Maple 2021 Questions and Posts

These are Posts and Questions associated with the product, Maple 2021

restart``

with(plots); with(RealDomain)

``

c := 1; cr := 0.3e-1*c; u := 1; sExp := 0.6e-1*c; s := .65*c

v := 3*c

``

NULL``

FirmModelHmax := proc (alpha, beta, delta) local q, p, pr, FirmpfSiS, F1, G1, G2, G3, RecpfSiS, sol, UnsoldSiS, EnvironSiS, p0, OldSoldPrim, xi, h, ps, qs, prs, prof1, prof2; xi := 1; prs := ps-delta*v; prof1 := qs*(ps-c)+(1/2)*(beta^2*xi^2*qs^2/(1-alpha)-(1+beta*xi)^2*qs^2)(ps-s)/u+(prs-sExp)(beta*xi*qs-(1/2)*beta^2*xi^2*qs^2/(u*(1-alpha))); prof2 := qs*(ps-c)-(1/2)*(ps-s)*qs^2*(prs-sExp)(beta*xi*qs-(1/2)*beta^2*xi^2*qs^2/(u*(1-alpha)))/(alpha*u); if alpha <= 1/(1+beta*xi) then [p, q] := solve({diff(prof1, qs) = 0, qs = alpha*u*(v-ps)/(v-s), 0 < ps}, [ps, qs]); G2 := (1/2)*beta^2*xi^2*q^2/(u*(1-alpha)^2); G3 := (1/2)*q^2*(1+beta*xi)^2/u; h := (p-delta*v-sExp)/(p-delta*v); FirmpfSiS := eval(prof1, [ps = p, qs = q, prs = p-delta*v]); RecpfSiS := ((1-h)*(p-delta*v)-sExp)*(beta*xi*q-G2)+sExp*xi*q-cr*xi*q; UnsoldSiS := G3-(1-alpha)*G2; EnvironSiS := q+UnsoldSiS; OldSoldPrim := beta*xi*q-(1-alpha)*G2 else [p, q] := solve({diff(prof2, qs) = 0, qs = alpha*u*(v-ps)/(v-s), 0 < ps}, [ps, qs]); q := alpha*u*(v-p)/(v-s); F1 := beta*xi*q/(u*(1-alpha)); G1 := (1/2)*q^2/(u*alpha^2); G2 := (1/2)*beta^2*xi^2*q^2/(u*(1-alpha)^2); G3 := (1/2)*q^2*(1+beta*xi)^2/u; h := (p-delta*v-sExp)/(p-delta*v); FirmpfSiS := eval(prof2, [ps = p, qs = q, prs = p-delta*v]); RecpfSiS := ((1-h)*(p-delta*v)-sExp)*(beta*xi*q-G2)+sExp*xi*q-cr*xi*q; UnsoldSiS := alpha*G1; EnvironSiS := q+UnsoldSiS; OldSoldPrim := beta*xi*q-(1-alpha)*G2 end if; return p, q, FirmpfSiS, RecpfSiS, EnvironSiS, h, UnsoldSiS, OldSoldPrim, xi end proc

``

NULL

``

WhyNot3 := proc (alpha, delta) if not [alpha, delta]::(list(numeric)) then return ('procname')(args) end if; FirmModelHmax(alpha, .2, delta)[3] end proc:

pltHmax1 := plot(
  [seq(WhyNot3(alpha, delta),delta=0.1..0.5,0.2)]  
  , alpha=0..2/(2 + 0.2*(1 - sqrt((c - s)/(v - s))))     
  , linestyle=[dot,dashdot,dash]    
  , legend=[seq('delta'=delta,delta=0.1..0.5,0.2)]    
  , legendstyle=[location=left]    
  , labels=["alpha","Firm profit"]    
  , labeldirections =["horizontal", "vertical"]  
  , legendstyle=[location=bottom]
):

display(pltHmax1)

Warning, unable to evaluate the functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

 

 

NULL

Download HmaxProc.mw

I am currently unable to type in maple 2021, there is no cursor, nothing shows up when I type etc. I am also unable to save files. I went into document mode, nothing. Some of the dialogs don't show up. Where does maple save documents and how do I change that setting? That might be my problem. Furthermore, there are no tabs visable, like I can't access any documents I open.

Dear Maple Expeets, In the attached Maple file, I have three procedures that are run smoothly. I am trying to compare outputs from each procedure to see which one if larger than the others. For changes on two parameters (alpha and delta), I used implicitplot and inequal commands to identify each region by a specific color. But the outcome is not reasonable. Would you please help with this? Thanks in advance!

NULLNULL

restart

with(plots)

c := 1; cr := 0.3e-1*c; u := 1; sExp := 0.6e-1*c; s := .65*c; v := 3*c

NULL

FirmModelPP := proc (alpha, delta) local p0, xi0, q0, Firmpf0, G0, Recpf0, Unsold0, Environ0, SoldPre0; option remember; xi0 := 1; p0 := min(s+sqrt((v-s)*(c-s)), delta*v+sExp); q0 := u*(v-p0)/(v-s); f(N) := 1/u; F(N) := N/u; G0 := int(F(N), N = 0 .. q0); Firmpf0 := (p0-c)*q0-(p0-s)*G0; Recpf0 := (sExp-cr)*xi0*q0; Environ0 := q0+G0; Unsold0 := G0; SoldPre0 := 0; return p0, q0, Firmpf0, Recpf0, Environ0, Unsold0, SoldPre0 end proc

