*sin(ang[i]) ]
    ),
    i = 1 .. 3
  ):
  seq
  ( dsegment
    ( `||`(seg, i),
      [ `||`(P, i), `||`(P, irem(i, 3) + 1) ]
    ),
    i = 1 .. 3
  ):
  circle
  ( cir,
    [ point(OO, [0, 0]), R ]
  ):
  display
  ( [ draw
      ( [ P1(color = black, symbol = solidcircle, symbolsize = 12),
          P2(color = black, symbol = solidcircle, symbolsize = 12),
          P3(color = black, symbol = solidcircle, symbolsize = 12),
          cir(color = blue)
        ]
      ),
      textplot
      ( [ [coordinates(P1)[], "P1"],
          [coordinates(P2)[], "P2"],
          [coordinates(P3)[], "P3"]
        ],
        align = [above, right]
      )
    ],
    axes = none
  );

 

 
> 

 

Download simpleGeo.mw

 

 

 

 

Your basic problem...

tomleslie 13821
January 13 2023
2 1

is that you have

 x := C[1] + n[1]*t;
y := C[2] + n[2]*t; 
EQ := eq = 0;
 tt := solve(subs(x = C[1] + n[1]*t, y = C[2] + n[2]*t, EQ), t);

Since 'x' and 'y' have been assigned values,  the subs() commmand will actually evaluate to

subs( C[1] + n[1]*t= C[1] + n[1]*t,  C[2] + n[2]*t= C[2] + n[2]*t, EQ)

which I'm guessing isn't what you want

Maybe you intended something like the attached?

PS if you really want to know the projection of a point on to a line, you can do this with the geometry:-projection() command

> 

restart;
with(LinearAlgebra):
A := [1, -2]:
B := [-2, 3]:
C := [1, 1]:
M := [x, y]:
ProjPL := proc(C, A, B)
       local M, AB, AM, Q, eq, EQ, eq1, a, b, c, t, tt, n, dist,
             x, y, xH, yH, H, CH, no;
             M := [x, y];
             AM := M - A;
             AB := B - A;
             Q := Matrix(2, [AM, AB]);
             eq := Determinant(Q);
             a := coeff(eq, x);
             b := coeff(eq, y);
             c := tcoeff(eq);
             dist := abs(a + b + c)/sqrt(a^2 + b^2);
             n := [a, b];
             EQ:=eq = 0;
             tt := solve(subs([x=C[1] + n[1]*t,y=C[2] + n[2]*t], EQ), t);
             x := C[1] + n[1]*t;
             y := C[2] + n[2]*t;
             xH := subs(t = tt, x);
             yH := subs(t = tt, y);
             H := [xH, yH];
             CH := H - C;
             no := sqrt(CH[1]^2 + CH[2]^2);
             return EQ, dist, H, no;
        end proc:
ProjPL(C, A, B);

1+5*x+3*y = 0, (9/34)*34^(1/2), [-11/34, 7/34], (9/34)*34^(1/2)

 (1)
> 

 

Download proj.mw

Anything wrong...

tomleslie 13821
January 11 2023
0 0

with the most basic use of the dsolve() command, as in the attached

> 

  restart:
  odeSys:= diff(y__1(x),x)=y__3(x)-cos(x),
           diff(y__2(x),x)=y__3(x)-exp(x),
           diff(y__3(x), x)=y__1(x)-y__2(x):
  ics:= y__1(0)=0,
        y__2(0)=0,
        y__3(0)=0:

  dsolve([odeSys, ics]);
        

{y__1(x) = -2*x-(1/2)*x^2+exp(x)-1, y__2(x) = sin(x)-2*x-(1/2)*x^2, y__3(x) = cos(x)+exp(x)-x-2}

 (1)
> 

 

Download simpleODE.mw

To get the desired form...

tomleslie 13821
January 10 2023
1 0

is a bit more complicated - see the attached

> 

  restart;
  u(x,t):=<u1(x,t),u2(x, t)>;
  pde:=diff(u(x,t), t) = Matrix([[0, mu*k^2/2], [2*A^2 - mu*k^2/2, 0]]).u(x,t);
  ans:=pdsolve
       ( simplify~
         ( subs
           ( isolate
             ( w^2 = -mu^2*k^4/4 + mu*k^2*A^2,
               mu
              ),
              pde
           )
         )
       );

