## To overlay one column graph on top of another...

Is it possible overlay one column graph on top of another ? And if, how do I do it?

Regards

```I have here a function
"sin(x)/x"

and suppose sin(x)/x = 0
Can I now use MapleAI to retrieve the correct command for this in Maple..could I?

The intersection points with the x-axis are positive and negative multiples of Pi
I have put these in an ordered list, but Maple gives this:
For x domain = -20...20
X := {x = Pi}, {x = 2*Pi}, {x = 3*Pi}, {x = 4*Pi}, {x = 5*Pi}, {x = 6*Pi}, {x = -6*Pi}, {x = -5*Pi}, {x = -4*Pi}, {x = -3*Pi}, {x = -2*Pi}, {x = -Pi};

X := sort(eval~(x, [X]));
X := [, -6 Pi, -5 Pi, -4 Pi, -3 Pi, -2 Pi, -Pi, 2 Pi, 3 Pi, 4 Pi, 5 Pi, 6 Pi]

A strange ranking that Maple comes up with ?

with(NaturalLanguage);
[Explain, GetCommand, GetMath, Query, RawQuery]

GetCommand("give for Maple solve command all options?");
"solve(equations, variables, options);"

Explain("give for Maple solve command all options?");

"Maple is a symbolic and numeric computing environment. Its

"solve" command is used to find solutions (roots) of a given

equation or a system of equations.

There are a number of options (or "parameters") which can be

specified in this command to alter its behavior:

1. `Allsolutions`: This option makes Maple to generate all

possible solutions of an equation.

2. `Real`: This option only provides the real solutions. If

equations do not have real solutions, it will return an

empty set.

3. `Positive`: It only includes positive solutions in the

output.

4. `explicit`: If specified, Maple attempts to isolate roots

and provide an explicit solution for each variable.

5. `assume = real`: This option restrict the solutions to

only real numbers.

6. `parametric`: This option allows Maple to write the

solutions in a parametric form.

7. `avoid ={x = a}`: This option makes solve exclude the

possibility `x = a` as a solution.

8. `MaxDegree = d`: This option allows you to limit the

degree of the polynomial equations to be considered.

9. `maxdepth = d`: This sets a limit on recursive depth to

which the computation should go to seek a solution.

10. `multiplicities`: This option reports multiplicity of the

roots.

11. `solutions = vars`: This option tells Maple to look for

solutions for specific variables.

12. `numeric`: This option makes solve find a numeric

solution to the equation.

13. `symbolic`: This option makes solve find a symbolic

solution to the equation.

14. `simplify`: This option simplifies the solutions returned

by solve.

15. `sqrt`: This option allows square roots in the output.

It is important to note that not all options are suited for

use with all types of equations. Also, the "solve" command

in Maple can be occasionally limited by the complexity of

the equation, and may sometimes fail to find solutions that

more specialized software or methods can find."

```

## solve sets of equations...

I am trying to solve the following set of equations, I am able to find solutions for a simplified case (b=0) using the command solve but cannot seem to solve it for general b.

Is there a better way to attempt to find a solution?
solve.mw

 >
 >
 >
 >
 >

## how to improve my home made full_simplify() in Map...

Maple does not have full_simplify() command like with Mathematica.

So I figured why not make one?

Here is a basic implementation. All what it does is blindly tries different simplifications methods I know about and learned from this forum then at the end sorts the result by leaf count and returns to the user the one with smallest leaf count.

I tried it on few inputs.

Advantage of full_simplify() is that user does not have to keep trying themselves. One disadvantage is that this can take longer time. timelimit can be added to this to make it not hang.

Can you see and make more improvement to this function?

May be we all together can make a better full_simplify() in Maple to use. Feel free to edit and change.

```#version 1.0
#increment version number each time when making changes.

full_simplify:=proc(e::anything)
local result::list;
local f:=proc(a,b)
RETURN(MmaTranslator:-Mma:-LeafCount(a)<MmaTranslator:-Mma:-LeafCount(b))
end proc;

result:=[simplify(e),
simplify(e,size),
simplify(combine(e)),
simplify(combine(e),size),
simplify(evala( combine(e) )),
evala(factor(e)),
simplify(e,ln),
simplify(e,power),
simplify(e,RootOf),
simplify(e,sqrt),
simplify(e,trig),
simplify(convert(e,trig)),
simplify(convert(e,exp)),
combine(e)
];
RETURN( sort(result,f)[1]);

end proc:
```

