Let  denote the factors of the "absolute factorization" of the following bivariate polynomial (i.e., ): 

p := product(x^3*k^2 + (x*(y + 2) + 2)*k - x^3 + y^3 + y + 1, k = RootOf(_Z^3 + _Z + 1)):
f__0 := (evala@AFactors)(p)[2, .., 1]; # Assume that we do not know the extension field in advance.

It is unfortunate that the output is not easy to read, so I have to simplify it here. However, it appears that none of the results (i.e., , , and ) is eminently readable. 
 

Download fully_simplify_f_0.mw

The  above (whose "size" is smaller) comes from manual simplification, but this is not a easy work. Is there a way to get the much simplified result programmatically?

I am not able to make a MWE for this error, as it only shows in the debugger. So it seems Maple internal memory changes or some other library is loaded to cause this. Inside the debugger, I get to a function which does this

DBG> simplify(JacobiDN(x,k)^2*n)

Error, invalid input: simplify/Jacobi/JacobiDN expects its 1st argument, k, to be of type posint, but received 0

Version 2023 on windows 10

In a worksheet, the above works just fine

restart;
simplify(JacobiDN(x,k)^2*n)

Back to the debugger, if I write (2*n) instead of 2*n, then the error goes away

DBG> simplify(JacobiDN(x,k)^(2*n))
JacobiDN(x,k)^(2*n)

The values of x,k,n are all symbols and have no values in the code running:

I have no idea why this happend when I run the code only. It think x is zero in the above for some reason.

Sorry can't make MWE, I wish I can. Something strange happens when I run the code that does not show otherwise. 

Any suggestions how to invetigate this more? Stepping into the simplify code it fails in

DBG> next
`simplify/check_constant`:
   3   return type(r,'And(constant,Or(Not(function),satisfies(f -> evalb(op(f)
         <> NULL))))')

DBG> r
JacobiDN(x,k)^2*n^2

DBG> type(r,'And(constant,Or(Not(function),satisfies(f -> evalb(op(f)          <> NULL))))')
false

DBG> step
`simplify/Jacobi`
`simplify/do`:
  84               userinfo(1,simplify,'applying',new_simp,
                     `function to expression`);

 85               new_r := new_simp(r,symb_mode);  

Here it generate the error.

It has nothing to do with simplify. Here is a call to integrate which gives same error

DBG> lhs(ode)
diff(diff(xi(x),x),x)-k^2*JacobiSN(x,k)*JacobiCN(x,k)/JacobiDN(x,k)*diff(xi(x),x)+(-k^2*JacobiCN(x,k)^2+k^2*JacobiSN(x,k)^2-k^4*JacobiSN(x,k)^2*JacobiCN(x,k)^2/JacobiDN(x,k)^2-JacobiSN(x,k)^2*k^2*n^2+n^2)*xi(x)

DBG> int(lhs(ode),x)
Error, invalid input: simplify/Jacobi/JacobiDN expects its 1st argument, k, to be of type posint, but received 0

DBG> x
x

DBG> k
k

DBG> xi(x)
xi(x)

alias(b = JacobiCN(sqrt(2)*sqrt(x), sqrt(2)*_Z/2)^2);
                          lessthan, b

I could not find an explanation on the help page.

I would have expected simply b as the return value.

Update:
A worksheet that generates the output

Download alias_with_lessthan_output.mw

On this day 181 years ago, Christian Doppler first presented the effect that would later become known as the Doppler effect. In his paper “On the coloured light of the binary stars and some other stars of the heavens”, he proposed (with a great deal of confidence and remarkably little evidence) that the observed frequency of a wave changes if either the source or observer is moving. Luckily for Doppler, he did turn out to be right! Or at least, right about the effect, not right about supernovas actually being binary stars that are moving really fast. The effect was experimentally confirmed a few years later, and it’s now used in a whole variety of interesting applications.

To learn more about how the Doppler effect works, take a look at this Maple MathApp. You can adjust the speed of the jet to see how the frequency of the sound changes, and add an observer to see what they perceive the sound as. You can even break the sound barrier, although the poor observer might not like that so much!

