MaplePrimes Questions

How to draw the given data?


 

 

restart

``

0, 0.

 

0.5e-1, 0.7453559923e-1

 

.10, .1054092553

 

.15, .1290994449

 

.20, .1490711985

 

.25, .1666666667

 

.30, .1825741858

 

.35, .1972026594

 

.40, .2108185107

 

.45, .2236067977

 

.50, .2357022604

 

.55, .2472066162

 

.60, .2581988897

 

.65, .2687419249

 

.70, .2788866755

 

.75, .2886751346

 

.80, .2981423970

 

.85, .3073181486

 

.90, .3162277660

 

.95, .3248931448

 

1.00, .3333333333

 

``


 

Download aaa.mw

 

 

pde := diff(u(x, t), x $ 4) = diff(u(x, t), t $ 2);

iv:= subs(L = 100, {u(0, t) = 0, u(L, t) = 0, u(x, 0) = sin(x), D[2](u)(x, 0) = 2*x, D[1, 1](u)(0, t) = 0, D[1, 1](u)(L, t) = 0});

de := pdsolve(pde, iv, numeric):

sa1 := de:-value(output = listprocedure);

sa1:=[x=proc() ... end proc,t=proc() ... end proc,u(x,t)=proc() .. end proc]

    With the above procedure it works, but in the most compact form below it does not work.

pdsolve(pde, iv, numeric,output = listprocedure):

Error, (in pdsolve/numeric/par_hyp) invalid arguments for theta scheme: [output = listprocedure]
 

I have been using simplify() in number of places, and not really expecting it will do any harm. At worst, it will have no effect, or it will change the expression to different form, but the semantics will remain the same.

Until I noticed that odetest() fail on some of my solutions because I called simplify  on the solution before.

One example why this happens, is that Maple simplifies cos(2*x)*sqrt(1/cos(2*x)^2) to csgn(1/cos(2*x)) and this makes odetest fail. Adding assuming x::real has no effect on making odetest happy.

So now I changed simplify(sol) to simplify(sol,size) and this seems so far not to have this adverse effect. 

My main reason for calling simplify  is to make the expression smaller. In Mathematica that is what I do, In Mathematica there is no "size" option to Simplify.

So now, I am very worried about calling simplify() as is.

Could some Maple experts share some of their experience on this? Should one call simplify() only when an explicit option, like size, trig, exp, etc....is also used and not call simplify as is?

restart;

ode:= diff(y(x),x) = 2+2*sec(2*x)+2*y(x)*tan(2*x);
my_sol:= y(x) = ((2*x+sin(2*x))/(cos(2*x)*sqrt(1/cos(2*x)^2))+_C1)*sqrt(1+tan(2*x)^2);
odetest(my_sol,ode);

diff(y(x), x) = 2+2*sec(2*x)+2*y(x)*tan(2*x)

y(x) = ((2*x+sin(2*x))/(cos(2*x)*(1/cos(2*x)^2)^(1/2))+_C1)*(1+tan(2*x)^2)^(1/2)

0

#now simplify the solution first
simplify(my_sol);
odetest(%,ode);

y(x) = (_C1*csgn(1/cos(2*x))+sin(2*x)+2*x)/cos(2*x)

csgn(1, 1/cos(2*x))*_C1/cos(2*x)

simplify(my_sol) assuming x::real;
odetest(%,ode);

y(x) = (_C1*signum(cos(2*x))+sin(2*x)+2*x)/cos(2*x)

signum(1, cos(2*x))*_C1/cos(2*x)

simplify(my_sol,size);
odetest(%,ode);

y(x) = ((2*x+sin(2*x))/(cos(2*x)*(1/cos(2*x)^2)^(1/2))+_C1)*(1+tan(2*x)^2)^(1/2)

0

simplify(cos(2*x)*sqrt(1/cos(2*x)^2))

csgn(1/cos(2*x))

 

 

Download 072519.mw

 

 

Hello. Let's say I have expressions of different lengths - linear combinations of some functions with some coefficients. And there is a free member. Is there a way to get out of these expressions free member? That is func(A)=78.34

Dear Users!

I have made a code using loops. But when I exceute it I go unwanted expression please see the files and try to fix it. I shall be very thankful. 

 

Help.mw

Special request to:

@acer @Kitonum @Preben Alsholm @Carl Love

My question seems simple but after using google and maple help I was still unsuccesfully in plotting a simple line with a function on the same coordinate.