worksheet below

 > #version 1.0   #increment version number each time when making changes. full_simplify:=proc(e::anything)    local result::list;    local f:=proc(a,b)       RETURN(MmaTranslator:-Mma:-LeafCount(a)
 > #test cases T:=[(-192*cos(t)^6 + 288*cos(t)^4 - 912*cos(t)^3 - 108*cos(t)^2 + 684*cos(t) - 54)/(4608*cos(t)^9 - 10368*cos(t)^7 + 6208*cos(t)^6 + 7776*cos(t)^5 - 9312*cos(t)^4 - 2440*cos(t)^3 + 3492*cos(t)^2 + 372*cos(t) - 1169), (10*(5+sqrt(41)))/(sqrt(70+10*sqrt(41))*sqrt(130+10*sqrt(41))), ((6-4*sqrt(2))*ln(3-2*sqrt(2))+(3-2*sqrt(2))*ln(17-12*sqrt(2))+32-24*sqrt(2))/(48*sqrt(2)-72)*(ln(sqrt(2)+1)+sqrt(2))/3, (1/2)*exp((1/2)*x)*(cosh((1/2)*x)-cosh((3/2)*x)+sinh((1/2)*x)+sinh((3/2)*x)) ];

 > full_simplify~(T)

 >

## Saving Style Sets & Using Them With "Format>Managi...

I just installed Maple 2024.0 and I discovered a problem in that the "Manage Style Sets" under the "Format" menu DOESN'T WORK!!! Type the following to understand how this feature works and see if you have the same problem:

>?workshhet,documenting,styles

Follow the instructions.  They are pretty simple.  Find a worksheet that has the styles you like and open it up and then save this Style Set in Maple 2024.0.  Then close it.  Open a new worksheet.  Go to "Format" and then click on "Managing Style Sets" and then click on the Style Set file name you saved previously and you will find that it does not set the style set you saved previously.

Another problem you will find is that it doesn't save your Style Set file where it is supposed to save it.  It needs to be saved in a Maple 2024.0 created folder known as "data" and then in a folder under "data" called "stylesets".  I had to manually go find my Style Set file and copy and paste it there.

Please check this out and see if I am wrong.  I use the "Format" "Manage Style Sets" option a lot when I download files from this blog and ".mw"  have fonts size 12 and they default to the nearly impossible to read font!  After I have applied the "Manage Style Sets" I can see what I have! But for some reason in Maple 2024.0 this feature was not tested or something has changed in Maple 2024.0 to break this feature!

## Something about the new function AllGraphs ...

`AllGraphs` is a new function in Maple 2024. Good things！

However, it seems that most of its functionalities are already provided by `NonIsomorphicGraphs`, and its speed even lags behind that of `NonIsomorphicGraphs`

I'm curious about what truly sets this function apart from existing ones. It generates isomorphic graphs if `nonisomorphic=false`But I donot know what its application is. Supporting directed graphs is a new thing, but its speed is not well.

``````iterator := GraphTheory[AllGraphs](vertices = 6, edges =6..7, connected, nonisomorphic)
s:=[seq(p, p = iterator)]:
nops(s)
``````

Note that this function is suitable for generating non-isomorphic connected graphs with 6 vertices and either 6 or 7 edges. It doesn't hold an advantage in terms of speed， and`NonIsomorphicGraphs` also provides an iteration option.

## How to draw a streamlines ...

Hello,

I have plotted psi [1] and psi [2] by using contourplot, but I want to show streamline or Flow nets on curves psi[1] and psi[2].

Thanks

streamline.mw

## How to (fully) simplify logical combinations of eq...

Here is a "toy" instance.
As the title suggests, I would like to simplify the following boolean combinations: (Note that the  should be taken into account.)

```formula__0 :=
convert(And(
Non(`xor`(Or(0 >- 0, y ** 3=x),
And(((y*x - 0^0)^2 + (y*y - x*x)^2)*(y^2 + x^2) >
0, 0 <- (y**3 - x)*(y - x**3)**3,
`implies`(y + x*2 >= y ** 3*2 + x**3,
Or(y + x < y*y*y + x*x*x)), Not((y**3 - x)*(y - x**3) = 0),
0 >= 0), y <> x*x*x))), 'boolean_function'):```

Regretfully, the built-in command `simplify` is unable to simplify :

```simplify(formula__0, assume = real); # only rudimentary simplifications
=

```

The library function `SMTLIB:-Simplify` seems to simplify it, but the result is incorrect

```(SMTLIB:-Simplify(formula__0) assuming real); # check {y = 1, x = 0}
=
/   /   / 3           3\\\
And\Not\And\y  = x, y = x ///

```

The only procedure I can find that is capable of rewriting it appears to be `RealDomain:-solve`