For Maple users, you can also check out the MathApp on the relativistic Doppler effect. You’ll find it in the Natural Sciences section, under Astronomy and Earth Sciences. Settle in to watch those colours come to life!

But wait, I mentioned interesting applications, didn’t I? And don’t worry, I’m not just here to talk about sirens moving past you or figuring out the speed of stars (although admittedly, that one is pretty interesting too). No, I’m talking about robots. Some robots make use of the Doppler effect to help monitor their own speed, by bouncing sound waves off the floor and measuring the frequency of the reflected wave. A large change in frequency means that robot is zooming!

The Doppler effect is also used in the medical field—Doppler ultrasonography uses the Doppler effect to determine and visualize the movement of tissues and body fluids like blood. It works by bouncing sound waves off of moving objects (like red blood cells) and measuring the result. The difference in frequency tells you the speed and direction of the blood flow, in accordance with the Doppler effect! Pretty neat, if you ask me.

And like any good scientific phenomena, the Doppler effect can be used for both work and pleasure. The Leslie speaker is a type of speaker invented in the 1940s that modifies the sound by rotating a baffle chamber, or drum, in front of the loudspeakers. The change in frequency dictated by the Doppler effect causes the pitch to fluctuate, creating a distinct sound that I can only describe as “woobly”. The speaker can be set to either “chorus” or “tremolo”, depending on how much woobliness the user wants. It was typically used with the Hammond organ, and you can hear it in action here!

You know who else uses the Doppler effect? Bats. Since they rely on echolocation to get around, they need some way to account for the fact that the returning sound waves won’t be at the same pitch that they were sent out at. This fantastic video explains it far better than I ever could, and involves putting bats on a swing, which I think should be enough of a recommendation all on its own.

That’s it for our little foray into the Doppler effect, although there’s still a lot more that could be said about it. Try checking out those Maple MathApps for inspiration—who knows, maybe you’ll find a whole new use for this fascinating effect!

Apparently functions working on lines do not work on segments.

I can't see any logical explanation why that should be so.

Please consider expanding functionality in future Maple versions.

segprojection.mw

Hei

Vet noen om Windows 11 støtter Maple 2020? Eller støttes det bare av Windows 10.

If I understand right, the form  is equivalent to  (where the optional index variable is omitted), which produces a sequence of n occurrences of y. But how to explain the following output (of )? 

Download singular_behaviour_of_`seq`.mw

Main code: 

p1 := proc()
    local a := 1, b := 2;
    seq('assign(('a', 'b') = (a + 1, 2*b))', 3);
    print(a, b)
end:

p1():

How can an equation containing a logarithmic function be converted into a polynomial?

Is there a way in the physics package to get my index to run from 0 to 3 instead of 1 to 4/0?

Hi,

I have a data structure/plotting question. How do I plot the 3 lambdas (singleaxis) and the 6 betas (dualaxis) for 12 calibrations (1000 runs each)? All the details are in the script 230523_different-calibrations.mw. Thank you!

For the beta plots and subplots, please follow the dualaxis example output format at the bottom of my script for each of the 12 calibrations.

For the lambda plots, I'd like to combine a few of them as follows (each plot with lambda_1 subplot, lambda_2 subplot, and lambda_3 subplot - note that the lambda plot example at the bottom of the script is dualaxis but I just need singleaxis):

PLOT 1 (singleaxis): lambda_1, _2, _3 for ncal2 and ncal3 (superimposed, 2 data series for each subplot)

PLOT 2 (singleaxis):  lambda_1, _2, _3 for ncal7 and ncal8 (superimposed, 2 data series for each subplot)

PLOT 3 (singleaxis):  lambda_1, _2, _3 for ncal4, ncal5, ncal6 (superimposed, 3 data series for each subplot)

PLOT 4 (singleaxis):  lambda_1, _2, _3 for ncal9, ncal10, ncal11 (superimposed, 3 data series for each subplot)

there’s few redundant values. I just want the positive values. How it can be done?

Download fyp_2.mw

Hi,

I am exploring the Grading package in Maple, and I want to create a random question about limits. (Question 9). Any ideas for the correct code? Thank you

QUIZZTestMaple.mw