NULL

FirmModelFC := proc (alpha, beta, delta) local p00, xi00, q00, Firmpf00, G00, Recpf00, Unsold00, Environ00, pr00, SoldPre00; option remember; xi00 := 1; p00 := s+sqrt((v-s)*(c-s)); if p00 < delta*v+sExp then q00 := u*(v-p00)/(v-s); f(N) := 1/u; F(N) := N/u; G00 := int(F(N), N = 0 .. q00); Firmpf00 := (p00-c)*q00-(p00-s)*G00; Recpf00 := `&xi;00*q00*`(sExp-cr); Unsold00 := G00; Environ00 := q00+Unsold00 else q00 := alpha*u*(v-p00)/(v-s); f(N) := 1/u; F(N) := N/u; G00 := int(F(N), N = 0 .. q00/alpha); pr00 := p00-delta*v; Firmpf00 := (p00-c)*q00-alpha*(p00-s)*G00; Recpf00 := (sExp-cr)*xi00*q00+(beta*xi00*q00-(1/2)*beta^2*xi00^2*q00^2/(u*(1-alpha)))*(pr00-sExp); Unsold00 := G00; Environ00 := q00+Unsold00; SoldPre00 := beta*xi00*q00-(1/2)*beta^2*xi00^2*q00^2/(u*(1-alpha)) end if; return p00, q00, Firmpf00, Recpf00, Environ00, Unsold00, SoldPre00 end proc

NULLNULL

NULL

FirmModelHmax := proc (alpha, beta, delta) local q, p, pr, FirmpfSiS, F1, G1, G2, G3, RecpfSiS, sol, UnsoldSiS, EnvironSiS, p0, OldSoldPrim, xi, h; option remember; xi := 1; if alpha <= 1/(1+beta*xi) then p := max(`assuming`([solve(u*(psol-c+(psol-delta*v-sExp)*beta*xi)/(beta^2*xi^2*(psol-delta*v-sExp)/(1-alpha)-(beta^2*xi^2/(1-alpha)-(1+beta*xi)^2)*(psol-s)) = alpha*u*(v-psol)/(v-s), psol, useassumptions)], [0 < psol])); q := alpha*u*(v-p)/(v-s); G2 := (1/2)*beta^2*xi^2*q^2/(u*(1-alpha)^2); G3 := (1/2)*q^2*(1+beta*xi)^2/u; h := (p-delta*v-sExp)/(p-delta*v); FirmpfSiS := (p-c)*q+(p-s)*((1-alpha)*G2-G3)+h*(p-delta*v)*(beta*xi*q-(1-alpha)*G2); RecpfSiS := ((1-h)*(p-delta*v)-sExp)*(beta*xi*q-G2)+sExp*xi*q-cr*xi*q; UnsoldSiS := G3-(1-alpha)*G2; EnvironSiS := q+UnsoldSiS; OldSoldPrim := beta*xi*q-(1-alpha)*G2 else p := max(`assuming`([solve(u*(psol-c+(psol-delta*v-sExp)*beta*xi)/((psol-s)/u+beta^2*xi^2*(psol-delta*v-sExp)/(1-alpha)) = alpha*u*(v-psol)/(v-s), psol, useassumptions)], [0 < psol])); q := alpha*u*(v-p)/(v-s); F1 := beta*xi*q/(u*(1-alpha)); G1 := (1/2)*q^2/(u*alpha^2); G2 := (1/2)*beta^2*xi^2*q^2/(u*(1-alpha)^2); G3 := (1/2)*q^2*(1+beta*xi)^2/u; h := (p-delta*v-sExp)/(p-delta*v); FirmpfSiS := (p-c)*q-alpha*(p-s)*G1+h*(p-delta*v)*(beta*xi*q-(1-alpha)*G2); RecpfSiS := ((1-h)*(p-delta*v)-sExp)*(beta*xi*q-G2)+sExp*xi*q-cr*xi*q; UnsoldSiS := alpha*G1; EnvironSiS := q+UnsoldSiS; OldSoldPrim := beta*xi*q-(1-alpha)*G2 end if; return p, q, FirmpfSiS, RecpfSiS, EnvironSiS, h, UnsoldSiS, OldSoldPrim, xi end proc

NULL

NULLNULL

FirmModelH := proc (alpha, beta, delta, h) local q, p, pr, FirmpfSiS, F1, G1, G2, G3, RecpfSiS, sol, UnsoldSiS, EnvironSiS, p0, OldSoldPrim, xi; option remember; xi := 1; if alpha <= 1/(1+beta*xi) then p := max(`assuming`([solve(u*(psol-c+h*(psol-delta*v)*beta*xi)/(beta^2*xi^2*h*(psol-delta*v)/(1-alpha)-(beta^2*xi^2/(1-alpha)-(1+beta*xi)^2)*(psol-s)) = alpha*u*(v-psol)/(v-s), psol, useassumptions)], [0 < psol])); q := alpha*u*(v-p)/(v-s); G2 := (1/2)*beta^2*xi^2*q^2/(u*(1-alpha)^2); G3 := (1/2)*q^2*(1+beta*xi)^2/u; FirmpfSiS := (p-c)*q+(p-s)*((1-alpha)*G2-G3)+h*(p-delta*v)*(beta*xi*q-(1-alpha)*G2); RecpfSiS := ((1-h)*(p-delta*v)-sExp)*(beta*xi*q-G2)+sExp*xi*q-cr*xi*q; UnsoldSiS := G3-(1-alpha)*G2; EnvironSiS := q+UnsoldSiS; OldSoldPrim := beta*xi*q-(1-alpha)*G2 else p := max(`assuming`([solve(u*(psol-c+h*(psol-delta*v)*beta*xi)/((psol-s)/u+beta^2*xi^2*h*(psol-delta*v)/(1-alpha)) = alpha*u*(v-psol)/(v-s), psol, useassumptions)], [0 < psol])); q := alpha*u*(v-p)/(v-s); F1 := beta*xi*q/(u*(1-alpha)); G1 := (1/2)*q^2/(u*alpha^2); G2 := (1/2)*beta^2*xi^2*q^2/(u*(1-alpha)^2); G3 := (1/2)*q^2*(1+beta*xi)^2/u; FirmpfSiS := (p-c)*q-alpha*(p-s)*G1+h*(p-delta*v)*(beta*xi*q-(1-alpha)*G2); RecpfSiS := ((1-h)*(p-delta*v)-sExp)*(beta*xi*q-G2)+sExp*xi*q-cr*xi*q; UnsoldSiS := alpha*G1; EnvironSiS := q+UnsoldSiS; OldSoldPrim := beta*xi*q-(1-alpha)*G2 end if; return p, q, FirmpfSiS, RecpfSiS, EnvironSiS, h, UnsoldSiS, OldSoldPrim, xi end proc

