tomleslie

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9 years, 275 days

MaplePrimes Activity


These are answers submitted by tomleslie

In the attached worksheet (on my machine)

  1. it starts with Physics:-Version 419 and everything works
  2. it sets the Physics:-Version to 426 repeats the commands, and all integrals return unevaluated!!
  3. it sets the Physics:-Version back to 419 and everything works again

If you re-execute this worksheet, your experience will be somewhat different, because you will be starting  with Physics:-Version 426, so the first two sets of commands *should* give the same "unevaluated integrals. But what happens with the last set of commands where you should be using Physicss:-Version 419??

restart;

version()

 User Interface: 1399874

         Kernel: 1399874
        Library: 1399874

 

1399874

(1)

interface(version)

`Standard Worksheet Interface, Maple 2019.1, Windows 7, May 21 2019 Build ID 1399874`

(2)

Physics:-Version();

`The "Physics Updates" version "419" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox\2019\Physics Updates\lib\Physics Updates.maple, created 2019, September 21, 9:30 hours`

(3)

restart;

int(exp(x),x=0..1)

-1+exp(1)

(4)

int(sin(n*x),x=0..Pi)

-(-1+cos(Pi*n))/n

(5)

int(tan(x),x=0..Pi)

undefined

(6)

int(cos(x),x=0..1)

sin(1)

(7)

int(sin(x),x=0 .. Pi)

2

(8)

int(cos(x),x)

sin(x)

(9)

int(x,x=0 .. 1)

1/2

(10)

Physics:-Version(426);

Warning, this package updates content shipped in a standard Maple install.  Use the 'restart' command to clear your session before using these commands.

 

`The "Physics Updates" version "426" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox/2019/Physics Updates/lib\Physics Updates.maple, created 2019, September 21, 9:34 hours`

(11)

restart;

int(exp(x),x=0..1)

int(exp(x), x = 0 .. 1)

(12)

int(sin(n*x),x=0..Pi)

int(sin(n*x), x = 0 .. Pi)

(13)

int(tan(x),x=0..Pi)

int(tan(x), x = 0 .. Pi)

(14)

int(cos(x),x=0..1)

int(cos(x), x = 0 .. 1)

(15)

int(sin(x),x=0 .. Pi)

int(sin(x), x = 0 .. Pi)

(16)

int(cos(x),x)

sin(x)

(17)

int(x,x=0 .. 1)

1/2

(18)

Physics:-Version(419);

Warning, this package updates content shipped in a standard Maple install.  Use the 'restart' command to clear your session before using these commands.

 

`The "Physics Updates" version "419" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox/2019/Physics Updates/lib\Physics Updates.maple, created 2019, September 21, 9:34 hours`

(19)

restart;

int(exp(x),x=0..1)

-1+exp(1)

(20)

int(sin(n*x),x=0..Pi)

-(-1+cos(Pi*n))/n

(21)

int(tan(x),x=0..Pi)

undefined

(22)

int(cos(x),x=0..1)

sin(1)

(23)

int(sin(x),x=0 .. Pi)

2

(24)

int(cos(x),x)

sin(x)

(25)

int(x,x=0 .. 1)

1/2

(26)

 


 

Download PhysVer.mw

If you want better control over the x-values at which the function is evaluated, use the attached.

You will have to change the filename in the Export() command to something appropriate for your machine

  restart;
  f:= x->x^3-2*x:
  startVal:= 1;
  stopVal:= 10;
  spacing:= 0.1;
  M:= Matrix
      ( 1+round((stopVal-startVal)/spacing),
        2,
        (i,j)-> `if`( j=1,
                      startVal+(i-1)*spacing,
                      f( startVal+(i-1)*spacing)
                    )
      );
  Export("C:/Users/TomLeslie/Desktop/data.csv", M);

startVal := 1

 

stopVal := 10

 

spacing := .1

 

_rtable[18446744074396479230]

 

1037

(1)

 


 

Download expData.mw

 

Your ODE is third order. You therefore need three intial conditions

The only thing you really need to remember is that is that ODEs and BCs/ICs have to be supplied to dsolve() as a simple list. Not a pair of lists, or a listlist or anything else. Just a plain ordinary simple list.

So I'd fix your problem as shown in the attached

Lindas signal transduction model

 

NULLNULLNULLNULL

Mod1 := [diff(Depot(t), t) = piecewise(t = 0, -Ka*Depot(t)+150, t = 24, -Ka*Depot(t)+150, -Ka*Depot(t)), diff(Central(t), t) = Ka*Depot(t)-ce*Ke, diff(EGFR(t), t) = Kin*(1-ce/IC50-ce)-Kout*EGFR(t), diff(PPi3k(t), t) = (EGFR(t)-PPi3k(t))/t1, diff(PAKT(t), t) = (PPi3k(t)-PAKT(t))/t1, diff(PRas(t), t) = (EGFR(t)-PRas(t))/t1, diff(PRaf(t), t) = (PRas(t)-PRaf(t))/t1, diff(PMEK(t), t) = (PRaf(t)-PMEK(t))/t1, diff(PERK(t), t) = (PMEK(t)-PERK(t))/t1, diff(Pmyc(t), t) = (PAKT(t)+PERK(t)-Pmyc(t))/t1, diff(ACII(t), t) = Pmyc(t)-ACII(t)*ACIIdeg, diff(SPC(t), t) = ACIIloss-SPC(t)*Ke0]

