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the maximize of equation...

Asked by: beidouxing 10
max maximize
December 18 2014
0  6

I want to solve maximize of equation,but the maximize failed to solve it,who can help me.thanks.

c[1] := (1/8)*w*{(1/((x+y+z)^2+1))^(3/2)+(1/((x+y)^2+1))^(3/2)+(1/((x+z)^2+1))^(3/2)+(1/((y+z)^2+1))^(3/2)+(1/(x^2+1))^(3/2)+(1/(y^2+1))^(3/2)+(1/(z^2+1))^(3/2)+1}+(1/8)*{x/((x+y+z)^2+1)+x/((x+y)^2+1)+x/((x+z)^2+1)+x/(x^2+1)}:

c[2] := (1/8)*w*{(1/((x+y+z)^2+1))^(3/2)+(1/((x+y)^2+1))^(3/2)+(1/((x+z)^2+1))^(3/2)+(1/((y+z)^2+1))^(3/2)+(1/(x^2+1))^(3/2)+(1/(y^2+1))^(3/2)+[1/(z^2+1)]^(3/2)+1}+(1/8)*{y/((x+y+z)^2+1)+y/((x+y)^2+1)+y/((y+z)^2+1)+y/(y^2+1)}:

t[1] := diff(c[1], x);

(1/8)*w*{-(3/2)*(1/((x+y+z)^2+1))^(1/2)*(2*x+2*y+2*z)/((x+y+z)^2+1)^2-(3/2)*(1/((x+y)^2+1))^(1/2)*(2*x+2*y)/((x+y)^2+1)^2-(3/2)*(1/((x+z)^2+1))^(1/2)*(2*x+2*z)/((x+z)^2+1)^2-3*(1/(x^2+1))^(1/2)*x/(x^2+1)^2}+(1/8)*{1/((x+y+z)^2+1)-x*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-x*(2*x+2*y)/((x+y)^2+1)^2+1/((x+z)^2+1)-x*(2*x+2*z)/((x+z)^2+1)^2+1/(x^2+1)-2*x^2/(x^2+1)^2}

 (1)

t[2] := diff(c[2], y);

(1/8)*w*{-(3/2)*(1/((x+y+z)^2+1))^(1/2)*(2*x+2*y+2*z)/((x+y+z)^2+1)^2-(3/2)*(1/((x+y)^2+1))^(1/2)*(2*x+2*y)/((x+y)^2+1)^2-(3/2)*(1/((y+z)^2+1))^(1/2)*(2*y+2*z)/((y+z)^2+1)^2-3*(1/(y^2+1))^(1/2)*y/(y^2+1)^2}+(1/8)*{1/((x+y+z)^2+1)-y*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-y*(2*x+2*y)/((x+y)^2+1)^2+1/((y+z)^2+1)-y*(2*y+2*z)/((y+z)^2+1)^2+1/(y^2+1)-2*y^2/(y^2+1)^2}

 (2)

eliminate({t[1], t[2]}, w);

