Markiyan Hirnyk

Markiyan Hirnyk
8 years, 275 days


These are answers submitted by Markiyan Hirnyk

Order of commands

Yesterday at 12:51 AM Markiyan Hirnyk 6023
1 1

If you carefully read Maple Help, you will understand why this works

x;

x

Don't hesitate to ask for further explanation in need.

Under assumption

Yesterday at 12:35 AM Markiyan Hirnyk 6023
1 7

It is clear that the parameter z is positive. In view of it this works


restart; f := proc (t) options operator, arrow; piecewise(t < 0, 0, 0 <= t and t < z, t, z < t, z) end proc; r := convert(f(t), Heaviside)

r := `assuming`([inttrans[laplace](r, t, s)], [z > 0]);

(1-exp(-s*z))/s^2

(1)

NULL

NULL


Download LT.mw

Not reinventing the wheel,

August 17 2014 Markiyan Hirnyk 6023
3 1

this can be done as follows:

 

addcoords(affine, [x, y], [x-(1/2)*y, y])

Warning, not an orthogonal coordinate system - no scale factors calculated.

 

plots:-coordplot(affine, [-1 .. 1, -1 .. 1], axes = box, gridlines = false)

 

``

The image of [-1,1]x[-1,1] is displayed.

Download affine.mw

Here are my arguments.

 

restart

t := (cos(y)/sqrt(y^2+1)+I*sqrt(y^3+2)*sin(y))*BesselJ(0, y):NULL

plot([Re(t), Im(t)], y = 0 .. 10, view = [0 .. 10, -.1 .. .1], color = [blue, red])

 

 

 

RootFinding:-Analytic(t, re = 0 .. 10, im = -1 .. 1)

5.520078110, .5378363550+.6749359945*I, 9.424781460+0.3642288221e-2*I, 8.653727915, 6.283224045+0.9939802100e-2*I, 2.404825558, 3.143645495+0.5271012320e-1*I

(1)

DirectSearch:-SolveEquations([Re(eval(t, y = u+I*v)), Im(eval(t, y = u+I*v))], {u >= 0, v >= -1, u <= 10, v <= 1}, AllSolutions)

Matrix(7, 4, {(1, 1) = 0.1039502792e-25, (1, 2) = Vector(2, {(1) = HFloat(-9.533264822182746e-14), (2) = HFloat(-3.614850074426784e-14)}), (1, 3) = [u = 8.65372791291102, v = -0.1979993520e-13], (1, 4) = 82, (2, 1) = 0.1278977452e-25, (2, 2) = Vector(2, {(1) = HFloat(-1.0187983564929878e-13), (2) = HFloat(-4.9094537444784927e-14)}), (2, 3) = [u = 2.40482555769580, v = -0.7611829592e-13], (2, 4) = 90, (3, 1) = 0.7373586454e-25, (3, 2) = Vector(2, {(1) = HFloat(2.6305853196235286e-13), (2) = HFloat(-6.735037714109912e-14)}), (3, 3) = [u = 9.42478145908336, v = 0.364228821925537e-2], (3, 4) = 83, (4, 1) = 0.1496284254e-24, (4, 2) = Vector(2, {(1) = HFloat(3.782392021918967e-13), (2) = HFloat(8.10156237189513e-14)}), (4, 3) = [u = .537836355054287, v = .674935994442906], (4, 4) = 60, (5, 1) = 0.5718766083e-24, (5, 2) = Vector(2, {(1) = HFloat(7.546656323302453e-13), (2) = HFloat(-4.854267870843557e-14)}), (5, 3) = [u = 3.14364549478210, v = 0.527101232016948e-1], (5, 4) = 79, (6, 1) = 0.6236084378e-23, (6, 2) = Vector(2, {(1) = HFloat(2.0150338629103837e-12), (2) = HFloat(-1.4750331892844617e-12)}), (6, 3) = [u = 6.28322404368377, v = 0.993980209970338e-2], (6, 4) = 69, (7, 1) = 0.6101471069e-21, (7, 2) = Vector(2, {(1) = HFloat(2.39681750166319e-11), (2) = HFloat(-5.9727458767628956e-12)}), (7, 3) = [u = 5.52007811028837, v = 0.7782349966e-11], (7, 4) = 83})

(2)

 

NULL

 

Download roots.mw

You are right

August 14 2014 Markiyan Hirnyk 6023
0 0

Here is a proof (PS. i. e. a counterexample) done with Maple:

 

``

NULL

with(GroupTheory):

G := CyclicGroup(n)

GroupTheory:-CyclicGroup(n)

(1)

IsNilpotent(G);

                                true
                              true

(2)

H := DihedralGroup(8)

GroupTheory:-DihedralGroup(8, form = "permgroup")

(3)

IsNilpotent(H)

true

(4)

IsAbelian(H)

false

(5)

``


However, it should be noted the properties of CyclicGroup(n) are simply implemented in Maple.