[diff(Depot(t), t) = piecewise(t = 0, -Ka*Depot(t)+150, t = 24, -Ka*Depot(t)+150, -Ka*Depot(t)), diff(Central(t), t) = Ka*Depot(t)-ce*Ke, diff(EGFR(t), t) = Kin*(1-ce/IC50-ce)-Kout*EGFR(t), diff(PPi3k(t), t) = (EGFR(t)-PPi3k(t))/t1, diff(PAKT(t), t) = (PPi3k(t)-PAKT(t))/t1, diff(PRas(t), t) = (EGFR(t)-PRas(t))/t1, diff(PRaf(t), t) = (PRas(t)-PRaf(t))/t1, diff(PMEK(t), t) = (PRaf(t)-PMEK(t))/t1, diff(PERK(t), t) = (PMEK(t)-PERK(t))/t1, diff(Pmyc(t), t) = (PAKT(t)+PERK(t)-Pmyc(t))/t1, diff(ACII(t), t) = Pmyc(t)-ACII(t)*ACIIdeg, diff(SPC(t), t) = ACIIloss-SPC(t)*Ke0]

(1.1)

pars := [Ka = .95, Ke = 0.18e-1, IC50 = 0.786872e-2, Kin = .1, Kout = 0.1e-1, ACIIdeg = .1, t1 = 6, Ke0 = 0.1e-1]

[Ka = .95, Ke = 0.18e-1, IC50 = 0.786872e-2, Kin = .1, Kout = 0.1e-1, ACIIdeg = .1, t1 = 6, Ke0 = 0.1e-1]

(1.2)

Initial := [Depot(0) = 0, Central(0) = 0, EGFR(0) = 100, PPi3k(0) = 0, PAKT(0) = 0, PRas(0) = 0, PRaf(0) = 0, PMEK(0) = 0, PERK(0) = 0, Pmyc(0) = 0, ACII(0) = 100, SPC(0) = 0]

[Depot(0) = 0, Central(0) = 0, EGFR(0) = 100, PPi3k(0) = 0, PAKT(0) = 0, PRas(0) = 0, PRaf(0) = 0, PMEK(0) = 0, PERK(0) = 0, Pmyc(0) = 0, ACII(0) = 100, SPC(0) = 0]

(1.3)

transform model to put ce and ACIIloss in terms of the variables

trans := [ce = (1/233000)*Central(t), ACIIloss = 100/ACII(t)]

[ce = (1/233000)*Central(t), ACIIloss = 100/ACII(t)]

(1.4)

Mod2 := subs(trans, Mod1)

[diff(Depot(t), t) = piecewise(t = 0, -Ka*Depot(t)+150, t = 24, -Ka*Depot(t)+150, -Ka*Depot(t)), diff(Central(t), t) = Ka*Depot(t)-(1/233000)*Central(t)*Ke, diff(EGFR(t), t) = Kin*(1-(1/233000)*Central(t)/IC50-(1/233000)*Central(t))-Kout*EGFR(t), diff(PPi3k(t), t) = (EGFR(t)-PPi3k(t))/t1, diff(PAKT(t), t) = (PPi3k(t)-PAKT(t))/t1, diff(PRas(t), t) = (EGFR(t)-PRas(t))/t1, diff(PRaf(t), t) = (PRas(t)-PRaf(t))/t1, diff(PMEK(t), t) = (PRaf(t)-PMEK(t))/t1, diff(PERK(t), t) = (PMEK(t)-PERK(t))/t1, diff(Pmyc(t), t) = (PAKT(t)+PERK(t)-Pmyc(t))/t1, diff(ACII(t), t) = Pmyc(t)-ACII(t)*ACIIdeg, diff(SPC(t), t) = 100/ACII(t)-SPC(t)*Ke0]

(1.5)

Numerically integrate

 