NULL

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diffr1 := proc (alpha, delta) if not [alpha, delta]::(list(numeric)) then return ('procname')(args) end if; FirmModelPP(alpha, delta)[3]-FirmModelHmax(alpha, .2, delta)[3] end proc

diffr2 := proc (alpha, delta) if not [alpha, delta]::(list(numeric)) then return ('procname')(args) end if; FirmModelFC(alpha, delta)[3]-FirmModelHmax(alpha, .2, delta)[3] end proc

diffr3 := proc (alpha, delta) if not [alpha, delta]::(list(numeric)) then return ('procname')(args) end if; FirmModelFC(alpha, delta)[3]-FirmModelPP(alpha, delta)[3] end proc

P1 := implicitplot(diffr1, 0 .. 1, 0 .. 1, color = gray, thickness = 1)

P2 := implicitplot(diffr2, 0 .. 1, 0 .. 1, color = black, thickness = 1)

P3 := implicitplot(diffr3, 0 .. 1, 0 .. 1, color = pink, thickness = 1)

``

``

 

 

NULL

``

NULL

P7 := inequal({diffr1(alpha, delta) > 0, diffr2(alpha, delta) > 0, diffr3(alpha, delta) > 0}, alpha = 0 .. 1, delta = 0 .. 1, color = "LightBlue")

P8 := inequal({diffr1(alpha, delta) > 0, diffr2(alpha, delta) > 0, diffr3(alpha, delta) < 0}, alpha = 0 .. 1, delta = 0 .. 1, color = yellow)``

P9 := inequal({diffr1(alpha, delta) > 0, diffr3(alpha, delta) > 0, diffr2(alpha, delta) < 0}, alpha = 0 .. 1, delta = 0 .. 1, color = cyan)

P10 := inequal({diffr1(alpha, delta) > 0, diffr2(alpha, delta) < 0, diffr3(alpha, delta) < 0}, alpha = 0 .. 1, delta = 0 .. 1, color = grey)

P11 := inequal({diffr2(alpha, delta) > 0, diffr3(alpha, delta) > 0, diffr1(alpha, delta) < 0}, alpha = 0 .. 1, delta = 0 .. 1, color = green)

P12 := inequal({diffr2(alpha, delta) > 0, diffr1(alpha, delta) < 0, diffr3(alpha, delta) < 0}, alpha = 0 .. 1, delta = 0 .. 1, color = red)

P13 := inequal({diffr3(alpha, delta) > 0, diffr1(alpha, delta) < 0, diffr2(alpha, delta) < 0}, alpha = 0 .. 1, delta = 0 .. 1, color = pink)

P14 := inequal({diffr1(alpha, delta) < 0, diffr2(alpha, delta) < 0, diffr3(alpha, delta) < 0}, alpha = 0 .. 1, delta = 0 .. 1, color = coral)

NULL

display(P7, P8, P9, P10, P11, P12, P13, P14, textplot([.2, .9, "some text"]), scaling = constrained, view = [0 .. 1, 0 .. 1], labels = [alpha, delta])

 

``


 

Download Compare_three_regions.mw

the final plot does not look reasonable. Would you please guide me?

aRandStep2D := proc(X0, Y0, dx, dy)
  local X, Y, P, R;
  P := Array(1 .. 2);
  R := rand(1 .. 8)();
  if R = 1 then X := X0 - dx; Y := Y0 + dy; end if;
  if R = 2 then X := X0; Y := Y0 + dy; end if;
  if R = 3 then X := X0 + dx; Y := Y0 + dy; end if;
  if R = 4 then X := X0 - dx; Y := Y0; end if;
  if R = 5 then X := X0 + dx; Y := Y0; end if;
  if R = 6 then X := X0 - dx; Y := Y0 - dy; end if;
  if R = 7 then X := X0; Y := Y0 - dy; end if;
  if R = 8 then X := X0 + dx; Y := Y0 - dy; end if;
  P[1] := X; P[2] := Y;
  return P;
end proc 

SetStart := proc(b)
  local alpha, R, P;
  P := Array(1 .. 2);
  alpha := rand(1 .. b)();
  P[1] := alpha*b;
  P[2] := alpha*b;
  return P;
end proc 

RandomFactTpq := proc(N, pb, dx, dy)
  local alpha, X, Y, f, P, counter, B, n, T;
  P := Array(1 .. 2);
  counter := 0; f := 1;
  B := floor(evalf(sqrt(N))); #Set maximal searching steps
  T := floor(evalf(sqrt(N))); #For SetStart's use
  P := SetStart(T);
  X := P[1]; Y := P[2];
  while f = 1 and counter < B do  #loop
    n := pb - X - Y;
    f := gcd(N, n);
    if f > 1then break; end if;
    P := aRandStep2D(X, Y, dx, dy); #A random move
    X := P[1]; Y := P[2];
    if X < 1 or Y < 1 or N - pb - 1 < X or X <= Y then
      P := SetStart(T);       # Restart when out of borders
      X := P[1]; Y := P[2];
    end if;
    counter := counter + 1;    #Counting the searched steps
  end do;
  if  f>1  then print(Find at point (X, Y), found divisor = f, searching steps = counter);
  else print(This*time*finds*no*result, test*again!); end if;
end proc


wxbRandWalkTpqNew4.pdf

How can I produce a graph with various values for parameters? I also attached a sample of my Maple code.

