Maple 2017 Questions and Posts

These are Posts and Questions associated with the product, Maple 2017

I was trying to answer a question by torabi 25, August 14, 2017 to speed up his calculations. I got this idea of converting the original code to a procedure - that was not easy, run the procedure and obtain a value of time() to establish a baseline, and making sure the answer from the procedure was the same as from torabi 25. So far so good. Then I would compile the procedure, execute it, and get another value for time(). Hopefully the compiled procedure will be faster than the uncompiled procedure. I am close, but - please see if you can fix my compiler error. Thanks!


 

restart

pa := proc (k::integer, h::float, N::float, nu::float, E_m::float, E_c::float, rho_m::float, rho_c::float, d::(Matrix()))::float; local lambda_m::float, lambda_c::float, mu_m::float, mu_c::float, Z::float, U::float, S::float, e2::float, f::float, W::float, z::float, b::integer, alpha::integer, beta::integer; lambda_m := nu*E_m/((1+nu)*(1-2*nu)); lambda_c := nu*E_c/((1+nu)*(1-2*nu)); mu_m := E_m/(2+2*nu); mu_c := E_c/(2+2*nu); Z := rho_m+(rho_c-rho_m)*(1/2+z/h)^N; U := lambda_m+(lambda_c-lambda_m)*(1/2+z/h)^N; S := mu_m+(mu_c-mu_m)*(1/2+z/h)^N; e2 := 0.; for alpha from 0 to k-2 do for b from 0 to k-2 do for beta from 0 to k-1 do f := 2*S*d[beta+1, alpha+1]*W(beta)*sqrt(alpha+1/2)*orthopoly:-P(alpha, z)*d[2, b+1]*sqrt(b+1/2)*orthopoly:-P(b, z); e2 := e2-(int(f, z = -(1/2)*h .. (1/2)*h)) end do end do end do end proc

NULL

k := 6; h := 1.; N := .5; nu := .3; E_m := 7.0*10^10; E_c := 3.80*10^11; rho_m := 2702.; rho_c := 3800.; d := Matrix([evalf([0, 0, 0, 0, 0, 0, 0, 0]), evalf([sqrt(3), 0, 0, 0, 0, 0, 0, 0]), evalf([0, sqrt(15), 0, 0, 0, 0, 0, 0]), evalf([sqrt(7), 0, sqrt(35), 0, 0, 0, 0, 0]), evalf([0, sqrt(27), 0, sqrt(63), 0, 0, 0, 0]), evalf([sqrt(11), 0, sqrt(55), 0, sqrt(99), 0, 0, 0]), evalf([0, sqrt(39), 0, sqrt(91), 0, sqrt(143), 0, 0]), evalf([sqrt(15), 0, sqrt(75), 0, sqrt(135), 0, sqrt(195), 0])], datatype = float[8])

time(pa(k, h, N, nu, E_m, E_c, rho_m, rho_c, d))

2.156

(1)

pa(k, h, N, nu, E_m, E_c, rho_m, rho_c, d)

-0.3192307695e12*W(1)+0.4396880666e12*W(3)-0.1474586302e12*W(5)-0.9235575679e11*W(2)+0.1979090107e12*W(4)

(2)

# Original Answer:        -3.192307692*10^11*W(1)+4.396880662*10^11*W(3)-1.474586301*10^11*W(5)-9.235575669*10^10*W(2)+1.979090105*10^11*W(4);NULL

cpa := Compiler:-Compile(pa)

Error, (in Compiler:-Compile) Array parameter types must specify a hardware datatype

 

time(cpa(k, h, N, nu, E_m, E_c, rho_m, rho_c, d))

0.

(3)

cpa(k, h, N, nu, E_m, E_c, rho_m, rho_c, d)

NULL


 

Download for_(5).mw

 

There seems to be a bug with improper integration:

integrate(cos(t)*exp(-x*t),t=-infinity..infinity)

gives

0

Substituting any number for x, or assuming x >= 0  (or x<=0) does give the correct result,

The problem also persists when assuming x>-1 (or x>-Maple_floats(MIN_FLOAT))

mathcontainerUses_Doubt.mw
 

restart; d[1] := [2.36, 26.90], [2.75, 30.0], [3.14, 31.9], [3.53, 32.8], [3.93, 33.4], [4.32, 32.8], [4.71, 31.9]

[2.36, 26.90], [2.75, 30.0], [3.14, 31.9], [3.53, 32.8], [3.93, 33.4], [4.32, 32.8], [4.71, 31.9]

(1)

NULL

d[2] := [2.36, 32.40], [2.75, 34.90], [3.14, 36.90], [3.53, 38.00], [3.93, 38.40], [4.32, 37.8], [4.71, 36.5]

[2.36, 32.40], [2.75, 34.90], [3.14, 36.90], [3.53, 38.00], [3.93, 38.40], [4.32, 37.8], [4.71, 36.5]

(2)

d[3] := [2.36, 27.9], [2.75, 28.3], [3.14, 30.0], [3.53, 30.9], [3.93, 31.3], [4.32, 30.8], [4.71, 29.7]

[2.36, 27.9], [2.75, 28.3], [3.14, 30.0], [3.53, 30.9], [3.93, 31.3], [4.32, 30.8], [4.71, 29.7]

(3)

y := a*x^2+b*x+c; for i to 3 do d[i] := [d[i]]; c[i] := CurveFitting[LeastSquares](d[i], x, curve = y) end do

HFloat(8.047886108501745)+HFloat(11.793324911833839)*x-HFloat(1.5172878997894277)*x^2

(4)

 

curve1 := [c[1], c[2]]; k[1] := [1, 2]; curve1p := [d[1], d[2]]; l[1] := "plot 1"

"plot 1"

(5)

curve2 := [c[2], c[3]]; k[2] := [2, 3]; curve2p := [d[2], d[3]]; l[2] := "plot 2"

"plot 2"

(6)

curve3 := [c[1], c[3]]; k[3] := [1, 3]; curve3p := [d[1], d[3]]; l[3] := "plot 3"

"plot 3"

(7)
Table 1

 

xlabel := "Brake Power"; ylabel := "Efficiency"

"Efficiency"

(8)

p1 := plot(curve1, x = 2.0 .. 5.0, labels = [xlabel, ylabel], labeldirections = ["horizontal", "vertical"], color = [black], linestyle = [1, 2], thickness = [3, 1], title = Title, caption = "Fig. 1 cool  Example 1", legend = ["curve1", "curve2"]); p2 := plot(curve1p, style = point, color = [black], symbol = [soliddiamond, box], symbolsize = 10); plots:-display(p1, p2)

 

p1 := plot(curve2, x = 2.0 .. 5.0, labels = [xlabel, ylabel], labeldirections = ["horizontal", "vertical"], color = [black], linestyle = [1, 2], thickness = [3, 1], title = Title, caption = "Fig. 1 cool  Example 1", legend = ["curve1", "curve2"]); p2 := plot(curve2p, style = point, color = [black], symbol = [box, point], symbolsize = 10); plots:-display(p1, p2)

 

p1 := plot(curve3, x = 2.0 .. 5.0, labels = [xlabel, ylabel], labeldirections = ["horizontal", "vertical"], color = [black], linestyle = [1, 2], thickness = [3, 1], title = Title, caption = "Fig. 1 cool  Example 1", legend = ["curve1", "curve2"]); p2 := plot(curve3p, style = point, color = [black], symbol = [soliddiamond, point], symbolsize = 10); plots:-display(p1, p2)

 

 

"for j from 1 to 3 do  print( Report on l[j]); for i in k[j] do x1(i):=solve((&DifferentialD;)/(&DifferentialD; x)c[i]);  y1(i):=eval( c[i], [x = x1(i)]):  print( Maximum brake thermal efficiency of,y1(i) "%"occurs at brake power value of , x1(i)kW);  end do;  end do;"

Maximum*brake*thermal*efficiency*of, HFloat(30.964188366461613)*"%"*occurs*at*brake*power*value*of, 3.886317459*kW

(9)

NULL


 

Download mathcontainerUses_Doubt.mw

Can any one state the uses of mathcontainer?

