Maple 2024 Questions and Posts

These are Posts and Questions associated with the product, Maple 2024

I have a lot of maple code for analysing electronic design uncertainties and would like to place a clip from the schematic before outputing the analysis results.  I have been working for hours on this with no success but I'm sure it must be simple.

I see that ImageTools,Preview kind of works but it outputs a very small, blurry image.  Is there just a simple command that I can read in my .png image and output it to the display?

undesired_textplot_format.mw

When using textplot() AND display(), how do I ensure that the expression I want in the figure is not modified by display()? See my attached spreadsheet where I demostrate this undesired behaviour. 

i did seperating but but is seems is not correct what is mistake in here?

issue1.mw

in here  for jacobieliptic i got two lambda[0] same as paper did but in second one is different and is true make my ode be zero, but is so different from paper 

test-Dr.D.mw

...but it's easily solvable with the help of a trick. My main concern is the path to the solution for the attached Diophantine equation. I was able to solve the problem both with pen and paper and then in Maple. There's certainly a more elegant way. I'm particularly interested in a special Maple command. However, I don't want to ask for it here yet, as it would give a hint of the trick and spoil the fun of solving the puzzle.

 

419*x^2+116*x*y-426*x*z+78*y^2-142*y*z+133*z^2-1604*x-682*y+1086*z+2306 = 0

NULL

Download Diophant.mw

in here i want the system which when i found the system it contain a singularity but by some changing of system we can remove it, i know how he did that but i can't do it by coding, also after removing which i did by hand , there is another problem which equalibruiom points is to long how i can make it be shorter becuase contain two function i don't know how do that can i change the coiefecient of any function by another letter? also for phase portrait i need `conserved quantity` which last code is not work for finding this kind of system ? and how decide about jacobian if the `conserved quantity` is know by that after determine the points it will be clear on plots, i write the code untill finding the `conserved quantity` becuase code not run i didn't find jacobian and phase portrait but i will put the code of jacobian and phase portrait too! 

bi-1.mw

In here i replaced but i don't know why still the D[1](f)(x, y, 0, t) is remain in my function in equation eqt1, beside this my function contain imaginary part we can plot this or we have to remove that somehow?

eval.mw

I defined a 2×2 matrix V with entries involving operator-valued fields u(x,t), ω(x,t), and scalar function β(t). On macOS with Maple 2024.0, when I try to compute the derivative with respect to x using 

Vx := (diff, V, x);

Maple does not return a result. It just shows “Evaluating”

restart

kernelopts(version)

`Maple 2024.0, APPLE UNIVERSAL OSX, Mar 01 2024, Build ID 1794891`

(1)

with(LinearAlgebra)

with(Physics)

with(PDEtools); undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(2)

interface(showassumed = 0)

Setup(mathematicalnotation = true)

[mathematicalnotation = true]

(3)

quantumOperators := {omega, u}

{omega, u}

(4)

Setup(quantumoperators = quantumOperators)

[quantumoperators = {omega, u}]

(5)

assume(x::real); assume(t::real)

declare(u(x, t), omega(x, t), B(x, t), alpha(t), beta(t), v1(x, t))

u(x, t)*`will now be displayed as`*u

 

omega(x, t)*`will now be displayed as`*omega

 

B(x, t)*`will now be displayed as`*B

 

alpha(t)*`will now be displayed as`*alpha

 

beta(t)*`will now be displayed as`*beta

 

v1(x, t)*`will now be displayed as`*v1

(6)

V := -(1/2)*Matrix([[beta(t)*(diff(omega(x, t), t)), -(diff(u(x, t), t))], [-(diff(u(x, t), t)), -beta(t)*(diff(omega(x, t), t))]])/lambda

Matrix(%id = 36893488152030778900)

(7)

Vx := diff(V, x)

Download derivativve.mw

in this method i don't know in most of short equation i try to find the parameter but is just evaluating and nothing come up i don't know my way is wrong or write but i think i am right  but parameter not coming out, beside this in this equation give  me a warning regarding the parameters which say number of solution is more than 100 and dint show me that , how i can find the solution better than this?

f-p-.mw

In the attached file "test," a system of ordinary differential equations is solved. I was able to create the (r, phi) plot. But how are the (t, r(t)) and (t, phi(t)) plots executed with the calculation results?
What does "range" mean in the (r, phi) plot command? Is there a more precise numerical method than the Runge-Kutta method used in "test" (perhaps a finer t-division of the axis?)?