restart

with(plots);
with(plottools);
with(DEtools);

eqn1 := diff(V(t), t) = pi*p - (alpha + mu)*V(t), V(0) = ic1

eqn2 := diff(S(t), t) = alpha*V(t) + (1 - p)*pi - beta*S(t)*In(t)/N - mu*S(t), S(0) = ic2

eqn3 := diff(In(t), t) = beta*S(t)*In(t)/N - (mu + delta + gamma)*In(t), In(0) = ic3

eqn4 := diff(R(t), t) = gamma*In(t) - mu*R(t), R(0) = ic4

pi := 487845;
p := 0.948;
alpha := 0.054;
beta := 0.955;
mu := 0.005;
delta := 0.03;
localgamma := 0.935;
ic1 := 484465;
ic2 := 31999760;
ic3 := 26305;
ics4 := 12470;
dsol := dsolve([eqn1, eqn2, eqn3, eqn4], numeric);

odeplot(dsol, [[t, V(t), color = plum], [t, S(t), color = blue], [t, In(t), color = cyan], [t, R(t), color = green]], t = 0 .. 1000, view = [0 .. 1000, 0 .. 300000000], thickness = 3)
 

Let's say I want to produce a graph for eqn1 with various values of parameter p: p = 0.2, p = 0.5, p = 0.7, p = 0.8. How should I produce it?

I have created a several matrices for my analysis. I want to plot the determinant value of matrix vs the omega. The matrix that should be plotted is named as FINAL. I am not able to do that due to large value of matrix determinant. How to simplify the matrix and get  plot.

restart

with(LinearAlgebra)

k1 := 4172976683.88513

k2 := 3322653306.61138``

nu := 62.83

l[9] := .676

l[8] := .676

l[7] := .218

l[6] := .255+.4*0

l[5] := .435+.4*0

l[4] := .435

l[3] := .456

l[2] := .577*.5

l[11] := .577*.5

l[12] := .577*.5

l[1] := .577*.5

i[9] := (1/64)*Pi*.355^4

i[8] := (1/64)*Pi*.355^4

i[7] := (1/64)*Pi*.419^4

i[6] := (1/64)*Pi*.543^4

i[5] := (1/64)*Pi*.698^4

i[4] := (1/64)*Pi*.698^4

i[3] := (1/64)*Pi*.67^4

i[2] := (1/64)*Pi*.45^4

i[11] := (1/64)*Pi*.45^4

i[12] := (1/64)*Pi*.45^4

i[1] := (1/64)*Pi*.45^4

m[0] := 2800

m[1] := 7850*(.25*Pi*.45^2*1.154)*(1/3)

NULLm[3] := 7850*(.25*Pi*.67^2*.456)

m[4] := 7850*(.25*Pi*.698^2*.870)

m[5] := 7850*(.25*Pi*.590^2*.8)+30715

m[6] := 7850*(.25*Pi*.543^2*.255)

m[7] := 7850*(.25*Pi*.419^2*.218)

m[8] := 7850*(.25*Pi*.355^2*1.132)NULL

E := 210*10^9

Id[0] := .5*825

Id[5] := (1/2)*(18.4*1000)+(30715/12)*.8^2*0+7850*(.25*Pi*.590^2*.8)*(.5*.590)^2*(1/4)+(.8*((1/12)*Pi*.590^2*.25)*7850)*.8^2*0

NULL

NULL

F9 := Matrix([[1, l[9], l[9]^2/(2*E*i[9]), l[9]^3/(6*E*i[9]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, l[9]/(E*i[9]), l[9]^2/(2*E*i[9]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, l[9], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, l[9], l[9]^2/(2*E*i[9]), l[9]^3/(6*E*i[9]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, l[9]/(E*i[9]), l[9]^2/(2*E*i[9]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, l[9], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, l[9], l[9]^2/(2*E*i[9]), l[9]^3/(6*E*i[9]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[9]/(E*i[9]), l[9]^2/(2*E*i[9]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[9], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[9], l[9]^2/(2*E*i[9]), l[9]^3/(6*E*i[9]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[9]/(E*i[9]), l[9]^2/(2*E*i[9]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[9], 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])
``

NULL
F8 := Matrix([[1, l[8], l[8]^2/(2*E*i[8]), l[8]^3/(6*E*i[8]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, l[8]/(E*i[8]), l[8]^2/(2*E*i[8]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, l[8], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, l[8], l[8]^2/(2*E*i[8]), l[8]^3/(6*E*i[8]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, l[8]/(E*i[8]), l[8]^2/(2*E*i[8]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, l[8], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, l[8], l[8]^2/(2*E*i[8]), l[8]^3/(6*E*i[8]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[8]/(E*i[8]), l[8]^2/(2*E*i[8]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[8], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[8], l[8]^2/(2*E*i[8]), l[8]^3/(6*E*i[8]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[8]/(E*i[8]), l[8]^2/(2*E*i[8]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[8], 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

NULL

F7 := Matrix([[1, l[7], l[7]^2/(2*E*i[7]), l[7]^3/(6*E*i[7]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, l[7]/(E*i[7]), l[7]^2/(2*E*i[7]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, l[7], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, l[7], l[7]^2/(2*E*i[7]), l[7]^3/(6*E*i[7]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, l[7]/(E*i[7]), l[7]^2/(2*E*i[7]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, l[7], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, l[7], l[7]^2/(2*E*i[7]), l[7]^3/(6*E*i[7]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[7]/(E*i[7]), l[7]^2/(2*E*i[7]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[7], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[7], l[7]^2/(2*E*i[7]), l[7]^3/(6*E*i[7]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[7]/(E*i[7]), l[7]^2/(2*E*i[7]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[7], 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

