I follow below question to generate binary sequence
but number of sequence is 6 not 5, why 011001 is wrong?

number of sequence should be catalan number.

how to generate this kind of sequence correctly?

For ecah positive integer n, how many 2n-digit binary sequence
 b1,b2,b2n with n "0" and n "1" are there such that
for each i=1,2,...2n, the number of "0" is larger than or equal 
to the number of "1" in the subsequence b1,b2,...bi?

with(combinat):
with(ListTools):
with(SumTools):
source := permute(Flatten([seq([0,0,0,1,1,1], k=1..1)]), 6);
aavxa := []:
for z in source do
if Summation(z[k], k = 1 .. nops(z)) = 3 then
if z[nops(z)] = 1 and z[1] = 0 then
if Reverse(z) in aavxa then
else
aavxa := [op(aavxa), z];
end if:
end if:
end if:
od:
nops(aavxa);
aavxa;
 

I am learning Typesetting so I can get better Latex.

I'd like to have all derivatives generated as y'(x) and not dy/dx regardless of what the derivative variable is. (It is more clear this way).

I found I can't even give Maple a list of the variables. But must do it each time one at a time.

I have thousands of ODE's I need to typeset, (they use different variables (depending on the textbook), and not always x or t, but the set of variables is not large).

so having to check and keep changing this setting each time is awkward (but I think is doable, as I know what the independent variable is for each ode so I can call Typesetting at start of each ode processing, once I know what the variable is).   

It wil be much easier if there is a way to tell Maple to do this for all variables. May be there is a good reason why Maple does not seem to allow such an option?

Here is an example

Typesetting:-Settings(usedot=false,prime=t,typesetprime=true):
ode:=diff(y(t),t$2)+diff(y(t),t)+y(t)= 0:
Physics:-Latex(ode);

Which gives the Latex I want

But if the variable was x instead of t, I have to do this

Typesetting:-Settings(usedot=false,prime=x,typesetprime=true):
ode:=diff(y(x),x$2)+diff(y(x),x)+y(x)= 0:
Physics:-Latex(ode);

I tried doing prime=[x,t] but Maple did not like this.

Is there a way or trick to tell Maple to use typesetprime=true for any letter?  I looked at https://fr.maplesoft.com/support/help/Maple/view.aspx?path=Typesetting%2fSettings but do not see a way so far.

Maple 2020.1 with Physics 776

I am trying the new Physics:-Latex command in version 774.

Couple of isssues I found:

1) One test I have failed with this error

Error, (in anonymous procedure called from anonymous procedure called from anonymous procedure called from anonymous procedure called from Physics:-*) invalid boolean expression: NULL
 

Using the normal latex() command works OK. I hope it is not too hard to fix since this new version seems to have fixed the fraction problem in latex(). Please see

restart;
sol:=dsolve(t*(t-2)^2*diff(diff(y(t),t),t)+t*diff(y(t),t)+y(t) = 0,y(t));
latex(sol);  #OK

Physics:-Latex(sol); #error

2) Maple now generates Latex using maple macro, which I do not know what it is.  Comparing

restart;
ode:=t*(t-2)^2*diff(diff(y(t),t),t)+t*diff(y(t),t)+y(t) = 0;
latex(ode)

which gives 

t \left( t-2 \right) ^{2}{\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}y
 \left( t \right) +t{\frac {\rm d}{{\rm d}t}}y \left( t \right) +y
 \left( t \right) =0

compare to

Physics:-Latex(ode)

which gives

t \left(t -2\right)^{2} \Mapleoverset{\ldots}{y}\left(t \right)
      +t \Mapleoverset{.}{y}\left(t \right)+y \left(t \right) = 0

What is \Mapleoverset ? googling around, these look like part of internal Maple style sheet for Latex?

Does this mean when using the new Physics Latex command, now one needs to use the package maplestd2e.sty?  With the normal latex() command, this was not needed. 

Just trying to understand the new setup.

I'm having hard time to do the following substitution. Please help

diff(x(t), t, t) := -R*diff(psi(t), t)*diff(phi(t), t)*sin(phi(t)) + R*diff(psi(t), t, t)*cos(phi(t)) <---- this is my expression xdoubledot

I want to substitute it in following equation

`Eq__&lambda;1` := diff(x(t), t, t) - R*diff(psi(t), t, t)*cos(phi(t)) + R*diff(psi(t), t)*diff(phi(t), t)*sin(phi(t))  <----this is my equation

I have turned on physics and algebra mobdules. it still not substitiutes. even though you see diff here I have dots in my maple output I don't know why it changes when I copy paste here.

I tried subs, solve,simplify commands. None of them works

Thank you for your help in advance

Hello,

I'm new to Maple and I'm struggling with dsolve output.