Vector(2, {(1) = u1(x, t), (2) = u2(x, t)})

  

Vector[column](%id = 36893488148079001460) = Vector[column](%id = 36893488148078993524)

  

{u1(x, t) = _F1(x)*exp(-w*t)+_F2(x)*exp(w*t), u2(x, t) = w*(_F1(x)*exp(-w*t)-_F2(x)*exp(w*t))/(-A^2+((A^2-w)*(A^2+w))^(1/2))}

 (1)
> 

 

Download solPDE.mw

Still no worksheet!!!...

tomleslie 13821
January 09 2023
1 2

In the absence of a worksheet, I have to hack your cut+paste entry to get something executable. It generates the error message

Error, (in geometry:-triangle) The three given points are AreCollinear

This error message is produced by the command

triangle(TR, [M1, M2, A]):

because two of these points (A and M1) have the same coordinates, so no triangle can be constructed. Coordinates of all three points are shown below

A=[2, 4.582575695]
M1=[2.000000000, 4.582575695]
M2=[1.330063498, -4.819847621]

Since your algorithm is therefore incorrect, and I don't know what the "poncelet theorem for the triangle" is, the error is impossible for me to fix It *seems* as if you are doing something vaguely related to Poncelet's Closure Theorem (aka Poncelet's porism) described in

https://en.wikipedia.org/wiki/Poncelet%27s_closure_theorem

so, just for amusement I have included an illustration of this Theorem in the worksheet attached. It *may* be of use in whatever construction you are trying to produce

> 

  restart;
  with(geometry):
  with(plots):
  _EnvHorizontalName='x':
  _EnvVerticalName='y':
  R := 5.0:
  ang := evalf~([2/3*Pi, -3*Pi*1/4, -Pi*1/6]):
  seq( point( `||`(P, i),
              [ R*cos(ang[i]),
                R*sin(ang[i])
              ]
            ),
       i = 1 .. 3
     ):
  triangle( T1,
            [seq(`||`(P, j), j=1..3)]
          ):
  incircle(C1, T1):
  circumcircle(C2, T1):

  porism:= proc(t)
                local theta:=ang[1]+t,
                      P1, P2, P3, L, II, T1,j;
              #
              # local point P1 is somewhere on the (global)
              # circumcircle C2
              #
                point( P1,
                       [ R*cos(theta),
                         R*sin(theta)
                       ]
                     ):
              #
              # Get the tangent lines from (local) P1 to
              # the (global) incircle C1
              #
                TangentLine(L, P1, C1):
              #
              # Find the intersection of these tangent lines
              # with the (global) circumcircle C2. Note that
              # each tangent line, intersects C2 at two points,
              # one of which is (local) point(P1). So for
              # both tangent lines, determine the intersection
              # point whihc isn't P1
              #
                intersection(II, L[1], C2):
                if   distance(II[1], P1) > distance(II[2], P1)
                then point( P2,
                            coordinates(II[1])
                          );
                else point( P2,
                            coordinates(II[2])
                          );
                fi:
                intersection( 'II', L[2], C2):
                if   distance(II[1], P1) > distance(II[2], P1)
                then point( P3,
                            coordinates(II[1])
                          );
                else point( P3,
                            coordinates(II[2])
                          );
                fi:
                triangle( T1,
                          [P1, P2, P3]
                        ):
                display
                ( [ draw
                    ( [ P1(color=black, symbol=solidcircle, symbolsize = 12),
                        P2(color=black, symbol=solidcircle, symbolsize = 12),
                        P3(color=black, symbol=solidcircle, symbolsize = 12),
                        T1(color=red),
                        C1(color=blue),
                        C2(color=green)
                      ]
                    ),
                    textplot
                    ( [ [ coordinates(P1)[], "P1"],
                        [ coordinates(P2)[], "P2"],
                        [ coordinates(P3)[], "P3"]
                      ],
                      align=[above, right]
                    )
                  ],
                  axes=none
                );
        end proc:
  nf:=60:
  display
  ( [ seq
      ( porism(j),
        j=0..evalf(2*Pi*(1-1/nf)), evalf(2*Pi/nf)
      )
    ],
    insequence=true
  );

 
> 

 

Download ponTheo.mw

 

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