NULL

F6 := Matrix([[1, l[6], l[6]^2/(2*E*i[6]), l[6]^3/(6*E*i[6]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, l[6]/(E*i[6]), l[6]^2/(2*E*i[6]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, l[6], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, l[6], l[6]^2/(2*E*i[6]), l[6]^3/(6*E*i[6]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, l[6]/(E*i[6]), l[6]^2/(2*E*i[6]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, l[6], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, l[6], l[6]^2/(2*E*i[6]), l[6]^3/(6*E*i[6]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[6]/(E*i[6]), l[6]^2/(2*E*i[6]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[6], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[6], l[6]^2/(2*E*i[6]), l[6]^3/(6*E*i[6]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[6]/(E*i[6]), l[6]^2/(2*E*i[6]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[6], 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

````

F5 := Matrix([[1, l[5], l[5]^2/(2*E*i[5]), l[5]^3/(6*E*i[5]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, l[5]/(E*i[5]), l[5]^2/(2*E*i[5]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, l[5], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, l[5], l[5]^2/(2*E*i[5]), l[5]^3/(6*E*i[5]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, l[5]/(E*i[5]), l[5]^2/(2*E*i[5]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, l[5], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, l[5], l[5]^2/(2*E*i[5]), l[5]^3/(6*E*i[5]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[5]/(E*i[5]), l[5]^2/(2*E*i[5]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[5], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[5], l[5]^2/(2*E*i[5]), l[5]^3/(6*E*i[5]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[5]/(E*i[5]), l[5]^2/(2*E*i[5]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[5], 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

F4 := Matrix([[1, l[4], l[4]^2/(2*E*i[4]), l[4]^3/(6*E*i[4]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, l[4]/(E*i[4]), l[4]^2/(2*E*i[4]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, l[4], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, l[4], l[4]^2/(2*E*i[4]), l[4]^3/(6*E*i[4]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, l[4]/(E*i[4]), l[4]^2/(2*E*i[4]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, l[4], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, l[4], l[4]^2/(2*E*i[4]), l[4]^3/(6*E*i[4]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[4]/(E*i[4]), l[4]^2/(2*E*i[4]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[4], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[4], l[4]^2/(2*E*i[4]), l[4]^3/(6*E*i[4]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[4]/(E*i[4]), l[4]^2/(2*E*i[4]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[4], 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

F3 := Matrix([[1, l[3], l[3]^2/(2*E*i[3]), l[3]^3/(6*E*i[3]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, l[3]/(E*i[3]), l[3]^2/(2*E*i[3]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, l[3], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, l[3], l[3]^2/(2*E*i[3]), l[3]^3/(6*E*i[3]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, l[3]/(E*i[3]), l[3]^2/(2*E*i[3]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, l[3], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, l[3], l[3]^2/(2*E*i[3]), l[3]^3/(6*E*i[3]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[3]/(E*i[3]), l[3]^2/(2*E*i[3]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[3], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[3], l[3]^2/(2*E*i[3]), l[3]^3/(6*E*i[3]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[3]/(E*i[3]), l[3]^2/(2*E*i[3]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[3], 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

F2 := Matrix([[1, l[2], l[2]^2/(2*E*i[2]), l[2]^3/(6*E*i[2]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, l[2]/(E*i[2]), l[2]^2/(2*E*i[2]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, l[2], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, l[2], l[2]^2/(2*E*i[2]), l[2]^3/(6*E*i[2]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, l[2]/(E*i[2]), l[2]^2/(2*E*i[2]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, l[2], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, l[2], l[2]^2/(2*E*i[2]), l[2]^3/(6*E*i[2]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[2]/(E*i[2]), l[2]^2/(2*E*i[2]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[2], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[2], l[2]^2/(2*E*i[2]), l[2]^3/(6*E*i[2]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[2]/(E*i[2]), l[2]^2/(2*E*i[2]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[2], 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

F1 := Matrix([[1, l[1], l[1]^2/(2*E*i[1]), l[1]^3/(6*E*i[1]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, l[1]/(E*i[1]), l[1]^2/(2*E*i[1]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, l[1], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, l[1], l[1]^2/(2*E*i[1]), l[1]^3/(6*E*i[1]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, l[1]/(E*i[1]), l[1]^2/(2*E*i[1]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, l[1], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, l[1], l[1]^2/(2*E*i[1]), l[1]^3/(6*E*i[1]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[1]/(E*i[1]), l[1]^2/(2*E*i[1]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[1], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[1], l[1]^2/(2*E*i[1]), l[1]^3/(6*E*i[1]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[1]/(E*i[1]), l[1]^2/(2*E*i[1]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[1], 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