1. It can store only one algebraic expression at a time?

2. Can it handle list of algebraic expressions?

3. Can it store list data points (x,y) for a list of curves?

4. Can there be any use for click to edit this component?

More than a simple Yes or No a simple example for each yes answer would be very helpful.

I enclose a document with list of coordinates for for three curves, expression for curve fitting, three expressions derived for these plot points (coordinates), a command for optimum y for each of the three curves (maximum y and corresponding x value), 

Thanks for answering.

Ramakrishnan V

Hey there. 

I recently had to install maple 2017, because the licensens for 2016 had expired. 

And in the new version, whenever i want to copy a matrix from a result, it gives me an _rtable, and a number. The result is the same, but it makes it harder to read and i am not able to edit values in this copied matrix. 

How do i change this?

hi..how i can rewrite section of this code as another form i,e ''for section''

I have a lot of line as this and runnig cise is time consuming.

is there another way to write this section in order to the runtime of the program is reduced??

thanks

for.mw
 

restart;

with(LinearAlgebra):

with(VectorCalculus):

#Digits:=5:
k:=6:

l:=0:

h:=1:

m:=4:

n:=4:

l1:=2*h:

l2:=2*h:

N:=0.5:

nu:=.3:

E_m:=70e9:

E_c:=380e9:

rho_m:=2702:

rho_c:=3800:

lambda_m:=nu*E_m/((1+nu)*(1-2*nu)):

lambda_c:=nu*E_c/((1+nu)*(1-2*nu)):

mu_m:=E_m/(2*(1+nu)):

mu_c:=E_c/(2*(1+nu)):

with(orthopoly):

for i from 0 to 5 do:
L(i):=sqrt((2*i+1)/2)*P(i,z):
end do:

Z:=rho_m+(rho_c-rho_m)*((1/2)+(z/h))^N;

2702+1098*(1/2+z)^.5

(1)

U:=lambda_m+(lambda_c-lambda_m)*((1/2)+(z/h))^N;

0.4038461538e11+0.1788461538e12*(1/2+z)^.5

(2)

S:=mu_m+(mu_c-mu_m)*((1/2)+(z/h))^N;

0.2692307692e11+0.1192307692e12*(1/2+z)^.5

(3)

d:=Matrix([[0,0,0,0,0,0,0,0],[sqrt(3),0,0,0,0,0,0,0],[0,sqrt(15),0,0,0,0,0,0],[sqrt(7),0,sqrt(35),0,0,0,0,0],[0,sqrt(27),0,sqrt(63),0,0,0,0],[sqrt(11),0,sqrt(55),0,sqrt(99),0,0,0],[0,sqrt(39),0,sqrt(91),0,sqrt(143),0,0],[sqrt(15),0,sqrt(75),0,sqrt(135),0,sqrt(195),0]]);

d := Matrix(8, 8, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (2, 1) = 3^(1/2), (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (3, 1) = 0, (3, 2) = 15^(1/2), (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (4, 1) = 7^(1/2), (4, 2) = 0, (4, 3) = 35^(1/2), (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (5, 1) = 0, (5, 2) = 3*3^(1/2), (5, 3) = 0, (5, 4) = 3*7^(1/2), (5, 5) = 0, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (6, 1) = 11^(1/2), (6, 2) = 0, (6, 3) = 55^(1/2), (6, 4) = 0, (6, 5) = 3*11^(1/2), (6, 6) = 0, (6, 7) = 0, (6, 8) = 0, (7, 1) = 0, (7, 2) = 39^(1/2), (7, 3) = 0, (7, 4) = 91^(1/2), (7, 5) = 0, (7, 6) = 143^(1/2), (7, 7) = 0, (7, 8) = 0, (8, 1) = 15^(1/2), (8, 2) = 0, (8, 3) = 5*3^(1/2), (8, 4) = 0, (8, 5) = 3*15^(1/2), (8, 6) = 0, (8, 7) = 195^(1/2), (8, 8) = 0})

(4)

``

``

e2 := 0;

0

 

-0.3192307692e12*W(1)+0.4396880662e12*W(3)-0.1474586301e12*W(5)-0.9235575669e11*W(2)+0.1979090105e12*W(4)

(5)

``


 

Download for.mw

 

hi...

how I can dsolve this differential equations. parameter p is unkown.

I want to gain w(x) and u(x) and psi(x) and p.

thanks

sade.mw
 

restart; eq1 := (diff(psi(x), x))^2+(diff(u(x), x)+(8*(1/2))*(diff(w(x), x))^2)((diff(psi(x), x))^2)+3*(diff(w(x), x, x))+5*(diff(w(x), x, x))*(diff(psi(x), x))-7*(diff(u(x), x, x, x)+(8*(1/2))*(diff(w(x), x, x))^2+(3/2)*(diff(w(x), x, x, x))*(diff(w(x), x)))+3 = p

(diff(psi(x), x))^2+(diff(u(x), x))((diff(psi(x), x))^2)+4*(diff(w(x), x))((diff(psi(x), x))^2)^2+3*(diff(diff(w(x), x), x))+5*(diff(diff(w(x), x), x))*(diff(psi(x), x))-7*(diff(diff(diff(u(x), x), x), x))-28*(diff(diff(w(x), x), x))^2-(21/2)*(diff(diff(diff(w(x), x), x), x))*(diff(w(x), x))+3 = p

(1)

eq2 := (51-31)(diff(psi(x), x, x))+(52-2)(diff(w(x), x, x, x))+8*(diff(psi(x), x, x, x, x))-7*(diff(w(x), x)-psi(x)) = 0

70+8*(diff(diff(diff(diff(psi(x), x), x), x), x))-7*(diff(w(x), x))+7*psi(x) = 0

(2)

eq3 := 4*(diff(w(x), x, x)-(diff(psi(x), x)))+(23+11)(diff(psi(x), x, x, x))+(14+12)*(diff(w(x), x, x, x, x)) = 0

4*(diff(diff(w(x), x), x))-4*(diff(psi(x), x))+34+26*(diff(diff(diff(diff(w(x), x), x), x), x)) = 0

