MaplePrimes Questions

Dear Sir(Madam) 

I plot a spacecurve,which is an intersection of two surface,x+y+z=5 and x*y+y*z+z*x=0.The curve is shown below.

Then I want the curve's color changes accroding to the value of x*y*z.From the help page,I learn that the colorscheme option can make the color of different parts of a surface change accroding to the value of an user given function.However,it does not apply to all Plots' package command.You need to use the display command,colorscheme option with the option "overrideoptions",to force the graph's color to changed to desired.

P1 is the graph of the curve.

The first code works well,it is just a test.

display(P1,colorscheme=["Orange","Blue"],overrideoptions)

The second code fail to chage color(In my document,I use 2-D Math Input,following the example)

display(P1, colorscheme = ["xyzcoloring", proc (x, y, z) options operator, arrow; x*y*z end proc], overrideoptions)

This is the trouble I encountered.So,please help me use this option correctly,or is there any other way to achieve my goal?

Thank you in advance.

The file here.

problem_with_colorscheme_option.mw

Hi all,

I have a system of nonlinear equations with for equations, 4 variables I want to solve for, and 2 parameters. All of the variables and parameters must be non-negative.

The code I used to try to do this is:

Where eqi (i = 1, ... , 4) are expression (not equations in themselves). For example, eq1 is:

 

When I try to run this code I get the following error:

"Error, (in SolveTools:-Inequality:-Piecewise) piecewise takes at least 2 parameters"

 

Can anyone help me how I can make Maple do what I want here? :)

 

Thank you in advance,

JTamas

 

Hello,

I have the general function F(x,g(y)), and I don't understand the following notation of the derivative of  F w.r.t  y in Maple ?  What is D2(F) ?  Can we provide a concrete example ?

Thank you!

When I try to find the trace of the product of Dirac Gamma matrices with variable indices, I get a different answer than in textbook. The product is Dgamma[~mu]Dgamma[~nu]Dgamma[~rho]Dgamma[~sigma]Dgamma[~5]. The answer I get using Maple is 0. The textbook answer is -4*i*epsilon[~mu,~nu,~rho,~sigma](Levi-Civita symbol). I verified this using Maple with using 1,2,3,4 and 2,1,3,4 for mu,nu,rho,sigma. I think I'm probably the one doing something wrong. Maple 2019 on Mac with Physics package default standard setup.

While using the Physics package in Maple 2018, I am facing a few hurdles. In the file tov.mw ,

1. I have defined a dual-vector with components $u_a$ in step 12, but when I am trying to compute $g(u,u)$ using SumOverRepeatedIndices  in step 15, it is not evaluating the sum.

2. I want to define a tensor $B_{ab}=\nabla_a u_b$. Do I just write Define(B{a,b}=D_[a] u[b]) ?

3. Is there any command to find the symmetric and antisymmetric components and trace of the tensor B or do we evaluate them by writing out the expressions?

Thank you.

Dear, 

Please, may I ask your help with the following problem? 

I have to print something like this: 

Days 4,5,6 is closed. 

4,5,6 is the content of a list.  I enter: 

d:=[4,5,6];

printf("Days %a is closed\n", d[]);

but Maple returns:

Days 4 is closed

Of course, if I enter  printf("Days %a, %a, %a is closed\n", d[]);

I get the correct result: Days 4,5,6 is closed. 

However, the numer of elements the list will have vary from case to case and according to the procedure I'm running so I cannot enter the command with the exact number of %a. How could I overcome this problem?

Many thanks for your help. 

 

Hi all,

I have the following function (with parameters/constants a, b, and p2A ):

 

I want to calculate its partial derivative with resprect to p1A. I entered the following code to do this:

But this returns a result that was (at least, for me) unexpected:

My problem is, I don't really get what the expressions 'D(...)' mean in this equation and why they are even there. a and p2A are supposed to be constant and thus their derivative should be zero (wtih respect to p1A ).

I think this should be an easy problem to solve for someone more familiar with Maple, but I am new to it and have been spending the last few hours trying to figure out how to solve this problem. Any help would be highly appriciated.