NULL

F11 := Matrix([[1, l[11], l[11]^2/(2*E*i[11]), l[11]^3/(6*E*i[11]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, l[11]/(E*i[11]), l[11]^2/(2*E*i[11]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, l[11], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, l[11], l[11]^2/(2*E*i[11]), l[11]^3/(6*E*i[11]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, l[11]/(E*i[11]), l[11]^2/(2*E*i[11]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, l[11], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, l[11], l[11]^2/(2*E*i[11]), l[11]^3/(6*E*i[11]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[11]/(E*i[11]), l[11]^2/(2*E*i[11]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[11], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[11], l[11]^2/(2*E*i[11]), l[11]^3/(6*E*i[11]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[11]/(E*i[11]), l[11]^2/(2*E*i[11]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[11], 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

NULL

F12 := Matrix([[1, l[12], l[12]^2/(2*E*i[12]), l[12]^3/(6*E*i[12]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, l[12]/(E*i[12]), l[12]^2/(2*E*i[12]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, l[12], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, l[12], l[12]^2/(2*E*i[12]), l[12]^3/(6*E*i[12]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, l[12]/(E*i[12]), l[12]^2/(2*E*i[12]), 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, l[12], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, l[12], l[12]^2/(2*E*i[12]), l[12]^3/(6*E*i[12]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[12]/(E*i[12]), l[12]^2/(2*E*i[12]), 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[12], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[12], l[12]^2/(2*E*i[12]), l[12]^3/(6*E*i[12]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[12]/(E*i[12]), l[12]^2/(2*E*i[12]), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, l[12], 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])
``

P0 := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -omega^2*Id[0], 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*Id[0]*nu*omega, 0, 0, 0], [m[0]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -omega^2*Id[0], 1, 0, 0, -2*Id[0]*nu*omega, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, m[0]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2*Id[0]*nu*omega, 0, 0, 0, -omega^2*Id[0], 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, m[0]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, -2*Id[0]*nu*omega, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -omega^2*Id[0], 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m[0]*omega^2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

NULL
P1 := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [m[1]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, m[1]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, m[1]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m[1]*omega^2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

NULL
P11 := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [m[1]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, m[1]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, m[1]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m[1]*omega^2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

NULL
P12 := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [m[1]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, m[1]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, m[1]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m[1]*omega^2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])
NULL

NULL
P3 := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [m[3]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, m[3]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, m[3]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m[3]*omega^2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])
``

NULL
P4 := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [m[4]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, m[4]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, m[4]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m[4]*omega^2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])
``NULL

P5 := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -omega^2*Id[5], 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*Id[5]*nu*omega, 0, 0, 0], [m[5]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -omega^2*Id[5], 1, 0, 0, -2*Id[5]*nu*omega, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, m[5]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2*Id[5]*nu*omega, 0, 0, 0, -omega^2*Id[5], 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, m[5]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, -2*Id[5]*nu*omega, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -omega^2*Id[5], 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m[5]*omega^2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

NULL
P6 := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [m[6]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, m[6]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, m[6]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m[6]*omega^2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