soln := dsolve([eval(Mod2[], pars), Initial[]], 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 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 12, (2) = 12, (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}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.3365105837227697e-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..12, {(1) = 100.0, (2) = .0, (3) = .0, (4) = 100.0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .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..12, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1, (6) = .1, (7) = .1, (8) = .1, (9) = .1, (10) = .1, (11) = .1, (12) = .1}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (7, 12) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (8, 12) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (9, 12) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (10, 12) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (11, 12) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (12, 12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (7, 12) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (8, 12) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (9, 12) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (10, 12) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (11, 12) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (12, 12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (7, 12) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (8, 12) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (9, 12) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (10, 12) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (11, 12) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (12, 12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0}, datatype = integer[8]), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..24, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..12, {(1) = 100.0, (2) = .0, (3) = .0, (4) = 100.0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = -10.0, (2) = .0, (3) = 150.0, (4) = -.9, (5) = .0, (6) = .0, (7) = .0, (8) = 16.666666666666664, (9) = .0, (10) = 16.666666666666664, (11) = .0, (12) = 1.0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = ACII(t), Y[2] = Central(t), Y[3] = Depot(t), Y[4] = EGFR(t), Y[5] = PAKT(t), Y[6] = PERK(t), Y[7] = PMEK(t), Y[8] = PPi3k(t), Y[9] = PRaf(t), Y[10] = PRas(t), Y[11] = Pmyc(t), Y[12] = SPC(t)]`; YP[1] := Y[11]-.1*Y[1]; YP[2] := .95*Y[3]-0.7725321888e-7*Y[2]; YP[3] := piecewise(X = 0, -.95*Y[3]+150, X = 24, -.95*Y[3]+150, -.95*Y[3]); YP[4] := .1-0.5497230584e-4*Y[2]-0.1e-1*Y[4]; YP[5] := (1/6)*Y[8]-(1/6)*Y[5]; YP[6] := (1/6)*Y[7]-(1/6)*Y[6]; YP[7] := (1/6)*Y[9]-(1/6)*Y[7]; YP[8] := (1/6)*Y[4]-(1/6)*Y[8]; YP[9] := (1/6)*Y[10]-(1/6)*Y[9]; YP[10] := (1/6)*Y[4]-(1/6)*Y[10]; YP[11] := (1/6)*Y[5]+(1/6)*Y[6]-(1/6)*Y[11]; YP[12] := 100/Y[1]-0.1e-1*Y[12]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = ACII(t), Y[2] = Central(t), Y[3] = Depot(t), Y[4] = EGFR(t), Y[5] = PAKT(t), Y[6] = PERK(t), Y[7] = PMEK(t), Y[8] = PPi3k(t), Y[9] = PRaf(t), Y[10] = PRas(t), Y[11] = Pmyc(t), Y[12] = SPC(t)]`; YP[1] := Y[11]-.1*Y[1]; YP[2] := .95*Y[3]-0.7725321888e-7*Y[2]; YP[3] := piecewise(X = 0, -.95*Y[3]+150, X = 24, -.95*Y[3]+150, -.95*Y[3]); YP[4] := .1-0.5497230584e-4*Y[2]-0.1e-1*Y[4]; YP[5] := (1/6)*Y[8]-(1/6)*Y[5]; YP[6] := (1/6)*Y[7]-(1/6)*Y[6]; YP[7] := (1/6)*Y[9]-(1/6)*Y[7]; YP[8] := (1/6)*Y[4]-(1/6)*Y[8]; YP[9] := (1/6)*Y[10]-(1/6)*Y[9]; YP[10] := (1/6)*Y[4]-(1/6)*Y[10]; YP[11] := (1/6)*Y[5]+(1/6)*Y[6]-(1/6)*Y[11]; YP[12] := 100/Y[1]-0.1e-1*Y[12]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] ))  ] ); _y0 := Array(0..12, {(1) = 0., (2) = 100., (3) = 0., (4) = 0., (5) = 100., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0., (11) = 0., (12) = 0.}); _vmap := array( 1 .. 12, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4), ( 5 ) = (5), ( 6 ) = (6), ( 7 ) = (7), ( 9 ) = (9), ( 8 ) = (8), ( 11 ) = (11), ( 10 ) = (10), ( 12 ) = (12)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, ACII(t), Central(t), Depot(t), EGFR(t), PAKT(t), PERK(t), PMEK(t), PPi3k(t), PRaf(t), PRas(t), Pmyc(t), SPC(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

(2.1)

plots:-odeplot(soln, [t, Depot(t)], t = 0 .. 10); plots:-odeplot(soln, [t, Central(t)], t = 0 .. 10); plots:-odeplot(soln, [t, PAKT(t)], t = 0 .. 10); plots:-odeplot(soln, [t, PERK(t)], t = 0 .. 10); plots:-odeplot(soln, [t, PMEK(t)], t = 0 .. 10); plots:-odeplot(soln, [t, PRaf(t)], t = 0 .. 10); plots:-odeplot(soln, [t, Pmyc(t)], t = 0 .. 10); plots:-odeplot(soln, [t, SPC(t)], t = 0 .. 10); plots:-odeplot(soln, [t, ACII(t)], t = 0 .. 10)

 

 

 

 

 

 

 

 

 

``

Download ode.mw

Attached are two files.

The first file  (makeRepos.mw) creates the Maple repository and store it in the specified place. I have used full path specification for the location of the repository, so you may have to change the value of the variable 'reposit' to something more appropriate for your machine

I attached the relevant repository (ie foo.mla) to an email, then sent it to myself. I then saved the attachment to my desktop.