[{w = -{1/((x+y+z)^2+1)-y*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-y*(2*x+2*y)/((x+y)^2+1)^2+1/((y+z)^2+1)-y*(2*y+2*z)/((y+z)^2+1)^2+1/(y^2+1)-2*y^2/(y^2+1)^2}/{-(3/2)*(1/(x^2+2*x*y+2*x*z+y^2+2*y*z+z^2+1))^(1/2)*(2*x+2*y+2*z)/((x+y+z)^2+1)^2-(3/2)*(1/(x^2+2*x*y+y^2+1))^(1/2)*(2*x+2*y)/((x+y)^2+1)^2-(3/2)*(1/(y^2+2*y*z+z^2+1))^(1/2)*(2*y+2*z)/((y+z)^2+1)^2-3*(1/(y^2+1))^(1/2)*y/(y^2+1)^2}}, {{1/((x+y+z)^2+1)-x*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-x*(2*x+2*y)/((x+y)^2+1)^2+1/((x+z)^2+1)-x*(2*x+2*z)/((x+z)^2+1)^2+1/(x^2+1)-2*x^2/(x^2+1)^2}*{-(3/2)*(1/(x^2+2*x*y+2*x*z+y^2+2*y*z+z^2+1))^(1/2)*(2*x+2*y+2*z)/((x+y+z)^2+1)^2-(3/2)*(1/(x^2+2*x*y+y^2+1))^(1/2)*(2*x+2*y)/((x+y)^2+1)^2-(3/2)*(1/(y^2+2*y*z+z^2+1))^(1/2)*(2*y+2*z)/((y+z)^2+1)^2-3*(1/(y^2+1))^(1/2)*y/(y^2+1)^2}-{1/((x+y+z)^2+1)-y*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-y*(2*x+2*y)/((x+y)^2+1)^2+1/((y+z)^2+1)-y*(2*y+2*z)/((y+z)^2+1)^2+1/(y^2+1)-2*y^2/(y^2+1)^2}*{-(3/2)*(1/(x^2+2*x*y+2*x*z+y^2+2*y*z+z^2+1))^(1/2)*(2*x+2*y+2*z)/((x+y+z)^2+1)^2-(3/2)*(1/(x^2+2*x*y+y^2+1))^(1/2)*(2*x+2*y)/((x+y)^2+1)^2-(3/2)*(1/(x^2+2*x*z+z^2+1))^(1/2)*(2*x+2*z)/((x+z)^2+1)^2-3*(1/(x^2+1))^(1/2)*x/(x^2+1)^2}}]

 (3)

w = -(1/((x+y+z)^2+1)-y*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-y*(2*x+2*y)/((x+y)^2+1)^2+1/((y+z)^2+1)-y*(2*y+2*z)/((y+z)^2+1)^2+1/(y^2+1)-2*y^2/(y^2+1)^2)/(-(3/2)*sqrt(1/(x^2+2*x*y+2*x*z+y^2+2*y*z+z^2+1))*(2*x+2*y+2*z)/((x+y+z)^2+1)^2-(3/2)*sqrt(1/(x^2+2*x*y+y^2+1))*(2*x+2*y)/((x+y)^2+1)^2-(3/2)*sqrt(1/(y^2+2*y*z+z^2+1))*(2*y+2*z)/((y+z)^2+1)^2-3*sqrt(1/(y^2+1))*y/(y^2+1)^2);

w = -(1/((x+y+z)^2+1)-y*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-y*(2*x+2*y)/((x+y)^2+1)^2+1/((y+z)^2+1)-y*(2*y+2*z)/((y+z)^2+1)^2+1/(y^2+1)-2*y^2/(y^2+1)^2)/(-(3/2)*(1/(x^2+2*x*y+2*x*z+y^2+2*y*z+z^2+1))^(1/2)*(2*x+2*y+2*z)/((x+y+z)^2+1)^2-(3/2)*(1/(x^2+2*x*y+y^2+1))^(1/2)*(2*x+2*y)/((x+y)^2+1)^2-(3/2)*(1/(y^2+2*y*z+z^2+1))^(1/2)*(2*y+2*z)/((y+z)^2+1)^2-3*(1/(y^2+1))^(1/2)*y/(y^2+1)^2)

 (4)

sub(w = -(1/((x+y+z)^2+1)-y*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-y*(2*x+2*y)/((x+y)^2+1)^2+1/((y+z)^2+1)-y*(2*y+2*z)/((y+z)^2+1)^2+1/(y^2+1)-2*y^2/(y^2+1)^2)/(-(3/2)*(1/(x^2+2*x*y+2*x*z+y^2+2*y*z+z^2+1))^(1/2)*(2*x+2*y+2*z)/((x+y+z)^2+1)^2-(3/2)*(1/(x^2+2*x*y+y^2+1))^(1/2)*(2*x+2*y)/((x+y)^2+1)^2-(3/2)*(1/(y^2+2*y*z+z^2+1))^(1/2)*(2*y+2*z)/((y+z)^2+1)^2-3*(1/(y^2+1))^(1/2)*y/(y^2+1)^2), c[1]);

