Maple 2017 Questions and Posts

These are Posts and Questions associated with the product, Maple 2017
restart;
sol:=dsolve(diff(y(x),x)= x/(sqrt(x^2-16))*1/(2*y(x)),y(x));

Gives

But the solution can also be written as

I just do not know how to transform the first solution to the second simpler one. I tried:

sol:=map(x->rhs(x),[sol]);
simplify(sol,radical);

Also tried simplify(sol,sqrt); simplify(sol,radical,symbolic); simplify(sol,size);

The simpler solution can be found as follows

restart;
sol:=dsolve(diff(y(x),x)= x/(sqrt(x^2-16))*1/(2*y(x)),y(x),'implicit');

But the term in the middle above is

Therefore the solution is really

eq:=y(x)^2-sqrt(x^2-16)-_C1 = 0;
solve(eq,y(x));

Which gives

What command to simplify the long solution to the shorter one obtained from the implicit?

 

The solution by Maple below is correct, but non-the-less, a little strange.

restart;
dsolve(diff(y(x),x)=3*x^2*(y(x)^2+1),y(x));

Gives

Ofcourse 3*constant is still constant. But it is a little strange and have no reason for it to be there.  When I solve it by hand

What could made Maple put the 3 in there? Again, solution is 100% correct, but it could be simpler.

Maple 2017.1

 

 

the following code results in an error message: Error, (in forget) lexically scoped parameter out of context

If I click on this error message, it brings me to a page which I visited too often.

if I uncomment the irrelevant minimize command, the error message disappears.

How can I prevent this error without giving irrelevant commands?

kind regards,

Harry Garst

hello.i have a problem for solving this equation.i dont why my past post about this is deleted.!!!

please help me

thanks,,,

9.mw
 

restart:

A1:= 27159:  n:= 0.59:  A2:= 70941:  h0:= 3e-4:   
L:= 0.8:  dpx := -98100:  uc:= 0.007:  k:=2.7:

ODE:= (A3,y)->
   (h0^(n+1)*L/sqrt(n)*(A1*exp(sqrt(n)*y/L)-A2*exp(-sqrt(n)*y/L))/k+dpx*y*h0^(n+1)/k+A3*(h0)^n/k)^(1/n)
;

proc (A3, y) options operator, arrow; (h0^(n+1)*L*(A1*exp(sqrt(n)*y/L)-A2*exp(-sqrt(n)*y/L))/(sqrt(n)*k)+dpx*y*h0^(n+1)/k+A3*h0^n/k)^(1/n) end proc

(1)

ODEINT:= proc(A3)
option remember;
local y;
   evalf(Int(ODE(A3,y), y= 0..1, epsilon= 1e-7)) - uc
end proc:

ReINT:= proc(A3x, A3y)
   Digits:= 15:
   Re(ODEINT(A3x + I*A3y))
end proc:

ImINT:= subs(Re= Im, eval(ReINT)):

Digits:= 7:
a3:= fsolve([ReINT, ImINT]);

fsolve([ReINT, ImINT])

(2)

A3:= Complex(a3[]);

Complex(fsolve([ReINT, ImINT])[])

(3)

Solve as IVP:

Digits:= 15:
sol:= dsolve({diff(u(y),y) = ODE(A3,y), u(0)=0}, numeric, range=0..1,  output=listprocedure):

Warning,  computation interrupted

 

NULL

``

NULL

NULL

plots:-odeplot(
   sol, [[y, Re(u(y))], [y, Im(u(y))]], y= 0..1,
   legend= [real, imag], labels= [y, u(y)]
);

Verify that boundary condition at u(1) is satisfied:

 

 

 

abs(eval(u(y), sol(1)) - uc);

sol(.5);

"\"

fy3 := eval(u(y), sol); with(CurveFitting); fy33 := PolynomialInterpolation([[0, fy3(0)], [.1, fy3(.1)], [.2, fy3(.2)], [.3, fy3(.3)], [.4, fy3(.4)], [.5, fy3(.5)], [.6, fy3(.6)], [.7, fy3(.7)], [.8, fy3(.8)], [.9, fy3(.9)], [1, fy3(1)]], y)

DEBI := int(fy33, y = 0 .. 1)

NULL

``

plot(DEBI, y = 0 .. 1)

``

``

``

``

``


 

Download 9.mw

 

Dear sir, 

 

I request your kind help with regard to the above cited subject.