The second file (recLib.mw) shows how the recipient would modify his/her library path to execute the contents of 'foo.mla' (ie the procedure canSpell). Again I have used full path specification for the location of the saved email attachment, so the value of the variable 'myDesk' will have to be changed correspond to wherever the attachment was saved

#
# Create a temporary directory where I can store the
# Maple repository. I'm using the 'temp' directory
# on a windows machine.
#
# I'm using *full* paths to the directory, just to
# avoid any possible confusion/ambiguity.
#
# OP may want to change the definition of 'reposit'
# to something suitable for his/her machine
#
# If the directory already exists, remove it to ensure
# a nice "clean" start
#
  reposit := "C:/temp/reposit":
  if   FileTools:-Exists(reposit)
  then FileTools:-RemoveDirectory(reposit, recurse=true)
  fi;
#
# Now create the empty directory
#
  mkdir( reposit ):

#
# Create an empty repository called 'foo.mla' in the
# above directory.
#
# Again I'm using full paths, just to avoid any possible
# confusion/ambiguity
#
  march( 'create', cat( reposit, "/foo.mla"), 100 ):

#
# Check the contents of the repository "foo.mla". At this
# stage it should be empty!
#
  march('list', cat( reposit, "/foo.mla"));

[]

(1)

#
# Define the OP's procedure and save it to the repository
# created above
#
  canSpell := proc(w)
                   option encrypted;
                   local blocks, i, j, word, found, N;
                   blocks := Array([{"B", "O"}, {"X", "K"}, {"D", "Q"}, {"C", "P"}, {"N", "A"},
                                    {"J", "W"}, {"H", "U"}, {"V", "I"}, {"A", "N"}, {"O", "B"},
                                    {"G", "T"}, {"R", "E"}, {"T", "G"}, {"Q", "D"}, {"F", "S"},
                                    {"E", "R"}, {"F", "S"}, {"L", "Y"}, {"P", "C"}, {"Z", "M"}]);
                   word := StringTools:-UpperCase(convert(w, string));
                   N := numelems(blocks);
                   for i to length(word) do
                       found := false;
                       for j to N do
                           if word[i] in blocks[j] then
                              blocks[j] := blocks[N];
                              N := N-1;
                              found := true;
                              break;
                           end if;
                       end do;
                       if not found then
                          return false;
                       end if;
                   end do;
                   return true;
             end proc:

  savelib(canSpell, cat( reposit, "/foo.mla")):

#
# Recheck the contents of the repository
#
# Everything *seems* to be working
#
  march('list', cat( reposit, "/foo.mla"));
  

[["canSpell.m", [2019, 9, 19, 11, 32, 46], 41984, 1814]]

(2)

 

Download makeRepos.mw


 

  restart;

#
# After creating the repository, I attached it to an email
# and sent it to myself. I then saved the attachment to my
# "Desktop", defined below.
#
# The value of 'myDesk' below will need to be changed by the
# recipient of OP's email to correspond to where (s)he saved
# the email attachment
#
  myDesk:="C:/Users/TomLeslie/Desktop":

#
# Check my default library path
#
  libname;
#
# Temporarily redefine the libname to include the "foo.mla"
# library on my desktop
#
  libname:=libname, cat( myDesk, "/foo.mla");

"C:\Users\TomLeslie\maple\toolbox\2019\Physics Updates\lib", "C:\Program Files\Maple 2019\lib", "C:\Users\TomLeslie\maple\toolbox\OrthogonalExpansions\lib", "C:\Users\TomLeslie\maple\toolbox\Syrup\lib"

 

"C:\Users\TomLeslie\maple\toolbox\2019\Physics Updates\lib", "C:\Program Files\Maple 2019\lib", "C:\Users\TomLeslie\maple\toolbox\OrthogonalExpansions\lib", "C:\Users\TomLeslie\maple\toolbox\Syrup\lib", "C:/Users/TomLeslie/Desktop/foo.mla"

(1)

#
# Check the contents of the added repository
#
  march('list', cat( myDesk, "/foo.mla") );

[["canSpell.m", [2019, 9, 19, 10, 41, 59], 41984, 1814]]

(2)

#
# Check encryption
#
  eval(canSpell);

proc (w) local blocks, i, j, word, found, N; option encrypted; "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" end proc

(3)

#
# Run the OP's procedure
#
  canSpell("good");

true

(4)

 


 

Download recLib.mw

Do all calculations with complex numbers

Just need a a couple of functions which convert inputs from "phasor" to complex and then converts output from complex back to phasor, as in the following

#
# Define a couple of simple functions which
#
# 1) Convert from "phasor" representation to
#    complex numbers
# 2) Convert from complex representation to
#    "phasor" representation
#
  fromP:= (r, theta)-> r*exp(I*Pi*theta/180);
  toP:= x-> evalf([abs(x), (180/Pi)*argument(x)]);
#
# Define "phasors" (and convert to complex
# reprentation)
#
  U__LI:= fromP(230, 0):
  I__LI:= fromP(20, -30):
  Z__L:=  fromP(0.097, 7.2):
  I__N:=  fromP(40,-120):
#
# Perform calculation, and convert to "phasor"
# representation
#
   ans:= toP(U__LI - I__LI * Z__L + I__N * Z__L);

proc (r, theta) options operator, arrow; r*exp(((1/180)*I)*Pi*theta) end proc

 

proc (x) options operator, arrow; evalf([abs(x), 180*argument(x)/Pi]) end proc

 

[226.7256261, -.7139358893]

(1)

 


 

Download phasors.mw

In the attached

  1. I removed some "comment" areas which appeared to be a mixture of "comment" and "executable code" - always tricky to tell the difference if you insist on using 2-D input
  2. I didn't like the syntax for the boundary condition D(u(0, t)) = 0, Slightly surprised that Maple didn't object to this, but I changed it to something which is definitely syntactically correct.

