tomleslie

12482 Reputation

19 Badges

12 years, 226 days

MaplePrimes Activity


These are answers submitted by tomleslie

because neither the output from a texplot() or polygonplot() command is a geometric object whihc can be handled by the geometry:-draw() command.

The correct way to achieve what you want is to use the display() command, as in

plots:-display( [ geometry:-draw(whatever),
                         plots:-textplot(whatever)
                         plots:-polygonplot(whatever)
                      ]
                    )

As shown in the attached

  restart:
  with(plots): with(geometry):
  _EnvHorizontalName := 'x':
  _EnvVerticalName := 'y':
  a := 7:
  point(E, 0, a*sqrt(3)/2):
  point(B, -a/2, 0):
  point(C, a/2, 0):
  point(o, 0, a*sqrt(3)/6):
  point(A, 0, a/2):
  point(H, 0, 0):
  R := (3-sqrt(3))*sqrt(2)*a/12:
  point(J, 0, a*sqrt(3)/6 - R):
  triangle(Tr1, [E, B, C]):
  triangle(Tr2, [A, B, C]):
  StretchRotation(E1, E, B, Pi/4, clockwise, sqrt(2)/2):
  coordinates(E1):
  StretchRotation(E2, E, C, Pi/4, counterclockwise, sqrt(2)/2):
  coordinates(E2):
  triangle(Tr3, [E, B, E1]):
  triangle(Tr4, [E, C, E2]):
  triangle(Tr5, [B, C, J]):
  circle(cir, [point(P1,[0,a*sqrt(3)/6]), R]):
  poly := Matrix( [ [0, a*sqrt(3)/2], [-7/4 + (7*sqrt(3))/4, -7/4 + (7*sqrt(3))/4],
                    [0, a/2],
                    [7/4 - (7*sqrt(3))/4, -7/4 + (7*sqrt(3))/4]
                  ],
                  datatype = float
                ):
  pol1 := polygonplot(poly, colour = "Magenta", transparency = 0.7, gridlines):
  tex := textplot([0.2, a*sqrt(3)/2, "zE"], 'align' = {'above', 'right'}):
  display( [ draw( [ Tr1(color = cyan),
                     Tr3(color = green),
                     cir(color=blue),
                     Tr2(color = red),
                     Tr4(color = grey),
                     Tr1(color=blue)],'view' = [-5 .. 5, 0 .. 7
                   ],
                   axes = normal,
                   scaling = constrained,
                   size=[800,800]
                   ),
            tex
           ]
          );

 

  line(L1, [B, o]):
  Equation(L1):
  line(L1, -(7*x*sqrt(3))/6 + (7*y)/2 - (49*sqrt(3))/12 = 0):
  reflection(J1, J, L1):
  triangle(Tr6, [B, J1, E]):
  line(L2, [C, o]):
  Equation(L2):
  line(L2, -(7*x*sqrt(3))/6 - (7*y)/2 + (49*sqrt(3))/12 = 0):
  reflection(J3, J, L2):
  triangle(Tr7, [C, J3, E]):
  triangle(T1, [E, J1, A]):
  triangle(T2, [E, C, E2]):
  triangle(T3, [B, H, J]):
  triangle(T4, [C, H, J]):

  display( [ draw( [ cir(color = orange, filled = true, transparency = 0.1),
                     Tr6(color = blue, filled = true, transparency = 0.2),
                     Tr5(color = blue, filled = true, transparency = 0.2),
                     Tr7(color = blue, filled = true, transparency = 0.2),
                     T1(color = green, filled = true, transparency = 0.2),
                     T2(color = green, filled = true, transparency = 0.2),
                     T3(color = green, filled = true, transparency = 0.2),
                     T4(color = green, filled = true, transparency = 0.2)
                   ],
                   axes = none,
                   scaling = constrained
                 ),
             pol1
           ]
         );

                   

 

 