Download NilpotentvsCyclic.mw

Explanation

August 12 2014 Markiyan Hirnyk 6023
0 2

Up to Statistics[Histogram],

"binwidth=positive, Sturges, Scott, or FreedmanDiaconis
This option controls the bin width (and consequently the number of bins) for the histogram. The bin width can be either specified explicitly (which overrides the maxbins and minbins options) or can be calculated using one of three methods: Sturges, Scott, or FreedmanDiaconis. The default value is Sturges"

Let us consider the following outputs with infolevel[Statistics]:=5 :

 

restart; infolevel[Statistics] := 5

Statistics:-Histogram([0.587944711e-1, 0.587944836e-1, 0.589720582e-1])

Histogram Type:  default
Data Range:      .0587944711 .. .0589720582
Bin Width:       5.91957000000027e-006
Number of Bins:  30
Frequency Scale: relative
Statistics:-Histogram - options passed on to the \`plot\` command: []

 

 

Statistics:-Histogram([0.587944711e-1, 0.587944836e-1, 0.589720582e-1], discrete = true, gridlines = false)

Discrete histogram chosen - ignoring averageshifted, binbounds, bincount, binwidth, maxbins, and minbins options
Histogram Type:  discrete
Data Range:      .0587944711 .. .0589720582
Number of Bins:  3
Frequency Scale: relative
Statistics:-Histogram - options passed on to the \`plot\` command: [gridlines = false]

 

 

``

``

``

 

 

``

``

``

``

``

``

``

``

``

``

``

``


We see the difference between the binwidths.

Download Histo.mw

Reference

August 11 2014 Markiyan Hirnyk 6023
0 0

See that article to this end.

This can be done by the use of an optimizer instead of Statistics:-NonLinearFit. Here is an example with the DirectSearch package which should be installed in your Maple.

X := Vector(10, proc (j) options operator, arrow; evalf(j) end proc);


Y := Vector(10, proc (j) options operator, arrow; evalf(j*exp(.1*j)+.1*sin(j)) end proc);


DirectSearch:-GlobalSearch(LinearAlgebra:-Norm(map(x -> a*x*exp(b*x)+c , X)-Y, 2), {a+b <= c+1}, solutions = 1);

DirectSearch:-DataFit(a*x*exp(b*x)+c, {a+b <= c+1}, X, Y, x, method = brent);

Download nonlinearfit.mw

Yes, it is possible

August 11 2014 Markiyan Hirnyk 6023
1 0

 This can be done in Maple Standard under Windows by switching from Inline  to Window in Menu/Tools/Options/Display/PlotDisplay

This works for me

July 28 2014 Markiyan Hirnyk 6023
0 0

sol := solve([u^2+v^2+x^2+y^2 = 1, 2*u*x+2*v*y, sqrt(y^2+x^2) = sqrt(v^2+u^2)], {u, v, x, y});

allvalues(sol[1]);

 

Explanation

July 25 2014 Markiyan Hirnyk 6023
0 5

Up to ?dsolve , Maple finds  closed form solutions for a single ODE.  The only closed form solution of the nonlinear ODE under consideration it can find is y(x)=0 (see the output of

restart; infolevel[dsolve] := 5;
ode := 2*a^2*y(x)-2*y(x)^3+3*a*(diff(y(x), x))+diff(y(x), `$`(x, 2)) = 0;
sol := dsolve(ode, y(x))  .

The command

sol1 := dsolve(ode, y(x), series);

outputs a general solution around x=0:

 

This ODE can be dsolved numerically, when assigning a and adding initial conditions. For example,

sol3 := dsolve({eval(ode, a = 2), y(0) = 0, (D(y))(0) = 1}, y(x), numeric);

plots:-odeplot(sol3, x = 0 .. 0.9e-1);

Example

July 25 2014 Markiyan Hirnyk 6023
1 0

Here is an example from S. Dempe, Foundations of Bilevel Programming, NY,...,Moscow, Kluwer Academic Publishers, 2002, done with Maple.