 

 

With warm regards.

 

Mr.M.Anand

Associate Professor in Mathematics.

Aurora's Technological & Research Institute, 

Hyderabad-INDIA

 To Whom It Might Concern,

I purchased Maple on Jun 5, 2017 for my Window laptop. However, my harddrive in my laptop was broken and i lost all my stuff including Maple. I am using my husband's laptop right now. How can re install Maple? I still have the transaction number (removed). Would you let me know what I can do to re-install the software? Also, my husband's laptop is a Mac. 

I am looking forward to hearing from you.

Nancy Phu.

I would like to create a Maple Workbook of my Lattice Package so I can put it on MapleCloud. I had an email exchange with Daniel Skoog from Maplesoft about this, and he even sent me an example that looked easy enough to adapt to my purposes. Alas, it does not work. Here is the code I wrote to assemble the already extant files:

restart;
                "Maple Initialization loaded..."
# Build Lattice workbook following example from Daniel Skoog, MapleSoft:
currentdir();
 "/Applications/Math_Calc/Maple 2015/Packages/Lattice/Lattice

    Version 1.1.0 release files"
# We have all files already from the App Center submission, so just assemble the workbook
PackageTools:-Create("Lattice.maple",\
"MLA file"="Lattice.mla",\
"Lattice.help",\
"Source"="Lattice1.1.mpl",\
"Build procedure"="Lattice1.1.mw",\
"Manual"="The Lattice Package Users Guide.mw",\
"Release Notes"="V1.1 Release Notes.rtf");
Error, (in march) unable to attach worksheet file The Lattice Package Users Guide.mw


When I look at the created workbook (Lattice.maple), the only members included are Lattice.help, the Build procedure Lattice1.1.mw and the source file Lattice.mpl. In particular, Lattice.mla is not there, which is the most important one.

What am I doing wrong? What does "march" (which sounds like machine architecture) have to do with it??

I also don't quite know how to "install" it. I assume I just put the whole workbook into a directory accessible through libname ?

Mac Dude

PS: I could have sorted this privately with Daniel, but this may be of interest to others as well so I hope he'll answer through this forum.

Lattice1.1_workbook_maker.mw

Maple help pages are terrible.  Sorry, but this is true.

I am looking for one example of how one is supposed to open a file and correctly check that the open was successful and no error occured, all done in code. As in a script.

All what help in fopen says is that if this and that, it generates an error.

            "

OK. But to check for this in code? Why not show an example? the help page on iostatus just lists possible errors. Again, not a SINGLE example of actual Maple code showing how to actually check or handle an error. It just says to call iostatus() and shows the output without an example of what to do next and what to check for.

Lets say one does this:


fileName := "C:\\foo.txt";
fd       := fopen(fileName,WRITE):

Now what? How to check the above was successful? Do I need a trap and catch? catch what? Do I need to check for fd being greater or equal to zero and also use trap in addition? And if an error happens, how to know what it is? How to to format the message, etc.. all in CODE (not interactive) and not by saying just look at the screen and see if there is an error message.

Spend 30 minutes in the help pages and could not find ONE example that shows how to actually check for errors.

I have no idea who writes Maple helps pages, but I find the help pages useless most of the time.

Compare the help for linux fopen for example, where is gives exact details of how to handle the error and find the exact error, all in code.