Download geomDraw.mw

  expr:= x+I*y-0.4646295e-3*tan(x+I*y)+0.2758717622e-2*tan(x+I*y)/(0.6000000000e-3*(x+I*y)^2-0.2760000000e-2);

and assume that you want simultaneous solutions for Re(expr)=0, Im(expr)=0, then one obtains three possible answers. See the attached

  restart;
  expr:=x+I*y-0.4646295e-3*tan(x+I*y)+0.2758717622e-2*tan(x+I*y)/(0.6000000000e-3*(x+I*y)^2-0.2760000000e-2):
#
# plot Re(expr)=0 and Im(expr)=0 - just to get
# some idea of where solutions might be
#
  plots:-implicitplot( [ Re(expr),Im(expr)],
                       x=-2..2,
                       y=-2..2,
                       color=[red,blue],
                       axes=boxed
                     );
#
# Hmmm solution (if any are very close to the origin
# so replot above with *much* smaller x,y ranges
#
  plots:-implicitplot( [ Re(expr),Im(expr)],
                         x=-0.0001..0.0001,
                         y=-0.0001..0.0001,
                         color=[red,blue],
                         axes=boxed
                       );
#
# Looks like there may be three solutions. From the above
# plot these are approximately
#
#          x= 0,       y=0
#          x=-0.00002, y=0
#          x= 0.00002, y=0
#
# Use fsolve with appropriate ranges to obtain these solutions
#
  f:=unapply( Re(expr), [x,y]):
  g:=unapply( Im(expr), [x,y]):
  fsolve( [f, g], [0..0.00005, -0.00005..0.00005]);
  fsolve( [f, g], [-0.00005..0, -0.00005..0.00005]);
  fsolve( [f, g], [-0.00001..0.00001, -0.00001..0.00001]);
 

 

 

[0.19535837429479822e-4, 0.]

 

[-0.19535837433966997e-4, 0.]

 

[0., 0.]

(1)

 

Download fsol.mw

the "simplification" whihch Maple is applying, it would probably be easier to enter it as a string in the first place, and then use parse() if you want the mathematical expression, as in the attached

  restart;
  q1:="2.800000000*10^(-30)*a+2.7800000000*10^(-29)*b+2.7800000000*10^(-31)+3.0*10^(-21)+2.*10^(-32)*c+3.*10^(-30)*d";
  parse(q1);

"2.800000000*10^(-30)*a+2.7800000000*10^(-29)*b+2.7800000000*10^(-31)+3.0*10^(-21)+2.*10^(-32)*c+3.*10^(-30)*d"

 

0.2800000000e-29*a+0.2780000000e-28*b+0.3000000000e-20+0.2000000000e-31*c+0.3000000000e-29*d

(1)

 


 

Download parse.mw

You define a procedure which accepts three parameters - although the third parameter is never used within the procedure; so why does it exist? I can remove this in the attached and still get the same answer

The procedure computes a quanity called ` S`(pO2, P50(pH)), which is never used within the procedure - so why does the calculation exist. I have removed this in the attached and still get the same answer

The local variable 'T' is used within the procedure, but is defined nowhere - is this deliberate?

See the attached

restart

pH := `<,>`(7.398, 7.392); pO2 := `<,>`(121.6, 113.4); Tart := `<,>`(32.5, 32.9)

Vector[column](%id = 36893488148080515660)

(1)

NULL

NULL

test := proc (pO2, pH) local P50, P50_37, n, T37, T, P50a; n := 2.7; T37 := 37; P50(pH) := 26.6*10^(.48*(7.4-pH)); P50_37(P50(pH), T37) := P50(pH)*10^((-1)*.24*(37-T37)); P50a(P50_37(P50(pH), T37), T) := P50_37(P50(pH), T37)*10^((-1)*.24*(37-T)) end proc

NULL

NULL

`~`[test](pO2, pH, Tart)

Vector[column](%id = 36893488148101248532)

(2)

``

NULL

The correct answer for the above should be 20.78938 and 21.39546
solve
 

Download oddProc.mw

 

You have stated

ICBC:= {u(y,0) = 0, u(0,t) = cos(t), u(N, t) = 0};

so your first initial condition requires  that u(0,0)=0, and your second boundary condition requires that u(0,0)=cos(0)=1. Obviously both cannot be true, so before doing anything else you have to fix this

When I "experiment" with Maple's numeric solution for this situation, it appears as if u(0,0)=0 is always used - but rather obviously, this screws up the numeric solution for small values of 't', because of the discrepancy with your second boundary condition.