 

 

restart; with(simplex)

f := proc (y) options operator, arrow; minimize(-x, {8 <= 4*x+y, x+y <= 8, 2*x+y <= 13}, NONNEGATIVE) end proc:

f(2)

{x = 11/2}

(1)

 

 

plots:-inequal({4*x+y >= 8, x+y <= 8, 2*x+y <= 13}, y = 0 .. 8, x = 0 .. 8);

 

plot(proc (y) options operator, arrow; rhs(op(f(y))) end proc, 0 .. 8)

 

DirectSearch:-GlobalSearch(proc (y) options operator, arrow; 3*rhs(op(f(y)))+y end proc, {y >= 0, y <= 6})

Matrix(1, 3, {(1, 1) = 12.0000000000002, (1, 2) = Vector(1, {(1) = 5.999999999999885}, datatype = float[8]), (1, 3) = 15})

(2)

f(5.99999999999989)

{x = 2.000000000}

(3)

``

Because the upper level objective function is not differentiable, the DirectSearch package is used.

Download Bilevel_Programming.mw

The output of

ans2:=GlobalSearch(log(tarfun),constr,pointrange=constrp,maximize,evaluationlimit=30000,

tolerances=10^(-8),solutions=5);

 

suggests there are two different optimal solutions:

close to

[eta[p2] = -.820853583349005, mu[p] = 1., phi[1] = .759806839240713, phi[2] = .732170469304686,
phi[3] = .878063065537579, phi[4] = .815624200852221, phi[5] = .660085347688083,
 phi[6] = .722060536120714, phi[7] = .840690519184552, phi[8] = .829978889729624,
tau[p3] = -0.548513761568674e-1, tau[p4] = -.162913081930433, tau[p5] = -.115531722646346,
 tau[p6] = -.120266670080191, tau[p7] = -.128078874442439, tau[p8] = -0.965049847119155e-1,
 tau[p9] = -.179146416650995, w[1] = .638468266188749]


and close to

[eta[p2] = .825740931547679, mu[p] = .174259068452321, phi[1] = .780986442917954, phi[2] = .734520439265845,
 phi[3] = .847843754634582, phi[4] = .838306231949389, phi[5] = .637136562777000,
 phi[6] = .746598141197962, phi[7] = .841610094125539, phi[8] = .866597312970020,
 tau[p3] = -0.543251071903657e-1, tau[p4] = -.145991878661213, tau[p5] = -.118231611851851,
 tau[p6] = -.122477654914788, tau[p7] = -.129516460264233, tau[p8] = -0.722417009900789e-1,
tau[p9] = -.174259068452321, w[1] = .364946526201933]

The other outputs don't deny that proposition.

pr.mw

 

Explicit solution

July 23 2014 Markiyan Hirnyk 6023
2 9

After correcting the misprint in ao ( it should be a0) and replacing 0.5 by 1/2, explicit solution can be obtained in such a way.

 

restart; a0 := a01+I*a02; b1 := b11+I*b12; b0 := b01+I*b02; a1 := a11+I*a12; a2 := a21+I*a22; x := a+I*b; y := u+I*v; z := eta+I*xi; solve(evalc({Im(10*x+10*y*(1/4)+10*z = 10), Im(conjugate(a1)*x+b0*y+conjugate(a2)*conjugate(y)+a1*z = 0), Im(a0*x+a1*y+conjugate(a1)*conjugate(y)+a2*z+conjugate(a2)*conjugate(z) = 1/2), Re(10*x+10*y*(1/4)+10*z = 10), Re(conjugate(a1)*x+b0*y+conjugate(a2)*conjugate(y)+a1*z = 0), Re(a0*x+a1*y+conjugate(a1)*conjugate(y)+a2*z+conjugate(a2)*conjugate(z) = 1/2)}), {a, b, eta, u, v, xi}, domain = real)