 1. Let f(x) = xe^x^3 and denote by A the area bounded by f(x) = xe^x^3 , x-axis and the
line x = 1.
(a) Graph the function f over the interval [-1; 1].

 

I have no idea on how to plot  f(x) with the line x=1 on the same coordinate.

What is the solution to this error message when trying to run the Maple add-in for Excel?
"The specified module could not be found.  OpenMaple cannot find Maple engine library, maple.dll."

I am running Maple 19.1 and Excel 2016, both 32-bit, in Windows 7.  Excel appears to have successfully installed the Maple add-in.  For example, the Maple add-in icons appear on the Add-ins tab of Excel.  Excel shows the Maple add-in as active in the list of add-ins.  The location of he WMIMPLEX.xla is correct at "C:\Program Files (x86)\Maple\Excel\WMIMPLEX.xla.

Maple support tells me that Maple should add its "bin" folder to the PATH key for excel.exe in the registry key "Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\App Paths\excel.exe\Path".  This path information, however, is not in my computer's registry.  This missing path information might be an obvious problem.  But what is the correct registry entry so that Excel knows where to find the Maple engine library maple.dll?

I tried adding the path to maple.dll in the environmental path variables of Windows 7, but that approach did not work.  I have uninstalled, rebooted, and reinstalled Maple 2019 (32-bit) several times.  Still the same error message.

Thanks.

My name is Viorel Popescu and I am a Ph.D. candidate at University Politehnica of Bucharest, Europe. I was impressed by the article that I found on the internet about Series Solution to Differential Equation with Maple. I am trying to solve the equation g''(r)- r/R*g(r)=0 with initial condition g(2R)=0 and g'(0)=R where R>0 is a positive constant.

with(PDEtools);
pde := diff(c(x, t), x, x) - h*diff(c(x, t), x) = diff(c(x, t), t):

iv := c(0, t) = 0, c(a, t) = 0, c(x, 0) = c0:

de := pdsolve([pde, iv], c(x, t), build);

                         de := ( )

Does anyone know how to solve this PDE?
Thank you,

Oliveira

      

Is there any way to place a command to the right of an expression to perform a task? Because I only know the way that puts the command to the right.A simple example:

w1 := simplify(sin(x)2 + cos(x)2);

                       w1:=1

w2:=sin(x)2+cos(x)2:-simplify;
             Error, invalid module reference

I wonder if there is a way to put the commands, also to the right of the expressions, as above.

Thank you,

Oliveira
   

Hi,

I seeking for informations on the Statistics:-ChiSquareSuitableModelTest procedure:

  1. Once you have choose the number of bins, what strategy does this procedure use to define the bins (equal width, equal probability, other one?).
     
  2. It seems the procedure accepts any value for this number of bins and that its correct use then is under the sole responsability of the user. Am I right?


In the book below (but I'm sure this can also be found on the web) there is a detailed discussion concerning "good practices" in using the Chi-Square goodness of fit test: does anyone known is something comparable is used in ChiSquareSuitableModelTest ?

Statistical methods in experimental physics, W.T.Eadie, D. Drijard, F.F.James, M. Roos, B. Sadoulet
North-Holland 1971
Paragraph 11.2.3 "choosing optimal bin size"


Thanks in advance

Hi. I want to get a Fourier transform under the equation How to do this? Equation_is.docx

Greetings!

I am trying to solve a system of equations involving several symbols. The answer I am getting involves rootof...
I have tried to fix it, and read several post on MP, but in vain. Please help me to get a solution which does not involve root of solutions. Coz the paper I am follwing has a very elegant solution to these equations which i am failed to obtain via maple.rootof.mw



Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/rootof.mw .
 

Download rootof.mw

 

Most of the time, odetest() returns just zero if solution satisfies ode, and non-zero expression if solution does not satisfy ode.

So I was just checking for zero as return value to check if my solution was verified or not. This works for most cases.

But there are cases when odetest returns odetest/PIECEWISE` where some cases are zero and some are not.  Example is below.

For this, I still want to consider my solution as valid if one of the cases in piecwise is zero. But I am not sure what is a robust way to do this in code. Currently, I do the following

restart;
ode:=x*diff(y(x),x) = y(x)+2*(x*y(x))^(1/2);
my_sol:=y(x)=x*(ln(x/_C1)^2 - 1) - 2*(-1 + sqrt(ln(x/_C1)^2))*x;
res:=odetest(my_sol,ode);
if res<>0 then
   if type(res,'function') then #this meant to handle PIECWISE                      
      print("verified");
   else
      print("did not verify");
   fi;
else #if we come here, res=0, so I am sure it is valid.
   print("verified");
fi;

In the above, the check  type(res,'function')  is meant to catch PIECEWISE  return, since when I did type(res) Maple told me the type is function.