(3)

dsys3 := {eq1, eq2, eq3, psi(0) = 0, psi(1) = 0, u(0) = 0, u(1) = 0, w(0) = 0, w(1) = 0, ((D@@1)(psi))(0) = 0, ((D@@1)(psi))(1) = 0, ((D@@1)(w))(0) = 0, ((D@@1)(w))(1) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 1200, numeric, abserr = .1, output = array([.5]))

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 12, got 10

 

dsolve({eq2, eq3}, {psi(x), w(x)}):

with(PDEtools, casesplit, declare);

[casesplit, declare]

(4)

 


 

Download sade.mw

 

hi...

how i can dsolve this differential equations and obtain w(x) and U(x) and phi(x) analytical or numerically?

thanks

zah.mw
 

``

restart; L := 100; h := 1; eq1 := 1130*(diff(U(x), x, x))+1130*(diff(W(x), x))*(diff(W(x), x, x))+1130*(diff(U(x), x, x, x, x))

1130*(diff(diff(U(x), x), x))+1130*(diff(W(x), x))*(diff(diff(W(x), x), x))+1130*(diff(diff(diff(diff(U(x), x), x), x), x))

(1)

eq2 := 1130*(diff(W(x), x))*(diff(U(x), x, x)+(diff(W(x), x))*(diff(W(x), x, x)))+(diff(W(x), x, x))*(1130*(diff(U(x), x))+565*(diff(W(x), x))^2-2.2*(int(diff(varphi(z), z), z = -5/2 .. 5/2)))+(14125/6)*(diff(W(x), x, x, x, x, x, x))+(10405/6)*(diff(W(x), x, x, x, x))+10

1130*(diff(W(x), x))*(diff(diff(U(x), x), x)+(diff(W(x), x))*(diff(diff(W(x), x), x)))+(diff(diff(W(x), x), x))*(1130*(diff(U(x), x))+565*(diff(W(x), x))^2-2.2*(int(diff(varphi(z), z), z = -5/2 .. 5/2)))+(14125/6)*(diff(diff(diff(diff(diff(diff(W(x), x), x), x), x), x), x))+(10405/6)*(diff(diff(diff(diff(W(x), x), x), x), x))+10

(2)

eq3 := diff(varphi(z), z, z)-.35*(diff(W(x), x, x))

diff(diff(varphi(z), z), z)-.35*(diff(diff(W(x), x), x))

(3)

dsys3 := {eq1, eq2, eq3, U(0) = 0, U(L) = 0, W(0) = 0, W(L) = 0, `&varphi;`(-(1/2)*h) = 0, `&varphi;`(-(1/2)*h) = 2, ((D@@1)(W))(0) = 0, ((D@@1)(W))(L) = 0, ((D@@2)(W))(0) = 0, ((D@@2)(W))(L) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 1200, numeric, abserr = .1, output = array([.5]))

Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {x, z}

 

``


 

Download zah.mw

 


``

How can I convert the result (2) to equal to the trigonometric identity (kw/s^2)*tanh(a*s/2)?

``

g := kw*piecewise(t < a, t, t < 2*a, 2*a-t)

kw*piecewise(t < a, t, t < 2*a, 2*a-t)

(1)

simplify((int(exp(-s*t)*g, t = 0 .. a)+int(exp(-s*t)*g, t = a .. 2*a))/(1-exp(-2*a*s)))

-(exp(-a*s)-1)*kw/((exp(-a*s)+1)*s^2)

(2)

``


Download trigonometric_id.mw

 

 

Books free. Like!!!

Lenin Araujo Castillo

I have a module with quite a few procedures and it is getting too long and complex. Basicially I write each procedure in a seperate document, them copy and paste it into the module. I want to improve matters as save each proc and read it in to the module

e.g.  Qdim:=proc(A,B).........end proc

        save Qdim , "Qdim.?"   have tried .txt ,.mla , .m  They save fine.

in the module have tried

read "Qdim.txt" etc.   I have included Qdim in export but Qdim doesnt work Qdim(A,B) returns Qdim(A,B)

read "C:\Users\Ronan\Documents\MAPLE\Rational Trinonometry\Qdim.m";

which procuces an error

Error, (in unknown) could not open `C:UsersRonanDocumentsMAPLERational TrinonometryQdim.m` for reading

 

Not sure if this is documented explicitly to Maple users, but normally (prior to Maple 2017) interface(typesetting=extended) was all that was required to output display diff(y(x),x) as y'(x)

With Maple 2017 typesetting=extended is default and one must use with(Typesetting)  Settings(typesetprime=true) in order to output the display of diff(y(x),x) as y'(x).

Perhaps this is well documented somewhere, however I was unable to find the change. 

I'm plotting matrices using the proc in the attached file.

How do I move the rows in the plot closer to each other?
The first picture show the rows plotted in the values [13,14...19].
I want them to be plotted in values like [13,13.5,14,14.5...].

Second picture shows how I would like it to be. Created it in paint, from a different matrix.Matrix_plot.mw

hi..

I dont know why ''Y'' in this code does not calculate?

Also in Determinant  should exist term ''Omega''!!!

however this term not apear!!

please help

thanksZrO2.mw
 

restart

 

with(LinearAlgebra):

with(LinearAlgebra):

with(VectorCalculus):

E_c:=200e9:

rho_m:=2702:

rho_c:=5700:h:=1:Digits:=200:


E1 := `-`(4.2705019043175109408418470672541038566261199358253*10^11*V1(0))+`-`(2.3725010579541727449121372595856132536811777421250*10^11*V2(0))+1.5696340652026885245525677229595578452458265608494*10^11*W(1)+`-`(2.0979486841753331066266817163288024688566490248347*10^11*W(3))+5.4007241680476829082789400225291715487122216582787*10^10*W(5)+3.5809247085360964145389659227744194611678663499154*10^11*V1(2)+1.9894026158533868969660921793191219228710368610640*10^11*V2(2)+`-`(1.5013483257366249401397118595815208870951202899385*10^11*V1(4))+`-`(8.3408240318701385563317325532306715949728904996586*10^10*V2(4))+2850.*(omega^2)*V1(0)+`-`(2389.7976509529002380373043584565514766271608718347*(omega^2)*V1(2))+1001.9531250000000000000000000000000000000000000000*(omega^2)*V1(4):

 

E2 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.3725010579541727449121372595856132536811777421250, 10^11), V1(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(4.2705019043175109408418470672541038566261199358252, 10^11), V2(0)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.9894026158533868969660921793191219228710368610640, 10^11), V1(2))), VectorCalculus:-`*`(VectorCalculus:-`*`(3.5809247085360964145389659227744194611678663499153, 10^11), V2(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(8.3408240318701385563317325532306715949728904996586, 10^10), V1(4)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.5013483257366249401397118595815208870951202899385, 10^11), V2(4)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.5696340652026885245525677229595578452458265608494, 10^11), W(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.0979486841753331066266817163288024688566490248347, 10^11), W(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(5.4007241680476829082789400225291715487122216582787, 10^10), W(5))), VectorCalculus:-`*`(VectorCalculus:-`*`(2850., omega^2), V2(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2389.7976509529002380373043584565514766271608718347, omega^2), V2(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1001.9531250000000000000000000000000000000000000000, omega^2), V2(4))):

