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Am here again, pls help me check out this adm code, cant get a result.

below is the attached file

 adm_2_method.mw

system3d := a[1](a[1])+a[2]*a[4]+a[3]*a[7]-a[1](a[1])-a[2]*a[10]-a[3]*a[19], a[1]*a[2]-a[1]*a[2]+a[2]*a[5]-a[2]*a[11]+a[3]*a[8]-a[3]*a[20], a[1]*a[3]-a[1]*a[3]+a[2]*a[6]-a[2]*a[12]+a[3]*a[9]-a[3]*a[21], a[1]*a[4]-a[1]*a[4]-a[2]*a[13]-a[3]*a[22]+a[4]*a[5]+a[6]*a[7], a[2]*a[4]+a[5](a[5])+a[6]*a[8]-a[1]*a[5]-a[2]*a[14]-a[3]*a[23], a[3]*a[4]+a[5]*a[6]+a[6]*a[9]-a[1]*a[6]-a[2]*a[15]-a[3]*a[24], a[1]*a[7]+a[4]*a[8]+a[7]*a[9] = a[1]*a[7]+a[2]*a[16]+a[3]*a[25], a[2]*a[7]+a[5]*a[8]+a[8]*a[9] = a[1]*a[8]+a[2]*a[17]+a[3]*a[26], a[3]*a[7]+a[6]*a[8]+a[9](a[9]) = a[1]*a[9]+a[2]*a[18]+a[3]*a[27];
print(`output redirected...`); # input placeholder
a[2] a[4] - a[2] a[10] + a[3] a[7] - a[3] a[19],

a[2] a[5] - a[2] a[11] + a[3] a[8] - a[3] a[20],

a[2] a[6] - a[2] a[12] + a[3] a[9] - a[3] a[21],

-a[2] a[13] - a[3] a[22] + a[4] a[5] + a[6] a[7], a[2] a[4]

+ a[5](a[5]) + a[6] a[8] - a[1] a[5] - a[2] a[14] - a[3] a[23],
-a[1] a[6] - a[2] a[15] + a[3] a[4] - a[3] a[24] + a[5] a[6]

+ a[6] a[9], a[1] a[7] + a[4] a[8] + a[7] a[9] = a[1] a[7]

+ a[2] a[16] + a[3] a[25], a[2] a[7] + a[5] a[8] + a[8] a[9] =

a[1] a[8] + a[2] a[17] + a[3] a[26], a[3] a[7] + a[6] a[8]

+ a[9](a[9]) = a[1] a[9] + a[2] a[18] + a[3] a[27]

solve({system3d}, {a[1]*a[2], a[1]*a[3], a[1]*a[4], a[1]*a[5], a[1]*a[6], a[1]*a[7], a[1]*a[8], a[1]*a[9], a[2]*a[4], a[2]*a[5], a[2]*a[6], a[2]*a[7], a[2]*a[10], a[2]*a[11], a[2]*a[12], a[2]*a[13], a[2]*a[14], a[2]*a[15], a[2]*a[16], a[2]*a[17], a[2]*a[18], a[3]*a[4], a[3]*a[7], a[3]*a[8], a[3]*a[9], a[3]*a[19], a[3]*a[20], a[3]*a[21], a[3]*a[22], a[3]*a[23], a[3]*a[24], a[3]*a[25], a[3]*a[26], a[3]*a[27], a[4]*a[5], a[4]*a[8], a[5]*a[6], a[5]*a[8], a[6]*a[7], a[6]*a[8], a[6]*a[9], a[7]*a[9], a[8]*a[9], a[1](a[1]), a[5](a[5]), a[9](a[9])});
%;
Warning, solving for expressions other than names or functions is not recommended.
{a[1] a[2] = a[1] a[2], a[1] a[3] = a[1] a[3],

a[1] a[4] = a[1] a[4], a[1] a[5] = a[2] a[10] - a[3] a[7]