NULLNULL
P7 := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [m[7]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, m[7]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, m[7]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m[7]*omega^2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

NULLNULL
P8 := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [m[8]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, m[8]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, m[8]*omega^2, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m[8]*omega^2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])

NULL
UA := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-k1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -k1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -k1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -k1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])
``

NULL
UB := Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-k2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -k2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -k2, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -k2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])
NULL``

NULL

NULL

NULL

NULL

NULL

NULL

NULL

N0 := Multiply(UB, F9)

N1 := Multiply(N0, P8)

N2 := Multiply(N1, F8)

N3 := Multiply(N2, P7)

N4 := Multiply(N3, F7)

N5 := Multiply(N4, P6)

N6 := Multiply(N5, F6)

N7 := Multiply(N6, P5)

N8 := Multiply(N7, F5)

N9 := Multiply(N8, P4)

N10 := Multiply(N9, F4)

N11 := Multiply(N10, P3)

N12 := Multiply(N11, F3)

N13 := Multiply(N12, UA)

N14 := Multiply(N13, F2)

N15 := Multiply(N14, P12)

N16 := Multiply(N15, F12)

N17 := Multiply(N16, P11)

N18 := Multiply(N17, F11)

N19 := Multiply(N18, P1)

N20 := Multiply(N19, F1)

N21 := Multiply(N20, P0)NULL

NULL

NULL

NULL

NULL

NULL``

NULL

Z31 := N21[3, 1]``

Z32 := N21[3, 2]NULL

Z35 := N21[3, 5]

Z36 := N21[3, 6]NULL

Z39 := N21[3, 9]NULL

Z310 := N21[3, 10]``

Z313 := N21[3, 13]

Z314 := N21[3, 14]

NULL

Z41 := N21[4, 1]NULL

Z42 := N21[4, 2]``

Z45 := N21[4, 5]

Z46 := N21[4, 6]NULL

Z49 := N21[4, 9]``

Z410 := N21[4, 10]NULL

Z413 := N21[4, 13]

Z414 := N21[4, 14]

NULL

NULL

Z71 := N21[7, 1]``

Z72 := N21[7, 2]NULL

Z75 := N21[7, 5]

Z76 := N21[7, 6]NULL

Z79 := N21[7, 9]NULL

Z710 := N21[7, 10]``

Z713 := N21[7, 13]

Z714 := N21[7, 14]

NULLNULL

Z81 := N21[8, 1]NULL

Z82 := N21[8, 2]``

Z85 := N21[8, 5]

Z86 := N21[8, 6]NULL

Z89 := N21[8, 9]``

Z810 := N21[8, 10]NULL

Z813 := N21[8, 13]

Z814 := N21[8, 14]

NULL

NULLZ111 := N21[11, 1]``

Z112 := N21[11, 2]NULL

Z115 := N21[11, 5]

Z116 := N21[11, 6]NULL

Z119 := N21[11, 9]NULL

Z1110 := N21[11, 10]``

Z1113 := N21[11, 13]

Z1114 := N21[11, 14]

NULL

NULL

Z121 := N21[12, 1]NULL

Z122 := N21[12, 2]``

Z125 := N21[12, 5]

Z126 := N21[12, 6]NULL

Z129 := N21[12, 9]``

Z1210 := N21[12, 10]NULL

Z1213 := N21[12, 13]

Z1214 := N21[12, 14]

NULL

NULLZ151 := N21[15, 1]``

Z152 := N21[15, 2]NULL

Z155 := N21[15, 5]

Z156 := N21[15, 6]NULL

Z159 := N21[15, 9]NULL

Z1510 := N21[15, 10]``

Z1513 := N21[15, 13]

Z1514 := N21[15, 14]

NULL

Z161 := N21[16, 1]NULL

Z162 := N21[16, 2]``

Z165 := N21[16, 5]

Z166 := N21[16, 6]NULL

Z169 := N21[16, 9]``

Z1610 := N21[16, 10]NULL

Z1613 := N21[16, 13]

Z1614 := N21[16, 14]

NULL

FINAL := Matrix([[Z31, Z32, Z35, Z36, Z39, Z310, Z313, Z314], [Z41, Z42, Z45, Z46, Z49, Z410, Z413, Z414], [Z71, Z72, Z75, Z76, Z79, Z710, Z713, Z714], [Z81, Z82, Z85, Z86, Z89, Z810, Z813, Z814], [Z111, Z112, Z115, Z116, Z119, Z1110, Z1113, Z1114], [Z121, Z122, Z125, Z126, Z129, Z1210, Z1213, Z1214], [Z151, Z152, Z155, Z156, Z159, Z1510, Z1513, Z1514], [Z161, Z162, Z165, Z166, Z169, Z1610, Z1613, Z1614]])

NULLF := Determinant(FINAL)/10^77

HFloat(173.47261448575398)

(1)

NULL

Error, (in plot) unexpected option: 160 = 120 .. 130

 

NULL

Download Plot_determinant_value_vs_omega.mw

Can someone kind help me? I encountered two issues when using the pdsolve function in Maple to obtain numerical solutions for partial differential equations. The first issue pertains to setting up the initial/boundary conditions correctly, and the second issue relates to configuring the plotting options. I'm wondering how to modify them in order to run the code correctly and generate the desired plots.

question.mw

How to find Z(t) matrix(array) =[ [z[1,0](t),z[1,1](t)],[z[2,0](t),z[2,1](t)]]

restart;

with(IntegrationTools):with(Physics):

 

 

 

h1 := (m,n)->(n+1/2)*KroneckerDelta[n,m];

proc (m, n) options operator, arrow; Physics:-`*`(n+Physics:-`*`(1, Physics:-`^`(2, -1)), Physics:-KroneckerDelta[n, m]) end proc

(1)

h2 := (mu,nu,m2,l)->-(nu*Pi/l)^2/(2*m2)*KroneckerDelta[mu,nu];

proc (mu, nu, m2, l) options operator, arrow; Physics:-`*`(-1, Physics:-`*`(Physics:-`^`(Physics:-`*`(nu, Pi, Physics:-`^`(l, -1)), 2), Physics:-`^`(Physics:-`*`(2, m2), -1), Physics:-KroneckerDelta[mu, nu])) end proc

(2)

v1 := (m,n,m1)->sqrt(min(n,m)!/max(n,m)!)*(2*m1)^(-abs(n-m)/2)*exp(-1/(4*m1))*LaguerreL(min(n,m),abs(n-m),-1/(2*m1));

proc (m, n, m1) options operator, arrow; Physics:-`*`(sqrt(Physics:-`*`(factorial(min(n, m)), Physics:-`^`(factorial(max(n, m)), -1))), Physics:-`^`(Physics:-`*`(2, m1), Physics:-`*`(-1, Physics:-`*`(abs(n-m), Physics:-`^`(2, -1)))), exp(Physics:-`*`(-1, Physics:-`*`(1, Physics:-`^`(Physics:-`*`(4, m1), -1)))), LaguerreL(min(n, m), abs(n-m), Physics:-`*`(-1, Physics:-`*`(1, Physics:-`^`(Physics:-`*`(2, m1), -1))))) end proc

(3)

v2 := (mu,nu,l)->4*Pi^2*l*mu*nu*(exp(l/2)-(-1)^(mu+nu)*exp(-l/2))/((Pi*(mu+nu))^2+l^2)/((Pi*(mu-nu))^2+l^2);