sub(w = -(1/((x+y+z)^2+1)-y*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-y*(2*x+2*y)/((x+y)^2+1)^2+1/((y+z)^2+1)-y*(2*y+2*z)/((y+z)^2+1)^2+1/(y^2+1)-2*y^2/(y^2+1)^2)/(-(3/2)*(1/(x^2+2*x*y+2*x*z+y^2+2*y*z+z^2+1))^(1/2)*(2*x+2*y+2*z)/((x+y+z)^2+1)^2-(3/2)*(1/(x^2+2*x*y+y^2+1))^(1/2)*(2*x+2*y)/((x+y)^2+1)^2-(3/2)*(1/(y^2+2*y*z+z^2+1))^(1/2)*(2*y+2*z)/((y+z)^2+1)^2-3*(1/(y^2+1))^(1/2)*y/(y^2+1)^2), (1/8)*w*{(1/((x+y+z)^2+1))^(3/2)+(1/((x+y)^2+1))^(3/2)+(1/((x+z)^2+1))^(3/2)+(1/((y+z)^2+1))^(3/2)+(1/(x^2+1))^(3/2)+(1/(y^2+1))^(3/2)+(1/(z^2+1))^(3/2)+1}+(1/8)*{x/((x+y+z)^2+1)+x/((x+y)^2+1)+x/((x+z)^2+1)+x/(x^2+1)})

 (5)

subs(w = -(1/((x+y+z)^2+1)-y*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-y*(2*x+2*y)/((x+y)^2+1)^2+1/((y+z)^2+1)-y*(2*y+2*z)/((y+z)^2+1)^2+1/(y^2+1)-2*y^2/(y^2+1)^2)/(-(3/2)*(1/(x^2+2*x*y+2*x*z+y^2+2*y*z+z^2+1))^(1/2)*(2*x+2*y+2*z)/((x+y+z)^2+1)^2-(3/2)*(1/(x^2+2*x*y+y^2+1))^(1/2)*(2*x+2*y)/((x+y)^2+1)^2-(3/2)*(1/(y^2+2*y*z+z^2+1))^(1/2)*(2*y+2*z)/((y+z)^2+1)^2-3*(1/(y^2+1))^(1/2)*y/(y^2+1)^2), c[2]);

-(1/8)*(1/((x+y+z)^2+1)-y*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-y*(2*x+2*y)/((x+y)^2+1)^2+1/((y+z)^2+1)-y*(2*y+2*z)/((y+z)^2+1)^2+1/(y^2+1)-2*y^2/(y^2+1)^2)*{(1/((x+y+z)^2+1))^(3/2)+(1/((x+y)^2+1))^(3/2)+(1/((x+z)^2+1))^(3/2)+(1/((y+z)^2+1))^(3/2)+(1/(x^2+1))^(3/2)+(1/(y^2+1))^(3/2)+[1/(z^2+1)]^(3/2)+1}/(-(3/2)*(1/(x^2+2*x*y+2*x*z+y^2+2*y*z+z^2+1))^(1/2)*(2*x+2*y+2*z)/((x+y+z)^2+1)^2-(3/2)*(1/(x^2+2*x*y+y^2+1))^(1/2)*(2*x+2*y)/((x+y)^2+1)^2-(3/2)*(1/(y^2+2*y*z+z^2+1))^(1/2)*(2*y+2*z)/((y+z)^2+1)^2-3*(1/(y^2+1))^(1/2)*y/(y^2+1)^2)+(1/8)*{y/((x+y+z)^2+1)+y/((x+y)^2+1)+y/((y+z)^2+1)+y/(y^2+1)}

 (6)

"#"Iwant to maximize the equation (5)and (6),under the conditon of x,y,z are negative or positive at the same time.

 

NULL

 

Download maximize.mw

http://www.crystaloffice.com/contact.html...

Asked by: das1404 135
December 18 2014
1  1

 

I recently downloaded a Maple reader software program from

http://www.crystaloffice.com/

I'mpuzzled as I'm not sure if this has anything to do with the Maple mathematics software,  On cursory observation it just looks like a text editor.

  I was curious to know if there was any software available which would allow people to read & execute a Maple program on the Internet. 