Even then I still get an error that

Error, (in pdsolve/numeric/plot) unable to compute solution for t>HFloat(0.0): matrix is singular

Now I can't be certain why this error message is occurring, but since the problem seems to occur at (x,t)=(0,0), one thing that bothers me is the BCs/ICs at (0,0).

You have the initial condition

u(x, 0) = 0.1*sin(2*Pi*x)

which must be true for all 'x' - so the above requires that u(0,0)=0.

However you also have the boundary condtion

u(0, t) = 0.5*cos(2*Pi*t)

which is true for all 't', so this requires that u(0,0)=0.5 in conflict with initial condition above

A similar conflict occurs with the BCs/ICs for v(0,0): the relevant initial condition has v(0,0)=0, wheres the relevant boundary condition has v(0,0)=0.2

You might want to give some thought to these boundary/initial condition conflicts

m := 1; hBar := 1

pdeu := diff(u(x, t), t)+u(x, t)*(diff(u(x, t), x)) = -0.1e-1

diff(u(x, t), t)+u(x, t)*(diff(u(x, t), x)) = -0.1e-1

(1)

pdev := diff(v(x, t), t)+u(x, t)*(diff(v(x, t), x))-hBar*(diff(u(x, t), `$`(x, 2)))/(2*m)+v(x, t)*(diff(u(x, t), x))/m = -0.2e-1

diff(v(x, t), t)+u(x, t)*(diff(v(x, t), x))-(1/2)*(diff(diff(u(x, t), x), x))+v(x, t)*(diff(u(x, t), x)) = -0.2e-1

(2)

IC := {u(x, 0) = .1*sin(2*Pi*x), v(x, 0) = .2*sin((1/2)*Pi*x)}

{u(x, 0) = .1*sin(2*Pi*x), v(x, 0) = .2*sin((1/2)*Pi*x)}

(3)

BC := {u(0, t) = .5*cos(2*Pi*t), v(0, t) = .2*cos(2*Pi*t), (D[1](u))(0, t) = 0}

{u(0, t) = .5*cos(2*Pi*t), v(0, t) = .2*cos(2*Pi*t), (D[1](u))(0, t) = 0}

(4)

``

IBC := `union`(IC, BC)

{u(0, t) = .5*cos(2*Pi*t), u(x, 0) = .1*sin(2*Pi*x), v(0, t) = .2*cos(2*Pi*t), v(x, 0) = .2*sin((1/2)*Pi*x), (D[1](u))(0, t) = 0}

(5)

pds := pdsolve({pdeu, pdev}, IBC, numeric, time = t, range = 0 .. 1)

_m747256992

(6)

p1 := pds:-plot(t = 10, numpoints = 1000, color = blue)

Error, (in pdsolve/numeric/plot) unable to compute solution for t>HFloat(0.0):
matrix is singular

 

NULL

Download pdeProb2.mw

In the atached,  removed a few things you probably(?) don't need.

Everything seems to be working correctly

What exactly do you want to do?

restart

with(plots)

L := 1; alpha := 1; epsilon := .1; `&Xscr;` := x^2

Inverse := diff(C(x, t), t) = -epsilon*(diff(C(x, t), x, x, x, x))-alpha*(diff(C(x, t), x, x))

IBCI := C(x, 0) = `&Xscr;`, C(0, t) = 0, C(L, t) = 0, (D[1, 1](C))(0, t) = 0, (D[1, 1](C))(L, t) = 0

pdsI := pdsolve(Inverse, [IBCI], numeric); pdsI:-plot3d(C(x, t), t = 0 .. 10, x = 0 .. 1); pdsI:-plot(t = 10, x = 0 .. 1); pdsI:-plot(x = .25, t = 0 .. 10)

_m696589984

 

 

 

 

``


 

Download pdeProb.mw

when performing multiple substitutions, like x=..., t=.., then these have to grouped in a list, as in [x=.., t=..] as in the attached

For future reference, when posting here, please use the big green up-arrow in the Mapleprimes toolbar to upload code. 'Pictures' of code are not editable, not executable, and so not very useful

  restart:

  f:=7*exp(-3*t)-(3*x):
  s:=0.05:
  T:=0.1:
  n:=round(T/s):
  t0:=0:
  x[0]:=6:
  for i from 0 by 1 to n-1 do
    #
    # Note the square brackets enclosing
    # the multiple substitutions
    #
    # the simplify() 'wrapper' is just so that
    # exp(0) gets evaluated to a floating point
    # which isn't really necessary at this stage
    #
      x[i+1]:=simplify(x[i]+s*subs( [x=x[0], t=t0+i*s], f)):
  od;

5.45

 

4.851247792

(1)

restart

f := 7*exp(-3*t)-3*x
s := 0.5e-1
T := .1
n := round(T/s)
t0 := 0

x[0] := 6

for i from 0 to n-1 do x[i+1] := simplify(x[i]+s*subs([x = x[0], t = i*s+t0], f)) end do

5.45

 

4.851247792

(2)

 

Download doSub.mw

Try adding more-or-less plausibe constraints to the values of the solution variables - as in the attached