For more detailed information see the attached.

  restart:
  with(plots):
  with(plottools):
  N:=10:
  t_upper:=evalf(Pi):
  s_step:=0.01:
   
  PDE:=diff(u(y, t), t) = diff(u(y, t), y, y);
  ICBC:= [u(y,0) = 0, u(0,t) = cos(t), u(N, t) = 0];
#
# Note that boundary conditions are contradictory. The
# first requires u(0,0)=0 and the second requires
# u(0,0)=cos(0)=1. Not sure what Maple is going to do
# with this

diff(u(y, t), t) = diff(diff(u(y, t), y), y)

 

[u(y, 0) = 0, u(0, t) = cos(t), u(10, t) = 0]

(1)

#
# Set up plots of the boundary conditions so that
# these can be included in a general plot of the
# solution surface - just as a check!!!
#
  f1:= plottools:-transform((x, y) -> [0, x, y]):
  f2:= plottools:-transform((x, y) -> [x, 0, y]):
  q1:=plot( cos(x), x=0..t_upper):
  q2:=plot( 0,      x=0..t_upper):
  q3:=plot( 0,      x=0..N):
  pbc:=display( [ f1(q1), f1(q2), f3(q3) ],
                color=green,
                thickness=4
              );

 

#
# Solve system using Maple defaults for spacestep and timestep
# and plot with boundary conditions. Note that spacestep will
# default to (N-0)/20, ie 0.5 and timestep will default to this
# value of spacestep
#
# Looks like Maple is *trying* to use the boundary condition
# u(0, t)=cos(t) along y=0 - except close to t=0, where it is
# using u(0,0)=0
#
  sol1:= pdsolve(PDE,ICBC,numeric):
  display( [ sol1:-plot3d( u(y, t),
                           y=0..N,
                           t=0..t_upper,
                           color=red,
                           style=surface
                         ),
              pbc
            ]
          );

 

#
# So check the returned value for t=0, y=0
#
# 1. from the boundary condition  u(y, 0)=0 the
#    answer for u(0,0) should return 0
# 2. from the boundary condition  u(y, 0)=cos(t)
#    the answer should be 1, when t=0
#
  uVal := sol1:-value(u(y,t), t=0):
  eval(u(y,t), uVal(0));
#
# So we seem to be obeying the u(y, 0)=0 condition
#
  

HFloat(0.0)

(2)

 

#
# In the above the boundary condition u(0,t) = cos(t), can get a
# better fit along y=0, by reducing the spacestep (which will
# reduce the timestep, and the reduced timestep will improve
# the fit along u(0,t) = cos(t)
#
  sol2:= pdsolve(PDE,ICBC,numeric, spacestep=s_step):
  display( [ sol2:-plot3d( u(y, t),
                           y=0..N,
                           t=0..t_upper,
                           color=blue,
                           style=surface
                         ),
              pbc
            ]
          );
 

 

#
# So check the returned value for t=0, y=0
#
# 1. from the boundary condition  u(y, 0)=0 the
#    answer for u(0,0) should return 0
# 2. from the boundary condition  u(y, 0)=cos(t)
#    the answer should be 1, when t=0
#
  uVal := sol2:-value(u(y,t), t=0):
  eval(u(y,t), uVal(0));
#
# So we seem to be obeying the u(y, 0)=0 condition
#

HFloat(0.0)

(3)

#
# Plot the both solutions along the line y=0, for comparison with
# the boundary condition u(0,t)=cos(t), Both solutions are very
# wrong at t=0, although sol2 (with reduced spacestep and timestep)
# is much better thereafter. Note that by default sol1, will have
# a (default) timestep of 0.5, whereas for sol2 it is set by s_step
# (defined as 0.01 above)
#
  display( [ sol1:-plot(y=0, t=0..t_upper, color=red),
             sol2:-plot(y=0, t=0..t_upper, color=blue),
             plot( cos(t), t=0..t_upper, color=green)
           ]
         );

 

 

Download PDEissue2.mw

the coerce() parameter modifier, as shown in the attached.

See also the help at ?Data Type Coercion

  restart;
  myProc := proc( s::coerce( (s::equation)-> [s],
                             (s::set)-> convert(s, list),
                             (s::Vector)-> convert(s, list),
                             (s::list)-> s
                           )
                )
                s;
            end proc:
  myProc(  a=b  );
  myProc( {a=b, c=d} );
  myProc( <a=b, c=d> );
  myProc( [a=b, c=d] );

[a = b]

 

[a = b, c = d]

 

[a = b, c = d]

 

[a = b, c = d]

(1)

 


Download coerce.mw

but it depends so much on what you really, really want!

  restart;
  with(plots):
  display( seq( pointplot
                ( [ seq
                    ( [i,sqrt(i)],
                      i=1..j
                    )
                  ],
                  symbol=solidcircle,
                  symbolsize=20,
                  color=red
                ),
                j=1..22
              ),
              insequence=true
           );

 

 

Download anim.mw

 

It is not obvious (to me) why you should need the Degrees() package if you are specifying units - because 'degrees' is a perfectly acceptable unit for plane angle. If you are having problems with using degrrees in a worksheet whihc does not use units, then please post the worksheet using the big green up-arrow in the MApleprimes toolbar.

