Markiyan Hirnyk

Markiyan Hirnyk
9 years, 6 days


These are answers submitted by Markiyan Hirnyk

Making two plots

November 24 2014 Markiyan Hirnyk 6208
1 0

This can be done as follows.



Download twoplots.mw

There is no problem here in Maple 18.02:

Converting to sets

November 23 2014 Markiyan Hirnyk 6208
0 5

This can be done as follows.

L1 := [(diff(y(x), x))*(diff(y(x), x, x)), diff(y(x), x, x, x), (diff(y(x), x, x))^2, diff(y(x), x, x, x), diff(y(x), x, x, x)]:

L2 := [(diff(y(x), x))*(diff(y(x), x, x)), diff(y(x), x, x, x), diff(y(x), x), (diff(y(x), x, x))^2, diff(y(x), x, x)]:

S1 := convert(L1, set):

S2 := convert(L2, set):


 S1 subset S2;

true

S2 subset S1

false

No real solutions for N:=6

November 23 2014 Markiyan Hirnyk 6208
0 31

N:=6:

plot(s,l=-20..100);

plot(s,l=40..60);

plot_to_Shklovski.mw

This works for me

November 21 2014 Markiyan Hirnyk 6208
0 1

You redifine M and the second definition

M := [[x*y,y,x],[x^2+x,y+x^2,y],[-y,x,y],[x^2,x,y]];

is not correct. Compare with http://www.maplesoft.com/support/help/Maple/view.aspx?path=Groebner/Basis_details

(Maybe, a typo is made.).

This works for me.

restart; with(Groebner):

F := [x+y+z, x*y+x*z+y*z, x*y*z-1];

M := [seq(s^3*F[i]+s^(3-i), i = 1 .. 3)];

with(Ore_algebra): A := poly_algebra(x, y, z, s);

T := MonomialOrder(A, lexdeg([s], [x, y, z]), {s});

G := Groebner[Basis](M, T);

[s*x*y*z-x*y-x*z-y*z-s, s^2*x*y+s^2*x*z+s^2*y*z-s*x-s*y-s*z, s^2*x*z^2+s^2*y*z^2-s*x*z-s*y*z-s*z^2+s^2+x+y+z, s^2*y^2*z^2-s*y^2*z-s*y*z^2+s^2*y+s^2*z+y^2+y*z+z^2-s, s^3*x+s^3*y+s^3*z+s^2, s^3*y^2+s^3*y*z+s^3*z^2+s^2*y+s^2*z-s, s^3*z^3+s^2*z^2-s^3-s*z+1]

 

Download basis.mw

The fsolve command works

November 19 2014 Markiyan Hirnyk 6208
0 0

Digits:=30:

fsolve([E[1]=0, E[2]=0,E[3]=0],complex);

{C[1] = 6.98650717794746147307883510970*10^(-28), C[2] = 3.16097084442000738841620848477*10^(-27), C[3] = -3.59332234088736387376082663291}

The verification:

eval([E[1] = 0, E[2] = 0, E[3] = 0], {C[1] = 6.98650717794746147307883510970*10^(-28), C[2] = 3.16097084442000738841620848477*10^(-27), C[3] = -3.59332234088736387376082663291});

[6.8*10^(-28) = 0, 2.9*10^(-28) = 0, 1.0*10^(-28) = 0]

answer.mw

 

Using exp(A+B)=exp(A).exp(B)

November 18 2014 Markiyan Hirnyk 6208
1 8

Correcting your syntax, this can be done as follows.


restart; with(LinearAlgebra)

``

dF := -.525*exp(-7*t)+2.625*exp(-3*t)+.8*exp(-4*t);

-.525*exp(-7*t)+2.625*exp(-3*t)+.8*exp(-4*t)

(1)

``

e3 := `<,>`(1, 1, 1); E := proc (m) options operator, arrow; IdentityMatrix(m) end proc; beta := `<|>`(.1, .6, .3); S := `<|>`(`<,>`(-3, 1, 1), `<,>`(1, -5, 2), `<,>`(0, 2, -4)); S0 := -S.e3

beta := Vector[row](3, {(1) = .1, (2) = .6, (3) = .3})

 

S := Matrix(3, 3, {(1, 1) = -3, (1, 2) = 1, (1, 3) = 0, (2, 1) = 1, (2, 2) = -5, (2, 3) = 2, (3, 1) = 1, (3, 2) = 2, (3, 3) = -4})

 

S0 := Vector(3, {(1) = 2, (2) = 2, (3) = 1})

(2)

``

NULL

Z := `<|>`(x, y, z)

Z := Vector[row](3, {(1) = x, (2) = y, (3) = z})

(3)

``

NULL

``

``

ME := MatrixFunction(evalf(S), exp(t), t).MatrixFunction(S0.Z, exp(t), t)