NB I don't know enough about fluids to determine whether the constraints in the attached are plausible or not - I just guessed. You may be able to "relax" these constraints quite a bit and still get a solution. As a general rule, any constraint you can add to an fsolve() problem (even something as simple as requiring all variables to be positive) increase the chances of obtaining a solution

Anyhow, for what it is worth, the second fsolve() command in the attached "works" in Maple 2019

  restart;
  interface(version);

`Standard Worksheet Interface, Maple 2019.1, Windows 7, May 21 2019 Build ID 1399874`

(1)

  with(ThermophysicalData);
  with(ThermophysicalData[CoolProp]);
  fluid := "R717"; T__in := 310; p__in := 11*10^5; v__in := 10;  A := 0.005;
  h__in := Property(massspecificenthalpy, T = T__in, P = p__in, fluid);
  rho__in := Property(density, T = T__in, P = p__in, fluid);
  m := A*v__in*rho__in;
  p__out := 2*10^5;
  eq1 := h__out = Property("massspecificenthalpy", "temperature" = T__out, "P" = p__out, fluid);
  eq2 := rho__out = Property("D", "temperature" = T__out, "P" = p__out, fluid);
  eq3 := h__in + v__in^2/2 = h__out + v__out^2/2;
  eq4 := m = A*v__out*rho__out;
  res := fsolve({eq1, eq2, eq3, eq4});
#
# Try adding plausible(?) constraints on the ranges
# of the variables
#
  res := fsolve( {eq1, eq2, eq3, eq4},
                 {T__out=200..500, h__out=0..5e06, v__out=0..100, rho__out=0..5}
               );

[Chemicals, CoolProp, PHTChart, Property, PsychrometricChart, TemperatureEntropyChart]

 

[HAPropsSI, PhaseSI, Property, Props1SI, PropsSI]

 

"R717"

 

310

 

1100000

 

10

 

0.5e-2

 

1655590.94730295590

 

8.15132757401520713

 

.4075663787

 

200000

 

h__out = ThermophysicalData:-CoolProp:-Property("massspecificenthalpy", "temperature" = T__out, "P" = 200000, "R717")

 

rho__out = ThermophysicalData:-CoolProp:-Property("D", "temperature" = T__out, "P" = 200000, "R717")

 

1655640.947 = h__out+(1/2)*v__out^2

 

.4075663787 = 0.5e-2*v__out*rho__out

 

fsolve({.4075663787 = 0.5e-2*v__out*rho__out, 1655640.947 = h__out+(1/2)*v__out^2, h__out = ThermophysicalData:-CoolProp:-Property("massspecificenthalpy", "temperature" = T__out, "P" = 200000, "R717"), rho__out = ThermophysicalData:-CoolProp:-Property("D", "temperature" = T__out, "P" = 200000, "R717")}, {T__out, h__out, v__out, rho__out})

 

{T__out = 285.0179004, h__out = 1654113.289, v__out = 55.27490598, rho__out = 1.474688637}

(2)

 

Download tProp.mw

 

 

something like the attached - although I don't think you gain much (if anything) when compared to using 'D-operator' notation


 

  restart;

#
# Define function
#
  doDiff:= (p,q,r)-> diff(p(q), q$r);
#
# A couple of examples
#
  doDiff( f, x, 3);
  doDiff( g, y, 2);
  doDiff( h, z, n);

proc (p, q, r) options operator, arrow; diff(p(q), `$`(q, r)) end proc

 

diff(diff(diff(f(x), x), x), x)

 

diff(diff(g(y), y), y)

 

diff(h(z), [`$`(z, n)])

(1)

#
# But is this any better that using
# D-operator notation?
#
  D[1$3](f)(x);
  D[1$2](g)(y);
  D[1$n](h)(z);
  convert(%%%, diff);
  convert(%%%, diff);
  convert(%%%, diff);

((D@@3)(f))(x)

 

((D@@2)(g))(y)

 

((D@@n)(h))(z)

 

diff(diff(diff(f(x), x), x), x)

 

diff(diff(g(y), y), y)

 

diff(h(z), [`$`(z, n)])

(2)

 

 


 

Download doDiff.mw

to use the command

MmaTranslator[FromMmaNotebook]()

which according to its help page

The FromMmaNotebook(Mma_notebook_filename) and the convert(Mma_notebook_filename, FromMmaNotebook) commands translate a Mathematica notebook to a Maple worksheet and saves the results to disk. These commands enable Mathematica users to automatically translate their Mathematica notebooks to Maple worksheets.

 

but can't find it?!

So far as I can tell, an analytic solution is not possible - so one is forced to look for a numeric solution

In a numeric solution, it is not possible to use "infinity" as one of the boundaries. The "conventional" approach is to use an appropriately "large" number as a "proxy" for infinity.

Even doing this, I had various problems producing a numeric solution which "worked" over a range of values for 'delta', which resulted in the selection of a few specific options for the dsolve(....., numeric) command.

The attached *appears* to be OK for the required range of delta-values, including delta=0

Anyhow for what it is worth, check the attached.