+ a[3] a[19] + a[5](a[5]) + a[6] a[8] - a[2] a[14]

- a[3] a[23], a[1] a[6] = -a[2] a[15] + a[3] a[4] - a[3] a[24]

+ a[5] a[6] + a[6] a[9], a[1] a[7] = a[1] a[7], a[1] a[8] = a[

2] a[7] - a[2] a[17] - a[3] a[26] + a[5] a[8] + a[8] a[9], a[1]

a[9] = a[3] a[7] + a[6] a[8] + a[9](a[9]) - a[2] a[18]

- a[3] a[27], a[2] a[4] = a[2] a[10] - a[3] a[7] + a[3] a[19],

a[2] a[5] = a[2] a[11] - a[3] a[8] + a[3] a[20],

a[2] a[6] = a[2] a[12] - a[3] a[9] + a[3] a[21],

a[2] a[7] = a[2] a[7], a[2] a[10] = a[2] a[10],

a[2] a[11] = a[2] a[11], a[2] a[12] = a[2] a[12],

a[2] a[13] = -a[3] a[22] + a[4] a[5] + a[6] a[7],

a[2] a[14] = a[2] a[14], a[2] a[15] = a[2] a[15],

a[2] a[16] = -a[3] a[25] + a[4] a[8] + a[7] a[9],

a[2] a[17] = a[2] a[17], a[2] a[18] = a[2] a[18],

a[3] a[4] = a[3] a[4], a[3] a[7] = a[3] a[7],

a[3] a[8] = a[3] a[8], a[3] a[9] = a[3] a[9],

a[3] a[19] = a[3] a[19], a[3] a[20] = a[3] a[20],

a[3] a[21] = a[3] a[21], a[3] a[22] = a[3] a[22],

a[3] a[23] = a[3] a[23], a[3] a[24] = a[3] a[24],

a[3] a[25] = a[3] a[25], a[3] a[26] = a[3] a[26],

a[3] a[27] = a[3] a[27], a[4] a[5] = a[4] a[5],

a[4] a[8] = a[4] a[8], a[5] a[6] = a[5] a[6],

a[5] a[8] = a[5] a[8], a[6] a[7] = a[6] a[7],

a[6] a[8] = a[6] a[8], a[6] a[9] = a[6] a[9],

a[7] a[9] = a[7] a[9], a[8] a[9] = a[8] a[9],

a[1](a[1]) = a[1](a[1]), a[5](a[5]) = a[5](a[5]),

a[9](a[9]) = a[9](a[9])}

 

 

 

the program runs however the warning message pops ...what can i do to eliminate the problem??? 

Hey,

I want to solve this equation and looking at the plot there are at least 3 solutions. I want the greatest/smallest negative solution. Unfortunately using solve with assumptions produces no results and solve without assumptions only finds two solutions.

Can you please help me?

#select greatest negative value from solution

restart:

expr:= ax*cos(lambda)+ay*sin(lambda)-(a+b*lambda)

ax*cos(lambda)+ay*sin(lambda)-b*lambda-a

(1)

ax:=1:ay:=2:a:=0.5:b:=0.25: #examplanatory values

plot(expr)

 

 

assume(-2*Pi<lambda,lambda<0): #does not work

 

sol_lambda:=[solve(expr=0,lambda, useassumptions)];# returns empty list even though without assumption one solution is found

Warning, solutions may have been lost

 

[]

(2)

sol_lambda:=[solve(expr=0,lambda)]; #returns only two solutions even though looking at the plot 3 are there

Warning, solve may be ignoring assumptions on the input variables.

 

Warning, solutions may have been lost

 

[2.190357220, -.2688724573]

(3)

sol_l_v:=evalb~(sol_lambda<~0); #dirty workaraound

[false, true]

(4)

sol_l_add:=[ListTools:-SearchAll(true,sol_l_v)] ; #this seems overly complicated

 

[2]

(5)

lambda:=sol_lambda[sol_l_add[-1]];  #to select the last entry

 

-.2688724573

(6)

expr; #test

 

0.