 

Sometimes dsolve returns solution as implicit, even when not using the `implicit` option. For example

restart;
ode:=diff(y(x),x)=(x*y(x))^(1/2):
sol:=dsolve(ode,y(x));

Gives

Which is the same result if I had used 'implicit'.

Is there a way to tell dsolve not to do this? is it becuase it can't solve for y(x) from the above?

Maple 2017.1

 

when i want to get awenser i have to solve it for 36 equation and 36 variabales
but maple will not give me a solution (just toss me back my variabales ) i dont know whats wrong
it will give me an awenser for lower like 20equ and 20var ?
parameters :

there is m for power an equation (equation^m) its between 2 , 2.5 , 3 , 4
and N give 2N+2var and 2N+2equ
its a hard calculation i copy it here hope u get it

h= "a number "

p := proc (x) c[-N-1]*x^2+1 end proc

dp := diff(p(x), x)

ddp := diff(p(x), x, x)

DELTA2 := piecewise(k <> j, -2*(-1)^(j-k)/(j-k)^2, k = j, -(1/3)*Pi^2)/h^2

DELTA1 := piecewise(k <> j, (-1)^(j-k)/(j-k), k = j, 0)/h

DELTA0 := piecewise(k <> j, 0, k = j, 1)

PHI := proc (x) ln(sinh(x)) end proc

dPHI := diff(PHI(x), x)

ddPHI := diff(PHI(x), x, x)
 

for i from -N-1 to N do x[i] := ln(exp(i*h)+(exp(2*i*h)+1)^(1/2)) end do

variabales : c[-N-1],c[-N],c[-N+1]...c[N-1],c[N] total 2N+2 var



My equations

POL := seq(simplify(eval(sum(c[k]*((eval(2*dPHI*DELTA1), x = x[j])+eval(x[j]*ddPHI*DELTA1, x = x[j])+x[j]*(eval(dPHI^2, x = x[j]))*DELTA2), k = -N .. N)+eval(ddp, x = x[j])+2*(sum(c[k]*(eval(x[j]*dPHI*DELTA1, x = x[j])+DELTA0), k = -N .. N)+eval(dp, x = x[j]))/x[j]+(c[j]*x[j]+p(x[j]))^m, x = x[j])), j = -N-1 .. N)

solving

K := fsolve({seq(POL[v] = 0, v = 1 .. 2*N+2)})

it can calculate for m=2.5 , N=15 , h=0.29669

if you can calculate it for m=3 , N=17 , h=0.41600

Everytime I start Maple 2017 I get a window asking me to accept incoming connection even though I did not put any restriction in System Preferences-Security-Firewall.

Is it normal?

 

Thank you

hello...how i can remove this error?

thanks

33.mw
 

restart; Digits := 15

15

(1)

