Maple Questions and Posts

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Hi,

I'm working on formatting my tables for export to PDF. Is there a way to align the text in the cells (to the left, for example)?

Thanks

GenerateSimilar_Ala.mw

I do not understand why select(has,-a^2,x); returns 1 but select(has,a^2,x); returned undefined.

Should not both return undefined, since there is no anywhere in the expression?

I looked at help and do not see a clue so far.

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1849 and is the same as the version installed in this computer, created 2025, March 12, 12:37 hours Pacific Time.`

restart;

C:=a^2;
select(has,C,x);

a^2

undefined

C:=-a^2;
select(has,C,x);

-a^2

1

 

 

Download select_question_march_23_2025.mw

Here is another variation, where I changed a^2 to a

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1849 and is the same as the version installed in this computer, created 2025, March 12, 12:37 hours Pacific Time.`

restart;

C:=a;
r:=select(has,C,x);

a

C:=-a;
r:=select(has,C,x);

-a

1

 

 

Download select_question_v2_march_23_2025.mw

The good thing is that has(C,x) returns false in both case. So the problem is not with the has call. It is select which decided to return 1 when there is negative sign. But why?

restart;

C:=a;
r:=has(C,x);

a

false

C:=-a;
r:=has(C,x);

-a

false

 

 

Download select_question_v3_march_23_2025.mw

a lot of time i have this issue when i want delete something it take a lot time to show the in this worksheet it happen too what is issue it is becuase all the text are not in text modde or what? and when i want copy and past my function to place with text is write null for me, what is problem?
and why in end of my display there is two graph?

2-line-label-done.mw

Trying to use plot to connect a series of points for illustrative purposes, but the functionality seems to have broken in 2024 or else I'm overlooking something. Related/unrelated: When I copy the related code from the cell and paste it into another application (like a browser) the list of points is reversed: e.g. `

plot({[-1, -2], [-1, 1], [-1, 6], [3, -2], [3, 6]}, x = -3 .. 4, y = -4 .. 10, style = line)` 

(That was literally me copy and pasting the relevant code from Maple into this form.)

The plot in question can be seen below. Also to note, if I leave off the last [3,-2] point, it will correctly plot the graph. It's ony when I add in that last point that I suddenly get the shape I do below. 

In 1-D Math, subscripts can be found with crtl-F

In 2-D Math this does not work. 

Also powers of (^) cannot be searched in 2D-Math.

Are there any ways to perfom searches on subscripts or superscripts in 2-D Math?

Hi MaplePrimes,
I made a quick code to calculate Aliquot Sequences.

The code works.

I was inspired by a Numberphile YouTube video.

see

aliquot_sequence_cut_1.mw

aliquot_sequence_cut_1.pdf

This should be helpful.

Regards,

Matt

LIMITS

Limits in maths are defined as the values that a function approaches the output for the given input values. Limits play a vital role in calculus and mathematical analysis and are used to define integrals, derivatives, and continuity. It is used in the analysis process, and it always concerns the behavior of the function at a particular point. The limit of a sequence is further generalized in the concept of the limit of a topological net and related to the limit and direct limit in the theory category. Generally, the integrals are classified into two types namely, definite and indefinite integrals. For definite integrals, the upper limit and lower limits are defined properly. Whereas indefinite integrals are expressed without limits, and it will have an arbitrary constant while integrating the function.

Sometimes we can't work something out directly ... but we can see what it should be as we get closer and closer!

Example 1

"restart;  f(x):=(|x|-3)/(x-3);"

proc (x) options operator, arrow, function_assign; (abs(x)-3)/(x-3) end proc

(1)

plot(f(x), x = -10 .. 10, discont = true, color = "Green")

 

f(3)

Error, (in f) numeric exception: division by zero

 

Now 0/0 is a difficulty! We don't really know the value of 0/0 (it is "indeterminate"), so we need another way of answering this.