(7)

 


Download select_solution.mw

Thanks!

Honigmelone

I have two deformed planes, that i would like to draw with 3dplot, as well as drawing a curve marking their intersection.

the curves are given by the expressions:


C = -(k[d2]*B[2]+I*k[m]+k[d1]*B[1])/((B[1]+B[2]-R)*k[a1]+(B[1]+B[2]-R)*k[a2]-k[m]),

C = k[d1]*B[1]/(k[a1]*(R-B[1]-B[2]))

 

evaluated at

Pars := [k[a1] = 6*10^(-4), k[d1] = 7*10^(-3), k[a2] = 5*10^(-4), k[d2] = 10^(-2), R = .5, k[m] = 10^(-4), C[T] = 100, h = 10^(-6)]

with the variables B[1],B[2] and C within the bounds [0..0.5],[0..0.5],[0..100].

 

My method was to try and use solve to find a formula for the intersection curve- but i couldn't get 3dplot to plot it!

Still a little unclear what this error means tho

-f(X)/(X*(ln(X)-Psi(1-f(X))-Psi(f(X)))*GAMMA(1-m))+X*(ln(X)-Psi(1-f(X))-Psi(f(X)))/(f(X)*GAMMA(1-m)) = 0

 

Download dispatchTOshillCORE.mw

Hi,

I am trying to solve a set of homogeneous equations for the non-trivial solutions. Mathematically it is possible to get it. But is there any way to get it in Maple. Please find the attached maple sheet for the question. Please help me regarding this.

Regards

Sunit

restart

with(plots):

with(LinearAlgebra):

eq[1] := diff(x[1](t), t)-x[2](t)

diff(x[1](t), t)-x[2](t)

(1)

eq[2] := diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(2)

eq[3] := diff(phi[1](t), t)-phi[2](t)

diff(phi[1](t), t)-phi[2](t)

(3)

eq[4] := diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(4)

for k to 4 do eqn[k] := simplify(coeff(map(expand, eval(eq[k], [x[1] = (proc (t) options operator, arrow; x[1]*exp(lambda*t) end proc), x[2] = (proc (t) options operator, arrow; x[2]*exp(lambda*t) end proc), phi[1] = (proc (t) options operator, arrow; phi[1]*exp(lambda*t) end proc), phi[2] = (proc (t) options operator, arrow; phi[2]*exp(lambda*t) end proc)])), exp(lambda*t))) end do

x[1]*lambda-x[2]

 

x[2]*lambda+2*zeta*beta*x[2]+beta^2*x[1]-n*psi*v*phi[1]+n*psi*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*psi*x[1]-n*psi*x[1]*exp(-2*lambda*Pi/(n*omega0))

 

phi[1]*lambda-phi[2]

 

phi[2]*lambda+2*kappa*phi[2]+phi[1]-n*v*phi[1]+n*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*x[1]-n*x[1]*exp(-2*lambda*Pi/(n*omega0))

(5)

A, b := GenerateMatrix([seq(eqn[k], k = 1 .. 4)], [x[1], x[2], phi[1], phi[2]])

A, b := Matrix(4, 4, {(1, 1) = lambda, (1, 2) = -1, (1, 3) = 0, (1, 4) = 0, (2, 1) = beta^2+n*psi-n*psi*exp(-2*lambda*Pi/(n*omega0)), (2, 2) = 2*Zeta*beta+lambda, (2, 3) = n*psi*v*exp(-2*lambda*Pi/(n*omega0))-n*psi*v, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = lambda, (3, 4) = -1, (4, 1) = n-n*exp(-2*lambda*Pi/(n*omega0)), (4, 2) = 0, (4, 3) = -n*v+1+n*v*exp(-2*lambda*Pi/(n*omega0)), (4, 4) = 2*kappa+lambda}), Vector(4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0})