restart

eq1 := diff(r(t), t)+1+cos(`ϕ`(t)) = 0; eq2 := diff(`ϕ`(t), t)+1-sin(`ϕ`(t))/r(t) = 0

diff(r(t), t)+1+cos(varphi(t)) = 0

 

diff(varphi(t), t)+1-sin(varphi(t))/r(t) = 0

(1)

``

ics := r(0) = 2.0, `ϕ`(0) = Pi/(1.5)

r(0) = 2.0, varphi(0) = 2.094395103

(2)

soln := dsolve({eq1, eq2, ics}, {r(t), `ϕ`(t)}, numeric, start = 0, range = 0 .. 3)

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, ( "right" ) = 3., ( "left" ) = 0. ] ) _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) = 1, (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) = 3.0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = .19535812688284548, (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) = 2.0, (2) = 2.094395103}, 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) = .22047804756371955, (2) = 2.873107829856247}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = -0.3386381880498868e-1, (2) = .17766918858144054}, 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) = -0.3386381880498868e-1, (1, 2) = -0.377585836518608e-1, (1, 3) = -0.3708633582928045e-1, (1, 4) = -0.34124098676952874e-1, (1, 5) = -0.3363280624230314e-1, (1, 6) = -0.3641604213065852e-1, (2, 1) = .17766918858144054, (2, 2) = .22761845480999643, (2, 3) = .2192661580732893, (2, 4) = .18085452152511095, (2, 5) = .17405774363177118, (2, 6) = .2108205409669659}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8]), Array(1..2, {(1) = .22040658040387567, (2) = 2.873512341267432}, datatype = float[8], order = C_order), Array(1..2, {(1) = .21910457742849349, (2) = 2.8806072512024623}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0.17347438180381758e-7, (2) = 0.10386005389051434e-7}, datatype = float[8], order = C_order), Array(1..2, {(1) = .22270057794927467, (2) = 2.8597843388449604}, datatype = float[8], order = C_order), Array(1..2, {(1) = -0.3569387106220412e-1, (2) = .20146120823190228}, 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) = 2.0, (2) = 2.094395103}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = -.4999999994744918, (2) = -.5669872982594819}, 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] = r(t), Y[2] = varphi(t)]`; YP[1] := -1-cos(Y[2]); YP[2] := -1+sin(Y[2])/Y[1]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = r(t), Y[2] = varphi(t)]`; YP[1] := -1-cos(Y[2]); YP[2] := -1+sin(Y[2])/Y[1]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 27 ) = (""), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0), ( 28 ) = (0)  ] )), ( 3 ) = (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) = 1, (9) = 0, (10) = 1, (11) = 85, (12) = 85, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 155, (19) = 30000, (20) = 5, (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) = 3.0, (2) = 0.10e-5, (3) = .10304186874784538, (4) = 0.500001e-14, (5) = .0, (6) = .19535812688284548, (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) = 2.0, (2) = 2.094395103}, 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) = .22047804756371955, (2) = 2.873107829856247}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = -0.3386381880498868e-1, (2) = .17766918858144054}, 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) = -0.3386381880498868e-1, (1, 2) = -0.377585836518608e-1, (1, 3) = -0.3708633582928045e-1, (1, 4) = -0.34124098676952874e-1, (1, 