MaplePrimes Questions

I want the legend to be produced to look like the third to last example. https://fr.maplesoft.com/support/help/Maple/view.aspx?path=plots/contourplot 

However, mine keeps coming out like this.

hello how do i solve these equations and what type exactly are they ? so i can find more information

(i dont understand if this is a partial-something)

for the following function

f(y,z)=y*sin(z) + 2*cos(y)

i need to evaluate it at the following point

fy(pi/2,pi)  and  fz(pi/2,pi)

this is the part i dont understand how to do, i keep getting 0 in the equation.

 

thanks for you! and your time

I would like to "run" or execute parts of my code that I put in a same section. Unfortunately, selecting "Execute" when right-clicking on a section does nothing...

For entering system of linear ode's, from textbook, such as this example

I can either use x[1],x[2]  or x__1 and x__2.

Maple dsolve works with both. The Latex generated is also exactly the same Which is x_{1} and x_{2}.

The only minor difference I see is on the screen in the worksheet (I only use 1D), where the subscript looks a little nicer in the case of x[1] vs. x__1

The subscript in the case of x[1] is upright while the one in x__1 is italic. I like the first one more.

Other than this cosmetic difference, Are there are subtle sematic differences between the two forms in terms of computation? I know x[1] create table x. OK.  While x__1 is a separate symbol. No table is created.,

Which would be  a safer/better option to use in this case?   Or is it just a matter of choice?

sys:=[ diff(x[1](t),t)=x[1](t)+x[2](t),diff(x[2](t),t)=x[1](t)+3*x[2](t)];
sys:=[ diff(x__1(t),t)=x__1(t)+x__2(t),diff(x__2(t),t)=x__1(t)+3*x__2(t)];

In some way, using x__1(t) might be a little easier to read on the eye than x[1](t) since there is only one type of paranthesis involved.

ps. I tried to search for __ in Maple help to read more about it, but ?__ do not show it. I am sure __ is in the help under some other name.

How do I insert an empty or null value into a matrix imported from a csv file?  The imported data assumes the value is zero.

For display only purposes, to get the Latex looking better, I replace the constant of integrations Maple using which is _C1, _C2., etc... to c[1],c[2],..... 

This is something I do at the very end of computation, just before I get the Latex of the expression.

The way I do this now, is not good. .And I am asking if there is a better way to do this replacement. In Mathematica, I can do this using a patterm where I tell it to replace  C?  by c[?] where ? means anything.

Is it possible to do something like this in Maple? Here is an example

sol:=dsolve(diff(x(t),t$3) = x(t));

This gives solution as

And just before ask for the Latex of this, I change it to 

This is done using a function. Please see worksheet below.

The problem with the current solution is that I do not know how many _C there are, so I assumed 10 as worst case, which works for my case. But I prefer a more general solution, may be using pattern in the subs command?


 

restart;

replace_all_C:=proc(expr::anything)
local n,N,c;
local new_expr;
local max_count :=10; #worst case, since do not know how many

    new_expr:=expr;
    for n from 1 to max_count do
        N:=convert(n,string);
        new_expr:=subs( :-parse(cat("_C",N))=:-parse(cat("c[",N,"]")),new_expr);
    od:
    return new_expr;
end proc:

sol:=dsolve(diff(x(t),t$3) = x(t));
tmp:=replace_all_C(sol)

x(t) = _C1*exp(t)+_C2*exp(-(1/2)*t)*sin((1/2)*3^(1/2)*t)+_C3*exp(-(1/2)*t)*cos((1/2)*3^(1/2)*t)

x(t) = c[1]*exp(t)+c[2]*exp(-(1/2)*t)*sin((1/2)*3^(1/2)*t)+c[3]*exp(-(1/2)*t)*cos((1/2)*3^(1/2)*t)

 


 

Download q.mw

And now I get the latex of tmp in the above, instead of sol which looks better.

 

 

Can anyone help with plotting the logistic map as a function in Maple

Logistic map x_(n+1)=f(x_n); f(x_n)=r*X(1-x) with the following values:

r=2.0; x(1)=0.3 f=r.*x.*(1-x)

Please help? Thanks.

