I am creating an algebra that includes shift operators. These operators commute with one another, but do not commute with anything else. I know that the Physics package enables you to make symbols non-commutative, but I would still like these operators to commute with one another. How can I do that?

Maple code example p.136 programming guide.

Explain the function of the word "divisible" in this maple code?

Why isn't divisible defined with an operator like -> ?

>L:= [seq( i, i=2..100)]:

> divisor := 2:

>while ( numelems( L ) > 0 )

do

divisible, L := selectremove( i->(i mod divisor = 0), L ):

n := numelems( divisible );

if ( n > 0 ) then

printf( "%d integer%s whose smallest prime divisor is %d\n",

n, `if`( n > 1, "s", "" ), divisor ):

end if;

divisor:=nextprime(divisor);

end do:

If a point is chosen in the Euclidean plane, then it is red or black.
It must be proven that there is then an equilateral triangle with corners of the same color.

dsolve gets stuck on a problem. Attached is the worksheet.

In Case I, dsolve solves the two ODEs separately. In Case II, dsolve solves them together, but only if I define a constant. In Case III the constant is not defined. dsolve never returns, and I have to hit the stop sign. The question I have: Is there a consistent method to the failure so that I can avoid the problem in the future with other ODEs?

dsolve_bug.mw

Question: Is there a style for the icons from the palettes? 

(The rest of this post is a screenshot because MaplePrimes can't show the change in fonts.)s a

How do I get alpha to display as the Greek letter in DataFrame Row column?

Download 2024-12-01_Q_Data_Table_alpha_as_Greek_Letter.mw

An oddly shaped Christmas package is a collection of centrally stacked cube-shaped boxes with ever smaller sides. From bottom to top, the edge lengths of the stacked cubes run like the sequence of the reciprocals of the sequence of the square roots of the natural numbers. How high is the package? How much paper is needed to wrap the package? What is the total volume enclosed by all the packages?

why i take intgral from equation it must apply for each term but just by sign is show up how it will work?

Download int.mw

I have a set of four equations along with specific parameter values provided in the dataset. I need to create a graph where I can dynamically adjust the values of parameters g2 and y within the specified range given in the sheet.
question_plot_slider.mw

Could you provide a maple code that allows for this flexibility, ideally with interactive controls (like the slider buttons shown in the example figure)

Hello,

I am working on a problem involving Newton's Law of Cooling in Maple, I want to:

1. Solve for the cooling constant k,
2. Find how long it takes for the pizza to cool to 300 F,

Here is the code I am currently using:

with(plots):

T__s := 75;  # Surrounding temperature
ode := diff(T(t), t) = k*(T(t) - T__s);

# General solution
general_solution := dsolve(ode, T(t));

# Initial condition: T(0) = 350
T := t -> 75 + exp(k*t)*c__1;
C := solve(350 = 75 + exp(0)*C__1, C__1);

# Solve for k using T(5) = 340
k := solve(340 = 75 + 275*exp(5*k), k);
k := evalf(k);

# Solve for time to reach T = 300
time_to_reach := solve(300 = 75 + 275*exp(k*t), t);
time_to_reach := evalf(time_to_reach);

# Define T(t) with solved constants
T := t -> 75 + 275*exp(k*t);

# Plot temperature over time
temp := plot(T, t = 0 .. 280, 75 .. 360, title = "Exponential Decay of Pizza Temperature", labels = ["t (minutes)", "T(t) (°F)"], color = blue);

# Plot T__s as a horizontal line
T__sur := plot(T__s, t = 0 .. 280, color = red, linestyle = dash);

# Combine and display plots
display([temp, T__sur]);

The code works, but I am wondering if there is a more efficient or genuine way.

I would greatly appreciate any advice or alternative approaches to solving and visualizing this in Maple.

Thank you in advance for your insights!

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With the latest version of Maple I get an indenting space when I click "Shift+Enter".
For example 

But I don't like it: suggestion? Thanks

Hint: we can vanish the different power of x and t!

Download params.mw

params.mw

Hi, how to rsolve this recursive sequence auto? 

The manual calculation is taking the reciprocal of both sides of the equation, and then do some simple calculations to get the answer:1/(3·2^n-5).

Download ask_recrusive_sequence_of_A[n].mw

I want to solve n nonlinear equations in n unknowns named lambda[1], lambda[2], ..., lambda[n]. For simplicity, I assume n=3. Each of the three equations includes matrices and dot products.

Running solve() takes forever...I assume this is because Maple is trying to find the explicit form. I am not sure, but I have reasons to believe that a solution exists.

Questions:

1. Did I set up the three equations correctly? Is there a simpler or smarter way to set up my problem?
2. Is it okay for Maple that lambda[i] sometimes appears isolated and sometimes as a component of a vector?  
3. Is there a way to keep my quantities (except the lambda vector I guess, since it containts the lambda[i] component I need to solve for) undefined/implicit while making sure Maple correctly deals with matrices and dot products?
   e.g., the solution should display terms like p^%T.R.w as such, rather than the corresponding explicit computation...

Worksheet:

Download dot_products.mw

I'm having some trouble finding how to do this: given some field with spacetime indices, say h[mu,nu] and a Lagrangian L of that field, I want to do a n+1 split to find the canonical momentum pi[~mu,~nu]. I can do the splitting fine, but it's calculating the canonical momentum that is the problem. I've tried a couple of different methods using diff and SubstituteTensorIndices but I can't get it to work: I either get the wrong answer or zero (also wrong). Anyone with any ideas or a working example of this, I'd appreciate to hear from!