But I am not sure if this is a robust way to check for this, as it might be possible maple will return non zero, and also a function, but it will not be what I think it is (i.e. PIECEWISE) and then I would flag my solution as valid when it is not.

worksheet attached also.


 

restart;
ode:=x*diff(y(x),x) = y(x)+2*(x*y(x))^(1/2);
my_sol:=y(x)=x*(ln(x/_C1)^2 - 1) - 2*(-1 + sqrt(ln(x/_C1)^2))*x;
res:=odetest(my_sol,ode);
if res<>0 then
   if type(res,'function') then
      print("verified");
   else
      print("did not verify");
   fi;
else
   print("verified");
fi;

ode := x*(diff(y(x), x)) = y(x)+2*sqrt(x*y(x))

my_sol := y(x) = x*(ln(x/_C1)^2-1)-(2*(-1+sqrt(ln(x/_C1)^2)))*x

`odetest/PIECEWISE`([0, x/exp((-x+(x*y(x))^(1/2))/x) = _C1], [0, x/exp((x+(x*y(x))^(1/2))/x) = _C1], [-4*(-x^2*(-ln(x/_C1)^2+2*(ln(x/_C1)^2)^(1/2)-1))^(1/2), x/exp(-(-x+(x*y(x))^(1/2))/x) = _C1], [-4*(-x^2*(-ln(x/_C1)^2+2*(ln(x/_C1)^2)^(1/2)-1))^(1/2), x/exp(-(x+(x*y(x))^(1/2))/x) = _C1])

"verified"

 

 

Download how_to_check_odetest.mw


 

restart; _local(gamma); _local(I); m := 3; A := 10; delta := .112; rho := .23; beta := 1.4; alpha := 2.1; gamma := 1.02; q := 2.3; b1 := 50; b2 := 10; b3 := 5; b4 := 20; S(0) := b1; B(0) := b2; V(0) := b3; R(0) := b4; mu := .13; i = 1; for k from 0 to m do S(k+1) := (A*delta*k-(rho+mu)*S(k)-beta*(sum(S(m)*B(j-m), j = 0 .. m)))/(k+1); B(k+1) := -(-(mu+alpha+gamma)*B(k)+beta*(sum(S(m)*B(j-m), j = 0 .. m)))/(k+1); V(k+1) := (rho*S(k)-(1-q)*S(k)-mu*V(k))/(k+1); R(k+1) := (gamma*B(k)-mu*R(k))/(k+1) end do; s := sum(S(kk)*t^kk, kk = 0 .. m); b := sum(B(kk)*t^kk, kk = 0 .. m); v := sum(V(kk)*t^kk, kk = 0 .. m); r := sum(R(kk)*t^kk, kk = 0 .. m); SS(0) := s; BB(0) := b; VV(0) := v; RR(0) := r; S(0) := subs(t = T(i), s); B(0) := subs(t = T(i), b); V(0) := subs(t = T(i), v); R(0) := subs(t = T(i), r)

I

 

Warning, The imaginary unit, I, has been renamed _I

 

3

 

10

 

.112

 

.23

 

1.4

 

2.1

 

1.02

 

2.3

 

50

 

10

 

5

 

20

 

50

 

10

 

5

 

20

 

.13

 

i = 1

 

-18.00-1.4*S(3)*B(-3)-1.4*S(3)*B(-2)-1.4*S(3)*B(-1)-14.0*S(3)

 

32.50-1.4*S(3)*B(-3)-1.4*S(3)*B(-2)-1.4*S(3)*B(-1)-14.0*S(3)

 

75.85

 

7.60

 

3.800000000-.4480000000*S(3)*B(-3)-.4480000000*S(3)*B(-2)-.4480000000*S(3)*B(-1)-4.480000000*S(3)

 

52.81250000-2.975000000*S(3)*B(-3)-2.975000000*S(3)*B(-2)-2.975000000*S(3)*B(-1)-29.75000000*S(3)

 

-18.70025000-1.071000000*S(3)*B(-3)-1.071000000*S(3)*B(-2)-1.071000000*S(3)*B(-1)-10.71000000*S(3)

 

16.08100000-.7140000000*S(3)*B(-3)-.7140000000*S(3)*B(-2)-.7140000000*S(3)*B(-1)-7.140000000*S(3)