{a = -(1/2)*a01*(16*a11^3+64*a11^2*a21-64*a11^2*b01+16*a11*a12^2-128*a11*a12*b02-16*a11*a21^2-16*a11*a21*b01-16*a11*a22^2+16*a11*a22*b02+64*a12^2*a21+64*a12^2*b01-16*a12*a21*b02-16*a12*a22*b01-64*a21^3-64*a21*a22^2+64*a21*b01^2+64*a21*b02^2-a11^2+8*a11*b01-a12^2+8*a12*b02+16*a21^2+16*a22^2-16*b01^2-16*b02^2)/(a01^2*a11^2-8*a01^2*a11*b01+a01^2*a12^2-8*a01^2*a12*b02-16*a01^2*a21^2-16*a01^2*a22^2+16*a01^2*b01^2+16*a01^2*b02^2-2*a01*a11^2*a21+60*a01*a11*a12*a22+64*a01*a11*a12*b02+16*a01*a11*a21*b01-62*a01*a12^2*a21-64*a01*a12^2*b01+16*a01*a12*a22*b01+32*a01*a21^3+32*a01*a21*a22^2-32*a01*a21*b01^2-32*a01*a21*b02^2+a02^2*a11^2-8*a02^2*a11*b01+a02^2*a12^2-8*a02^2*a12*b02-16*a02^2*a21^2-16*a02^2*a22^2+16*a02^2*b01^2+16*a02^2*b02^2-16*a02*a11^2*a12-2*a02*a11^2*a22-60*a02*a11*a12*a21+64*a02*a11*a12*b01+16*a02*a11*a22*b01-16*a02*a12^3-62*a02*a12^2*a22+64*a02*a12^2*b02+16*a02*a12*a21^2-16*a02*a12*a21*b01+16*a02*a12*a22^2+32*a02*a21^2*a22+32*a02*a22^3-32*a02*a22*b01^2-32*a02*a22*b02^2), b = (1/2)*a02*(16*a11^3+64*a11^2*a21-64*a11^2*b01+16*a11*a12^2-128*a11*a12*b02-16*a11*a21^2-16*a11*a21*b01-16*a11*a22^2+16*a11*a22*b02+64*a12^2*a21+64*a12^2*b01-16*a12*a21*b02-16*a12*a22*b01-64*a21^3-64*a21*a22^2+64*a21*b01^2+64*a21*b02^2-a11^2+8*a11*b01-a12^2+8*a12*b02+16*a21^2+16*a22^2-16*b01^2-16*b02^2)/(a01^2*a11^2-8*a01^2*a11*b01+a01^2*a12^2-8*a01^2*a12*b02-16*a01^2*a21^2-16*a01^2*a22^2+16*a01^2*b01^2+16*a01^2*b02^2-2*a01*a11^2*a21+60*a01*a11*a12*a22+64*a01*a11*a12*b02+16*a01*a11*a21*b01-62*a01*a12^2*a21-64*a01*a12^2*b01+16*a01*a12*a22*b01+32*a01*a21^3+32*a01*a21*a22^2-32*a01*a21*b01^2-32*a01*a21*b02^2+a02^2*a11^2-8*a02^2*a11*b01+a02^2*a12^2-8*a02^2*a12*b02-16*a02^2*a21^2-16*a02^2*a22^2+16*a02^2*b01^2+16*a02^2*b02^2-16*a02*a11^2*a12-2*a02*a11^2*a22-60*a02*a11*a12*a21+64*a02*a11*a12*b01+16*a02*a11*a22*b01-16*a02*a12^3-62*a02*a12^2*a22+64*a02*a12^2*b02+16*a02*a12*a21^2-16*a02*a12*a21*b01+16*a02*a12*a22^2+32*a02*a21^2*a22+32*a02*a22^3-32*a02*a22*b01^2-32*a02*a22*b02^2), eta = -(1/2)*(8*a01^2*a11*a21+8*a01^2*a11*b01-8*a01^2*a12*a22+8*a01^2*a12*b02+32*a01^2*a21^2+32*a01^2*a22^2-32*a01^2*b01^2-32*a01^2*b02^2-16*a01*a11^3-64*a01*a11^2*a21+64*a01*a11^2*b01+16*a01*a11*a12^2-128*a01*a11*a12*a22+16*a01*a11*a22^2-16*a01*a11*a22*b02+64*a01*a12^2*a21+64*a01*a12^2*b01-16*a01*a12*a21*a22-16*a01*a12*a22*b01+8*a02^2*a11*a21+8*a02^2*a11*b01-8*a02^2*a12*a22+8*a02^2*a12*b02+32*a02^2*a21^2+32*a02^2*a