sys3 := {-.233333333333333*(diff(g5(y), y, y))+0.5e-1*g3(y)-.820000000000000*g5(y)*omega2-0.150000000000000e-1*g4(y)*omega2+0.500000000000000e-4*(diff(g1(y), y))*omega2-0.999999999999999e-4*(diff(g2(y), y))*omega2-1.44142830009497*(diff(g2(y), y, y, y, y, y))+864.856980056984*(diff(g5(y), y, y, y, y)), 2.61572184429325*10^(-10)*(diff(g3(y), y, y, y, y, y, y, y, y))+3.32396399331216*10^(-7)*(diff(g3(y), y, y, y, y, y, y))-0.193818732289211e-2*(diff(g3(y), y, y, y, y))+0.199166451610413e-1*(diff(g1(y), y, y, y, y, y))+0.598690451303844e-1*(diff(g2(y), y, y, y, y, y))-5.40849801271536*(diff(g1(y), y, y, y))-5.40846938859685*(diff(g2(y), y, y, y))-.101409302553410*(diff(g3(y), y, y))+0.240924444444445e-5*(diff(g4(y), y, y, y, y)), -.233333333333333*(diff(g4(y), y, y))-0.5e-1*g3(y)-.820000000000000*g4(y)*omega2-0.150000000000000e-1*g5(y)*omega2+0.999999999999999e-4*(diff(g1(y), y))*omega2-0.500000000000000e-4*(diff(g2(y), y))*omega2-0.225354497440541e-3*(diff(g3(y), y, y, y, y, y, y))-76.1509512630580*(diff(g1(y), y, y, y, y, y))-11.7785283950617*(diff(g2(y), y, y, y, y, y))+1874.44512820514*(diff(g4(y), y, y, y, y))+6.88355555555557*10^(-7)*(diff(g3(y), y, y, y, y))-8413.23456790121*(diff(g2(y), y, y, y))+8413.23456790121*(diff(g1(y), y, y, y)), 7118.49071746442*(diff(g2(y), y, y, y, y))+0.266666666666666e-2*(diff(g3(y), y))-93.3333333333333*g2(y)+93.3333333333333*g1(y)+.820000000000000*g2(y)*omega2-0.999999999999999e-4*(diff(g5(y), y))*omega2+1.66666666666666*10^(-7)*(diff(g1(y), y, y))*omega2-0.500000000000000e-4*(diff(g4(y), y))*omega2-3.33333333333333*10^(-7)*(diff(g2(y), y, y))*omega2+0.150000000000000e-1*g1(y)*omega2+980.282047736626*(diff(g1(y), y, y, y, y))+0.987816663816580e-2*(diff(g3(y), y, y, y, y, y))-2.84647769547324*(diff(g1(y), y, y, y, y, y, y))-1.77181281840245*(diff(g2(y), y, y, y, y, y, y))+5.40846577473014*(diff(g3(y), y, y, y))+5.07598485596708*10^5*(diff(g1(y), y, y))-5.07598485596708*10^5*(diff(g2(y), y, y))-16826.4691358025*(diff(g4(y), y, y, y))-0.210330864197531e-4*(diff(g3(y), y, y, y, y, y, y, y)), 1.66666666666666*10^(-7)*(diff(g2(y), y, y))*omega2+0.500000000000000e-4*(diff(g5(y), y))*omega2-3.33333333333333*10^(-7)*(diff(g1(y), y, y))*omega2+0.999999999999999e-4*(diff(g4(y), y))*omega2+0.150000000000000e-1*g2(y)*omega2+.820000000000000*g1(y)*omega2-5.53911151967922*(diff(g1(y), y, y, y, y, y, y))-2.55201448559671*10^5*(diff(g4(y), y, y, y))-0.355523547493069e-4*(diff(g3(y), y, y, y, y, y, y, y))+0.266666666666666e-2*(diff(g3(y), y))-4.05637062704760*(diff(g3(y), y, y))-11.4677117829418*(diff(g3(y), y, y, y))-0.338031746031747e-2*(diff(g3(y), y, y, y, y))-0.890132662315342e-2*(diff(g3(y), y, y, y, y, y))-378.595555555555*(diff(g2(y), y, y, y))-482.358781893005*(diff(g2(y), y, y, y, y))-2.84647769547324*(diff(g2(y), y, y, y, y, y, y))-93.3333333333333*g1(y)-4.35805550617285*10^5*(diff(g1(y), y, y))-378.595555555555*(diff(g1(y), y, y, y))+45299.9927158183*(diff(g1(y), y, y, y, y))+93.3333333333333*g2(y)+5.07598485596708*10^5*(diff(g2(y), y, y))}:

bcs3 := {-0.350267076923078e-2*((D@@3)(g2))(0)+7.00534153846156*((D@@2)(g5))(0) = 0, -0.350267076923078e-2*((D@@3)(g2))(1)+7.00534153846156*((D@@2)(g5))(1) = 0, -0.2100e-1*(D(g5))(0)+0.350267076923078e-2*((D@@5)(g2))(0)-7.00534153846156*((D@@4)(g5))(0) = 0, -0.2100e-1*(D(g5))(1)+0.350267076923078e-2*((D@@5)(g2))(1)-7.00534153846156*((D@@4)(g5))(1) = 0, 1.71617510204081*10^(-14)*((D@@4)(g3))(0)+2.93357776746121*10^(-11)*((D@@2)(g3))(0)+0.912685714285722e-5*(D(g1))(0)-0.912685714285712e-5*(D(g2))(0)-5.09278628571429*10^(-7)*((D@@2)(g4))(0)+8.04988799999997*10^(-9)*((D@@3)(g1))(0)+4.59993600000001*10^(-9)*((D@@3)(g2))(0) = 0, 1.71617510204081*10^(-14)*((D@@4)(g3))(1)+2.93357776746121*10^(-11)*((D@@2)(g3))(1)+0.912685714285722e-5*(D(g1))(1)-0.912685714285712e-5*(D(g2))(1)-5.09278628571429*10^(-7)*((D@@2)(g4))(1)+8.04988799999997*10^(-9)*((D@@3)(g1))(1)+4.59993600000001*10^(-9)*((D@@3)(g2))(1) = 0, -1.64283428634155*10^(-7)*((D@@4)(g3))(0)-.133295923200000*((D@@3)(g1))(0)-0.286218240000000e-1*((D@@3)(g2))(0)+15.1830055384616*((D@@2)(g4))(0)+5.57568000000000*10^(-9)*((D@@2)(g3))(0)-227.157333333333*(D(g2))(0)+227.157333333333*(D(g1))(0) = 0, -1.64283428634155*10^(-7)*((D@@4)(g3))(1)-.133295923200000*((D@@3)(g1))(1)-0.286218240000000e-1*((D@@3)(g2))(1)+15.1830055384616*((D@@2)(g4))(1)+5.57568000000000*10^(-9)*((D@@2)(g3))(1)-227.157333333333*(D(g2))(1)+227.157333333333*(D(g1))(1) = 0, -1.71617510204081*10^(-14)*((D@@5)(g3))(0)-2.12981181756245*10^(-10)*((D@@3)(g3))(0)+0.813595871901550e-5*(D(g3))(0)-0.393365900022856e-4*((D@@2)(g1))(0)-0.136355081430858e-3*((D@@2)(g2))(0)+5.09278628571429*10^(-7)*((D@@3)(g4))(0)-8.04988799999997*10^(-9)*((D@@4)(g1))(0)-4.59993600000001*10^(-9)*((D@@4)(g2))(0) = 0, -1.71617510204081*10^(-14)*((D@@5)(g3))(1)-2.12981181756245*10^(-10)*((D@@3)(g3))(1)+0.813595871901550e-5*(D(g3))(1)-0.393365900022856e-4*((D@@2)(g1))(1)-0.136355081430858e-3*((D@@2)(g2))(1)+5.09278628571429*10^(-7)*((D@@3)(g4))(1)-8.04988799999997*10^(-9)*((D@@4)(g1))(1)-4.59993600000001*10^(-9)*((D@@4)(g2))(1) = 0, -0.2100e-1*(D(g4))(0)+1.64283428634155*10^(-7)*((D@@6)(g3))(0)+.185046811569231*((D@@5)(g1))(0)+0.286218240000000e-1*((D@@5)(g2))(0)-15.1830055384616*((D@@4)(g4))(0)-5.57568000000000*10^(-9)*((D@@4)(g3))(0)+227.157333333333*((D@@3)(g2))(0)-227.157333333333*((D@@3)(g1))(0) = 0, -0.2100e-1*(D(g4))(1)+1.64283428634155*10^(-7)*((D@@6)(g3))(1)+.185046811569231*((D@@5)(g1))(1)+0.286218240000000e-1*((D@@5)(g2))(1)-15.1830055384616*((D@@4)(g4))(1)-5.57568000000000*10^(-9)*((D@@4)(g3))(1)+227.157333333333*((D@@3)(g2))(1)-227.157333333333*((D@@3)(g1))(1) = 0, 371.200498864795*((D@@2)(g1))(0)-0.125033665514056e-4*((D@@3)(g3))(0)-0.454911629784616e-2*((D@@4)(g1))(0)-0.207508224000000e-2*((D@@4)(g2))(0)-.90862933333333*((D@@2)(g2))(0)-.219044470756571*(D(g3))(0)+.317542124307693*((D@@3)(g4))(0)-7.77529998367344*10^(-9)*((D@@5)(g3))(0) = 