ME := Matrix(3, 3, {(1, 1) = HFloat(0.07968493772050299)*(2*x*exp(z+2*y+2*x)+2*y+z)/(z+2*y+2*x)+HFloat(0.11021977788550943)*x*(exp(z+2*y+2*x)-1)/(z+2*y+2*x), (1, 2) = HFloat(0.18808083120538238)*y*(exp(z+2*y+2*x)-1)/(z+2*y+2*x)+HFloat(0.04075441106056652)*(2*y*exp(z+2*y+2*x)+2*x+z)/(z+2*y+2*x), (1, 3) = HFloat(0.24087869756213903)*z*(exp(z+2*y+2*x)-1)/(z+2*y+2*x)+HFloat(0.028710955764376392)*(z*exp(z+2*y+2*x)+2*x+2*y)/(z+2*y+2*x), (2, 1) = HFloat(0.06946536682494289)*(2*x*exp(z+2*y+2*x)+2*y+z)/(z+2*y+2*x)+HFloat(0.1639939206130015)*x*(exp(z+2*y+2*x)-1)/(z+2*y+2*x), (2, 2) = HFloat(0.19172860000664235)*y*(exp(z+2*y+2*x)-1)/(z+2*y+2*x)+HFloat(0.055598027128122465)*(2*y*exp(z+2*y+2*x)+2*x+z)/(z+2*y+2*x), (2, 3) = HFloat(0.25012678790613074)*z*(exp(z+2*y+2*x)-1)/(z+2*y+2*x)+HFloat(0.052797866356756575)*(z*exp(z+2*y+2*x)+2*x+2*y)/(z+2*y+2*x), (3, 1) = HFloat(0.08382084470713112)*(2*x*exp(z+2*y+2*x)+2*y+z)/(z+2*y+2*x)+HFloat(0.20194817090220213)*x*(exp(z+2*y+2*x)-1)/(z+2*y+2*x), (3, 2) = HFloat(0.2352831718385749)*y*(exp(z+2*y+2*x)-1)/(z+2*y+2*x)+HFloat(0.06715334423894474)*(2*y*exp(z+2*y+2*x)+2*x+z)/(z+2*y+2*x), (3, 3) = HFloat(0.30194837789215173)*z*(exp(z+2*y+2*x)-1)/(z+2*y+2*x)+HFloat(0.06764148242431263)*(z*exp(z+2*y+2*x)+2*x+2*y)/(z+2*y+2*x)})

(4)

MEint := map(proc (c) options operator, arrow; int(c, t = 0 .. infinity) end proc, ME*dF)

MEint := Matrix(3, 3, {(1, 1) = 0.1000000000e-17*(0.2695896533e18*x*exp(z+2.*y+2.*x)-0.1102197779e18*x+0.1593698754e18*y+0.7968493772e17*z)/(z+2.*y+2.*x), (1, 2) = 0.2000000000e-18*(0.1347948267e19*y*exp(z+2.*y+2.*x)+0.4075441106e18*x-0.9404041560e18*y+0.2037720553e18*z)/(z+2.*y+2.*x), (1, 3) = 0.2000000000e-18*(0.1347948267e19*z*exp(z+2.*y+2.*x)+0.2871095576e18*x+0.2871095576e18*y-0.1204393488e19*z)/(z+2.*y+2.*x), (2, 1) = 0.4000000000e-18*(0.7573116357e18*x*exp(z+2.*y+2.*x)-0.4099848015e18*x+0.3473268341e18*y+0.1736634171e18*z)/(z+2.*y+2.*x), (2, 2) = 0.2000000000e-18*(0.1514623271e19*y*exp(z+2.*y+2.*x)+0.5559802713e18*x-0.9586430000e18*y+0.2779901356e18*z)/(z+2.*y+2.*x), (2, 3) = 0.2000000000e-18*(0.1514623271e19*z*exp(z+2.*y+2.*x)+0.5279786636e18*x+0.5279786636e18*y-0.1250633940e19*z)/(z+2.*y+2.*x), (3, 1) = 0.1000000000e-17*(0.3695898603e18*x*exp(z+2.*y+2.*x)-0.2019481709e18*x+0.1676416894e18*y+0.8382084471e17*z)/(z+2.*y+2.*x), (3, 2) = 0.1000000000e-18*(0.3695898603e19*y*exp(z+2.*y+2.*x)+0.1343066885e19*x-0.2352831718e19*y+0.6715334424e18*z)/(z+2.*y+2.*x), (3, 3) = 0.2000000000e-18*(0.1847949302e19*z*exp(z+2.*y+2.*x)+0.6764148242e18*x+0.6764148242e18*y-0.1509741889e19*z)/(z+2.*y+2.*x)})

(5)

Equate, "unable to equate these objects"

{x = .1307909150, y = .1006896044, z = 0.9590171029e-1}

(6)

``

``

NULL

NULL

NULL

NULL

``


Download ex.mw

 

 

Lambert

November 17 2014 Markiyan Hirnyk 6208
1 2

solve(b*x*ln(x)-x*ln(a)+a = 0, x);

 

exp((LambertW(-a*exp(-ln(a)/b)/b)*b+ln(a))/b)

See ?Lambert.