So instead of trying to work it out for x=3 let's try approaching it closer and closer:

f(3.01)

1.000000000

(2)

f(3.0000001)

1.000000000

(3)

f(2.9999999)

1.000000000

(4)

Limit(f(x), x = 3)

Limit((abs(x)-3)/(x-3), x = 3)

(5)

limit(f(x), x = 3)

1

(6)

limit(f(x), x = 3, left)

1

(7)

limit(f(x), x = 3, right)

1

(8)

Example 2

Sometimes some functions are not continuous. That is, they appear to be approaching two different values when they are approached from two sides.

"g(x):=piecewise(0<x<2,1/(2 x-x^(2)),2 <x<=3,2 -x,3<x<4,x-4, 4<=x,Pi,undefined);"

proc (x) options operator, arrow, function_assign; piecewise(0 < x and x < 2, 1/(2*x-x^2), 2 < x and x <= 3, 2-x, 3 < x and x < 4, x-4, 4 <= x, Pi, undefined) end proc

(9)

plot(g(x), x = -10 .. 10, y = -1 .. 10, discont = true, color = "Red")

 

Suppose we want to approach 2 and see the function’s limit. This naturally leads to directions from which we can approach. Left-hand side and the right-hand side limits.

The right-hand side limit is the value of the function that it takes while approaching it from the right-hand side of the desired point. Similarly, the left-hand side limit is the value of function while approaching it from the left-hand side.

eval(g(x), x = 2)

undefined

(10)

limit(g(x), x = 2, left)

infinity

(11)

limit(g(x), x = 2, right)

0

(12)

limit(g(x), x = 2)

undefined

(13)

And the ordinary limit "does not exist".

g(4)

Pi

(14)

limit(g(x), x = 4, left)

0

(15)

limit(g(x), x = 4, right)

Pi

(16)

limit(g(x), x = 4)

undefined

(17)

And the ordinary limit "does not exist".

with(Student[Calculus1]); LimitTutor()

Example 3

Estimate the value of the following limit limit(h(x)*where, x = 2), h(x) = piecewise(x <> 2, x+12, x = 2, 4).

"h(x):={[[x+12,x<>2],[4,x=2]];"

proc (x) options operator, arrow, function_assign; piecewise(x <> 2, x+12, x = 2, 4) end proc

(18)

plot(h(x), x = -10 .. 10, discont = true, color = "#40e0d0")

 

limit(h(x), x = 2)

14

(19)

The limit is NOT 2025!Remember from the first example that limits do not care what the function is actually doing at the point in question. Limits are only concerned with what is going on around the point. Since the only thing about the function that we actually changed was its behavior at x = 2 this will not change the limit.

Example 4

" w(x):=piecewise( x<0,-x+5,x>=0,2 x);"

proc (x) options operator, arrow, function_assign; piecewise(x < 0, -x+5, 0 <= x, 2*x) end proc

(20)

plot(w(x), x = -10 .. 10, y = -10 .. 10, discont = true, color = "Blue")

 

limit(w(x), x = 5)

10

(21)

limit(w(x), x = 6, left)

12

(22)

limit(w(x), x = 1, right)

2

(23)

Example 5

" k(x):=piecewise( x<5,x+4,x>=5, x^(2)-2);"

proc (x) options operator, arrow, function_assign; piecewise(x < 5, x+4, 5 <= x, x^2-2) end proc

(24)

plot(k(x), x = -10 .. 10, discont = true, color = orange)

 

limit(k(x), x = 2)

6

(25)

limit(k(x), x = 5, left)

9

(26)

limit(k(x), x = 5, right)

23

(27)

limit(k(x), x = 5)

undefined

(28)

limit(k(x), x = 6)

34

(29)

Example 6

restart

" l(x):=piecewise( x<=1,(x-8)/(x-3),x>=3, sqrt(x^(2)+x+2), undefined);"

proc (x) options operator, arrow, function_assign; piecewise(x <= 1, (x-8)/(x-3), 3 <= x, sqrt(x^2+x+2), undefined) end proc