0, 371.200498864795*((D@@2)(g1))(1)-0.125033665514056e-4*((D@@3)(g3))(1)-0.454911629784616e-2*((D@@4)(g1))(1)-0.207508224000000e-2*((D@@4)(g2))(1)-.90862933333333*((D@@2)(g2))(1)-.219044470756571*(D(g3))(1)+.317542124307693*((D@@3)(g4))(1)-7.77529998367344*10^(-9)*((D@@5)(g3))(1) = 0, -1.71617510204081*10^(-14)*((D@@8)(g3))(0)-2.42316975112457*10^(-10)*((D@@6)(g3))(0)+0.156993173154261e-4*((D@@4)(g3))(0)-0.483974477413303e-4*((D@@5)(g1))(0)-0.145481779666834e-3*((D@@5)(g2))(0)+.146029446343315*((D@@3)(g1))(0)+.146028673492115*((D@@3)(g2))(0)+0.912683722980687e-2*((D@@2)(g3))(0)-1.95148800000000*10^(-8)*((D@@4)(g4))(0) = 0, -1.71617510204081*10^(-14)*((D@@8)(g3))(1)-2.42316975112457*10^(-10)*((D@@6)(g3))(1)+0.156993173154261e-4*((D@@4)(g3))(1)-0.483974477413303e-4*((D@@5)(g1))(1)-0.145481779666834e-3*((D@@5)(g2))(1)+.146029446343315*((D@@3)(g1))(1)+.146028673492115*((D@@3)(g2))(1)+0.912683722980687e-2*((D@@2)(g3))(1)-1.95148800000000*10^(-8)*((D@@4)(g4))(1) = 0, 54.7703335314617*((D@@2)(g2))(0)+5.87769600000000*((D@@2)(g1))(0)+0.148770877878858e-4*((D@@3)(g3))(0)-0.207508224000000e-2*((D@@4)(g1))(0)-0.129031719384616e-2*((D@@4)(g2))(0)+.146028885677714*(D(g3))(0)+.143109120000000*((D@@3)(g4))(0)+0.350267076923078e-2*((D@@3)(g5))(0)-4.59993600000001*10^(-9)*((D@@5)(g3))(0) = 0, 54.7703335314617*((D@@2)(g2))(1)+5.87769600000000*((D@@2)(g1))(1)+0.148770877878858e-4*((D@@3)(g3))(1)-0.207508224000000e-2*((D@@4)(g1))(1)-0.129031719384616e-2*((D@@4)(g2))(1)+.146028885677714*(D(g3))(1)+.143109120000000*((D@@3)(g4))(1)+0.350267076923078e-2*((D@@3)(g5))(1)-4.59993600000001*10^(-9)*((D@@5)(g3))(1) = 0, 1.71617510204081*10^(-14)*((D@@6)(g3))(0)+2.42316975112457*10^(-10)*((D@@4)(g3))(0)-0.715265022412607e-5*((D@@2)(g3))(0)+0.483974477413303e-4*((D@@3)(g1))(0)+0.145481779666834e-3*((D@@3)(g2))(0)-3.28345600000000*10^(-7)*(D(g1))(0)+3.28345600000000*10^(-7)*(D(g2))(0)+2.11875840000000*10^(-8)*((D@@2)(g4))(0)-5.09278628571429*10^(-7)*((D@@4)(g4))(0)+8.04988799999997*10^(-9)*((D@@5)(g1))(0)+4.59993600000001*10^(-9)*((D@@5)(g2))(0) = 0, 1.71617510204081*10^(-14)*((D@@6)(g3))(1)+2.42316975112457*10^(-10)*((D@@4)(g3))(1)-0.715265022412607e-5*((D@@2)(g3))(1)+0.483974477413303e-4*((D@@3)(g1))(1)+0.145481779666834e-3*((D@@3)(g2))(1)-3.28345600000000*10^(-7)*(D(g1))(1)+3.28345600000000*10^(-7)*(D(g2))(1)+2.11875840000000*10^(-8)*((D@@2)(g4))(1)-5.09278628571429*10^(-7)*((D@@4)(g4))(1)+8.04988799999997*10^(-9)*((D@@5)(g1))(1)+4.59993600000001*10^(-9)*((D@@5)(g))(1) = 0, g1(0) = 0, g1(1) = 0, g2(0) = 0, g2(1) = 0, ((D@@2)(g1))(0) = 0, ((D@@2)(g1))(1) = 0, ((D@@2)(g2))(0) = 0, ((D@@2)(g2))(1) = 0}:

dsys4 := {bcs3, sys3}:

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("5", 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("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("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("5", 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("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:-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:-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("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:-mn("7", 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("7", 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:-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 = "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&minus;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 = "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("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 = "0.2777778em", 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("end", 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("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 = "0.0em", 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 = "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("to", 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 = "0.0em", 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", 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:-mfrac(Typesetting:-mrow(Typesetting:-mi("sqrt", italic = "false", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("10", 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 = "0.1111111em", rspace = "0.1111111em"), Typesetting:-mn("25", 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 = "0.1666667em", rspace = "0.1666667em"), Typesetting:-mi("P", 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")), Typesetting:-mrow(Typesetting:-mn("2", font_style_name = "2D Input", mathvariant = "normal"), 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:-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 = "]")), 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:-mfenced(Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mrow(Typesetting:-mi("seq", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("y", 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("cat", italic = "true", 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(""))

"unable to store %1 when datatype=%2", -HFloat(9.659865599999965e-7)+0.459993600000001e-8*((D@@5)(g))(1), float[8]

(2)

``


 

Download 33.mw

 

in my solution is 0.0000 . how can show it 0 and how can i show the solutions for example 10^-30 to zero(round to zero)

 

1.mw

 

I want to plot a function f(x,y)=x^3-2x^2y. But I only want to plot values where $x^2+y^2 <= 1$. So far I specified the plotting range in the standard way, but I really need to specify it like I described. I want to use plot3d.

hello...how I can pdsolve three equations with related boundary conditions?

please help me.

thanks...

J := f1(r, z)*f2(r, z)*f3(r, z):

`f&theta;` := f2(r, z)*f3(r, z)/fz:

m0 := 1:

``

g := r*ph/l:

sy := (1/2)*arctan(2*g*fz^2/(-fz^2+g^2+`f&theta;`^2-1)):

I4 := (f2(r, z)^2*cos(sy)^2+f3(r, z)^2*sin(sy)^2-(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2))*cos(b)^2+.5*f2(r, z)*f3(r, z)*(f2(r, z)^2-f3(r, z)^2)*sin(2*sy)*sin(2*b)/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)+((f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)^2+(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2))*sin(b)^2:

I6 := (f2(r, z)^2*cos(sy)^2+f3(r, z)^2*sin(sy)^2-(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2))*cos(b)^2-.5*f2(r, z)*f3(r, z)*(f2(r, z)^2-f3(r, z)^2)*sin(2*sy)*sin(2*b)/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)+((f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)^2+(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2))*sin(b)^2:

L := (I4-1)*exp(K2*(I4-1)^2-1):

N := (I6-1)*exp(K2*(I6-1)^2-1):

P23 := -f2(r, z)*f3(r, z)*sin(b)*cos(b)+(.5*(f2(r, z)^2-f3(r, z)^2))*sin(sy)^2*sin(b)^2:

P32 := -f2(r, z)*f3(r, z)*sin(b)*cos(b)+(.5*(f2(r, z)^2-f3(r, z)^2))*sin(sy)^2*sin(b)^2:

P33 := (f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)*sin(b)^2:

P22 := ((f2(r, z)^2*cos(sy)^2+f3(r, z)^2*sin(sy)^2)^2-(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2)*cos(b)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)-f2(r, z)*f3(r, z)*(f2(r, z)^2-f3(r, z)^2)*sin(2*sy)*sin(b)*cos(b)/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)+(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2*sin(b)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2):

S23 := f2(r, z)*f3(r, z)*sin(b)*cos(b)+(.5*(f2(r, z)^2-f3(r, z)^2))*sin(sy)^2*sin(b)^2:

S32 := f2(r, z)*f3(r, z)*sin(b)*cos(b)+(.5*(f2(r, z)^2-f3(r, z)^2))*sin(sy)^2*sin(b)^2:

S33 := (f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)*sin(b)^2:

S22 := ((f2(r, z)^2*cos(sy)^2+f3(r, z)^2*sin(sy)^2)^2-(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2)*cos(b)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)+f2(r, z)*f3(r, z)*(f2(r, z)^2-f3(r, z)^2)*sin(2*sy)*sin(b)*cos(b)/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)+(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2*sin(b)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2):

Trr := k0*(J-1)+(1/3)*m0*(2*f1(r, z)^2-f2(r, z)^2-f3(r, z)^2)/J^(5/3):

`T&theta;&theta;` := k0*(J-1)+m0*(f2(r, z)^2*cos(sy)^2+f3(r, z)^2*sin(sy)^2-(1/3)*f1(r, z)^2-(1/3)*f2(r, z)^2-(1/3)*f3(r, z)^2)/J^(5/3)+2*k1*(L*S22+N*P22)/J:

`T&theta;z` := m0*(f2(r, z)^2-f3(r, z)^2)*sin(sy)*cos(sy)/J^(5/3)+2*k1*(L*S23+N*P23)/J:

`Tz&theta;` := m0*(f2(r, z)^2-f3(r, z)^2)*sin(sy)*cos(sy)/J^(5/3)+2*k1*(L*S23+N*P23)/J:

Tzz := k0*(J-1)+m0*(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2-(1/3)*f1(r, z)^2-(1/3)*f2(r, z)^2-(1/3)*f3(r, z)^2)/J^(5/3)+2*k1*(L*S33+N*P33)/J:

`Tr&theta;` := 0:

`T&theta;r` := 0:

Trz := 0:

Tzr := 0:

NULLpartial equations

equ(1) := r*(diff(Trr, r))+Trr-`T&theta;&theta;`:

equ(2) := diff(`T&theta;z`, z):

equ(3) := diff(Tzz, z):

# BOUNDARY CONDITIONS

Trr := proc (ro, z) options operator, arrow; 0 end proc:

int((`T&theta;&theta;`-Trr)/r, r, ri, ro) := 13.3*10^3:

2*Pi*(int(Tzz*r, r, ri, ro))-13.3*Pi*ri^2*10^3

Error, (in int) wrong number (or type) of arguments: invalid options or option values passed to indefinite integration. Unknown options: {ro, .8333333333*f1(r, z)*f2(r, z)}

 

int(`T&theta;z`*r^2, r, ri, ro) := 10:

NULL


 

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hello...how I can pdsolve three equation with related boundary conditions?

please help me.

thanks...

for_site.mw

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