(6)

right_vector := Matrix(4, 1, [r[1], r[2], r[3], r[4]])

right_vector := Matrix(4, 1, {(1, 1) = r[1], (2, 1) = r[2], (3, 1) = r[3], (4, 1) = r[4]})

(7)

junk := MatrixVectorMultiply(subs(lambda = I*omega, A), right_vector)

junk := Matrix(4, 1, {(1, 1) = I*omega*r[1]-r[2], (2, 1) = (beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*Zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3], (3, 1) = I*omega*r[3]-r[4], (4, 1) = (n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(-n*v+1+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]})

(8)

junk(1)

I*omega*r[1]-r[2]

(9)

for k to 4 do eqnn[k] := junk(k) end do

I*omega*r[1]-r[2]

 

(beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3]

 

I*omega*r[3]-r[4]

 

(n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(1-n*v+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]

(10)

solve({seq(eqnn[k], k = 1 .. 4)}, {seq(r[k], k = 1 .. 4)})

{r[1] = 0, r[2] = 0, r[3] = 0, r[4] = 0}

(11)

``

``

``

 

Download question4.mw

pls help review this code, its doesnt return a solution

 

 

restart;
Digits := 16;
M := .5; lambda := .5; Pr := .72; beta := 1; L[w] := 0; m := 1; R := 1; Ec := 1;
N := 7;
for j from 0 to N do J[j] := sum(f[k](t)*(diff(f[j-k](t), `$`(t, 2))), k = 0 .. j) end do;
for i from 0 to N do K[i] := sum((diff(f[k](t), t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
for j from 0 to N do G[j] := sum(f[k](t)*(diff(theta[j-k](t), t)), k = 0 .. j) end do;
for j from 0 to N do H[j] := sum((diff(f[k](t), t))*theta[j-k](t), k = 0 .. j) end do;
for i from 0 to N do P[i] := sum((diff(f[k](t), t, t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
epsilon := 1; delta := 0;
f[0] := proc (t) options operator, arrow; L[w]+epsilon+delta*A*t+(1/2)*A*t^2 end proc;
1 2
t -> L[w] + epsilon + delta A t + - A t
2
theta[0] := proc (t) options operator, arrow; 1+B*t end proc;
t -> 1 + B t
NULL;
;
NULL;
NULL;
NULL;
NULL;

for i to N do f[i] := simplify(-((m+1)*(1/2))*(int(int(int(J[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))+m*(int(int(int(1-K[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-M*(int(int(int(diff(f[i-1](t), t)-1, t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-lambda*(int(int(int(theta[i-1](t), t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))); f[i] := unapply(f[i], eta); theta[i] := simplify(-3*Pr*R*(((m+1)*(1/2))*(int(int(G[i-1], t = 0 .. eta), t = 0 .. eta))-(2*m-1)*(int(int(H[i-1], t = 0 .. eta), t = 0 .. eta))+Ec*(int(int(P[i-1], t = 0 .. eta), t = 0 .. eta)))/(4+3*R)); theta[i] := unapply(theta[i], eta) end do;

NULL;
F(eta):=collect((&sum;)f[z](eta),eta):
Theta(eta):=collect((&sum;)theta[z](eta),eta):
with(numapprox);
for k from 2 to 5 do W[k] := pade(diff(F(eta), eta), eta, [k, k]); Q[k] := pade(Theta(eta), eta, [k, k]); SOLL1[k] := expand(coeff(numer(W[k]), eta^k)) = 1; SOLL2[k] := expand(coeff(numer(Q[k]), eta^k)) = 0; SOL[k] := solve({SOLL1[k], SOLL2[k]}, {A, B}); print([k] = SOL[k]) end do;
Warning, computation interrupted

 

 

 

 

 

 

i want parametrix answer for z in terms of w, what should i do ? please help

 

 

``

restart:

P:=w-10*z-1/5*z^2-1/200*z^3-1/500*z^4-z^5-1/1000*z^6

w-10*z-(1/5)*z^2-(1/200)*z^3-(1/500)*z^4-z^5-(1/1000)*z^6

(1)

solve(P,z)

RootOf(_Z^6+1000*_Z^5+2*_Z^4+5*_Z^3+200*_Z^2+10000*_Z-1000*w)

(2)

 

 

 

``

 

Download solve.mw

I am trying to solve an equation using surd and I get a strange result.

solve(surd(x^4,8)=-2)
    4, -4, 4 I, -4 I

These solutions are clearly wrong.