E3 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.8980008463633381959297098076684906029449421937001, 10^11), W(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.0464227101351256830350451486397052301638843738996, 10^11), V1(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.3986324561168887377511211442192016459044326832232, 10^11), V1(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(3.6004827786984552721859600150194476991414811055185, 10^10), V1(5)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.5915220926827095175728737434552975382968294888513, 10^11), W(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(6.6726592254961108450653860425845372759783123997272, 10^10), W(4)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.0464227101351256830350451486397052301638843738996, 10^11), V2(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.3986324561168887377511211442192016459044326832232, 10^11), V2(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(3.6004827786984552721859600150194476991414811055185, 10^10), V2(5)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2850., omega^2), W(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2389.7976509529002380373043584565514766271608718347, omega^2), W(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1001.9531250000000000000000000000000000000000000000, omega^2), W(4))):

E4 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.0464227101351256830350451486397052301638843738997, 10^11), W(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.2214716299255315813643079206596798103103761378024, 10^11), V1(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(3.3768909335128648548928127154266879343498252829884, 10^11), V1(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.9781847824423219358080619338342989761407203990375, 10^11), V1(5)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.7549042347962743784892618717635313196920712292577, 10^11), W(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.2808745009976567622404499724256074938728417212344, 10^11), W(4)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(5.9312526448854318622803431489640331342029443553127, 10^10), V2(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.0192655329160445762728144798285002567196893656192, 10^11), V2(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(8.7843041320517842057351587174649326412354044181698, 10^10), V2(5)))), VectorCalculus:-`*`(VectorCalculus:-`*`(712.50000000000000000000000000000000000000000000000, omega^2), V1(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1224.4069434960135017602438595742022681505344916052, omega^2), V1(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1055.2267908337921786307617355195123093332341255338, omega^2), V1(5))):

E5 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.0464227101351256830350451486397052301638843738997, 10^11), W(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.2214716299255315813643079206596798103103761378024, 10^11), V2(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(3.3768909335128648548928127154266879343498252829884, 10^11), V2(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.9781847824423219358080619338342989761407203990375, 10^11), V2(5)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.7549042347962743784892618717635313196920712292577, 10^11), W(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.2808745009976567622404499724256074938728417212344, 10^11), W(4)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(5.9312526448854318622803431489640331342029443553127, 10^10), V1(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.0192655329160445762728144798285002567196893656192, 10^11), V1(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(8.7843041320517842057351587174649326412354044181698, 10^10), V1(5)))), VectorCalculus:-`*`(VectorCalculus:-`*`(712.50000000000000000000000000000000000000000000000, omega^2), V2(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1224.4069434960135017602438595742022681505344916052, omega^2), V2(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1055.2267908337921786307617355195123093332341255338, omega^2), V2(5))):

E6 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.5696340652026885245525677229595578452458265608495, 10^11), V1(0)), VectorCalculus:-`*`(VectorCalculus:-`*`(1.5696340652026885245525677229595578452458265608495, 10^11), V2(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(4.5129617500523730105208889903786611122746970868863, 10^11), W(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(6.2131578362567818226243648649366563582660969795536, 10^11), W(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.0922794659196454621738794738143334638130489666375, 10^11), W(5)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.9011462543626305766967003610771589296664104983626, 10^11), V1(2)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.9011462543626305766967003610771589296664104983626, 10^11), V2(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.8271521540250046106119733650076103042314699809888, 10^11), V1(4))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.8271521540250046106119733650076103042314699809888, 10^11), V2(4))), VectorCalculus:-`*`(VectorCalculus:-`*`(712.50000000000000000000000000000000000000000000000, omega^2), W(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1224.4069434960135017602438595742022681505344916052, omega^2), W(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1055.2267908337921786307617355195123093332341255338, omega^2), W(5))):

E7 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.9011462543626305766967003610771589296664104983626, 10^11), W(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(4.7119107128007866217743468531741155729216807681740, 10^11), V1(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(5.0748128190543187340378117893989426968741725224549, 10^11), V1(4))), VectorCalculus:-`*`(VectorCalculus:-`*`(3.0995137005629364198630176713255719374808867211330, 10^11), W(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.3168284715873139556329481351343925356696602976947, 10^11), W(5)))), VectorCalculus:-`*`(VectorCalculus:-`*`(3.5809247085360964145389659227744194611678663499154, 10^11), V1(0))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.9894026158533868969660921793191219228710368610640, 10^11), V2(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.8164461224961635078233550893702351473496517088145, 10^11), V2(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.0724123476084663741457840654142141615476683079173, 10^11), V2(4))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2389.7976509529002380373043584565514766271608718347, omega^2), V1(0)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2182.0312500000000000000000000000000000000000000000, omega^2), V1(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1288.2502962167977845669843807304847803693289074734, omega^2), V1(4)))):

E8 := -1.9011462543626305766967003610771589296664104983626*10^11*W(1)-4.7119107128007866217743468531741155729216807681740*10^11*V2(2)+5.0748128190543187340378117893989426968741725224549*10^11*V2(4)+3.0995137005629364198630176713255719374808867211330*10^11*W(3)-2.3168284715873139556329481351343925356696602976947*10^11*W(5)+1.9894026158533868969660921793191219228710368610640*10^11*V1(0)+3.5809247085360964145389659227744194611678663499153*10^11*V2(0)-1.8164461224961635078233550893702351473496517088145*10^11*V1(2)+1.0724123476084663741457840654142141615476683079173*10^11*V1(4)-2389.7976509529002380373043584565514766271608718347*omega^2*V2(0)+2182.0312500000000000000000000000000000000000000000*omega^2*V2(2)-1288.2502962167977845669843807304847803693289074734*omega^2*V2(4)

E9 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.7549042347962743784892618717635313196920712292577, 10^11), V1(1)), VectorCalculus:-`*`(VectorCalculus:-`*`(1.7549042347962743784892618717635313196920712292577, 10^11), V2(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(6.5012338210738538831817609945731111948027982901282, 10^11), W(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.1863576954843550511330528903118121550547428135047, 10^12), W(4))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.9040488725995079969887733136744097432253353062867, 10^11), V1(3)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.9040488725995079969887733136744097432253353062867, 10^11), V2(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2.2665101950561447195804856166187258422604042194633, 10^11), V1(5))), VectorCalculus:-`*`(VectorCalculus:-`*`(2.2665101950561447195804856166187258422604042194633, 10^11), V2(5))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.5915220926827095175728737434552975382968294888513, 10^11), W(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2389.7976509529002380373043584565514766271608718347, omega^2), W(0)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2182.0312500000000000000000000000000000000000000000, omega^2), W(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1288.2502962167977845669843807304847803693289074734, omega^2), W(4)))):

E10 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.3986324561168887377511211442192016459044326832232, 10^11), W(0)), VectorCalculus:-`*`(VectorCalculus:-`*`(3.3768909335128648548928127154266879343498252829884, 10^11), V1(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(6.1222023070711042519748179963162700048903049636371, 10^11), V1(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(5.9722762993987285423665483888817556162282387212450, 10^11), V1(5))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.9040488725995079969887733136744097432253353062868, 10^11), W(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(4.4534580327025486258972640897961855979523955862006, 10^11), W(4))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.0192655329160445762728144798285002567196893656192, 10^11), V2(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.7886433757232630459689159808594662420330754071490, 10^11), V2(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.6315367543759662237835567740527270814718925725463, 10^11), V2(5))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1224.4069434960135017602438595742022681505344916052, omega^2), V1(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2148.6328125000000000000000000000000000000000000000, omega^2), V1(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1959.9062914564655436920860212499538090252187294161, omega^2), V1(5)))):