(30)

plot(l(x), x = -10 .. 10, discont = true, color = "Blue")

 

limit(l(x), x = 0)

8/3

(31)

limit(l(x), x = 1, left)

7/2

(32)

limit(l(x), x = 1, right)

undefined

(33)

limit(l(x), x = 2)

undefined

(34)

Example 7

Estimate the value of the following limit. limit(H(t), t = 0)where, H(t) = piecewise(t < 0, 0, t >= 0, 1)

"  H(t):=piecewise( t<0,0,t>=0, 1);"

proc (t) options operator, arrow, function_assign; piecewise(t < 0, 0, 0 <= t, 1) end proc

(35)

This function is often called either the Heaviside or step function. We could use a table of values to estimate the limit, but it’s probably just as quick in this case to use the graph so let’s do that. Below is the graph of this function.

plot(H(t), t = -10 .. 10, discont = true, color = "Blue")

 

limit(H(t), t = 0, left)

0

(36)

limit(H(t), t = 0, right)

1

(37)

We can see from the graph that if we approach t = 0from the right side the function is moving in towards a yvalue of 1. Well actually it’s just staying at 1, but in the terminology that we’ve been using in this section it’s moving in towards 1.

Also, if we move in towards t = 0 from the left the function is moving in towards a yvalue of 0.

According to our definition of the limit the function needs to move in towards a single value as we move in towards t = a (from both sides). This isn’t happening in this case and so in this example we will also say that the limit doesn’t exist.

 

NULL

Download limits.mw

i did plot without reducing the decimal but when i reduce to 2 decimal this error is showing up How i fix this issue?
plot.mw

Looking back at this question:

https://www.mapleprimes.com/questions/37691-How-Do-I-Change-The-Background-Colour

the reply by Hmm in 2009

"In Linux there is an X11 resource file for the classic worksheet, one of the settings controls the background color.  The distributed file is located in the maple/X11_defaults directory."

suggested a solution only thiis does not work for me in Maple2024. Perhaps because this worked for the classic view.

Why is there still no way to do this after 16 years or perhaps I just cannot find the option?

Is there away to change the background colour or even invert all colours?

I occasionally find myself inexplicably in a region of my worksheet that does not respond to my editing, fe.g., I cannot erae or I cannot copy. I recently typed a command-there was an error of some form and I tried unsuccessfully to edit it. Then I tried to copy the code and enter it at a prompt. It refused to enter it at the prompt but copied it below the prompt in a strnge region that I do not understand. When I retyped the command at a prompt it worked fine. I do not understand th dead regions that pop up mysteriously. (I am using Maple 2024 on a Mac) The page is too long to copy but I could upload it if given directions.

in this equation we have a list of a lot paramter which i have to find it but in prgress to find it some issue are appear i don't know how many term i have to replacing by algsubs there is any way for showing that something like lpring just for factoring and replacing if we did something like that in one step we can replacing all and then find our parameter there is any way for finding parameter like that?

Download pro.mw

in this integral PDE author did a substitution and the integral is simplify and removing how i can do that as mention in picture i did try but i think need a technique

Download int.mw

All three expressions define the same initial velocity condition in different notations.
ic1 := u(x, 0) = f, D[2](u)(x, 0) = g
ic2 := u(x, 0) = f, diff(u(x, 0), t) = g;
ic3 := u(x, 0) = f, u__t(x, 0) = g;  

Why does only ic1 work while ic2 and ic3 do not? Should I use another way?

wave_equation_1D.mw

Working on updating a very large and out of date guidebook and I need the content of execution cells to be 'Text' for illustrative purposes. It's tedious to constantly have to hit F5 for every, single, new, cell as I'm working through this. Is there a way I can just have the default style be 'Text' instead of 'Math'?  I can't seem to find that as an option anywhere.

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