5) = -0.3363280624230314e-1, (1, 6) = -0.3641604213065852e-1, (2, 1) = .17766918858144054, (2, 2) = .22761845480999643, (2, 3) = .2192661580732893, (2, 4) = .18085452152511095, (2, 5) = .17405774363177118, (2, 6) = .2108205409669659}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8]), Array(1..2, {(1) = .22040658040387567, (2) = 2.873512341267432}, datatype = float[8], order = C_order), Array(1..2, {(1) = .21910457742849349, (2) = 2.8806072512024623}, datatype = float[8], order = C_order), Array(1..2, {(1) = 0.17347438180381758e-7, (2) = 0.10386005389051434e-7}, datatype = float[8], order = C_order), Array(1..2, {(1) = .22270057794927467, (2) = 2.8597843388449604}, datatype = float[8], order = C_order), Array(1..2, {(1) = -0.3569387106220412e-1, (2) = .20146120823190228}, 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) = .22270057794927467, (2) = 2.8597843388449604}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = -0.3386381880498868e-1, (2) = .17766918858144054}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..2, {(1, 1) = 2.938831384122585, (1, 2) = .22270057794927467, (2, 0) = .22270057794927467, (2, 1) = 2.8597843388449604, (2, 2) = 2.9634858657986514, (3, 0) = 2.9634858657986514, (3, 1) = .221748342025735, (3, 2) = 2.8656651287650265, (4, 0) = 2.8656651287650265, (4, 1) = 2.988140347474718, (4, 2) = .22083401075704298, (5, 0) = .22083401075704298, (5, 1) = 2.871070168038091, (5, 2) = 3.012794829150785, (6, 0) = 3.012794829150785, (6, 1) = .21995387131675959, (6, 2) = 2.876038628847415}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = r(t), Y[2] = varphi(t)]`; YP[1] := -1-cos(Y[2]); YP[2] := -1+sin(Y[2])/Y[1]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (Array(1..85, 0..2, {(1, 1) = .0, (1, 2) = 2.0, (2, 0) = 2.0, (2, 1) = 2.094395103, (2, 2) = 0.4883953172071137e-1, (3, 0) = 0.4883953172071137e-1, (3, 1) = 1.9749957636720312, (3, 2) = 2.0670025471235336, (4, 0) = 2.0670025471235336, (4, 1) = 0.9767906344142274e-1, (4, 2) = 1.9488280959770066, (5, 0) = 1.9488280959770066, (5, 1) = 2.04021084709857, (5, 2) = .1465185951621341, (6, 0) = .1465185951621341, (6, 1) = 1.9215068608366304, (6, 2) = 2.0140263347936975, (7, 0) = 2.0140263347936975, (7, 1) = .19535812688284548, (7, 2) = 1.893044054829213, (8, 0) = 1.893044054829213, (8, 1) = 1.988457425914424, (8, 2) = .280900476384457, (9, 0) = .280900476384457, (9, 1) = 1.8404843242365583, (9, 2) = 1.9451906076368206, (10, 0) = 1.9451906076368206, (10, 1) = .36644282588606847, (10, 2) = 1.7845598519772645, (11, 0) = 1.7845598519772645, (11, 1) = 1.9039191638716142, (11, 2) = .4519851753876799, (12, 0) = .4519851753876799, (12, 1) = 1.7253847367916073, (12, 2) = 1.8647415453538858, (13, 0) = 1.8647415453538858, (13, 1) = .5375275248892915, (13, 2) = 1.6630931456083156, (14, 0) = 1.6630931456083156, (14, 1) = 1.827785275008053, (14, 2) = .616075451639432, (15, 0) = .616075451639432, (15, 1) = 1.603283300376125, (15, 2) = 1.7959429678186245, (16, 0) = 1.7959429678186245, (16, 1) = .6946233783895726, (16, 2) = 1.5411171896322202, (17, 0) = 1.5411171896322202, (17, 1) = 1.7662563673049378, (17, 2) = .7731713051397131, (18, 0) = .7731713051397131, (18, 1) = 1.4767537695478887, (18, 2) = 1.7389080337794152, (19, 0) = 1.7389080337794152, (19, 1) = .8517192318898537, (19, 2) = 