By Explore

November 15 2014 Markiyan Hirnyk 6208
0 1

How about

Explore(plot(_C1*exp(-1.*t)*sin(.57736*t)+_C2*exp(-1.*t)*cos(.57736*t), t = -2 .. 2));,

choosing _C1=-10.0..10.0 and _C2=-10.0..10.0?

In detail

November 12 2014 Markiyan Hirnyk 6208
2 7

The summand in N1 has singularities at the nonnegative integers:

.

The ones can be removed in such a way.

.

At last,

sum.mw

Bug in inequal

November 10 2014 Markiyan Hirnyk 6208
0 3

Your question is unclearly formulated. If you mean

plots:-inequal((2*c-1)/(3*c-1)>0,c=0..1.5,Alpha=0..1);

which produces an empty plot, then it is a bug. There is a workaround

plots:-implicitplot((2*c-1)/(3*c-1) > 0, c = 0 .. 1.5, alpha = 0 .. 1, filled);

As far as I remember it, this is a known bug in inequal: an inequality in one variable is not correctly displayed as an inequality in two variables.

Through parametrization

November 08 2014 Markiyan Hirnyk 6208
0 0

This can be found in usual way of calculus.  First, we find the parametrization of the space curve under consideration:

sol := solve({z = x^2+2*y^2, z = -2*x^2-y^2+3}, {x, y});

{x = RootOf(_Z^2+z-2), y = RootOf(_Z^2-z+1)}

Next,

allvalues(sol);

{x = sqrt(-z+2), y = sqrt(z-1)}, {x = sqrt(-z+2), y = -sqrt(z-1)}, {x = -sqrt(-z+2), y = sqrt(z-1)}, {x = -sqrt(-z+2), y = -sqrt(z-1)}

Now the variables x and y are expressed through z in the interval from 1 to 2. It should be noted that the curve splits in the four parametrized curves having the same length.

We plot it by

A := plots:-spacecurve([sqrt(-z+2), sqrt(z-1), z], z = 1 .. 2); B := plots:-spacecurve([sqrt(-z+2), -sqrt(z-1), z], z = 1 .. 2); C := plots:-spacecurve([-sqrt(-z+2), sqrt(z-1), z], z = 1 .. 2); E := plots:-spacecurve([-sqrt(-z+2), -sqrt(z-1), z], z = 1 .. 2);
plots:-display([A, B, C, E], axes = frame);

Second, we find its length numerically:

VectorCalculus:-ArcLength(z -><sqrt(-z+2), sqrt(z-1), z>, 1 .. 2, inert); 4*evalf(%);

7.640395580

 

Singularity?

November 06 2014 Markiyan Hirnyk 6208
0 0

Trying it with the DirectSearch package (the one should be downloaded and installed in your Maple.) instead of GlobalOptimization, I obtain

err(.5, 10, 200, .5, 7000, 2, .5, 1, 3);

                  HFloat(0.004863795374811606)
DirectSearch:-GlobalOptima(err, {A = .5 .. 2, B = 1 .. 5, c0 = 0 .. 1, h1 = 100 .. 15000, h2 = 0 .. .5, kp = 0 .. 1, ks = 0 .. 1, n = 1 .. 20, s0 = 150 .. 250});

Error, (in st1) cannot evaluate the solution further right of .78462143, probably a singularity

Likely no solutions

October 28 2014 Markiyan Hirnyk 6208
0 0

You deal with a system of 10 equation in more than 10 unknowns: 

sol1 := fsolve({eq[0], eq[1], eq[2], eq[3], eq[4], eq[5], eq[6], eq[7], eq[8], eq[9], eq[10]}, {f[-2], f[1], f[2], f[3], f[4], f[5], f[6], f[7], f[8], f[9], f[10]}, {theta[1], theta[2], theta[3], theta[4], theta[5], theta[6], theta[7], theta[8], theta[9], theta[10]});

Your syntax is not correct. The fsolve command deals only with systems having the same number of equations and unknowns. I tried it with the Direct Search:-SolveEquations with the AllSolutions option: it cannot find any feasible point.

By parametric=full option

October 25 2014 Markiyan Hirnyk 6208
0 0

This can be solved as follows.

solve({eq1, eq2}, z, parametric = full);

piecewise(-x1-x2-x3-x4+m = 0, [{z = -a*m}], -x1-x2-x3-x4+m <> 0, [])

By Statistics[TwoSampleTTest]

October 24 2014 Markiyan Hirnyk 6208
0 1

Take a look at Statistics[TwoSampleTTest].

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