The equation (x^4)^(1/8) = -2 has no solution.

This problem is equivalent to asking the computer to solve sqrt(x) = -2

which has no solution in R or C.

 

However if I type

solve((x^4)^(1/8) = -2) , then I get no answer, which is what I expected.

Why does surd behave in this unexpected way.

 

Also another thing I am wondering, why doesn't Maple simplify (x^4)^(1/8) to x^(1/2).

I tried the simplify command it didn't work.

 

i want to solve a system , A.b+B.X=0 , which A is 5*5 known matrix, B is 5*2 known matrix , and b is 5*1 and X is 2*1 unknown arbitary matrices ! i want to have solution for b and X . whatever they can be ! just equation to be solved !

restart:

A:=Matrix(5,[[-0.9800,0,0,-0.0160,0],[1.0000,0,0,0,0],[-2.1900,-9.7800,-0.0280,0.0740,0],[77.3600,-0.7700,-0.2200,-0.6700,0],[0,-79.9700,-0.0300,0.9900,0]]);

A := Matrix(5, 5, {(1, 1) = -.9800, (1, 2) = 0, (1, 3) = 0, (1, 4) = -0.160e-1, (1, 5) = 0, (2, 1) = 1.0000, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (3, 1) = -2.1900, (3, 2) = -9.7800, (3, 3) = -0.280e-1, (3, 4) = 0.740e-1, (3, 5) = 0, (4, 1) = 77.3600, (4, 2) = -.7700, (4, 3) = -.2200, (4, 4) = -.6700, (4, 5) = 0, (5, 1) = 0, (5, 2) = -79.9700, (5, 3) = -0.300e-1, (5, 4) = .9900, (5, 5) = 0})

(1)

B:=Matrix((5,2),[[-2.44,0.58],[0,0],[0.18,19.62],[-6.48,0],[0,0]]);

B := Matrix(5, 2, {(1, 1) = -2.44, (1, 2) = .58, (2, 1) = 0, (2, 2) = 0, (3, 1) = .18, (3, 2) = 19.62, (4, 1) = -6.48, (4, 2) = 0, (5, 1) = 0, (5, 2) = 0})

(2)

b:=Matrix((5,1),[y[1],y[2],y[3],y[4],y[5]]);

b := Matrix(5, 1, {(1, 1) = y[1], (2, 1) = y[2], (3, 1) = y[3], (4, 1) = y[4], (5, 1) = y[5]})

(3)

X:=Matrix((2,1),[[x[1]],[x[2]]])

X := Matrix(2, 1, {(1, 1) = x[1], (2, 1) = x[2]})

(4)

M:=A.b+B.X

M := Matrix(5, 1, {(1, 1) = -.9800*y[1]-0.160e-1*y[4]-2.44*x[1]+.58*x[2], (2, 1) = 1.0000*y[1], (3, 1) = -2.1900*y[1]-9.7800*y[2]-0.280e-1*y[3]+0.740e-1*y[4]+.18*x[1]+19.62*x[2], (4, 1) = 77.3600*y[1]-.7700*y[2]-.2200*y[3]-.6700*y[4]-6.48*x[1], (5, 1) = -79.9700*y[2]-0.300e-1*y[3]+.9900*y[4]})

(5)

eval(M,y[1]=0)