```RealDomain:-solve(formula__0, 'allsolutions'); # see below
=
Warning, solutions may have been lost
/            3\    /     3       \    /     3        \
{ x = x, y = x  }, { x = y , y = y }, { y = x , x < -1 },
\             /    \             /    \              /

/     3              \    /     3        \
{ y = x , 0 < x, x < 1 }, { x = y , y < -1 },
\                    /    \              /

/     3              \
{ x = y , 0 < y, y < 1 }
\                    /

```

Nevertheless, this is more or less overkill, since a complete solution set is somewhat unnecessary, and in practice, an simplified and compact but presumably unsolved form is more applicable to further manipulations. (For example, the simplest form of  (over ℝ²) should at least be x2y2＞1, yet  simply returns , which is definitely unsuitable here.) (A more real example can be found in the Ex３ of this compressed file.)

I believe that this is a common problem; curiously, I cannot find any related questions in this forum. So, are such simplifications (similar to SLFQ) available in Maple?

## Optional parameter naming...

I have a repetative set of parameter names used in procedures in a package. I settled on making all optional inputs in the format {name::type:=something}. Originally I wanted to use non capitalised names for the optional inputs. But the names clash with Maple commands. I have all sorts of quicky abbreviations like prnt etc. These are both messy and tacky. For many of my choices I would seem to have to use capitalised naming to give a meaningful name. The problem here is these names are used in other Maple packages. So sooner or later there is going to be a clash.

Is there a way a of handling this? Like can I defiine package parameter names? Or should I just stick with my abbreviations?

I read somewhere about this problem in the help years ago. I think Basis was the example used in different packages GroebinerBasis and Polynomial package and using PackageName:-Basis to avoid the clash with both loaded. But that is more a command level handling.

 > restart
 >
 > illegal:=proc(x,y,{Point:=[symbol=solidcircle,colour=purple]},{Line:=[colour=green,thickness=2]},{Colour:="Blue"},{Scale:=5},{Print:="y"}) print("1 Point= ",Point);  #I currently use points print("2 Line= ",Line);   #                 linetype print("3 Colour=  ",Colour); #              clr     this has nothing to do with plotting colour print("4 Scale= ",Scale);   #               scl    print("5 Print= ",Print);   #               prnt Scale*x/y end proc
 >
 (1)
 > illegal(3,7)
 (2)
 > illegal(3,7,line=[linestyle=dash,colour=black,thickness=4])
 (3)

## Graph of rectangular grid from 4 copies of the pat...

Want to make a rectangular graph (in the sense of Graph Theory) of 4 copies of the path A-B-C-D i.e. four rows of this path. Once the rectangular or matrix like graph is made its ediges are to be weighted as the matrix position of vertex stating from (1,1) at the upper left vertex i.e. "A". Help please.

## evalf gives a sum back...

Hi everyone! :)

I'm new to Maple, so please forgive me if the solution is obvious, but I could not find any fitting articles for my problem.

I have a transfer function and need to find the poles. Later, I want to calculate the constants to meet my filter requirements. For now, I'm focusing on getting a symbolic solution and evaluating the poles.

Here's my setup:

Here is the File NoiseFilter.mw

When I use the "evalf" function, it gives me a large sum, but I would like to get one complex numerical result.

I appreciate any help! :)

## How do I find the element-wise minimum of two Data...

I would expect I could do

```A := DataSeries([2, 3, 4], datatype = float)
B := DataSeries([1, 3, 19], datatype = float)
min~(A, B)```

but the last command gives me

```Error, (in DataSeries:-min) invalid boolean expression: 2.
```

How do I find the element-wise min (i.e. DataSeries([1,3,4], datatype=float)) of two DataSeries?

## Missing symbols in exported PDF?...

One may easily spot that the symbols “” and “” are missing here and here

These two PDF files were printed officially, so I think they can be considered examples of best practice for the export functionality. Does this mean that this functionality is still defective in the most recent release?

## Where does one find the python module "maple"?...

Where does one find the python module "maple" used to access open maple as in https://www.maplesoft.com/support/help/maple/view.aspx?path=OpenMaple%2fPython%2fAPI ?

## how to plot impulse points in the differential equ...

For t not equal to nT,

dS/dt = delta- mu*S+ omega*V;

dV/dt = -(omega+mu)*V

For t=nT,

S(nT+)=(1-gamma) S(nT);

V(nT+)=V(nT)+ gamma* S(nT),

with the initial conditions  S(0+)=s0

V(0+)=v0

how to plot the graph with this system of equations,impulsive points and initial conditions

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