I'm not sure that I understand your problem with linearr and angular velocity. I admit that the defualt unit for angular velocity ( ie m*s/m(radius) ) isn't the most obvious choice, but it is relatively simple to tell MAple to use either rad/sec or rpm as a default - see the attached. In order to convert from an angular velocity (whatever the unit), you have to multiply by something which has units of Unit(m(radius)) - again see the attached.

NB when rendered on this site, units display differently (with double square brackets [[]]) than the display in the worksheet itself - I don't know why!
 

  restart;
  with(Units):
  with(Units[Standard]):

Automatically loading the Units[Simple] subpackage
 

 

  av:= 2*Unit(rad)/10*Unit(sec); # wrong - because of operator precedenc
  av:= 2*Unit(rad)/(10*Unit(sec));# correct - but with an "odd" unit
#
# Convert to a linear velocity, using
#
# linear_velocity=angular_velocity*radius
#
  lv:= av*1*Unit(m(radius));

(1/5)*Units:-Unit(m*s/m(radius))

 

(1/5)*Units:-Unit(m/(s*m(radius)))

 

(1/5)*Units:-Unit(m/s)

(1)

#
# Specify a "sensible" default unit for angular speed and repeat
#
  UseUnit(rad/sec);
  av:= 2*Unit(rad)/10*Unit(sec); # wrong - because of operator precedence
  av:= 2*Unit(rad)/(10*Unit(sec));# correct - but with an "odd" unit
#
# Convert to a linear velocity, using
#
# linear_velocity = angular_velocity*radius
#
  lv:= av*1*Unit(m(radius));

false

 

(1/5)*Units:-Unit(m*s/m(radius))

 

(1/5)*Units:-Unit(rad/s)

 

(1/5)*Units:-Unit(m/s)

(2)

#
# Specify a different "sensible" default unit for angular speed
#
  UseUnit(rpm);
  av:= 2*Unit(rad)/10*Unit(sec); # wrong - because of operator precedence
  av:= 2*Unit(rad)/(10*Unit(sec));# correct - but with an "odd" unit
#
# Convert to a linear velocity, using
#
# linear_velocity = angular_velocity*radius
#
  lv:= av*1*Unit(m(radius));

true

 

(1/5)*Units:-Unit(m*s/m(radius))

 

6*Units:-Unit(rpm)/Pi

 

(1/5)*Units:-Unit(m/s)

(3)

 

Download unitProb.mw

 

a syntactically correct ode would be useful - otherwise I just have to guess what you mean. My guess is shown in the attached, along with its solution

Since you have a second-order ODE its solution will contain two arbitrary constants - represented in the attached by _C1 and _C2.

Before you can "plot" anything you will have to provide appropriate initial/boundary conditions so that numerical values for these arbitrary constants can be obtained.

Further what is the value of 'a'? You say you want to plot  "different regions like u<=-a , -a<=u<=a , u>=a". The name "a" does not appear in the ODE, or indeed anywhere!

   ode:=diff(x(u),u,u)+1/2*sech(u)^2*x(u)=0;
   dsolve(ode);

diff(diff(x(u), u), u)+(1/2)*sech(u)^2*x(u) = 0

 

x(u) = _C1*(2*cosh(2*u)-2)^(3/4)*hypergeom([3/4-(1/4)*3^(1/2), 3/4-(1/4)*3^(1/2)], [1-(1/2)*3^(1/2)], (1/2)*cosh(2*u)+1/2)*(2*cosh(2*u)+2)^(1/2)*cosh(u)^(-(1/2)*3^(1/2))/sinh(2*u)^(1/2)+_C2*(2*cosh(2*u)-2)^(3/4)*hypergeom([3/4+(1/4)*3^(1/2), 3/4+(1/4)*3^(1/2)], [1+(1/2)*3^(1/2)], (1/2)*cosh(2*u)+1/2)*(2*cosh(2*u)+2)^(1/2)*cosh(u)^((1/2)*3^(1/2))/sinh(2*u)^(1/2)

(1)

 

Download badode2.mw

defining the "square". First issue is that you use the name 'c', which is nowhere defined. Second issue is that for squares, (like othe polygons) the geometry package likes the points to be given in cyclic order - I don't think it matters whether you go clockwise or anticlockwise, but they do have to be in order!