Cheers

   David

 

How can I make a triangle with integer coordinates...

Asked by: toandhsp 305
geometry centroid
December 18 2014
1  10

I have some triangles ABC with vertices

1) A(-13,-5,5), B(-5,11,-11), C(-3,-9,15) has centre of out circle is (3, 3, 3), orthocentre (-27, -9, 3) and centroid (-7, -1, -3). 

2) A(-6,6,-1), B(-5,-1,-3), C(2,10,7) has centre of out circle is (1, 2, 3), orthocentre (-11, 11, -3) and centroid (-3, 5, 1). 

How can I write a program to find a triangle with integer coordinates of vertices, centroid, orthocenter and center of the triangle in geometry 3D? 

Directional derivative with tetrad...

Asked by: Michael_Watson 125
directional-derivatives
December 18 2014
0  1

Does anyone know how to incorporate the tetrad with the directional derivative? I tried using the SumOverIndices, but get crazy results. I know Maple can find the answer easily because I have done the same thing by hand. What am I missing?

The directional derivative should take the form f,1 = eaμ df/dxμ . The answer is Y,1 = dY/dζ – Ybar dY/du.  I obviously do not get this result.

 


restart; with(Physics); with(Tetrads)

0, "%1 is not a command in the %2 package", Tetrads, Physics

 (1)

`#msup(mi("ds",mathcolor = "#af00af"),mn("2",mathcolor = "#af00af"))` := Physics:-`*`(Physics:-`*`(2, dzeta), dzetabar)+Physics:-`*`(Physics:-`*`(2, du), dv)+Physics:-`*`(Physics:-`*`(2, H(zetabar, zeta, v, u)), (du+Physics:-`*`(Ybar(zetabar, zeta, v, u), dzeta)+Physics:-`*`(Y(zetabar, zeta, v, u), dzetabar)-Physics:-`*`(Physics:-`*`(Y(zetabar, zeta, v, u), Ybar(zetabar, zeta, v, u)), dv))^2)

2*dzeta*dzetabar+2*du*dv+2*H(zetabar, zeta, v, u)*(du+Ybar(zetabar, zeta, v, u)*dzeta+Y(zetabar, zeta, v, u)*dzetabar-Y(zetabar, zeta, v, u)*Ybar(zetabar, zeta, v, u)*dv)^2

 (2)

X = [zetabar, zeta, v, u]

X = [zetabar, zeta, v, u]

 (3)

PDEtools:-declare(`#msup(mi("ds",mathcolor = "#af00af"),mn("2",mathcolor = "#af00af"))`)

Ybar(zetabar, zeta, v, u)*`will now be displayed as`*Ybar

 (4)

Setup(automaticsimplification = true, coordinatesystems = (X = [zetabar, zeta, v, u]), metric = 2*dzeta*dzetabar+2*du*dv+2*H(zetabar, zeta, v, u)*(du+Ybar(zetabar, zeta, v, u)*dzeta+Y(zetabar, zeta, v, u)*dzetabar-Y(zetabar, zeta, v, u)*Ybar(zetabar, zeta, v, u)*dv)^2)

[automaticsimplification = true, coordinatesystems = {X}, metric = {(1, 1) = 2*H(X)*Y(X)^2, (1, 2) = 1+2*H(X)*Y(X)*Ybar(X), (1, 3) = -2*H(X)*Y(X)^2*Ybar(X), (1, 4) = 2*H(X)*Y(X), (2, 2) = 2*H(X)*Ybar(X)^2, (2, 3) = -2*H(X)*Ybar(X)^2*Y(X), (2, 4) = 2*H(X)*Ybar(X), (3, 3) = 2*H(X)*Y(X)^2*Ybar(X)^2, (3, 4) = 1-2*H(X)*Y(X)*Ybar(X), (4, 4) = 2*H(X)}]