1.4103708331171143, (20, 0) = 1.4103708331171143, (20, 1) = 1.7141191124530415, (20, 2) = .9177358538213208, (21, 0) = .9177358538213208, (21, 1) = 1.3531616403350515, (21, 2) = 1.6954560815446786, (22, 0) = 1.6954560815446786, (22, 1) = .983752475752788, (22, 2) = 1.2948000182859192, (23, 0) = 1.2948000182859192, (23, 1) = 1.6789696037423298, (23, 2) = 1.0497690976842553, (24, 0) = 1.0497690976842553, (24, 1) = 1.235434387752726, (24, 2) = 1.664875276796809, (25, 0) = 1.664875276796809, (25, 1) = 1.1157857196157224, (25, 2) = 1.1752283323792916, (26, 0) = 1.1752283323792916, (26, 1) = 1.6534251811289784, (26, 2) = 1.17181879714737, (27, 0) = 1.17181879714737, (27, 1) = 1.1236019582656207, (27, 2) = 1.6459973906746916, (28, 0) = 1.6459973906746916, (28, 1) = 1.2278518746790175, (28, 2) = 1.0716241501398995, (29, 0) = 1.0716241501398995, (29, 1) = 1.640888665777501, (29, 2) = 1.2838849522106648, (30, 0) = 1.2838849522106648, (30, 1) = 1.0194315393350855, (30, 2) = 1.6383329167946707, (31, 0) = 1.6383329167946707, (31, 1) = 1.3399180297423123, (31, 2) = .967173884862351, (32, 0) = .967173884862351, (32, 1) = 1.63859579173605, (32, 2) = 1.3895931786245055, (33, 0) = 1.3895931786245055, (33, 1) = .9209233700331131, (33, 2) = 1.6414255181271569, (34, 0) = 1.6414255181271569, (34, 1) = 1.4392683275066989, (34, 2) = .8748784230151254, (35, 0) = .8748784230151254, (35, 1) = 1.646939265151252, (35, 2) = 1.4889434763888922, (36, 0) = 1.4889434763888922, (36, 1) = .8291788145340493, (36, 2) = 1.6553957182885823, (37, 0) = 1.6553957182885823, (37, 1) = 1.5386186252710854, (37, 2) = .7839766015575426, (38, 0) = .7839766015575426, (38, 1) = 1.667077404650224, (38, 2) = 1.5687462276863915, (39, 0) = 1.5687462276863915, (39, 1) = .7568735457220451, (39, 2) = 1.67586213435023, (40, 0) = 1.67586213435023, (40, 1) = 1.5988738301016974, (40, 2) = .7300540461536099, (41, 0) = .7300540461536099, (41, 1) = 1.6860182095468146, (41, 2) = 1.6290014325170035, (42, 0) = 1.6290014325170035, (42, 1) = .7035599816612077, (42, 2) = 1.697620293665825, (43, 0) = 1.697620293665825, (43, 1) = 1.6591290349323096, (43, 2) = .6774351893350706, (44, 0) = .6774351893350706, (44, 1) = 1.7107443248264431, (44, 2) = 1.6892566373476157, (45, 0) = 1.6892566373476157, (45, 1) = .6517254613446625, (45, 2) = 1.7254668242982154, (46, 0) = 1.7254668242982154, (46, 1) = 1.7193842397629218, (46, 2) = .6264787480696691, (47, 0) = .6264787480696691, (47, 1) = 1.7418650301879928, (47, 2) = 1.7495118421782276, (48, 0) = 1.7495118421782276, (48, 1) = .6017446545171511, (48, 2) = 1.7600130123373363, (49, 0) = 1.7600130123373363, (49, 1) = 1.7796394445935337, (49, 2) = .5775742015482379, (50, 0) = .5775742015482379, (50, 1) = 1.7799796411830302, (50, 2) = 1.8061947635665625, (51, 0) = 1.8061947635665625, (51, 1) = .5567786183444859, (51, 2) = 1.7991366433344658, (52, 0) = 1.7991366433344658, (52, 1) = 1.832750082539591, (52, 2) = .5364978626253581, (53, 0) = .5364978626253581, (53, 1) = 1.8197927195419688, (53, 2) = 1.8593054015126196, (54, 0) = 1.8593054015126196, (54, 1) = .5167682561523157, (54, 2) = 1.8419764809526942, (55, 0) = 1.8419764809526942, (55, 1) = 1.8858607204856483, (55, 2) = .49762581223390895, (56, 0) = .49762581223390895, (56, 1) = 1.8657055776358582, (56, 2) = 1.9097149107830291, (57, 0) = 