E11 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.3986324561168887377511211442192016459044326832232, 10^11), W(0)), VectorCalculus:-`*`(VectorCalculus:-`*`(3.3768909335128648548928127154266879343498252829884, 10^11), V2(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(6.1222023070711042519748179963162700048903049636371, 10^11), V2(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(5.9722762993987285423665483888817556162282387212450, 10^11), V2(5))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.9040488725995079969887733136744097432253353062868, 10^11), W(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(4.4534580327025486258972640897961855979523955862006, 10^11), W(4))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.0192655329160445762728144798285002567196893656192, 10^11), V1(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.7886433757232630459689159808594662420330754071490, 10^11), V1(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.6315367543759662237835567740527270814718925725463, 10^11), V1(5))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1224.4069434960135017602438595742022681505344916052, omega^2), V2(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2148.6328125000000000000000000000000000000000000000, omega^2), V2(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1959.9062914564655436920860212499538090252187294161, omega^2), V2(5)))):

E12 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.0979486841753331066266817163288024688566490248347, 10^11), V1(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.0979486841753331066266817163288024688566490248347, 10^11), V2(0)))), VectorCalculus:-`*`(VectorCalculus:-`*`(6.2131578362567818226243648649366563582660969795536, 10^11), W(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.1590169508270918129082825092379880685934152633409, 10^12), W(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.1929514898827735667473357103796145708703426375351, 10^12), W(5))), VectorCalculus:-`*`(VectorCalculus:-`*`(3.0995137005629364198630176713255719374808867211330, 10^11), V1(2))), VectorCalculus:-`*`(VectorCalculus:-`*`(3.0995137005629364198630176713255719374808867211330, 10^11), V2(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(3.8470197411831163997629889061698911342985204774594, 10^11), V1(4)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(3.8470197411831163997629889061698911342985204774594, 10^11), V2(4)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1224.4069434960135017602438595742022681505344916052, omega^2), W(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2148.6328125000000000000000000000000000000000000000, omega^2), W(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1959.9062914564655436920860212499538090252187294161, omega^2), W(5)))):

E13 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.8271521540250046106119733650076103042314699809887, 10^11), W(1)), VectorCalculus:-`*`(VectorCalculus:-`*`(5.0748128190543187340378117893989426968741725224548, 10^11), V1(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(9.4675908045149947710569375270005700088105651033426, 10^11), V1(4)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(3.8470197411831163997629889061698911342985204774594, 10^11), W(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(4.8700076253112037420543824992554999016189996047000, 10^11), W(5))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.5013483257366249401397118595815208870951202899385, 10^11), V1(0)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(8.3408240318701385563317325532306715949728904996586, 10^10), V2(0)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.0724123476084663741457840654142141615476683079173, 10^11), V2(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.2408423807134586334931704209832226544674079633954, 10^11), V2(4)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1001.9531250000000000000000000000000000000000000000, omega^2), V1(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1288.2502962167977845669843807304847803693289074734, omega^2), V1(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1490.5792236328125000000000000000000000000000000000, omega^2), V1(4))):

E14 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.8271521540250046106119733650076103042314699809887, 10^11), W(1)), VectorCalculus:-`*`(VectorCalculus:-`*`(5.0748128190543187340378117893989426968741725224548, 10^11), V2(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(9.4675908045149947710569375270005700088105651033426, 10^11), V2(4)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(3.8470197411831163997629889061698911342985204774594, 10^11), W(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(4.8700076253112037420543824992554999016189996047000, 10^11), W(5))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(8.3408240318701385563317325532306715949728904996586, 10^10), V1(0)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.5013483257366249401397118595815208870951202899385, 10^11), V2(0)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.0724123476084663741457840654142141615476683079173, 10^11), V1(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.2408423807134586334931704209832226544674079633954, 10^11), V1(4)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1001.9531250000000000000000000000000000000000000000, omega^2), V2(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1288.2502962167977845669843807304847803693289074734, omega^2), V2(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1490.5792236328125000000000000000000000000000000000, omega^2), V2(4))):

E15 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.2808745009976567622404499724256074938728417212344, 10^11), V1(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.2808745009976567622404499724256074938728417212344, 10^11), V2(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.1863576954843550511330528903118121550547428135047, 10^12), W(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.6311934721878459214486844029094270431266234063024, 10^12), W(4)))), VectorCalculus:-`*`(VectorCalculus:-`*`(4.4534580327025486258972640897961855979523955862006, 10^11), V1(3))), VectorCalculus:-`*`(VectorCalculus:-`*`(4.4534580327025486258972640897961855979523955862006, 10^11), V2(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(5.0261223082938320761218206092817337666989622620092, 10^11), V1(5)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(5.0261223082938320761218206092817337666989622620092, 10^11), V2(5)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(6.6726592254961108450653860425845372759783123997272, 10^10), W(0)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1001.9531250000000000000000000000000000000000000000, omega^2), W(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1288.2502962167977845669843807304847803693289074734, omega^2), W(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1490.5792236328125000000000000000000000000000000000, omega^2), W(4))):

E16 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(3.6004827786984552721859600150194476991414811055197, 10^10), W(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.9781847824423219358080619338342989761407203990374, 10^11), V1(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(5.9722762993987285423665483888817556162282387212450, 10^11), V1(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.0811342250226880053021853608526459273776333972115, 10^12), V1(5)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2.2665101950561447195804856166187258422604042194634, 10^11), W(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(5.0261223082938320761218206092817337666989622620092, 10^11), W(4)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(8.7843041320517842057351587174649326412354044181698, 10^10), V2(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.6315367543759662237835567740527270814718925725463, 10^11), V2(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.7046921130066534482600041414890585709013821212606, 10^11), V2(5)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1055.2267908337921786307617355195123093332341255338, omega^2), V1(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1959.9062914564655436920860212499538090252187294161, omega^2), V1(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2047.7851867675781250000000000000000000000000000000, omega^2), V1(5))):

E17 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(3.6004827786984552721859600150194476991414811055197, 10^10), W(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.9781847824423219358080619338342989761407203990374, 10^11), V2(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(5.9722762993987285423665483888817556162282387212450, 10^11), V2(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.0811342250226880053021853608526459273776333972115, 10^12), V2(5)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2.2665101950561447195804856166187258422604042194634, 10^11), W(2))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(5.0261223082938320761218206092817337666989622620092, 10^11), W(4)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(8.7843041320517842057351587174649326412354044181698, 10^10), V1(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.6315367543759662237835567740527270814718925725463, 10^11), V1(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1.7046921130066534482600041414890585709013821212606, 10^11), V1(5)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1055.2267908337921786307617355195123093332341255338, omega^2), V2(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1959.9062914564655436920860212499538090252187294161, omega^2), V2(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2047.7851867675781250000000000000000000000000000000, omega^2), V2(5))):