proc (mu, nu, l) options operator, arrow; Physics:-`*`(4, Physics:-`^`(Pi, 2), l, mu, nu, exp(Physics:-`*`(l, Physics:-`^`(2, -1)))-Physics:-`*`(Physics:-`^`(-1, mu+nu), exp(Physics:-`*`(-1, Physics:-`*`(l, Physics:-`^`(2, -1))))), Physics:-`^`(Physics:-`^`(Physics:-`*`(Pi, mu+nu), 2)+Physics:-`^`(l, 2), -1), Physics:-`^`(Physics:-`^`(Physics:-`*`(Pi, mu-nu), 2)+Physics:-`^`(l, 2), -1)) end proc

(4)

h:=(m,n,mu,nu,m1,m2,l)->evalf(h1(m,n)+h2(mu,nu,m2,l)+v1(m,n,m1)+v2(mu,nu,l));

proc (m, n, mu, nu, m1, m2, l) options operator, arrow; evalf(h1(m, n)+h2(mu, nu, m2, l)+v1(m, n, m1)+v2(mu, nu, l)) end proc

(5)

m1:=1:m2:=1:l:=1:

H:= (m,n,mu,nu)->h(m,n,mu,nu,m1,m2,l);

proc (m, n, mu, nu) options operator, arrow; h(m, n, mu, nu, m1, m2, l) end proc

(6)

H(1,1,0,0);

2.668201175

(7)

eq1:= diff(z(m,nu,t),t)=-I*Sum(Sum(H(m,n,mu,nu)*z(n,mu,t),n=1..N),mu=0..M);

diff(z(m, nu, t), t) = -I*(Sum(Sum(((n+.5000000000)*Physics:-KroneckerDelta[m, n]-4.934802202*nu^2*Physics:-KroneckerDelta[mu, nu]+.7788007831*(factorial(min(m, n))/factorial(max(m, n)))^(1/2)*2.^(-.5000000000*abs(-1.*n+m))*LaguerreL(min(m, n), abs(-1.*n+m), -.5000000000)+39.47841762*mu*nu*(1.648721271-.6065306597*(-1.)^(mu+nu))/((9.869604404*(mu+nu)^2+1.)*(9.869604404*(mu-1.*nu)^2+1.)))*z(n, mu, t), n = 1 .. N), mu = 0 .. M))

(8)

 

zint := Array([[1,0],[0,1]]);

Matrix(2, 2, {(1, 1) = 1, (1, 2) = 0, (2, 1) = 0, (2, 2) = 1})

(9)

Z:= Array(1..2,1..2);
 for i from 1to 2 do
    for j from 1 to 2 do
        Z[i,j]:= dsolve({eq1,zint[i,j]},numeric,output=listprocedure);
    end do;
end do;

 

Matrix(2, 2, {(1, 1) = 0, (1, 2) = 0, (2, 1) = 0, (2, 2) = 0})

 

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

 

 

Download test3.mw

how to write the code for integration of the orthogonal cosine function with nu=mu or with nu<>mu

restart;

 

phi:= (mu,Q2)->sqrt(2/l)*sin(mu*Pi*(Q2+l/2)/l);    # E:=mu->(Pi*mu/sqrt(2)/l)^2, mu=1,2...

proc (mu, Q2) options operator, arrow; sqrt(2/l)*sin(mu*Pi*(Q2+(1/2)*l)/l) end proc

(1)

fh1:=simplify((-1/2/m2*Int(diff(phi(mu,Q2),Q2)*diff(phi(nu,Q2),Q2),Q2=-l/2..l/2)))

-mu*Pi^2*nu*(Int(cos((1/2)*mu*Pi*(2*Q2+l)/l)*cos((1/2)*nu*Pi*(2*Q2+l)/l), Q2 = -(1/2)*l .. (1/2)*l))/(l^3*m2)

(2)

convert(fh1,int) assuming(mu,integer,nu,integer);

0

(3)

fh1_subs := simplify(subs(nu = mu, fh1));

-mu^2*Pi^2*(Int(cos((1/2)*mu*Pi*(2*Q2+l)/l)^2, Q2 = -(1/2)*l .. (1/2)*l))/(l^3*m2)

(4)

convert(fh1_substituted,int)assuming (mu,integer,nu,integer);

-(1/2)*mu^2*Pi^2/(l^2*m2)

(5)

 

Download test1.mw

Hi all,

I would like to use the command ConvertIn() from the Galois Field package to convert polynomials to field elements.

This is what I've done:

G:=GF(2,4)
                        G := &Fopf;[16]

b:=G:-random()
                          b := T mod 2

s:=G:-ConvertIn(T)
Error, (in ConvertIn) only integer polynomials in T can be converted

Why is this error showing up?? My argument of the command ConvertIn IS an integer polynomial in T.

How can I avoid this error?

Thanks for your help!

BR David

restart;  
with(geometry):  
with(plots):  
_EnvHorizontalName = 'x':  _EnvVerticalName = 'y':
point(A, -1, 9):                                                                                                       
point(B, -5, 0):
point(C, 6, 0):
triangle(ABC,[A,B,C]):
midpoint(M1,A,C): midpoint(M2,B,C):midpoint(M3,A,B):
rotation(J, C, Pi/2, 'counterclockwise', M1):triangle(AJC,[A,J,C]):
rotation(Ii, C, Pi/2, 'counterclockwise', M2):triangle(BIC,[B,Ii,C]):
rotation(K, A, Pi/2, 'counterclockwise', M3):triangle(AKB,[A,K,B]):
midpoint(O1,K,J): coordinates(O1):
midpoint(O2,A,Ii): coordinates(O2):  
poly:=[coordinates(A),coordinates(J),coordinates(Ii),coordinates(K)]:   

display(draw([A(color = black, symbol = solidcircle, symbolsize = 12), 
B(color = black, symbol = solidcircle, symbolsize = 12), 
C(color = black, symbol = solidcircle, symbolsize = 12), 
J(color = black, symbol = solidcircle, symbolsize = 12), 
polygonplot(poly,color = "DarkGreen", transparency = 0.5),
ABC(color = red ),
BIC(color = green),
AKB(color = grey),
AJC(color =blue)]),
textplot([[coordinates(A)[], "A"],[coordinates(J)[], "J"],[coordinates(Ii)[], "I"],   
[coordinates(B)[], "B"], [coordinates(K)[], "K"], 
[coordinates(C)[], "C"]], 
align = [above, right]),  axes = none);
Error, (in geometry:-draw) the option must be of type equation or name. I don't see how to correct this error/
 

I have some large systems of linear equations.  The solutions are probability generating functions.  I can get solutions in a few minutes for systems of up to n= 200 eqns or so, but Maple just cycles indefinitely if I try to solve much larger systems.  I really only need to perform Gaussian Elimination, as I only need to solve for one of the n solutions.  The matrices are sparse, there are only 3 non-zero entries per row.  I tried to get help from the manuals but I get the impression that sparse solutions are only available for numeric computations.   Doesn't Maple allow for sparse symbolic solutions?  If so, how to do it?

Does anyone know how to remove this boring notation? I would like to know why Maple does not give me "± 2x". Thanks in advance.

 

I am trying to define a Tensor expression in the physics package but it seems to be taking eons to do so, it has been running for quite some time but still no result to the point where I halt the computation. 

Does anyone have any ideas on how I could accelerate the process? 

I have attached the file I am working with. 

Define.mw

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