NB I couldn't check this in Maple 17, because the earliest version I have loaded is Maple 18

  restart;
  with(plots):
  delta:=1:
  inf:=500*delta+1;
  sol:= dsolve( [ 2*diff(y(x),x,x,x)+y(x)*diff(y(x),x,x)=0,
                  y(0)=0,
                  D(y)(inf)=1,
                  D(y)(0)=delta*D[1,1](y)(0)
                ],
                numeric,
                approxsoln=[y(x)=x],
                maxmesh=4096,
                method=bvp[midrich]
              ):
  odeplot( sol, [x, y(x)], x=0..1);
  odeplot( sol, [x, y(x)], x=0..inf)

501

 

 

 

 


 

Download BVPprob.mw

For linear systems, one can use commands from the LinearAlgebra package to examine whether the system is consistent or underdetermined etc

As in the attached

  restart:
#
# Make sure enough digits are used for calculation
# but restrict how many are displayed, just for
# readibility
#
  Digits:=50:
  interface(displayprecision=4):
#
# Since system is 'linear' probably(?) better to use
# LinearAlgebra:-LinearSolve() rather than the more
# "straightforward" fsolve(). so load the relevant
# package
#
  with(LinearAlgebra):
#
# OP's system
#
  C[0]:= 3.19153824321146142351956847947*tau[1]-19.1492294592687685411174108768*tau[2]+111.703838512401149823184896781*tau[3]+3.19153824321146142351956847947*tau[4]-44.6815354049604599292739587124*tau[5]+622.349957426234977586315853494*tau[6]:
  C[1]:= 51.0646118913833827763130956714*tau[2]-612.775342696600593315757148056*tau[3]+51.0646118913833827763130956714*tau[5]-1429.80913295873471773676667880*tau[6]:
  C[2]:= -1.06073680388443795908856507616+3.19153824321146142351956847947*tau[1]+53.1609155734306093706448370717*tau[2]+1672.89412862088744108725223170*tau[3]+3.19153824321146142351956847947*tau[4]+27.6286096277389179824882892361*tau[5]+1026.57792701153122226218722129*tau[6]:
  C[3]:= -1.08847004231036963538035920033+3.19153824321146142351956847947*tau[1]+62.6399144226357196540662623767*tau[2]+2040.52109049201342887896297462*tau[3]+3.19153824321146142351956847947*tau[4]+37.1076084769440282659097145411*tau[5]+1242.54090729537544551915515930*tau[6]:
  C[4]:= -1.05523181556926815105314303389+3.19153824321146142351956847947*tau[1]+72.7671212023804312453829273862*tau[2]+2472.93216226733267613216245895*tau[3]+3.19153824321146142351956847947*tau[4]+47.2348152566887398572263795506*tau[5]+1512.91667059477930731128800348*tau[6]:
  C[5]:= -.922876006485286011069063957991+3.19153824321146142351956847947*tau[1]+82.9822841707707093164204255644*tau[2]+2971.36790137532483139495115633*tau[3]+3.19153824321146142351956847947*tau[4]+57.4499782250790179282638777288*tau[5]+1847.90980220852701343747673000*tau[6]:
#
# Convert to a matrix system and attempt a solution
#
  A,b:= GenerateMatrix
        ( [seq( C[j], j=0..5)],
          [seq( tau[j], j=1..6)]
        );
  LinearSolve(A,b);

A, b := Matrix(6, 6, {(1, 1) = 3.19153824321146142351956847947, (1, 2) = -19.1492294592687685411174108768, (1, 3) = 111.703838512401149823184896781, (1, 4) = 3.19153824321146142351956847947, (1, 5) = -44.6815354049604599292739587124, (1, 6) = 622.349957426234977586315853494, (2, 1) = 0, (2, 2) = 51.0646118913833827763130956714, (2, 3) = -612.775342696600593315757148056, (2, 4) = 0, (2, 5) = 51.0646118913833827763130956714, (2, 6) = -1429.80913295873471773676667880, (3, 1) = 3.19153824321146142351956847947, (3, 2) = 53.1609155734306093706448370717, (3, 3) = 1672.89412862088744108725223170, (3, 4) = 3.19153824321146142351956847947, (3, 5) = 27.6286096277389179824882892361, (3, 6) = 1026.57792701153122226218722129, (4, 1) = 3.19153824321146142351956847947, (4, 2) = 62.6399144226357196540662623767, (4, 3) = 2040.52109049201342887896297462, (4, 4) = 3.19153824321146142351956847947, (4, 5) = 37.1076084769440282659097145411, (4, 6) = 1242.54090729537544551915515930, (5, 1) = 3.19153824321146142351956847947, (5, 2) = 72.7671212023804312453829273862, (5, 3) = 2472.93216226733267613216245895, (5, 4) = 3.19153824321146142351956847947, (5, 5) = 47.2348152566887398572263795506, (5, 6) = 1512.91667059477930731128800348, (6, 1) = 3.19153824321146142351956847947, (6, 2) = 82.9822841707707093164204255644, (6, 3) = 2971.36790137532483139495115633, (6, 4) = 3.19153824321146142351956847947, (6, 5) = 57.4499782250790179282638777288, (6, 6) = 1847.90980220852701343747673000}), Vector(6, {(1) = 0, (2) = 0, (3) = 1.06073680388443795908856507616, (4) = 1.08847004231036963538035920033, (5) = 1.05523181556926815105314303389, (6) = .922876006485286011069063957991})