 

Thank you in advance,

JTamas

restart; with(plots); _EnvHorizontalName := 'x'; _EnvVerticalName := 'y'; para := -2*p*x+y^2 = 0; para1 := -2*p1*x+y^2 = 0; t := y-m*x-p/(2*m) = 0; t1 := y+x/m+(1/2)*p1*m = 0; sol := op(solve([t, t1], [x, y])); eliminate({rhs(sol[1]), rhs(sol[2])}, m); for example : m := 2; p := 1; p1 := -2; PARA := implicitplot(para, x = -3 .. 3, y = -3 .. 3, color = blue); PARA1 := implicitplot(para1, x = -3 .. 3, y = -3 .. 3, color = green); Tang := implicitplot(t, x = -3 .. 3, y = -3 .. 3, color = brown); Tang1 := implicitplot(t1, x = -3 .. 3, y = -3 .. 3, color = aquamarine); NULL; #m is not constant display([PARA, PARA1, Tang, Tang1], view = [-3 .. 3, -3 .. 3], scaling = constrained);#on what curve is the vertex of the angle of 2 tangents ? Thank you.

i have a function which contains Ln and arctan fanctions in which the output function is complex.
how can i implicitplot this complex function? tnx for the help
 

restart

with(plots, implicitplot)

ode := diff(y(w), w)+(sqrt((12*Pi)(y(w)^2+m^2*w^2))*y(w)+m^2*w)/y(w) = 0

diff(y(w), w)+(2*3^(1/2)*Pi(y(w)^2+m^2*w^2)^(1/2)*y(w)+m^2*w)/y(w) = 0

(1)

Ans := dsolve([ode])

[{ln(w)+(1/4)*ln(-m^4-2*m^2*y(w)^2/w^2-y(w)^4/w^4+12*y(w)^2*Pi/w^2)-(3/2)*arctan((1/4)*(-2*m^2-2*y(w)^2/w^2+12*Pi)/(3*Pi*m^2-9*Pi^2)^(1/2))*Pi/(3*Pi*m^2-9*Pi^2)^(1/2)+(1/4)*ln(2*Pi^(1/2)*3^(1/2)*y(w)/w-y(w)^2/w^2-m^2)-(3/2)*arctan((1/2)*(2*Pi^(1/2)*3^(1/2)-2*y(w)/w)/(m^2-3*Pi)^(1/2))/((3*m^2-9*Pi)/Pi)^(1/2)-(1/4)*ln(2*Pi^(1/2)*3^(1/2)*y(w)/w+m^2+y(w)^2/w^2)+(3/2)*arctan((1/2)*(2*y(w)/w+2*Pi^(1/2)*3^(1/2))/(m^2-3*Pi)^(1/2))/((3*m^2-9*Pi)/Pi)^(1/2)-_C1 = 0}]

(2)

P:=subs(y(w)=Y,eval(lhs(Ans[1, 1]), [_C1 = 0, m = 1]))

ln(w)+(1/4)*ln(-1-2*Y^2/w^2-Y^4/w^4+12*Y^2*Pi/w^2)-(3/2)*arctan((1/4)*(-2-2*Y^2/w^2+12*Pi)/(-9*Pi^2+3*Pi)^(1/2))*Pi/(-9*Pi^2+3*Pi)^(1/2)+(1/4)*ln(2*Pi^(1/2)*3^(1/2)*Y/w-Y^2/w^2-1)-(3/2)*arctan((1/2)*(2*Pi^(1/2)*3^(1/2)-2*Y/w)/(1-3*Pi)^(1/2))/((-9*Pi+3)/Pi)^(1/2)-(1/4)*ln(2*Pi^(1/2)*3^(1/2)*Y/w+1+Y^2/w^2)+(3/2)*arctan((1/2)*(2*Y/w+2*Pi^(1/2)*3^(1/2))/(1-3*Pi)^(1/2))/((-9*Pi+3)/Pi)^(1/2)

(3)

implicitplot(P,w=-10..0,Y=0..10)

 

evalf((eval(P,[w=1,Y=1])))

1.655474573+.8307038310*I

(4)

 

 


 

Download P2.mw

The sphere with radius 0.5 whose center has y coordinate = 0.5 and z coordinate = 0.5 is tangent internally to the ellipsoid centered on the origin with principal semi axes of 5, 3 and 2.

