I am working with a symbolic expression in Maple that combines exponential terms. How can exponential terms be fully converted into hyperbolic functions? 

Download simplify.mw

1. Further simplify the expression under three physical scenarios, assuming delta__1 > 0:

   • Case (i): When A__c = 0

   • Case (ii): When delta__1 > g * A__c

   • Case (iii): When delta__1 < g * A__c

I have created an animation of a flexible octahedron (following Bricard) with Maple.   It shows the six vertices and twelve edges.  How do I add the faces (triangles)?  Can the animation show their lines of intersection?

restart;
with(geometry);

triangle(ABC, [point(A, a, b), point(B, c, d), point(C, e, f)]);
AreCollinear: hint: could not determine if a*d-a*f-b*c+b*e+c*f-d*e is zero
Error, (in geometry:-triangle) not enough information: the three points might be AreCollinear

assume(a*d - a*f - b*c + b*e + c*f - d*e <> 0);

triangle(ABC, [point(A, a, b), point(B, c, d), point(C, e, f)]);
                              ABC

area(ABC);
                   

What does the ~ after the point variables supposed to mean?

The workbook includes the excel data file but I also included the worksheet and data file separate for versions that can't load workbooks.

Average_World_Temperature_workbook-.maple

Average_World_Temperature_since_1850_worksheet.mw

HadCRUT5.zip

I have just started to use Maple workbook (*.maple). In the workbook, there are 4 worksheets: "main.mw","calc1.mw","calc2.mw","calc3.mw". In "main.mw", I plot variables saved from "calc?.mw". This works. However, when I make changes in one of the worksheet "calc?.mw" and get the new expressions for the variables, they are not updated in "main.mw". I deleted the variables being changed but "main.mw" still run and show the old expressions of these variables.

How do I refresh so that "main.mw" will show the updated variables from "calc?.mw"?

Thanks.

Trying to produce two different font sizes within a plot title.  I can achieve it with Typesetting but I'm getting brackets and fluff I don't want.  Any other ideas?

For example

with(Typesetting):
plot(x^2, title = [cat(mtext("sort of", font = "TimesNewRoman", size = 30), mtext("works", size = 10))])

I’m trying to plot a 3D surface in Maple with variables l and m. I used numerical substitution to evaluate the function and the results are real and positive. However, when I plot the function over a range of l and m, the graph shows complex (imaginary) values instead.

This seems very strange to me and has been quite frustrating. I’ve tried many different approaches to resolve the issue, but nothing has worked so far.

Why is this happening? How can the function evaluate to real numbers with direct substitution, but show complex values during plotting?

Any suggestions or explanations would be greatly appreciated. Thank you!
gra423_Omega.mw

I'm not sure if this is fixed in newer Maples or if there's a work around. 

Whenever I size a 3d plot, that I'm trying to stretch out the width while keeping the height, never seems to work.  For example using the size=[3000,800] produces a plot area that's bigger but NOT actually a plot stretched in the x axis.  Going to size=[3000,3000] of course then makes the plot and the area bigger and so scales both x and y bigger.  However I don't want the y axis scaled up - I'm trying to scale the plot up - not the area.  And what happened to the window zoom, icon - we've lost zoom control to just magnify + and magnify - (at least in 2022) this seems like a regression. 

Is this plot size a bug or just a plot command that fails to function like it should? 

I am very confused by the y-value of the rightmost point on the plot below.

Download plotq.mw

I have a question about a calculation I was just trying to do. For some context, I am trying to calculate the pH of a solution of a weak acid in water. When the concentration of the weak acid is low enough, we need to consider the effect of ionization of the water itself (ie, autoprotolysis of water), since the order of magnitude of this ionization is the same as the order of magnitude of the ions due to the weak acid in this case of very low concentration.

There is a specific formula that can be used for this, which is shown below.

K_a is a constant that depends on the weak acid being considered, and K_w is a constant as well (for the autoprotolysis of water). I am interested in solving for the concentration of hydronium, given an initial concentration of the weak acid [HA]_initial.

I'd like to solve the equation for different values of [HA]_initial.

Download concentrations.mw

Today I was working on some plots involving pH, which is defined as -log_10 ([hydronium]), that is, the negative of the base 10 logarithm of the concentration of hydronium in a solution.

I reached an expression for a variable x that is a function of an initial concentration C_i.

I wanted to plot the pH given by -log_10 (0.0001+x).

Note that x(0)=0, and so for this latter plot we should have the point (0, 4).

I am not able to see any part of the plot near (0,4), as can be seen below.

Download plotatzero.mw

I aim to conduct a numerical frequency sweep analysis on a nonlinear, coupled two-degree-of-freedom vibration model and compare the results with the analytical solution. However, I am currently facing two main difficulties:

1. I am unsure how to determine whether the computed response has reached a steady state. If I simply use the maximum value to represent the steady-state amplitude, it can be misleading—since transient responses prior to reaching steady state may yield a higher peak, as seen in the uploaded code.

2. I do not know how to properly select the steady-state result from the previous frequency as the initial condition for the next frequency step.
   2.mw

Approximation_of_ODEs_with_Cubic_Splines.mw

Hi!

I am studying Burger's equation, and I would like to see the steps that Maple takes to solve this.  "ShowSteps" doesn't seem to work.

Unfortunately, I am unable to share the worksheet I made.

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How do we simplify the arguments of the exponential in (1)? Further how to express (1) into hyperbolic/trig functions? 
 

Download argument.mw