 (5)

g_[]

g_[mu, nu] = (Matrix(4, 4, {(1, 1) = 2*H(X)*Y(X)^2, (1, 2) = 1+2*H(X)*Y(X)*Ybar(X), (1, 3) = -2*H(X)*Y(X)^2*Ybar(X), (1, 4) = 2*H(X)*Y(X), (2, 1) = 1+2*H(X)*Y(X)*Ybar(X), (2, 2) = 2*H(X)*Ybar(X)^2, (2, 3) = -2*H(X)*Ybar(X)^2*Y(X), (2, 4) = 2*H(X)*Ybar(X), (3, 1) = -2*H(X)*Y(X)^2*Ybar(X), (3, 2) = -2*H(X)*Ybar(X)^2*Y(X), (3, 3) = 2*H(X)*Y(X)^2*Ybar(X)^2, (3, 4) = 1-2*H(X)*Y(X)*Ybar(X), (4, 1) = 2*H(X)*Y(X), (4, 2) = 2*H(X)*Ybar(X), (4, 3) = 1-2*H(X)*Y(X)*Ybar(X), (4, 4) = 2*H(X)}))

 (6)

``

NULL

NULL

eqn3 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(X)), e_[1, `~mu`]))

((Y(X)*Ybar(X)-1)*(diff(Y(X), zetabar))+(Y(X)*Ybar(X)-1)*(diff(Y(X), zeta))+(diff(Y(X), u)+diff(Y(X), v))*(Y(X)+Ybar(X)))*2^(1/2)/((-(Ybar(X)^2+1)*(Y(X)^2+1)/(Y(X)+Ybar(X))^2)^(1/2)*(2*Y(X)+2*Ybar(X)))

 (7)

NULL

``

NULL


Download Directional_Derivative.mw

How can I solve float(infinity)? please help me....

Asked by: wenny 25
December 17 2014
0  6

Dear All,

I'm trying to solve the following in Maple.

minimize(int(0.1e-3+.5*t+0.2e-2*t^2-b*t-a, t = 0 .. 300), location = true)

But Maple told me that the answer is

Float(-infinity), {[{a = Float(infinity), b = Float(infinity)}, Float(-infinity)]}.

I really need to get a kind of numerical answer. Would it be possible? Please Help me!!

how to convert integer or decimal number into any ...

Asked by: LeeHoYeung 535
logic
December 17 2014
0  4

https://social.msdn.microsoft.com/Forums/vstudio/en-US/cc2a85ad-30ec-44ed-8c75-636ff71eade2/how-to-convert-integer-or-decimal-number-into-any-base-number?forum=csharpgeneral

1. for example how to convert decimal or integer number into base 3 number, base 5 number etc.

2.how to do logical operation with custom logic table for example,

 

120 special operator 235 

01111000

11101011

 

special operator according to logical table is

1st op 2nd op output
0 0 1
0 1 0
1 0 1
1 1 0

 

  01111000

  11101011

=00010100 = 20

homokinetic joint definition...

Asked by: federave 15
December 17 2014
0  1

Hi everybody,

is it possible to define an homokinetic joint in MapleSim for multibody modeling? How can I do that?

 

thanks.

Solving non-linear ODE...

Asked by: joha 50
ode dsolve
December 17 2014
2  22

Hi,

I'm trying to solve the following non-linear ODE numerically:

by ececuting

but maple gives me this error-message:

"Error, (in dsolve/numeric/make_proc) Could not convert to an explicit first order system due to 'RootOf'"

I couldnt find any useful information in the manual. What does this error mean? Is there something wrong with my maple code or is there just no solution for this particulare differential equation?

 

Thanks in advance

Inhomogeneous wave equation...

Asked by: bobred 20
solve pde
December 17 2014
1  7

Hi

I have this PDE and was wondering how I can get Maple to solve it

utt+2ut-uxx=18sin(3πx/l)

with conditions u(0,t)=u(l,t)=0 and u(x,0)=ut(x,0)=0

Thanks

James

 

 

 

How can error in fsolve be corrected?...

Asked by: emmantop 40
student fsolve
December 17 2014
1  2

Could anyone assist in rectifying this error ''Error, (in fsolve) {f[1], f[2], f[3], f[4], f[5], f[6], f[7], f[8], f[9], f[10], f[11], theta[11]} are in the equation, and are not solved for''. Here is the worksheet FDM_Revisit_1.mw

readline - output not being cleared...