How can the x coordinate of the sphere's center be determined?

   I need to integrate x with a<=x<=b and k , l are constants.

I input foolowing code , it did not work. Maybe you have some good ideas to solve this! thanks!

int(sqrt(1+((k*Pi)/l*cos((Pi*x)/l))^2), x = a.. b) assuming x>=a, x<=b

I am trying to solve the pde:= (d/dt)^2v+(d/dx)^2v+v=0 with initial boundary conditions v=xexp(x^2)

I use pdsolve to get v but I wish to tell pdsolve to use a different numerical method because my output of v is coming out like a step function.

The time taken for thread is comparitively higher in following case. how to decrease time in threads

 

thread_time.mw

Dear reader,

Have to create digital questions in Mobius on quaternions. Aim is to teach students of robot engineering about rotations besides the matrix rotations. Made some code, it works but very simplistic. I could not load a quarternion-toolbox.

Any suggestions?

# quaternion product
# define two vecotrs p and q:
$p0=range(3,3,1);
$px=range(1,1,1);
$py=range(-2,-2,1);
$pz=range(1,1,1);
$q0=range(2,2,1);
$qx=range(-1,-1,1);
$qy=range(2,2,1);
$qz=range(3,3,1);
$p=maple("Vector([$px,$py,$pz])");
$q=maple("Vector([$qx,$qy,$qz])");
$displayp=maple("printf(MathML:-ExportPresentation($p))");
$displayq=maple("printf(MathML:-ExportPresentation($q))");
# p.q=p0.q0-(p.q)+p0.q+q0.p+p*q
# scalar part
$dot=maple("LinearAlgebra[DotProduct]($p,$q,conjugate=false)");
$scalar_part=$p0*$q0-$dot;
# vector part
$cross=maple("LinearAlgebra[CrossProduct]($p,$q)");
$p0q=maple("LinearAlgebra[MatrixMatrixMultiply]($p0,$q)");
$q0p=maple("LinearAlgebra[MatrixMatrixMultiply]($q0,$p)");
$pq=maple("LinearAlgebra[VectorAdd]($p0q,$q0p)");
$vector_part=maple("LinearAlgebra[VectorAdd]($pq,$cross)");
$displayvector_part=maple("printf(MathML:-ExportPresentation($vector_part))");
# unit vectors
$i=maple("Vector([1,0,0])");
$j=maple("Vector([0,1,0])");
$k=maple("Vector([0,0,1])");
# generate answers
$x=maple("LinearAlgebra[DotProduct]($vector_part,$i)");
$y=maple("LinearAlgebra[DotProduct]($vector_part,$j)");
$z=maple("LinearAlgebra[DotProduct]($vector_part,$k)");
 

Best regards,

Nico Booij

I have recently received a doc from my friend in privete group in maple cloud, the table showed both eye(view) icon and download icon).When I downloaded and run, the document does not run (maple 2019). 

When I sign in maple cloud and see the doc (only view button is ahow), the same document works fine. What could be the error?

I attach  a document extract showing the errors (unable to delimt   .../  identifiers).

Can any one help us please?

Thanks. Ramki.
 