22^2-32*a02^2*b01^2-32*a02^2*b02^2+32*a02*a11^2*a12+128*a02*a11*a12*a21-128*a02*a11*a12*b01-16*a02*a11*a21*a22-16*a02*a11*a22*b01+128*a02*a12^2*a22-128*a02*a12^2*b02-16*a02*a12*a22^2+16*a02*a12*a22*b02-64*a02*a21^2*a22-64*a02*a22^3+64*a02*a22*b01^2+64*a02*a22*b02^2+a01*a11^2-8*a01*a11*b01-a01*a12^2+8*a01*a12*a22-16*a01*a21^2-16*a01*a22^2+16*a01*b01^2+16*a01*b02^2-2*a02*a11*a12-8*a02*a12*a21+8*a02*a12*b01)/(a01^2*a11^2-8*a01^2*a11*b01+a01^2*a12^2-8*a01^2*a12*b02-16*a01^2*a21^2-16*a01^2*a22^2+16*a01^2*b01^2+16*a01^2*b02^2-2*a01*a11^2*a21+60*a01*a11*a12*a22+64*a01*a11*a12*b02+16*a01*a11*a21*b01-62*a01*a12^2*a21-64*a01*a12^2*b01+16*a01*a12*a22*b01+32*a01*a21^3+32*a01*a21*a22^2-32*a01*a21*b01^2-32*a01*a21*b02^2+a02^2*a11^2-8*a02^2*a11*b01+a02^2*a12^2-8*a02^2*a12*b02-16*a02^2*a21^2-16*a02^2*a22^2+16*a02^2*b01^2+16*a02^2*b02^2-16*a02*a11^2*a12-2*a02*a11^2*a22-60*a02*a11*a12*a21+64*a02*a11*a12*b01+16*a02*a11*a22*b01-16*a02*a12^3-62*a02*a12^2*a22+64*a02*a12^2*b02+16*a02*a12*a21^2-16*a02*a12*a21*b01+16*a02*a12*a22^2+32*a02*a21^2*a22+32*a02*a22^3-32*a02*a22*b01^2-32*a02*a22*b02^2), u = 4*(a01^2*a11^2+4*a01^2*a11*a21-4*a01^2*a11*b01+a01^2*a12^2-4*a01^2*a12*a22-4*a01^2*a12*b02-2*a01*a11^2*a21+16*a01*a11*a12^2-4*a01*a11*a12*a22-8*a01*a11*a21^2+8*a01*a11*a21*b01+2*a01*a12^2*a21-8*a01*a12*a21*a22-8*a01*a12*a21*b02+a02^2*a11^2+4*a02^2*a11*a21-4*a02^2*a11*b01+a02^2*a12^2-4*a02^2*a12*a22-4*a02^2*a12*b02-2*a02*a11^2*a22+4*a02*a11*a12*a21-8*a02*a11*a21*a22+8*a02*a11*a22*b01-16*a02*a12^3+2*a02*a12^2*a22+16*a02*a12*a21^2-16*a02*a12*a21*b01+8*a02*a12*a22^2+8*a02*a12*a22*b02-a01*a12^2+4*a01*a12*a22+4*a01*a12*b02-a02*a11*a12-4*a02*a12*a21+4*a02*a12*b01)/(a01^2*a11^2-8*a01^2*a11*b01+a01^2*a12^2-8*a01^2*a12*b02-16*a01^2*a21^2-16*a01^2*a22^2+16*a01^2*b01^2+16*a01^2*b02^2-2*a01*a11^2*a21+60*a01*a11*a12*a22+64*a01*a11*a12*b02+16*a01*a11*a21*b01-62*a01*a12^2*a21-64*a01*a12^2*b01+16*a01*a12*a22*b01+32*a01*a21^3+32*a01*a21*a22^2-32*a01*a21*b01^2-32*a01*a21*b02^2+a02^2*a11^2-8*a02^2*a11*b01+a02^2*a12^2-8*a02^2*a12*b02-16*a02^2*a21^2-16*a02^2*a22^2+16*a02^2*b01^2+16*a02^2*b02^2-16*a02*a11^2*a12-2*a02*a11^2*a22-60*a02*a11*a12*a21+64*a02*a11*a12*b01+16*a02*a11*a22*b01-16*a02*a12^3-62*a02*a12^2*a22+64*a02*a12^2*b02+16*a02*a12*a21^2-16*a02*a12*a21*b01+16*a02*a12*a22^2+32*a02*a21^2*a22+32*a02*a22^3-32*a02*a22*b01^2-32*a02*a22*b02^2), v = -4*(4*a01^2*a11*a22-4*a01^2*a11*b02+4*a01^2*a12*a21+4*a01^2*a12*b01-16*a01*a11^2*a12-8*a01*a11*a21*a22+8*a01*a11*a21*b02+8*a01*a12*a21^2+8*a01*a12*a21*b01+4*a02^2*a11*a22-4*a02^2*a11*b02+4*a02^2*a12*a21+4*a02^2*a12*b01+16*a02*a11*a12^2-8*a02*a11*a22^2+8*a02*a11*a22*b02+8*a02*a12*a21*a22-16*a02*a12*a21*b02-8*a02*a12*a22*b01+a01*a11*a12-4*a01*a12*a21-4*a01*a12*b01-a02*a12^2-4*a02*a12*a22+4*a02*a12*b02)/(a01^2*a11^2-8*a01^2*a11*b01+a01^2*a12^2-8*a01^2*a12*b02-16*a01^2*a21^2-16*a01^2*a22^2+16*a01^2*b01^2+16*a01^2*b02^2-2*a01*a11^2*a21+60*a01*a11*a12*a22+64*a01*a11*a12*b02+16*a01*a11*a21*b01-62*a01*a12^2*a21-64*a01*a12^2*b01+16*a01*a12*a22*b01+32*a01*a21^3+32*a01*a21*a22^2-32*a01*a21*b01^2-32*a01*a21*b02^2+a02^2*a11^2-8*a02^2*a11*b01+a02^2*a12^2-8*a02^2*a12*b02-16*a02^2*a21^2-16*a02^2*a22^2+16*a02^2*b01^2+16*a02^2*b02^2-16*a02*a11^2*a12-2*a02*a11^2*a22-60*a02*a11*a12*a21+64*a02*a11*a12*b01+16*a02*a11*a22*b01-16*a02*a12^3-62*a02*a12^2*a22+64*a02*a12^2*b02+16*a02*a12*a21^2-16*a02*a12*a21*b01+16*a02*a12*a22^2+32*a02*a21^2*a22+32*a02*a22^3-32*a02*a22*b01^2-32*a02*a22*b02^2), xi = (1/2)*(8*a01^2*a11*a22-8*a01^2*a11*b02+8*a01^2*a12*a21+8*a01^2*a12*b01-32*a01*a11^2*a12-16*a01*a11*a21*a22+16*a01*a11*a21*b02+16*a01*a12*a21^2+16*a01*a12*a21*b01+8*a02^2*a11*a22-8*a02^2*a11*b02+8*a02^2*a12*a21+8*a02^2*a12*b01-16*a02*a11^3-64*a02*a11^2*a21+64*a02*a11^2*b01+16*a02*a11*a12^2+128*a02*a11*a12*b02+16*a02*a11*a21^2+16*a02*a11*a21*b01-64*a02*a12^2*a21-64*a02*a12^2*b01+16*a02*a12*a21*a22-16*a02*a12*a21*b02+64*a02*a21^3+64*a02*a21*a22^2-64*a02*a21*b01^2-64*a02*a21*b02^2+2*a01*a11*a12-8*a01*a12*a21-8*a01*a12*b01+a02*a11^2-8*a02*a11*b01-a02*a12^2-8*a02*a12*a22-16*a02*a21^2-16*a02*a22^2+16*a02*b01^2+16*a02*b02^2)/(a01^2*a11^2-8*a01^2*a11*b01+a01^2*a12^2-8*a01^2*a12*b02-16*a01^2*a21^2-16*a01^2*a22^2+16*a01^2*b01^2+16*a01^2*b02^2-2*a01*a11^2*a21+60*a01*a11*a12*a22+64*a01*a11*a12*b02+16*a01*a11*a21*b01-62*a01*a12^2*a21-64*a01*a12^2*b01+16*a01*a12*a22*b01+32*a01*a21^3+32*a01*a21*a22^2-32*a01*a21*b01^2-32*a01*a21*b02^2+a02^2*a11^2-8*a02^2*a11*b01+a02^2*a12^2-8*a02^2*a12*b02-16*a02^2*a21^2-16*a02^2*a22^2+16*a02^2*b01^2+16*a02^2*b02^2-16*a02*a11^2*a12-2*a02*a11^2*a22-60*a02*a11*a12*a21+64*a02*a11*a12*b01+16*a02*a11*a22*b01-16*a02*a12^3-62*a02*a12^2*a22+64*a02*a12^2*b02+16*a02*a12*a21^2-16*a02*a12*a21*b01+16*a02*a12*a22^2+32*a02*a21^2*a22+32*a02*a22^3-32*a02*a22*b01^2-32*a02*a22*b02^2)}

(1)

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