1.9097149107830291, (57, 1) = .4809602717718633, (57, 2) = 1.8883435286863, (58, 0) = 1.8883435286863, (58, 1) = 1.93356910108041, (58, 2) = .4648218596764317, (59, 0) = .4648218596764317, (59, 1) = 1.9122277759833848, (59, 2) = 1.9574232913777907, (60, 0) = 1.9574232913777907, (60, 1) = .4492340389199136, (60, 2) = 1.9373409026689865, (61, 0) = 1.9373409026689865, (61, 1) = 1.9812774816751715, (61, 2) = .4342187292534649, (62, 0) = .4342187292534649, (62, 1) = 1.9636521189398293, (62, 2) = 2.004263852787264, (63, 0) = 2.004263852787264, (63, 1) = .4203101092586252, (63, 2) = 1.990098117377601, (64, 0) = 1.990098117377601, (64, 1) = 2.027250223899356, (64, 2) = .4069674582769166, (65, 0) = .4069674582769166, (65, 1) = 2.0175622542309486, (65, 2) = 2.050236595011448, (66, 0) = 2.050236595011448, (66, 1) = .3942039633751688, (66, 2) = 2.0459772536535046, (67, 0) = 2.0459772536535046, (67, 1) = 2.07322296612354, (67, 2) = .38203013565972604, (68, 0) = .38203013565972604, (68, 1) = 2.075261255402451, (68, 2) = 2.098058121270015, (69, 0) = 2.098058121270015, (69, 1) = .3695485759576045, (69, 2) = 2.107766300909261, (70, 0) = 2.107766300909261, (70, 1) = 2.1228932764164896, (70, 2) = .3577689175737098, (71, 0) = .3577689175737098, (71, 1) = 2.141033682628699, (71, 2) = 2.1477284315629643, (72, 0) = 2.1477284315629643, (72, 1) = .3466910657927155, (72, 2) = 2.174907057374285, (73, 0) = 2.174907057374285, (73, 1) = 2.1725635867094395, (73, 2) = .33631017357287435, (74, 0) = .33631017357287435, (74, 1) = 2.20921581927419, (74, 2) = 2.196849383761043, (75, 0) = 2.196849383761043, (75, 1) = .3268235884660522, (75, 2) = 2.2430115231100825, (76, 0) = 2.2430115231100825, (76, 1) = 2.221135180812647, (76, 2) = .3179799207626713, (77, 0) = .3179799207626713, (77, 1) = 2.276869570385799, (77, 2) = 2.2454209778642507, (78, 0) = 2.2454209778642507, (78, 1) = .309760915843174, (78, 2) = 2.3106091885511706, (79, 0) = 2.3106091885511706, (79, 1) = 2.2697067749158544, (79, 2) = .3021447460238304, (80, 0) = .3021447460238304, (80, 1) = 2.3440521970551167, (80, 2) = 2.2915527181738296, (81, 0) = 2.2915527181738296, (81, 1) = .2957879507637747, (81, 2) = 2.373738294552842, (82, 0) = 2.373738294552842, (82, 1) = 2.3133986614318047, (82, 2) = .28987791521959144, (83, 0) = .28987791521959144, (83, 1) = 2.402922916310279, (83, 2) = 2.3352446046897803, (84, 0) = 2.3352446046897803, (84, 1) = .28439275840127815, (84, 2) = 2.4314945706700617, (85, 0) = 2.4314945706700617, (85, 1) = 2.3570905479477555, (85, 2) = .27930964339102904}, datatype = float[8], order = C_order)), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = r(t), Y[2] = varphi(t)]`; YP[1] := -1-cos(Y[2]); YP[2] := -1+sin(Y[2])/Y[1]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 27 ) = (""), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0), ( 28 ) = (0)  ] )), ( 4 ) = (3)  ] ); _y0 := Array(0..2, {(1) = 0., (2) = 2.0}); _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 <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> 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 <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> 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, r(t), varphi(t)], (4) = []}); _vars := _dat[3]; _pars := map(lhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(3)