Observation:  The ellipse 'E' and the circle 'C1' do not intersect (see figure in the attached)., although for the supplied equations solve() or fsolve(..complex) will give a complex answer, of which you have taken the real part in the definition of the point 'T'. Not obvious to me that this is a "meaningful" operation

  restart;
  with(geometry):
  _EnvHorizontalName := x:
  _EnvVerticalName := y:
  a := 7:
  b := a*(1/2 + 1/6*sqrt(45 - 24*sqrt(3)))^2:
  r := b*sqrt(b)/(sqrt(a + b) + sqrt(a)):

  point(A, -a, -b):
  point(B, -a,  b):
  point(C,  a,  b):
  point(F,  a, -b):
  square(Sq, [A, B, C, F]):

  circle(C1, [point(P1, [r, 0]), r]):
  circle(C2, [point(P2, [(1 + sqrt(3))*r, r]), r]):
  circle(C3, [point(P3, [(1 + sqrt(3))*r, -r]), r]):
  ellipse(E, x^2/a^2 + y^2/b^2 = 1, [x, y]):
  solve({Equation(C1), x^2/a^2 + y^2/b^2 = 1}, {x, y}):
  point(T, [5.349255162, 2.829908743]):
  IsOnCircle(T, C1);
  draw( [ E(color = cyan),
          C1(color = yellow, filled = true),
          T(symbol = solidcircle, symbolsize = 20, color = red),
          Sq,
          C2(color = red),
          C3(color = red),
          Sq(color=blue)
        ],
        axes = normal,
        view = [-a .. a, -b .. b],
        scaling = constrained
      );
 

false

 

 

fsolve( {Equation(C1), x^2/a^2 + y^2/b^2 = 1}, complex);

{x = 2.829908741-5.349255152*I, y = -5.578472313-1.160682287*I}

(1)

 

Download ell1.mw

throughout by U(z). The first term is still integrable, and the second term is transformed to the well know quotient formula for diffferetniation/integration, so is also redily integrable.

See the attached

restart

with(PDEtools); with(plots); tr1 := -c*t+x = z; tr2 := {c = 1}

-c*t+x = z

 

{c = 1}

(1)

eq := U(z)^2*(diff(U(z), z))-((diff(U(z), z))*(diff(U(z), z, z))-(diff(U(z), z, z, z))*U(z))*c^2/U(z) = 0

U(z)^2*(diff(U(z), z))-((diff(U(z), z))*(diff(diff(U(z), z), z))-(diff(diff(diff(U(z), z), z), z))*U(z))*c^2/U(z) = 0

(2)

eq1 := map(int, lhs(eq), z)-C1 = 0

(1/3)*U(z)^3+int(-((diff(U(z), z))*(diff(diff(U(z), z), z))-(diff(diff(diff(U(z), z), z), z))*U(z))*c^2/U(z), z)-C1 = 0

(3)

  expand(eq/U(z));
  int(lhs(%),z);

U(z)*(diff(U(z), z))-(diff(diff(U(z), z), z))*c^2*(diff(U(z), z))/U(z)^2+c^2*(diff(diff(diff(U(z), z), z), z))/U(z) = 0

 

(1/2)*U(z)^2+(diff(diff(U(z), z), z))*c^2/U(z)

(4)

NULL

Download doInteg.mw

I can't get an analytic solution either, but a numeric one is trivial, as shown in the attached.

Note that where you have used e^(-u^2), I have assume that you mean exp(-u^2).