 

.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3)

 

55.85709723-1.296018889*S(3)*B(-3)-1.296018889*S(3)*B(-2)-1.296018889*S(3)*B(-1)-12.96018889*S(3)-.4666666667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4666666667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4666666667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)

 

2.748344167-.1820700000*S(3)*B(-3)-.1820700000*S(3)*B(-2)-.1820700000*S(3)*B(-1)-1.820700000*S(3)

 

17.25940667-.9805600000*S(3)*B(-3)-.9805600000*S(3)*B(-2)-.9805600000*S(3)*B(-1)-9.805600000*S(3)

 

-.2034933335+1.482334934*S(3)*B(-3)+1.482334934*S(3)*B(-2)+1.482334934*S(3)*B(-1)+14.82334934*S(3)-.3500000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.3500000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.3500000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)

 

44.36655818+.3921579862*S(3)*B(-3)+.3921579862*S(3)*B(-2)+.3921579862*S(3)*B(-1)+3.921579862*S(3)-.7291666668*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.7291666668*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.7291666668*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)

 

0.2185881458e-1-.1520195250*S(3)*B(-3)-.1520195250*S(3)*B(-2)-.1520195250*S(3)*B(-1)-1.520195250*S(3)

 

13.68262908-.2986166168*S(3)*B(-3)-.2986166168*S(3)*B(-2)-.2986166168*S(3)*B(-1)-2.986166168*S(3)-.1190000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.1190000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.1190000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)

 

50+(-22.06933333-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+5.780693334*S(3)*B(-3)+5.780693334*S(3)*B(-2)+5.780693334*S(3)*B(-1)+57.80693334*S(3))*T(i)+(2.497813333-.4480000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4480000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4480000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+1.849821867*S(3)*B(-3)+1.849821867*S(3)*B(-2)+1.849821867*S(3)*B(-1)+18.49821867*S(3))*T(i)^2+(-.9095153783-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+1.704919154*S(3)*B(-3)+1.704919154*S(3)*B(-2)+1.704919154*S(3)*B(-1)+17.04919154*S(3))*T(i)^3

 

10+(28.43066667-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+5.780693334*S(3)*B(-3)+5.780693334*S(3)*B(-2)+5.780693334*S(3)*B(-1)+57.80693334*S(3))*T(i)+(44.16516667-2.975000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-2.975000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-2.975000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+12.28397333*S(3)*B(-3)+12.28397333*S(3)*B(-2)+12.28397333*S(3)*B(-1)+122.8397333*S(3))*T(i)^2+(52.09000233-1.296018889*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-1.296018889*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-1.296018889*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+5.351348394*S(3)*B(-3)+5.351348394*S(3)*B(-2)+5.351348394*S(3)*B(-1)+53.51348394*S(3)-.4666666667*(-.9095153783-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+1.704919154*S(3)*B(-3)+1.704919154*S(3)*B(-2)+1.704919154*S(3)*B(-1)+17.04919154*S(3))*B(-3)-.4666666667*(-.9095153783-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+1.704919154*S(3)*B(-3)+1.704919154*S(3)*B(-2)+1.704919154*S(3)*B(-1)+17.04919154*S(3))*B(-2)-.4666666667*(-.9095153783-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+1.704919154*S(3)*B(-3)+1.704919154*S(3)*B(-2)+1.704919154*S(3)*B(-1)+17.04919154*S(3))*B(-1))*T(i)^3

 

5+75.85*T(i)+(-21.81329000-1.071000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-1.071000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-1.071000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+4.422230400*S(3)*B(-3)+4.422230400*S(3)*B(-2)+4.422230400*S(3)*B(-1)+44.22230400*S(3))*T(i)^2+(2.219127367-.1820700000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.1820700000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.1820700000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+.7517791681*S(3)*B(-3)+.7517791681*S(3)*B(-2)+.7517791681*S(3)*B(-1)+7.517791681*S(3))*T(i)^3

 

20+7.60*T(i)+(14.00564000-.7140000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.7140000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.7140000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+2.948153600*S(3)*B(-3)+2.948153600*S(3)*B(-2)+2.948153600*S(3)*B(-1)+29.48153600*S(3))*T(i)^2+(14.40924560-.9805600000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.9805600000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.9805600000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+4.048797611*S(3)*B(-3)+4.048797611*S(3)*B(-2)+4.048797611*S(3)*B(-1)+40.48797611*S(3))*T(i)^3

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