Matrix([[-0.160e-1*y[4]-2.44*x[1]+.58*x[2]], [0.], [-9.7800*y[2]-0.280e-1*y[3]+0.740e-1*y[4]+.18*x[1]+19.62*x[2]], [-.7700*y[2]-.2200*y[3]-.6700*y[4]-6.48*x[1]], [-79.9700*y[2]-0.300e-1*y[3]+.9900*y[4]]])

(6)

 

 

 

Download solve.mw


actually the problem to be solved is M=0 ! which directly goes to y[1]=0;
after that , how can i find other unknowns so that M=0 is ok. tnx

how can solve using assume option ?

restart:

F(z):=m*z^4-4*m*z^3+(3*m+3)*z^2-6*u;

m*z^4-4*m*z^3+(3*m+3)*z^2-6*u

(1)

solve(F(z),z assuming -0.5<m<0.5, 0<u<0.5)

Error, `<` unexpected

 

 

 

Download assume.mw

Hi

 

Im trying to copy my collegues work, he uses mathcad and I use maple. I have a problem when trying to solve a system of 7 equations and 7 unknows. For some reason he dosent seem to get the same problem of "Error, recursive assignment".

You can see a screen shot of his solution here:
http://i.imgur.com/U7nE7sU.png

 

And you can see my solution here:

http://i.imgur.com/vrBTLIY.jpg

 

As you can see the code dosent work, is there anyone that could help me understand why eactly this happens and how to fix this? 

 

Best Regards

Ivan N

 

 

Hello 

Is there a way to solve matrices symbolically?

an example would be A*X=B

where the answer would be 

X=A^-1B

 

I have tried to look for a thing in maple that will do this but so far i had no luck. Does anyone know ?

Thanks in advance

hi...please help me for solve this differential equation

thanks

warning.mw

restart; newsys := {-299.982222222220*(diff(G(x), x))-1.15384615384615*(diff(w(x), x, x, x, x))-299.999999999998*(diff(w(x), x, x))+0.128205128205129e-2*(diff(G(x), x, x, x)) = -omega2*(diff(G(x), x)), (diff(w(x), x, x))*(1.00895521199133*cos(.133333333333334*x)-1)-.134527361598845*(diff(w(x), x))*sin(.133333333333334*x)+.333333333333333*(diff(w(x), x, x))+.333333333333333*(diff(G(x), x))-0.128205128205129e-2*(diff(w(x), x, x, x, x))+0.128205128205129e-2*(diff(G(x), x, x, x)) = -omega2*w(x)}

bcs := {.333333333333333*(D(w))(1)+.333333333333333*G(1)-0.128205128205129e-2*((D@@3)(w))(1)+0.128205128205129e-2*((D@@2)(G))(1) = 0, G(0) = 0, w(0) = 0, (D(G))(1) = 0, (D(w))(0) = 0, ((D@@2)(w))(1) = 0}:

Typesetting:-mrow(Typesetting:-mi("extra_bcs", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", 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;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", 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("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("D", italic = "false", mathvariant = "normal"), Typesetting:-mo("@@", 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", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("G", italic = "true", mathvariant = "italic")), mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("a", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", 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", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", 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", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("2", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("a", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", 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", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mo(" ", 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", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("D", italic = "false", mathvariant = "normal"), Typesetting:-mo("@@", 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", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("w", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("a", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", 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", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", 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", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("3", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("a", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", 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", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mo(" ", 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", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "{", close = "}"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("minus", bold = "true", 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(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("lhs", italic = "true", mathvariant = "italic"), Typesetting:-mo("~", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.1111111em", rspace = "0.1111111em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bcs", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("newsys2", italic = "true", mathvariant = "italic"), Typesetting:-mo("&coloneq;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("subs", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("omega", italic = "false", mathvariant = "normal"), Typesetting:-mo("^", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.1111111em", rspace = "0.1111111em"), Typesetting:-mn("2", mathvariant = "normal"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("omega2", italic = "true", mathvariant = "italic"), Typesetting:-mo("&sdot;", 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:-mn("10", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mi(""), Typesetting:-mo(",", foreground = "[255,0,0]", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("newsys", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mo("for", bold = "true", 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(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("b", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", 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", 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(" ", 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", mathvariant = "italic"), Typesetting:-mo(" ", 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", 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:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", 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", 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(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", 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", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("b", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", 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(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", 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", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("b", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo("&coloneq;", 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", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("newsys2", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", 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", 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(" ", 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("b", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", 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", mathvariant = "normal")), mathvariant = "normal", open = "{", close = "}"), Typesetting:-mo(",", 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", mathvariant = "italic"), Typesetting:-mo(",", 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", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("2024", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("output", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", 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", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("approxsoln", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", 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("ω2", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn(".0001", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mrow(Typesetting:-mi("G", italic = "true", mathvariant = "italic"), Typesetting:-mo("&ApplyFunction;", family = "Times New Roman", size = "12", bold = "false", italic = "false", underline = "false", subscript = "false", superscript = "false", foreground = "[0,0,0]", background = "[255,255,255]", opaque = "false", executable = "false", readonly = "false", composed = "false", converted = "false", imselected = "false", placeholder = "false", `selection-placeholder` = "false", mathvariant = "normal", fence = "unset", separator = "unset", stretchy = "unset", symmetric = "unset", largeop = "unset", movablelimits = "unset", accent = "unset", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal")), Typesetting:-mo("=", 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:-mo("&uminus0;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mn("3", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mo("+", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mn("2", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mo("+", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic")), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mrow(Typesetting:-mi("w", italic = "true", mathvariant = "italic"), Typesetting:-mo("&ApplyFunction;", family = "Times New Roman", size = "12", bold = "false", italic = "false", underline = "false", subscript = "false", superscript = "false", foreground = "[0,0,0]", background = "[255,255,255]", opaque = "false", executable = "false", readonly = "false", composed = "false", converted = "false", imselected = "false", placeholder = "false", `selection-placeholder` = "false", mathvariant = "normal", fence = "unset", separator = "unset", stretchy = "unset", symmetric = "unset", largeop = "unset", movablelimits = "unset", accent = "unset", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal")), Typesetting:-mo("=", 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:-mi(""), Typesetting:-mrow(Typesetting:-mfrac(Typesetting:-mn("11068376068376057", mathvariant = "normal"), Typesetting:-mn("170940170940172", mathvariant = "normal"), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false"), Typesetting:-mo("&InvisibleTimes;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mn("4", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mi("")), Typesetting:-mo("&minus;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mrow(Typesetting:-mfrac(Typesetting:-mn("22179487179487157", mathvariant = "normal"), Typesetting:-mn("128205128205129", mathvariant = "normal"), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false"), Typesetting:-mo("&InvisibleTimes;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mn("3", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mi("")), Typesetting:-mo("+", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mrow(Typesetting:-mfrac(Typesetting:-mn("11153846153846143", mathvariant = "normal"), Typesetting:-mn("85470085470086", mathvariant = "normal"), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false"), Typesetting:-mo("&InvisibleTimes;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mn("2", mathvariant = "normal"), superscriptshift = "0")), Typesetting:-mi("")), Typesetting:-mi("")), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", 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", mathvariant = "italic"), Typesetting:-mo("=", 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;5", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(" ", 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", 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(":", 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(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", 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", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("lasterror", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mi(""), 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(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", 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", 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(" ", 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", 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:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", 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", 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(" ", 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", 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(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", 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;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", 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", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", 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", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("nops", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal"), Typesetting:-mo(":", 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", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(":", 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("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("subs", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("omega2", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", 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", mathvariant = "italic"), Typesetting:-mo("=", 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", mathvariant = "normal"), Typesetting:-mo("..", 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", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mo(" ", 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", mathvariant = "italic"), Typesetting:-mo("&coloneq;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("D", italic = "false", mathvariant = "normal"), Typesetting:-mo("@@", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("2", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("w", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"))

res[((D@@2)(w))(0)]

(1)

``


Download warning.mw

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