Obce again, no way I can check this in Maple12 - that's about 12 major releases ago!

  ode := diff(x(u), u, u) + 1/4*exp(-u^2)*x(u) = 0;
  sol := dsolve([ode, x(0) = 1, D(x)(0) = 0], numeric);
  plots:-odeplot( sol,
                  [ [u, x(u)],
                    [u, diff(x(u), u)]
                  ],
                  u=0..1,
                  color=[red, blue]
                );

diff(diff(x(u), u), u)+(1/4)*exp(-u^2)*x(u) = 0

 

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) = 2, (2) = 2, (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) = 0.20190635023366182e-1, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..2, {(1) = 1.0, (2) = .0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..2, {(1) = .1, (2) = .1}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0}, datatype = float[8], order = C_order), Array(1..2, 1..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}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8]), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .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..2, {(1) = 0, (2) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..2, {(1) = 1.0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = -.25}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..2, {(1, 1) = .0, (1, 2) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = x(u), Y[2] = diff(x(u),u)]`; YP[2] := -(1/4)*exp(-X^2)*Y[1]; YP[1] := Y[2]; 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] = x(u), Y[2] = diff(x(u),u)]`; YP[2] := -(1/4)*exp(-X^2)*Y[1]; YP[1] := Y[2]; 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..2, {(1) = 0., (2) = 1.}); _vmap := array( 1 .. 2, [( 1 ) = (1), ( 2 ) = (2)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _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) = [u, x(u), diff(x(u), u)], (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

 

 

NULL

Download simpODE.mw

 

you can get a solution as shown in the attached.

alpha[1](t), alpha[2](t), m[1](t) and m[2](t) all appear to be complex whereas z[1](t) and z[2](t) appear to be real.

(NB the plots are much nicer  in the worksheet than they render on this site - honest)
 

  restart;
  eqns := { diff(alpha[1](t), t) = -w[r]*alpha[1](t)*I - g*m[1](t)*I + J*alpha[2](t)*I,
            diff(alpha[2](t), t) = -w[r]*alpha[2](t)*I - g*m[2](t)*I + J*alpha[1](t)*I,
            diff(m[1](t), t) = -2*I*w[a]*m[1](t) + g*alpha[1](t)*z[1](t)*I,
            diff(m[2](t), t) = -2*I*w[a]*m[2](t) + g*alpha[2](t)*z[2](t)*I,
            diff(z[1](t), t) = -2*I*g*(alpha[1](t)*conjugate(m[1](t)) - conjugate(alpha[1](t))*m[1](t)),
            diff(z[2](t), t) = -2*I*g*(alpha[2](t)*conjugate(m[2](t)) - conjugate(alpha[2](t))*m[2](t))
          };
  cons := {J = 0.1, g = 1, w[a] = 100, w[r] = 100};
  ics := {alpha[1](0) = sqrt(20), alpha[2](0) = 0, m[1](0) = 0, m[2](0) = 0, z[1](0) = -1, z[2](0) = -1};

{diff(alpha[1](t), t) = -I*w[r]*alpha[1](t)-I*g*m[1](t)+I*J*alpha[2](t), diff(alpha[2](t), t) = -I*w[r]*alpha[2](t)-I*g*m[2](t)+I*J*alpha[1](t), diff(m[1](t), t) = -(2*I)*w[a]*m[1](t)+I*g*alpha[1](t)*z[1](t), diff(m[2](t), t) = -(2*I)*w[a]*m[2](t)+I*g*alpha[2](t)*z[2](t), diff(z[1](t), t) = -(2*I)*g*(alpha[1](t)*conjugate(m[1](t))-conjugate(alpha[1](t))*m[1](t)), diff(z[2](t), t) = -(2*I)*g*(alpha[2](t)*conjugate(m[2](t))-conjugate(alpha[2](t))*m[2](t))}

 

{J = .1, g = 1, w[a] = 100, w[r] = 100}

 

{alpha[1](0) = 2*5^(1/2), alpha[2](0) = 0, m[1](0) = 0, m[2](0) = 0, z[1](0) = -1, z[2](0) = -1}

(1)