E18 := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(5.4007241680476829082789400225291715487122216582806, 10^10), V1(0)), VectorCalculus:-`*`(VectorCalculus:-`*`(5.4007241680476829082789400225291715487122216582806, 10^10), V2(0))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.0922794659196454621738794738143334638130489666373, 10^11), W(1)))), VectorCalculus:-`*`(VectorCalculus:-`*`(1.1929514898827735667473357103796145708703426375351, 10^12), W(3))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.8463891254257486220146464851652785318259567235472, 10^12), W(5)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.3168284715873139556329481351343925356696602976947, 10^11), V1(2)))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(2.3168284715873139556329481351343925356696602976947, 10^11), V2(2)))), VectorCalculus:-`*`(VectorCalculus:-`*`(4.8700076253112037420543824992554999016189996046996, 10^11), V1(4))), VectorCalculus:-`*`(VectorCalculus:-`*`(4.8700076253112037420543824992554999016189996046996, 10^11), V2(4))), VectorCalculus:-`*`(VectorCalculus:-`*`(1055.2267908337921786307617355195123093332341255338, omega^2), W(1))), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(1959.9062914564655436920860212499538090252187294161, omega^2), W(3)))), VectorCalculus:-`*`(VectorCalculus:-`*`(2047.7851867675781250000000000000000000000000000000, omega^2), W(5))):

q := Matrix([[coeff(E1, V1(0)), coeff(E1, V2(0)), coeff(E1, W(0)), coeff(E1, V1(1)), coeff(E1, V2(1)), coeff(E1, W(1)), coeff(E1, V1(2)), coeff(E1, V2(2)), coeff(E1, W(2)), coeff(E1, V1(3)), coeff(E1, V2(3)), coeff(E1, W(3)), coeff(E1, V1(4)), coeff(E1, V2(4)), coeff(E1, W(4)), coeff(E1, V1(5)), coeff(E1, V2(5)), coeff(E1, W(5))], [coeff(E2, V1(0)), coeff(E2, V2(0)), coeff(E2, W(0)), coeff(E2, V1(1)), coeff(E2, V2(1)), coeff(E2, W(1)), coeff(E2, V1(2)), coeff(E2, V2(2)), coeff(E2, W(2)), coeff(E2, V1(3)), coeff(E2, V2(3)), coeff(E2, W(3)), coeff(E2, V1(4)), coeff(E2, V2(4)), coeff(E2, W(4)), coeff(E2, V1(5)), coeff(E2, V2(5)), coeff(E2, W(5))], [coeff(E3, V1(0)), coeff(E3, V2(0)), coeff(E3, W(0)), coeff(E3, V1(1)), coeff(E3, V2(1)), coeff(E3, W(1)), coeff(E3, V1(2)), coeff(E3, V2(2)), coeff(E3, W(2)), coeff(E3, V1(3)), coeff(E3, V2(3)), coeff(E3, W(3)), coeff(E3, V1(4)), coeff(E3, V2(4)), coeff(E3, W(4)), coeff(E3, V1(5)), coeff(E3, V2(5)), coeff(E3, W(5))], [coeff(E4, V1(0)), coeff(E4, V2(0)), coeff(E4, W(0)), coeff(E4, V1(1)), coeff(E4, V2(1)), coeff(E4, W(1)), coeff(E4, V1(2)), coeff(E4, V2(2)), coeff(E4, W(2)), coeff(E4, V1(3)), coeff(E4, V2(3)), coeff(E4, W(3)), coeff(E4, V1(4)), coeff(E4, V2(4)), coeff(E4, W(4)), coeff(E4, V1(5)), coeff(E4, V2(5)), coeff(E4, W(5))], [coeff(E5, V1(0)), coeff(E5, V2(0)), coeff(E5, W(0)), coeff(E5, V1(1)), coeff(E5, V2(1)), coeff(E5, W(1)), coeff(E5, V1(2)), coeff(E5, V2(2)), coeff(E5, W(2)), coeff(E5, V1(3)), coeff(E5, V2(3)), coeff(E5, W(3)), coeff(E5, V1(4)), coeff(E5, V2(4)), coeff(E5, W(4)), coeff(E5, V1(5)), coeff(E5, V2(5)), coeff(E5, W(5))], [coeff(E6, V1(0)), coeff(E6, V2(0)), coeff(E6, W(0)), coeff(E6, V1(1)), coeff(E6, V2(1)), coeff(E6, W(1)), coeff(E6, V1(2)), coeff(E6, V2(2)), coeff(E6, W(2)), coeff(E6, V1(3)), coeff(E6, V2(3)), coeff(E6, W(3)), coeff(E6, V1(4)), coeff(E6, V2(4)), coeff(E6, W(4)), coeff(E6, V1(5)), coeff(E6, V2(5)), coeff(E6, W(5))], [coeff(E7, V1(0)), coeff(E7, V2(0)), coeff(E7, W(0)), coeff(E7, V1(1)), coeff(E7, V2(1)), coeff(E7, W(1)), coeff(E7, V1(2)), coeff(E7, V2(2)), coeff(E7, W(2)), coeff(E7, V1(3)), coeff(E7, V2(3)), coeff(E7, W(3)), coeff(E7, V1(4)), coeff(E7, V2(4)), coeff(E7, W(4)), coeff(E7, V1(5)), coeff(E7, V2(5)), coeff(E7, W(5))], [coeff(E8, V1(0)), coeff(E8, V2(0)), coeff(E8, W(0)), coeff(E8, V1(1)), coeff(E8, V2(1)), coeff(E8, W(1)), coeff(E8, V1(2)), coeff(E8, V2(2)), coeff(E8, W(2)), coeff(E8, V1(3)), coeff(E8, V2(3)), coeff(E8, W(3)), coeff(E8, V1(4)), coeff(E8, V2(4)), coeff(E8, W(4)), coeff(E8, V1(5)), coeff(E8, V2(5)), coeff(E8, W(5))], [coeff(E9, V1(0)), coeff(E9, V2(0)), coeff(E9, W(0)), coeff(E9, V1(1)), coeff(E9, V2(1)), coeff(E9, W(1)), coeff(E9, V1(2)), coeff(E9, V2(2)), coeff(E9, W(2)), coeff(E9, V1(3)), coeff(E9, V2(3)), coeff(E9, W(3)), coeff(E9, V1(4)), coeff(E9, V2(4)), coeff(E9, W(4)), coeff(E9, V1(5)), coeff(E9, V2(5)), coeff(E9, W(5))], [coeff(E10, V1(0)), coeff(E10, V2(0)), coeff(E10, W(0)), coeff(E10, V1(1)), coeff(E10, V2(1)), coeff(E10, W(1)), coeff(E10, V1(2)), coeff(E10, V2(2)), coeff(E10, W(2)), coeff(E10, V1(3)), coeff(E10, V2(3)), coeff(E10, W(3)), coeff(E10, V1(4)), coeff(E10, V2(4)), coeff(E10, W(4)), coeff(E10, V1(5)), coeff(E10, V2(5)), coeff(E10, W(5))], [coeff(E11, V1(0)), coeff(E11, V2(0)), coeff(E11, W(0)), coeff(E11, V1(1)), coeff(E11, V2(1)), coeff(E11, W(1)), coeff(E11, V1(2)), coeff(E11, V2(2)), coeff(E11, W(2)), coeff(E11, V1(3)), coeff(E11, V2(3)), coeff(E11, W(3)), coeff(E11, V1(4)), coeff(E11, V2(4)), coeff(E11, W(4)), coeff(E11, V1(5)), coeff(E11, V2(5)), coeff(E11, W(5))], [coeff(E12, V1(0)), coeff(E12, V2(0)), coeff(E12, W(0)), coeff(E12, V1(1)), coeff(E12, V2(1)), coeff(E12, W(1)), coeff(E12, V1(2)), coeff(E12, V2(2)), coeff(E12, W(2)), coeff(E12, V1(3)), coeff(E12, V2(3)), coeff(E12, W(3)), coeff(E12, V1(4)), coeff(E12, V2(4)), coeff(E12, W(4)), coeff(E12, V1(5)), coeff(E12, V2(5)), coeff(E12, W(5))], [coeff(E13, V1(0)), coeff(E13, V2(0)), coeff(E13, W(0)), coeff(E13, V1(1)), coeff(E13, V2(1)), coeff(E13, W(1)), coeff(E13, V1(2)), coeff(E13, V2(2)), coeff(E13, W(2)), coeff(E13, V1(3)), coeff(E13, V2(3)), coeff(E13, W(3)), coeff(E13, V1(4)), coeff(E13, V2(4)), coeff(E13, W(4)), coeff(E13, V1(5)), coeff(E13, V2(5)), coeff(E13, W(5))], [coeff(E14, V1(0)), coeff(E14, V2(0)), coeff(E14, W(0)), coeff(E14, V1(1)), coeff(E14, V2(1)), coeff(E14, W(1)), coeff(E14, V1(2)), coeff(E14, V2(2)), coeff(E14, W(2)), coeff(E14, V1(3)), coeff(E14, V2(3)), coeff(E14, W(3)), coeff(E14, V1(4)), coeff(E14, V2(4)), coeff(E14, W(4)), coeff(E14, V1(5)), coeff(E14, V2(5)), coeff(E14, W(5))], [coeff(E15, V1(0)), coeff(E15, V2(0)), coeff(E15, W(0)), coeff(E15, V1(1)), coeff(E15, V2(1)), coeff(E15, W(1)), coeff(E15, V1(2)), coeff(E15, V2(2)), coeff(E15, W(2)), coeff(E15, V1(3)), coeff(E15, V2(3)), coeff(E15, W(3)), coeff(E15, V1(4)), coeff(E15, V2(4)), coeff(E15, W(4)), coeff(E15, V1(5)), coeff(E15, V2(5)), coeff(E15, W(5))], [coeff(E16, V1(0)), coeff(E16, V2(0)), coeff(E16, W(0)), coeff(E16, V1(1)), coeff(E16, V2(1)), coeff(E16, W(1)), coeff(E16, V1(2)), coeff(E16, V2(2)), coeff(E16, W(2)), coeff(E16, V1(3)), coeff(E16, V2(3)), coeff(E16, W(3)), coeff(E16, V1(4)), coeff(E16, V2(4)), coeff(E16, W(4)), coeff(E16, V1(5)), coeff(E16, V2(5)), coeff(E16, W(5))], [coeff(E17, V1(0)), coeff(E17, V2(0)), coeff(E17, W(0)), coeff(E17, V1(1)), coeff(E17, V2(1)), coeff(E17, W(1)), coeff(E17, V1(2)), coeff(E17, V2(2)), coeff(E17, W(2)), coeff(E17, V1(3)), coeff(E17, V2(3)), coeff(E17, W(3)), coeff(E17, V1(4)), coeff(E17, V2(4)), coeff(E17, W(4)), coeff(E17, V1(5)), coeff(E17, V2(5)), coeff(E17, W(5))], [coeff(E18, V1(0)), coeff(E18, V2(0)), coeff(E18, W(0)), coeff(E18, V1(1)), coeff(E18, V2(1)), coeff(E18, W(1)), coeff(E18, V1(2)), coeff(E18, V2(2)), coeff(E18, W(2)), coeff(E18, V1(3)), coeff(E18, V2(3)), coeff(E18, W(3)), coeff(E18, V1(4)), coeff(E18, V2(4)), coeff(E18, W(4)), coeff(E18, V1(5)), coeff(E18, V2(5)), coeff(E18, W(5))]]); RR := subs(omega = evalf(Omega*sqrt(E_c/rho_c)/h), q); Y := Determinant(RR); with(LinearAlgebra); Sol := [fsolve(Y, Omega)]; J := min(select(`>`, Sol, 0))