``

"Refraction Demonstration          restart:with(plots):  RefractionDemo:=proc(theta1, n2)  local theta2,ainput,ainside,aoutput,box,line1,line2,H,n2text,theta1text,theta2text;   if(theta1<0)or(theta1>Pi/(2.0001)) then return end if;   #theta1:=theta01*Pi180.;   theta2:=arcsin(1/(n2)*sin(theta1));   ainput:=arrow(?&ndash;cos(theta1),&ndash;sin(theta1)?,?cos(theta1),sin(theta1)?,color="Red"):   ainside:=arrow(?0,0?,?1,tan(theta2)?,color="DarkBlue",width=[0.05,relative=false]):   aoutput:=arrow(?1,tan(theta2)?,?cos(theta1),sin(theta1)?,color="Red"):   line1:=plot(0,x=&ndash;1..0,thickness=4,color=black);   line2:=plot(tan(theta2),x=1..2,thickness=4,color=black);   H:=1.8:   box:=plottools:&ndash;rectangle([0,&ndash;H],[1,H],color="LightBlue"):   n2text:=textplot([0.5,1.5,sprintf("n_2=%1.3 g",n2)]);   theta1text:=textplot([&ndash;0.5,0.4,sprintf("theta_1=%4.3 g",theta1)]);   theta2text:=textplot([0.5,&ndash;0.4,sprintf("theta_2=%4.3 g",theta2)]);   display([ainput,ainside,aoutput,box,line1,line2,n2text,theta1text,theta2text],scaling=constrained,view=[&ndash;1..2,&ndash;1..H]);   endproc:        Light enters from the air into a medium at an angle of theta1 relative to the normal. It is refracted to an angle of theta2and travels through the medium, returning back to the air.      You can vary two parameters:       theta1the angle of incidence       n2the index of refraction of the medium*(assuming the index of refraction of the air is essentially 1.0).     To do: Let it execute and start manipulating the sliders.     >Explore(RefractionDemo(theta1,n2),parameters=[theta1=0..Pi2.0015,n2=1..3.]);6""

Error, unable to delimit strings/identifiers

"Refraction Demonstration          restart:with(plots):  RefractionDemo:=proc(theta1, n2)  local theta2,ainput,ainside,aoutput,box,line1,line2,H,n2text,theta1text,theta2text;   if(theta1<0)or(theta1>Pi/2.0001) then return end if;   #theta1:=theta01*Pi180.;   theta2:=arcsin(1/n2*sin(theta1));   ainput:=arrow(&acirc;ï¿&frac12;&uml;&ndash;cos(theta1),&ndash;sin(theta1)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):   ainside:=arrow(&acirc;ï¿&frac12;&uml;0,0&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,color="DarkBlue",width=[0.05,relative=false]):   aoutput:=arrow(&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):   line1:=plot(0,x=&ndash;1..0,thickness=4,color=black);   line2:=plot(tan(theta2),x=1..2,thickness=4,color=black);   H:=1.8:   box:=plottools:&ndash;rectangle([0,&ndash;H],[1,H],color="LightBlue"):   n2text:=textplot([0.5,1.5,sprintf("n_2=%1.3 g",n2)]);   theta1text:=textplot([&ndash;0.5,0.4,sprintf("theta_1=%4.3 g",theta1)]);   theta2text:=textplot([0.5,&ndash;0.4,sprintf("theta_2=%4.3 g",theta2)]);   display([ainput,ainside,aoutput,box,line1,line2,n2text,theta1text,theta2text],scaling=constrained,view=[&ndash;1..2,&ndash;1..H]);   endproc:        Light enters from the air into a medium at an angle of theta1 relative to the normal. It is refracted to an angle of theta2and travels through the medium, returning back to the air.      You can vary two parameters:       theta1the angle of incidence       n2the index of refraction of the medium*(assuming the index of refraction of the air is essentially 1.0).     To do: Let it execute and start manipulating the sliders.     >Explore(RefractionDemo(theta1,n2),parameters=[theta1=0..Pi2.0015,n2=1..3.]);"

 

``

``

``

``Dear Prof.

The following code seems not copying properly (my communication error be allowed please)

 

"ainput:=arrow(?&"

Error, unable to delimit strings/identifiers

"ainput:=arrow(&acirc;ï¿&frac12;&uml;&ndash;cos(theta1),&ndash;sin(theta1)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):ainside:=arrow(&acirc;ï¿&frac12;&uml;0,0&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,color="DarkBlue",width=[0.05,relative=false]):aoutput:=arrow(&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):"

 

``

``

"I checked by typing separately. It works as below."

``

``

a1 := arrow([-cos(theta1), -sin(theta1)], color = "LightBlue")

 

``ainput := arrow([-1, 0], color = "Red")

 

"But the copied from your code does not work."

"ainput:=arrow([-1, 0],color= "`Red"`)"

Error, unable to delimit strings/identifiers

"ainput:=arrow([-1, 0],color= "`Red"`)"

 

``


 

Download forScotgould_Error_arrow.mw

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