I created some simple maple 9 code to do some z->w mappings long time ago, on my web page:

https://ingalidakis.com/math/ComplexMaps.html

Upon revising my webpage, I've stumbled upon a page for comformal mappings, by David Bau:

http://davidbau.com/conformal/#exp(z)

Here's the current version of my code in Maple 18:

rrestart;
NULL;
with(plots);
xMax := 1;
yMax := 1;
N := 10;
step := abs(xMax)/N;
GL := proc (x, y) options operator, arrow; x+I*y end proc;
f := sin;
G := {};
for k from -N+1 to N+1 do

G := `union`(G, {complexplot(f(GL(x, (k-1)*step)), x = -xMax .. xMax, color = brown)});

G := `union`(G, {complexplot(f(GL((k-1)*step, y)), y = -yMax .. yMax, color = brown)})

end do;
display(G, scaling = constrained);

The code is pretty simple: I am simply scanning the 1x1 unit square complex grid and create a complex plot of it on the w-plane, by passing it through whatever function is at: f:=x.

Does anyone have any idea why the grid lines on the w-plane do not agree with Bau's grid lines mapping of the w-plane? To try it for exp for example, input "exp(z)" in Bau's home page.

The difference is quite noticeable, especially on exp and log, where the orientation of the w-grid on the left and right half-planes, seem to be opposite of what my code displays.

The reason may be Mathematical, but from what I see from the description on Bau's page, there's no difference on the identity function, so I am clueless.

Many thanks in advance

Any idea why the result of the FirstChild function of the attached file is

_XML_Text("\n  ")

Test.zip

I also miss a more complete example on Maple Help for writing, reading and processing xml files.

restart;

W := proc ()

      global rf;

     rf := add(xx[ii]^2-nn, ii = 1 .. nn);

    return rf ;

   end proc;

Optimization:-Minimize(W(), nn = 1 .. 5, seq(xx[ii] = 1 .. 10, ii = 1 .. nn));


Error, (in W) unable to execute add

 

Please solve

A triangle ABC with fixed B and C vertex is considered in the plane, A being variable so that b+c remains constant and equal to a given length L.
We call P, T, T' the points of contact of the exinscrit circle in the angle B with the sides BC, AB and AC respectively.
Show that P is fixed and is one of the vertex of the ellipse described by point A. What are the locus of T and T'? How to animate the drawing when A move ? Thank you.

Hello! Sorry if this question was already asked, I just can't find my answer and I don't really know how to form the question since I'm new to using Maple. My question is: How can I find a point on a plot I did in Maple? When I use the cursor position(from when I click Probe info) I can never align it right enough for me to not get a decimal answer. For instance, I can't figure out the y-value for when x=2 because the closest I can get to 2 is like 2.1 which isn't exact enough for me. 

This is a very basic question and apologize for not being able to figure it out myself.     I would like to define a function that I can evaluate with a complicated argument.    For example for a simple function, the following works well

f:=x->x^2+x^3;

This allows me to plot f(x) or f(exp(-r)), etc.    

However the following syntax does not work in the same way.

g:=x->diff(f(x),x);

I can plot g(x) correctly, but g(exp(-r))  cannot be plotted or evaluated.    The error message is 

Error, (in g) invalid input: diff received exp(-r), which is not valid for its 2nd argument
Thanks in advance for your suggestions.

Hi guys,

an error appeared in solving a set of equations and plotting the solution, I dont know how to handle it!!

Thanks for your help

Best

 

problem.mw

please help me

 

 

restart:

Similar*solution

Similar*solution

(1)

eq11 := (10-9*lambda1)*n*diff(f(eta),eta,eta,eta)*(-diff(f(eta),eta,eta))^(n-1)-m*diff(f(eta),eta)^2+M^2*diff(f(eta),eta)+(m*(2*n-1)+1)/(n+1)*f(eta)*diff(f(eta),eta,eta)=0;

(10-9*lambda1)*n*(diff(diff(diff(f(eta), eta), eta), eta))*(-(diff(diff(f(eta), eta), eta)))^(n-1)-m*(diff(f(eta), eta))^2+M^2*(diff(f(eta), eta))+(m*(2*n-1)+1)*f(eta)*(diff(diff(f(eta), eta), eta))/(n+1) = 0

(2)

eq21 := (10-9*lambda1)*n*diff(theta(eta),eta,eta)*(-diff(theta(eta),eta))^(n-1)+(m*(2*n-1)+1)/(n+1)*f(eta)*diff(theta(eta),eta)-m*diff(f(eta), eta)*theta(eta)=0;

(10-9*lambda1)*n*(diff(diff(theta(eta), eta), eta))*(-(diff(theta(eta), eta)))^(n-1)+(m*(2*n-1)+1)*f(eta)*(diff(theta(eta), eta))/(n+1)-m*(diff(f(eta), eta))*theta(eta) = 0

(3)

bc21:= f(0)=0, D(f)(0)=1+alpha*(D@@2)(f)(0), D(f)(N)=0, theta(0)=1+b*D(theta)(0), theta(N)=0;

f(0) = 0, (D(f))(0) = 1+alpha*((D@@2)(f))(0), (D(f))(N) = 0, theta(0) = 1+b*(D(theta))(0), theta(N) = 0