Asked by: das1404 135
December 17 2014
0  5

The "program" below includes a readline statement.  This does not clear the former output when run again.  Is there any modification to correct this?

David

 

restart;
 with(plots):
 with(plottools):
 #f:=proc()
 #local c, numplayers:
 #numplayers:=4:
 #c:= rectangle([0,0], [11,11], color=red):
 #plots[display](c, scaling=constrained, view=[-0.8..11.5,-0.8..12],axes=BOXED);
 printf("Enter the number of players:\n");
 numplayers:=readline(terminal):
 printf("Number of players is %s\n",numplayers);
 #printf("Number of players is %d\n",numplayers);
 #return "foo";
 #end proc:
 #f();

Length of Output Exceeded Error when using tetrads...

Asked by: Michael_Watson 125
physics tetrads
December 16 2014
2  5

I am using the SumOverRepeatedIndices and get a Length of Output Exceeded error. Sometimes if I close the file and restart the program then I get a result and no error.  However, if I recalculate then I get the error.

 


restart; with(Physics); with(Tetrads)

[e_, eta_, gamma_, l_, lambda_, m_, mb_, n_]

 (1)

`#msup(mi("ds",mathcolor = "#af00af"),mn("2",mathcolor = "#af00af"))` := Physics:-`*`(Physics:-`*`(2, dzeta), dzetabar)+Physics:-`*`(Physics:-`*`(2, du), dv)+Physics:-`*`(Physics:-`*`(2, H(zeta, zetabar, u, v)), (du+Physics:-`*`(Ybar(zeta, zetabar, u, v), dzeta)+Physics:-`*`(Y(zeta, zetabar, u, v), dzetabar)-Physics:-`*`(Physics:-`*`(Y(zeta, zetabar, u, v), Ybar(zeta, zetabar, u, v)), dv))^2)

2*dzeta*dzetabar+2*du*dv+2*H(zeta, zetabar, u, v)*(du+Ybar(zeta, zetabar, u, v)*dzeta+Y(zeta, zetabar, u, v)*dzetabar-Y(zeta, zetabar, u, v)*Ybar(zeta, zetabar, u, v)*dv)^2

 (2)

X = [zeta, zetabar, u, v]

X = [zeta, zetabar, u, v]

 (3)

PDEtools:-declare(`#msup(mi("ds",mathcolor = "#af00af"),mn("2",mathcolor = "#af00af"))`)

Ybar(zeta, zetabar, u, v)*`will now be displayed as`*Ybar

 (4)

Setup(coordinates = (X = [zeta, zetabar, u, v]), metric = 2*dzeta*dzetabar+2*du*dv+2*H(zeta, zetabar, u, v)*(du+Ybar(zeta, zetabar, u, v)*dzeta+Y(zeta, zetabar, u, v)*dzetabar-Y(zeta, zetabar, u, v)*Ybar(zeta, zetabar, u, v)*dv)^2)

[coordinatesystems = {X}, metric = {(1, 1) = 2*H(X)*Ybar(X)^2, (1, 2) = 1+2*H(X)*Ybar(X)*Y(X), (1, 3) = 2*H(X)*Ybar(X), (1, 4) = -2*H(X)*Ybar(X)^2*Y(X), (2, 2) = 2*H(X)*Y(X)^2, (2, 3) = 2*H(X)*Y(X), (2, 4) = -2*H(X)*Y(X)^2*Ybar(X), (3, 3) = 2*H(X), (3, 4) = 1-2*H(X)*Ybar(X)*Y(X), (4, 4) = 2*H(X)*Y(X)^2*Ybar(X)^2}]