I solve this equation
 

ode:=diff(y(t),t)=-(4/3)*(a/eta)*(y(t)^3+1):
lambdaE:=dsolve({ode,y(0)=1},y(t),numeric,method=classical[rk4],parameters=[a,eta],output=listprocedure):
lambdaE(parameters=[theta[5,1],eta0]):

tCompute:=20*(lambda-~1)/(50/60): #vector with times I need 
# lambda is a 371 lines column vector

Then I need the value of the solution at each time to compute components of a matrix

J:=Matrix(371,5):
for i from 1 to 371 do
	J[i,1]:=2*(lambda[i]-1/lambda[i]^2);
	J[i,2]:=4*(lambda[i]^2-2/lambda[i]-3)*(lambda[i]-1/lambda[i]^2);
	J[i,3]:=6*(lambda[i]^2-2/lambda[i]-3)^2*(lambda[i]-1/lambda[i]^2);
	J[i,4]:=2*(1-1/lambda[i]^3);
	J[i,5]:=2*(lambdaE(tCompute[i])^2/lambda[i]-(1/lambdaE(tCompute[i])*lambda[i])); #here is where I need the value
end do;

However the output in the 5th column of J is something with y(t) and t inside

1.997498088*[t = 0.0300605520000000, y(t) = 0.999829465489350]^2 - 2.002505046/([t = 0.0300605520000000, y(t) = 0.999829465489350])

Would you have a solution to get only the numerical value ?

Thanks a lot in advance

Manon

In old studymaterial i could calculate  a gradient in (1,-1,2)   with obselote   package linalg 

f:= (x,y,z)->exp(x*y^3*z^2);

gradf(1, -1, 2); # werkt wel
              [-4 exp(-4), 12 exp(-4), -4 exp(-4)]

But i couldn't do it with the LinearAlgebra  or VectorCalculus package ?
LinearAlgebra has no gradient command, so left over Vector Calculus what is the right place 

This is the same example in previous post,

But here my question is how to produce smother plot of date. I tried the interpolation package but it not working.. 
 

I noticed this package is not introduced in Maple 17.. what is the alternative way to produce smother curve

Download interploation.mw

y(t)/diff(y(t),t)

how to dsolve when highest derivative at denominator?

For a from 1 to 2 do

convert(cat("k",a),symbol) := a;

od;

Error : can not do assignment 

how to do ?

This is strange.  It is true that this function (a modular form) goes to infinity as t -> 0 from the right.
But should plotting it it do this?

    |\^/|     Maple 2019 (APPLE UNIVERSAL OSX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> version();
 User Interface: 1435526
         Kernel: 1435526
        Library: 1435526
                                    1435526

> exp(-Pi*t/3)^8*JacobiTheta3(Pi*(4*I*t+1)/2,
> exp(-12*Pi*t))^8/(exp(-Pi*t/6)^4*
> JacobiTheta3(Pi*(2*I*t + 1)/2, exp(-6*Pi*t))^4);
                 Pi t 8              Pi (4 I t + 1)                8
           exp(- ----)  JacobiTheta3(--------------, exp(-12 Pi t))
                  3                        2
           ---------------------------------------------------------
                 Pi t 4              Pi (2 I t + 1)               4
           exp(- ----)  JacobiTheta3(--------------, exp(-6 Pi t))
                  6                        2

> plot(%,t=0..4);
memory used=48.4MB, alloc=45.3MB, time=0.45
Execution stopped: Stack limit reached.

CH10A.MWS

Hello

I need Nu[a] in the label of y-axis.

i am writing      labels = [eta, 'Nu[a]'(eta)] but I am not getting. Please help me for writing correct code.

Hello

I am trying to reproduce a simple result from Linear Control Theory using Laplace Transform.  Here are the steps:

assume(omega>0);assume(zeta>0 and zeta<1);
tf:=omega^2/(s^2+2*zeta*omega*s+omega^2);
y:=tf*1/s;
yt:=inttrans:-invlaplace(y,s,t);
dyt:=diff(yt,t);

So far, so good.  Now I need to find the values of t (time) such that the dyt=0.  

solve(dyt=0,t);

but Maple returns only the trivial solution, that is, zero.   How can I find the next one (Tp - peak time = Pi/(omega*sqrt(1-zetaˆ2)))?  

Many thanks

Dear All, 

When I checked the dynamic responses of second-order systems, I saw this:

While MATLAB step response shows a smooth curve (the blue one), Maple came up with wiggles (the blue one).

What might have worked on Maple's side to make the curve wiggling?

The Maple worksheet as well as MATLAB M script are attached. The MATLAB M script extension (.m) is not allowed, therefore it was modified to '.txt'. 

Sallen_Key.mw

SallenKey_check.txt