 

Error, (in LinearAlgebra:-BackwardSubstitute) inconsistent system

 

#
# Idle curiosity - check the reduced row echelon form
# of the augmented matrix. Three observations
#
# 1. the fact that row 6 is all zero implies that the
#    system is underdetermined - so any solution would
#    require a free parameter, however
# 2. row 5 is equivalent to the statement 0=1, so no
#    solution is possible
# 3. The fact that all of the coefficients in the RRF
#    *seem* to be *exact* makes one wonder exactly how
#    the original equation system was generated!
#
  M:=ReducedRowEchelonForm(<A|b>);
#
# Regenerate the system of equations from the reduced
# row echelon form. Check the fifth and sixth entry
# in the output list, which confirms the statements
# (1) and (2) above
#
  GenerateEquations(M, [seq( tau[j], j=1..6)]);

Matrix(6, 7, {(1, 1) = 1., (1, 2) = 0., (1, 3) = 0., (1, 4) = 1.0000000000000000000000000000000000000000000000000, (1, 5) = -7.9999999999999999999999999999498674345073799899517, (1, 6) = 0., (1, 7) = 0., (2, 1) = 0., (2, 2) = 1., (2, 3) = 0., (2, 4) = 0., (2, 5) = 1.0000000000000000000000000000000000000000000000000, (2, 6) = 0., (2, 7) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 1., (3, 4) = -0., (3, 5) = -0., (3, 6) = -0., (3, 7) = -0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 0., (4, 5) = 0., (4, 6) = 1., (4, 7) = 0., (5, 1) = 0., (5, 2) = 0., (5, 3) = 0., (5, 4) = 0., (5, 5) = 0., (5, 6) = 0., (5, 7) = 1., (6, 1) = 0., (6, 2) = 0., (6, 3) = 0., (6, 4) = 0., (6, 5) = 0., (6, 6) = 0., (6, 7) = 0.})

 

[1.*tau[1]+1.0000000000000000000000000000000000000000000000000*tau[4]-7.9999999999999999999999999999498674345073799899517*tau[5] = 0., 1.*tau[2]+1.0000000000000000000000000000000000000000000000000*tau[5] = 0., 1.*tau[3] = -0., 1.*tau[6] = 0., 0. = 1., 0. = 0.]

(1)

 

 

Download linSol.mw

 is shown in the attached (and I am sure there are many other ways!)

  restart;
#
# Implement the sieve of Eratosthenes. This will
# return all prime numbers up to the supplied
# argument (reasonably efficiently)
#
# EG on my machine all primes up to 1000000 can
# be generated in less than 1sec
#
  sieve := proc( Nval::integer)
                 local vec, k;
                 description "The Sieve of Eratosthenes";
                 uses ArrayTools, LinearAlgebra:
               #
               # Initialise a vector with all ones
               #
                 vec:= Vector[row]( Nval, 1 ):
               #
               # set the first entry in the vector to zero
               #        
                 vec[1]:= 0:
               #
               # Set all even entries with index >=4, to zero
               # (eliminates all the even indices which can't
               # be prime)
               #
                 Fill(0, vec, 3, 2);
               #
               # For each odd number, say k,  eliminate all
               # of its odd multiples (other than 1*k)
               #
                 seq( Fill
                      ( 0, vec, k^2-1, k ),
                      k=3..floor( sqrt(Nval) ),
                      2
                    ):
               #
               # return the indices for all non-zero values
               #
                 return Transpose
                        ( SearchArray
                          ( vec )
                        );
           end proc:
#
# Generate all the primes between 1 and N, Change
# the following assignment as necessary
#
  N:=1000000:
  prims:=sieve(N):
#
# Generate a random number between 1 and the
# number of primes in the vector 'prims'
#
  randomize():
  r:= rand( 1..op(1, prims)):

#
# Now generate (say) a hundred "random" prime
# numbers between 1 and N (defined above)
#
  seq( prims[ r() ], j=1..100);

575119, 538457, 296669, 748637, 180311, 486757, 223753, 52673, 854083, 257, 651769, 995173, 499253, 878641, 479287, 910603, 294923, 318863, 373151, 704251, 174487, 151471, 620183, 491527, 603391, 184241, 174859, 148763, 505339, 701653, 870031, 141269, 696433, 390107, 927833, 42061, 102533, 678779, 141679, 183377, 100537, 982687, 54091, 227363, 681061, 678581, 372013, 533909, 461861, 276883, 56591, 346039, 102233, 131743, 794413, 639371, 712493, 46327, 874763, 273719, 15307, 632743, 151483, 515639, 941209, 580913, 695677, 599303, 56311, 739217, 560137, 722411, 603613, 994067, 377623, 19937, 70241, 488321, 135449, 525949, 397939, 418909, 373, 125933, 909281, 465089, 840589, 201829, 268607, 104851, 559877, 967507, 44771, 829537, 24121, 911173, 215959, 625267, 672209, 958501

(1)

 

Download primRand.mw

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