plots[odeplot](soln, [r(t), `&varphi;`(t)])

 

Download test.mw

In this kind of contour plot i have two line but when i change time variable t just contour of one line wil move the other is not do any movement and is stop how i can  make the second plot one second line move too? also there is any way for ploting this kind any other option?

line-2-done.mw

i did for two of them base on the information but one of them is not make my odetest to be zero? where is problem

test.mw

It is possible to perform the simplest QFT calculations with second quantization, in Maple? Bosons in a box. See attached example. bosons_in_a_box.mw

Sure any general purpose programming language is capable of performing this task with enough effort. What I am interested in is if the physics tools has a standard way of dealing with these calculations. The general impedement when attempting the calculation is that integrations are perfomed by replacements with delta functions or kronecker delta functions, and its not clear how to force the Maple Physics package to recognize this or if that's possible. Part of the problem is that integrations in maple are defined in one dimension at a time where as in QFT the integration element is almost always atleast three dimensional, d^3x or dxdydzy, the later of which can get extremely cumbersome with even a small number of fields under consideration. I don't find much of what I am refering to mentioned in the help pages and I doubt these types of QFT calculations are possible to perform in Maple without addressing these issues.

bosons_in_a_box.mw

i don't  know  why my graph make a problem and what is issue i did plot  but this time make issue for me which i don't know where is problem there is anyone which can help and even modified the plot?

explore-chaotic.mw

i did substitution but my result is so different from the author i think he just take the linear term of theta but i didn't do that so how take just linear term of that function and find unknwon , and how afeter replacing eq(12) inside eq(11) we can remove thus exponential and find w? also i think author did a mistake which the equation 12 is theta(x,t) not Q(x,t)

restart

with(PDEtools)

undeclare(prime, quiet)

declare(u(x, t), quiet); declare(U(xi), quiet); declare(V(xi), quiet); declare(theta(x, t), quiet)

pde := diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2)))+(2*I)*(diff(u(x, t)*U^2, t))-(2*I)*alpha*s*(diff(u(x, t)*U^2, t))+I*(diff(u(x, t), `$`(x, 2), t))-I*beta*s*(diff(u(x, t), `$`(x, 3)))

diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x))+(2*I)*(diff(u(x, t), t))*U^2-(2*I)*alpha*s*(diff(u(x, t), t))*U^2+I*(diff(diff(diff(u(x, t), t), x), x))-I*beta*s*(diff(diff(diff(u(x, t), x), x), x))

(1)

T := u(x, t) = (sqrt(Q)+theta(x, t))*exp(I*(Q^2*epsilon*gamma+Q*q)*t); T1 := U = sqrt(Q)+theta(x, t)

u(x, t) = (Q^(1/2)+theta(x, t))*exp(I*(Q^2*epsilon*gamma+Q*q)*t)

 

U = Q^(1/2)+theta(x, t)

(2)

P := collect(eval(subs({T, T1}, pde)), exp)/exp(I*(Q^2*gamma*`&epsilon;`+Q*q)*t)

diff(diff(theta(x, t), t), t)+(2*I)*(diff(theta(x, t), t))*(Q^2*epsilon*gamma+Q*q)-(Q^(1/2)+theta(x, t))*(Q^2*epsilon*gamma+Q*q)^2-s^2*(diff(diff(theta(x, t), x), x))+(2*I)*(diff(theta(x, t), t)+I*(Q^(1/2)+theta(x, t))*(Q^2*epsilon*gamma+Q*q))*(Q^(1/2)+theta(x, t))^2-(2*I)*alpha*s*(diff(theta(x, t), t)+I*(Q^(1/2)+theta(x, t))*(Q^2*epsilon*gamma+Q*q))*(Q^(1/2)+theta(x, t))^2+I*(diff(diff(diff(theta(x, t), t), x), x)+I*(diff(diff(theta(x, t), x), x))*(Q^2*epsilon*gamma+Q*q))-I*beta*s*(diff(diff(diff(theta(x, t), x), x), x))

(3)

 

TT := Q = alpha[1]*exp(I*(k*x-t*w))+alpha[2]*exp(-I*(k*x-t*w))

Q = alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w))

(4)

S := eval(subs(TT, P))

diff(diff(theta(x, t), t), t)+(2*I)*(diff(theta(x, t), t))*(gamma*epsilon*(alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))^2+(alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))*q)-((alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))^(1/2)+theta(x, t))*(gamma*epsilon*(alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))^2+(alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))*q)^2-s^2*(diff(diff(theta(x, t), x), x))+(2*I)*(diff(theta(x, t), t)+I*((alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))^(1/2)+theta(x, t))*(gamma*epsilon*(alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))^2+(alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))*q))*((alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))^(1/2)+theta(x, t))^2-(2*I)*alpha*s*(diff(theta(x, t), t)+I*((alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))^(1/2)+theta(x, t))*(gamma*epsilon*(alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))^2+(alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))*q))*((alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))^(1/2)+theta(x, t))^2+I*(diff(diff(diff(theta(x, t), t), x), x)+I*(diff(diff(theta(x, t), x), x))*(gamma*epsilon*(alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))^2+(alpha[1]*exp((k*x-t*w)*I)+alpha[2]*exp(-I*(k*x-t*w)))*q))-I*beta*s*(diff(diff(diff(theta(x, t), x), x), x))

(5)

Download steps.mw

or for this equation 

steps-2.mw

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