 (5)

g_[]

g_[mu, nu] = (Matrix(4, 4, {(1, 1) = 2*H(X)*Ybar(X)^2, (1, 2) = 1+2*H(X)*Ybar(X)*Y(X), (1, 3) = 2*H(X)*Ybar(X), (1, 4) = -2*H(X)*Ybar(X)^2*Y(X), (2, 1) = 1+2*H(X)*Ybar(X)*Y(X), (2, 2) = 2*H(X)*Y(X)^2, (2, 3) = 2*H(X)*Y(X), (2, 4) = -2*H(X)*Y(X)^2*Ybar(X), (3, 1) = 2*H(X)*Ybar(X), (3, 2) = 2*H(X)*Y(X), (3, 3) = 2*H(X), (3, 4) = 1-2*H(X)*Ybar(X)*Y(X), (4, 1) = -2*H(X)*Ybar(X)^2*Y(X), (4, 2) = -2*H(X)*Y(X)^2*Ybar(X), (4, 3) = 1-2*H(X)*Ybar(X)*Y(X), (4, 4) = 2*H(X)*Y(X)^2*Ybar(X)^2}))

 (6)

NULL

``

eqn1 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[1, `~mu`])) = 0

`[Length of output exceeds limit of 1000000]`

 (7)

eqn2 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[2, `~mu`])) = 0

`[Length of output exceeds limit of 1000000]`

 (8)

eqn3 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[4, `~mu`])) = x

(1/2)*(-(diff(Y(Zeta, zetabar, u, v), zetabar))*(Y(X)*Ybar(X)+1)*2^(1/2)+(diff(Y(Zeta, zetabar, u, v), u))*2^(1/2)*(Y(X)-Ybar(X))-(diff(Y(Zeta, zetabar, u, v), v))*2^(1/2)*(Y(X)-Ybar(X)))/((-(Ybar(X)^2+1)*(Y(X)^2+1)/(Y(X)-Ybar(X))^2)^(1/2)*(Y(X)-Ybar(X))) = x

 (9)

eqn1 := `[Length of output exceeds limit of 1000000]` = 0

`[Length of output exceeds limit of 1000000]` = 0

 (10)

algsubs(`[Length of output exceeds limit of 1000000]` = 0, `[Length of output exceeds limit of 1000000]`)

0

 (11)

``

simplify(`[Length of output exceeds limit of 1000000]`)

``


Download Derive_Eq_4.4.mw

Integral of natural logarithm finction...

Asked by: Chia 160
December 16 2014
0  4

Hello everyone,

I'm using Maple18, I tried to integrate the function including natural logarithm:

 

But we get the answer:

Is there any simple way to directly convert the answer to the kind of form we want? I cannot not finish the conversion:

 

So the toolbox "IntegrationTools" was used, but finally, we couldn't compute the integral:

 

 However, we can get the correct answer by manually inputting the formula.

 

Using IntegrationTools is pretty nasty and not very convenient, such as the problem I mentioned.

Does anyone have another solution?

Linear Optimization with nonlinear inequality cons...

Asked by: tlee 10
inequal
December 16 2014
2  0

In brief the problem can be stated as follows:

 

Given dependent variables Qi i=1,...,N and independent variables xi, yi, and zi i=1,...,N

which are related via the following system of N linear equations with parameters P1, P2 and P3 :

Qi = P1xi+P2yi+P3zi   i=1,...,N

How to find the optimal values of  P1, P2 and P3 which satisfy the above system of linear equations subject to the following constraints:

Pi>=0   i=1,2,3

and  P1>=P2P3

 Without the requirement of P1>=P2P3, the problem can be solved with the Non-negative Least Squares Method of Lawson and Hanson.  But with this additional constraint, I am stuck.  

 

Your suggestions are welcome.

 

 

 

 

Latex typesetting of delayDotProduct...

Asked by: highsciguy 75
typesetting latex export
December 16 2014
2  0

I would like to implement a rule for typeseting delayDotProduct in latex exports (in which this expressions appears in plain form). It corresponds to dot products of vectors/matrices with the "." operator. I tried to define 

`latex/Typesetting:-delayDotProduct`:=proc(f1,f2,f3)
sprintf("{ {%s}{%s} }",cat(`latex/print`(f1)),cat(`latex/print`(f2)))
end proc:

which does not do the job. 

Edit:

A related question: How can I make

D[1,1](x)(t)

produce x''(t) in latex output?

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