(4)

 

n:=1.2: b:=0: M:=0: alpha:=0:

N:=6:

 

m:=0.8:

A11:=dsolve({eq11,eq21,bc21},numeric,continuation=lambda1,maxmesh=15000, output=array([seq( i, i=0..N,0.01 )])):

Error, (in unknown) unable to store '-HFloat(1.03827200589718e-4)+HFloat(7.543487679217342e-5)*I' when datatype=float[8]

 

m:=1.2:

A12:=dsolve({eq11,eq21,bc21},numeric,continuation=lambda1,maxmesh=15000, output=array([seq( i, i=0..N,0.01 )])):

Error, (in unknown) unable to store '-HFloat(1.239112373179345e-4)+HFloat(9.002678360924433e-5)*I' when datatype=float[8]

 

m:=2:

A13:=dsolve({eq11,eq21,bc21},numeric,continuation=lambda1,maxmesh=15000, output=array([seq( i, i=0..N,0.01 )])):

Error, (in unknown) unable to store '-HFloat(5.684098069533373e-5)+HFloat(4.129738980869168e-5)*I' when datatype=float[8]

 

 

 

with(plots):

p1:=odeplot(A11, [[eta,f(eta),color=red,linestyle=2]],0..N):
p2:=odeplot(A12, [[eta,f(eta),color=blue,linestyle=2]],0..N):
p3:=odeplot(A13, [[eta,f(eta),color=green,linestyle=2]],0..N):

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

 

display({p1,p2,p3}, axes=boxed,  title=`velerature Profiles:`);

Error, (in plots:-display) expecting plot structures but received: {p1, p2, p3}

 

 

 

for j from 1 to 100*(N-1) do eta[j]:=A11[2,1][j,1] end do:

for j from 1 to 100*(N-1) do vel1[j]:=A11[2,1][j,2] end do:

for j from 1 to 100*(N-1) do vel2[j]:=A12[2,1][j,2] end do:

for j from 1 to 100*(N-1) do vel3[j]:=A13[2,1][j,2] end do:

 

with(LinearAlgebra):
E1:= <<seq(eta[j], j=1..100*(N-1) )>|<seq(vel1[j], j=1..100*(N-1) )>|<seq(vel2[j], j=1..100*(N-1) )>|<seq(vel3[j], j=1..100*(N-1))>>;

_rtable[18446746174193268126]

(5)

 

#ExportMatrix("F:/D/Drive D/Local/Rashad/Paper 9/vel1.txt", E1, format = rectangular):

 

NULL

with(plots):

p1:=odeplot(A11, [[eta,theta(eta), color=red,linestyle=2]],0..N):
p2:=odeplot(A12, [[eta,theta(eta), color=blue,linestyle=2]],0..N):
p3:=odeplot(A13, [[eta,theta(eta), color=green,linestyle=2]],0..N):

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

 

display({p1,p2,p3}, axes=boxed,  title=`temperature Profiles:`);

Error, (in plots:-display) expecting plot structures but received: {p1, p2, p3}

 

 

``

"[[eta,F(eta),(&DifferentialD;)/(&DifferentialD;eta) F(eta),((&DifferentialD;)^2)/(&DifferentialD;eta^2) F(eta),Theta(eta),(&DifferentialD;)/(&DifferentialD;eta) Theta(eta),f(eta),(&DifferentialD;)/(&DifferentialD;eta) f(eta),((&DifferentialD;)^2)/(&DifferentialD;eta^2) f(eta),theta(eta),(&DifferentialD;)/(&DifferentialD;eta) theta(eta)]]"

for j from 1 to 100*(N-1) do eta[j]:=A11[2,1][j,1] end do:

for j from 1 to 100*(N-1) do temp1[j]:=A11[2,1][j,5] end do:

for j from 1 to 100*(N-1) do temp2[j]:=A12[2,1][j,5] end do:

for j from 1 to 100*(N-1) do temp3[j]:=A13[2,1][j,5] end do:

 

with(LinearAlgebra):
E2:= <<seq(eta[j], j=1..100*(N-1) )>|<seq(temp1[j], j=1..100*(N-1) )>|<seq(temp2[j], j=1..100*(N-1) )>|<seq(temp3[j], j=1..100*(N-1))>>;

_rtable[18446746174193227646]

(6)

#ExportMatrix("F:/D/Drive D/Local/Rashad/Paper 9/temp1.txt", E2, format = rectangular):

 

 

NULL

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