Error, selecting function must return true or false

 

``


 

Download ZrO2.mw

 

 

hi... I have a problem with dsolve.

"unable to convert to an explicit first-order system"

please help me

thanks

unable_to_convert_to_an_explicit_first-order_system.mw
 

sys3 := {-3.94190107376326*10^(-23)*(diff(g3(y), y, y, y, y, y, y))+1.07838202775510*10^(-20)*(diff(g3(y), y, y, y, y))-3.40658117485714*10^(-9)*(diff(g1(y), y, y, y, y, y))-4.01448960000000*10^(-7)*(diff(g1(y), y, y, y))-4.56192000000000*10^(-19)*(diff(g3(y), y, y)), -4032000*(diff(g5(y), y, y))+(9/1000000)*g3(y)-(237/500000000)*g5(y)*omega2-(237/4000000000)*g4(y)*omega2+(237/40000000000)*(diff(g1(y), y))*omega2-(237/20000000000)*(diff(g2(y), y))*omega2, -1.51200000000000*10^10*(diff(g4(y), y, y))-0.900000000000000e-5*g3(y)-4.74000000000000*10^(-7)*g4(y)*omega2-5.92500000000000*10^(-8)*g5(y)*omega2+1.18500000000000*10^(-8)*(diff(g1(y), y))*omega2-5.92500000000000*10^(-9)*(diff(g2(y), y))*omega2-1.15287906461538*10^8*(diff(g1(y), y, y, y, y, y)), 1.62147762523876*10^11*(diff(g1(y), y, y, y, y))+0.252000000000000e-5*(diff(g3(y), y))+5.6000000*10^7*g2(y)-5.6000000*10^7*g1(y)+4.74000000000000*10^(-7)*g1(y)*omega2+5.92500000000000*10^(-9)*(diff(g5(y), y))*omega2+5.92500000000000*10^(-10)*(diff(g2(y), y, y))*omega2+1.18500000000000*10^(-8)*(diff(g4(y), y))*omega2-1.18500000000000*10^(-9)*(diff(g1(y), y, y))*omega2+5.92500000000000*10^(-8)*g2(y)*omega2+3.40658117485714*10^(-9)*(diff(g3(y), y, y, y, y, y))-7.16872433152730*10^(-7)*(diff(g3(y), y, y, y))-1.09035520000000*10^7*(diff(g1(y), y, y))+1.09035520000000*10^7*(diff(g2(y), y, y)), 1.39966033920000*10^6*(diff(g2(y), y, y, y, y))+0.252000000000000e-5*(diff(g3(y), y))-5.6000000*10^7*g2(y)+5.6000000*10^7*g1(y)+4.74000000000000*10^(-7)*g2(y)*omega2-1.18500000000000*10^(-8)*(diff(g5(y), y))*omega2+5.92500000000000*10^(-10)*(diff(g1(y), y, y))*omega2-5.92500000000000*10^(-9)*(diff(g4(y), y))*omega2-1.18500000000000*10^(-9)*(diff(g2(y), y, y))*omega2+5.92500000000000*10^(-8)*g1(y)*omega2+5.29912627200000*10^5*(diff(g1(y), y, y, y, y))+3.40658117485714*10^(-9)*(diff(g3(y), y, y, y, y, y))-4.01448960000000*10^(-7)*(diff(g3(y), y, y, y))+1.09035520000000*10^7*(diff(g1(y), y, y))-1.09035520000000*10^7*(diff(g2(y), y, y))}:

bcs3 := {-(63/25000)*(D(g5))(0) = 0, -(63/25000)*(D(g5))(1) = 0, -(189/20)*(D(g4))(0)+1.12585846153846*10^(-15)*((D@@5)(g1))(0) = 0, -(189/20)*(D(g4))(1)+1.12585846153846*10^(-15)*((D@@5)(g1))(1) = 0, 9.62378191836733*10^(-51)*((D@@3)(g3))(0)-1.51215428571429*10^(-39)*(D(g3))(0)+3.32673942857143*10^(-32)*((D@@2)(g1))(0) = 0, 9.62378191836733*10^(-51)*((D@@3)(g3))(1)-1.51215428571429*10^(-39)*(D(g3))(1)+3.32673942857143*10^(-32)*((D@@2)(g1))(1) = 0, -9.62378191836733*10^(-51)*((D@@4)(g3))(0)+2.70027551020408*10^(-39)*((D@@2)(g3))(0)-3.32673942857143*10^(-32)*((D@@3)(g1))(0) = 0, -9.62378191836733*10^(-51)*((D@@4)(g3))(1)+2.70027551020408*10^(-39)*((D@@2)(g3))(1)-3.32673942857143*10^(-32)*((D@@3)(g1))(1) = 0, 6.33389697358892*10^(-8)*((D@@2)(g1))(0)+3.32673942857143*10^(-32)*((D@@3)(g3))(0)-6.27264000000000*10^(-21)*(D(g3))(0) = 0, 6.33389697358892*10^(-8)*((D@@2)(g1))(1)+3.32673942857143*10^(-32)*((D@@3)(g3))(1)-6.27264000000000*10^(-21)*(D(g3))(1) = 0, 5.46742320000000*10^(-13)*((D@@2)(g2))(0)+2.06997120000000*10^(-13)*((D@@2)(g1))(0)+3.32673942857143*10^(-32)*((D@@3)(g3))(0)-6.27264000000000*10^(-21)*(D(g3))(0) = 0, 5.46742320000000*10^(-13)*((D@@2)(g2))(1)+2.06997120000000*10^(-13)*((D@@2)(g1))(1)+3.32673942857143*10^(-32)*((D@@3)(g3))(1)-6.27264000000000*10^(-21)*(D(g3))(1) = 0, 9.62378191836733*10^(-51)*((D@@6)(g3))(0)-4.21242979591837*10^(-39)*((D@@4)(g3))(0)+3.32673942857143*10^(-32)*((D@@5)(g1))(0)+6.27264000000000*10^(-21)*((D@@3)(g1))(0)+2.85120000000000*10^(-28)*((D@@2)(g3))(0) = 0, 9.62378191836733*10^(-51)*((D@@6)(g3))(1)-4.21242979591837*10^(-39)*((D@@4)(g3))(1)+3.32673942857143*10^(-32)*((D@@5)(g1))(1)+6.27264000000000*10^(-21)*((D@@3)(g1))(1)+2.85120000000000*10^(-28)*((D@@2)(g3))(1) = 0, g1(0) = 0, g1(1) = 0, g2(0) = 0, g2(1) = 0}:

dsys4 := {bcs3, sys3}:

Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mrow(Typesetting:-mo("for", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("bb", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("in", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("extra_bcs", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("do", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("try", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("print", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bb", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-msup(Typesetting:-mn("10", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mo("&uminus0;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mn("13", font_style_name = "2D Input", mathvariant = "normal")), superscriptshift = "0")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("res", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bb", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo("&coloneq;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("dsolve", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("newsys2", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("union", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bb", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-msup(Typesetting:-mn("10", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mo("&uminus0;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mn("13", font_style_name = "2D Input", mathvariant = "normal")), superscriptshift = "0")), font_style_name = "2D Input", mathvariant = "normal", open = "{", close = "}"), Typesetting:-mo("union", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("bcs3", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("numeric", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("method", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("bvp", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("middefer", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("output", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("listprocedure", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("initmesh", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("3024", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("approxsoln", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("omega3", italic = "false", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.0000000001", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("g1", italic = "false", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("y", italic = "false", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-msup(Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mrow(Typesetting:-mn("3", font_style_name = "2D Input", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo("&sdot;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("&minus;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("3", font_style_name = "2D Input", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("g2", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mrow(Typesetting:-mn("3", font_style_name = "2D Input", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo("&sdot;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("&minus;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("3", font_style_name = "2D Input", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("g4", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mrow(Typesetting:-mi("")), superscriptshift = "0"), Typesetting:-mo("&sdot;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("&minus;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mi("")), superscriptshift = "0"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("g3", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mrow(Typesetting:-mi("")), superscriptshift = "0"), Typesetting:-mo("&sdot;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("&minus;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("5", font_style_name = "2D Input", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("g5", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mrow(Typesetting:-mi("")), superscriptshift = "0"), Typesetting:-mo("&sdot;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("&minus;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mi("")), superscriptshift = "0")), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("abserr", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("1e−9", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("catch", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("print", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("lasterror", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", font_style_name 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mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("&coloneq;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("indices", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("nolist", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mi("nops", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mi("res", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("P", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("&coloneq;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("seq", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("subs", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("i", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("omega3", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("..", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mi("nops", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]")), font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo("for", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("i", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("from", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("by", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = 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"false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("nops", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("do", 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largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("Pi", italic = "false", font_style_name = "2D Input", mathvariant = "normal")), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("od", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(";", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mi("plots", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(":-", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("odeplot", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = 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font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("g", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("..", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("5", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal")), Typesetting:-mi("")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mn("0", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("..", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("thickness", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("3", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal")), Typesetting:-mi(""))

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

``


 

Download unable_to_convert_to_an_explicit_first-order_system.mw

 

The following integral is obviously positive, but Maple returns 0:  (Maple 2017)

assume(gamma1>0, gamma2>0 , mu1, 'real', mu2, 'real')'
int( 1/sqrt( Pi^2 * gamma1 * gamma2 * (1+((x-mu1)/gamma1)^2) * (1+((x-mu2)/gamma2)^2) ), x=-infinity..infinity )
                               0

(This is the Bhattacharyya coefficient between two cauchy distributions). Numerical integration works.

 

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