  dsol:=dsolve( eval( `union`(eqns, ics), cons), numeric);
  dsol(0.1);
#
# Hmmmm - lookks as if alpha[1](t), alpha[2](t), m[1](t), m[2](t)
# are all complex whereas z[1](t) and z[2](t) are real.
#
  plots:-odeplot( dsol,
                  [ [t, Re(alpha[1](t))],
                    [t, Im(alpha[1](t))]
                  ],
                  t=0..0.2,
                  color=[red, blue],
                  title=typeset(Re(alpha[1](t)), " and ", Im(alpha[1](t))),
                  titlefont=[times, italic, 16]
                );
  plots:-odeplot( dsol,
                  [ [t, Re(alpha[2](t))],
                    [t, Im(alpha[2](t))]
                  ],
                  t=0..0.2,
                  color=[red, blue],
                  title=typeset(Re(alpha[2](t)), " and ", Im(alpha[2](t))),
                  titlefont=[times, italic, 16]
                );
  plots:-odeplot( dsol,
                  [ [t, Re(m[1](t))],
                    [t, Im(m[1](t))]
                  ],
                  t=0..0.2,
                  color=[red, blue],
                  title=typeset(Re(m[1](t)), " and ", Im(m[1](t))),
                  titlefont=[times, italic, 16]
                );
  plots:-odeplot( dsol,
                  [ [t, Re(m[2](t))],
                    [t, Im(m[2](t))]
                  ],
                  t=0..0.2,
                  color=[red, blue],
                  title=typeset(Re(m[2](t)), " and ", Im(m[2](t))),
                  titlefont=[times, italic, 16]
                );
  plots:-odeplot( dsol,
                  [ [t, z[1](t)],
                    [t, z[2](t)]
                  ],
                  t=0..0.2,
                  color=[black, green],
                  title=typeset( z[1](t), " and ", z[2](t)),
                  titlefont=[times, italic, 16]
                );

`Non-fatal error while reading data from kernel.`

 

[t = .1, alpha[1](t) = -3.75412937362476+2.42843979680634*I, alpha[2](t) = -0.242878255083043e-1-0.375392393317978e-1*I, m[1](t) = 0.536167658802068e-1-0.653827773144382e-1*I, m[2](t) = 0.187160998874069e-3+0.440484190777856e-3*I, z[1](t) = -.985597053964343+0.*I, z[2](t) = -.999999541889001+0.*I]

 

 

 

 

 

 

 

Download odeComp.mw

I have no idea what you are trying to achieve. For example in the code you present

Cen := proc(M, N, R) local eq1, eq2, sol;
eq1 := EqBIS(M, N, R) = 0;
eq2 := EqBIS(N, M, R) = 0;
sol := simplify(solve({eq1, eq2}, {x, y}));
RETURN([subs(sol, x), subs(sol, y)]);
end proc
  Ce := Cen(P, Dd, Q);

what are P, Dd, Q?

Am I expected to guess???

If I do make some more-or-less random guesses - required because of your inability to ask a sensible question or post reasonably functional code using the big green up-arrow in the Mapleprimes toolbar, then I'd probably come up with what is shown in the attached

I assume that if this answer is *satisfactory* then you will delete the whole thread?

  restart:
  with(geometry):
  _EnvHorizontalName:= x:
  _EnvVerticalName:= y:
  triangle( ABC,
            [ point(A, [4, 5]),
              point(B, [11, 7/3]),
              point(C, [11, 5])
            ]
          ):
  bisector( bA, A, ABC ):
  incircle( inc, ABC, centername=incc):
  evalf(coordinates(incc));

  draw( [  A(symbol=solidcircle, symbolsize=20, color=red),
           B(symbol=solidcircle, symbolsize=20, color=red),
           C(symbol=solidcircle, symbolsize=20, color=red),
           bA(color=black),
           ABC(color=red),
           inc(color=blue),
           incc(symbol=solidcircle, symbolsize=20, color=blue)
        ],
        axes=boxed,
        view=[0..12, 0..6],
        scaling=constrained
      );

[9.912034177, 3.912034175]

 

 

 

Download useGeom2.mw

same calculation using the geometry() package. See the attached

  restart;
  EqBIS:= proc(P, U, V)
               uses LinearAlgebra:
               local a, M1, t;
               a := (P - U)/Norm(P - U, 2) + (P - V)/Norm(P - V, 2);
               M1 := P + a*t;
               return eliminate( { x = M1[1], y = M1[2]},
                                 t
                               )[2][]=0;
          end proc:
  evalf
  ( isolate
    ( EqBIS( Vector([4, 5]),
             Vector([11, 7/3]),
             Vector([11, 5])
           ),
      y
    )
  );

y = 5.736102529-.1840256318*x

(1)

  restart:
  with(geometry):
  _EnvHorizontalName := x:
  _EnvVerticalName := y:
  triangle( ABC, [ point(A, [4, 5]),
                   point(B, [11, 7/3]),
                   point(C, [11, 5])
                 ]
          ):
  evalf
  ( isolate
    ( Equation
      ( bisector( bA, A, ABC )
      ),
      y
    )
  );

y = -.1840256319*x+5.736102529

(2)

 

Download useGeom.mw

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