## Can I simplify a variable power of a matrix?...

Hi, guys.

I have a question with D, where D is a diagonal matrix,k>=0,for example

D:=<<6, 0> | <0, -1>>

I want Dk to be simplified to the form

<<6k, 0> | <0, (-1)k>>

How can I get it?

## Common legend for different figures...

Hello,

Is it possible to have a common legend for different figures? I can plot them as Array of Plots (below) but then they each have a legend.

Is it possible to have the two figures side by side and a common legend in the middle?

Thank you!

restart:
with(plots):
A := Array(1 .. 2):
A[1] := plot([2*sin(x), 3*sin(x)], x = -Pi .. Pi, labels = [x, b*sin(x)], color = [blue, red], legend = ["Case of b=2", "Case of b=3"]):
A[2] := plot([2*cos(x), 3*cos(x)], x = -Pi .. Pi, labels = [x, b*cos(x)], color = [blue, red], legend = ["Case of b=2", "Case of b=3"]):
display(A);

## Is there a maple function comparable to RelationGr...

Recently, I tried to write a function to get the lexicographic product of two graphs.

In  graph theory the lexicographic product G ∙ H of graphs G and H is a graph such that
• the vertex set of G ∙ H is the cartesian product V(G) × V(H); and
• any two vertices (u,v) and (x,y) are adjacent in G ∙ H if and only if either u is adjacent with x in G or u = x and v is adjacent with y in H.

I'm trying to write this function as defined after making sure it doesn't exist in maple. I saw a similar post by mathematica stack.

There are many answers in the post, the most interesting to me is the following code, which follows the definition of lexicographic product.

lexicographicProduct[g1_?UndirectedGraphQ, g2_?UndirectedGraphQ, opt : OptionsPattern[]] :=
RelationGraph[
(* two nodes are connected if their corresponding nodes in the first graph are connected *)
EdgeQ[g1, First[#1] $UndirectedEdge] First[#2]] || (* or their corresponding nodes in the first graph are the same and their corresponding nodes in the second graph are connected *) (First[#1] === First[#2] && EdgeQ[g2, Last[#1] \[UndirectedEdge] Last[#2]]) &, (* the vertices are the cartesian product of the two vertex sets *) Tuples[{VertexList[g1], VertexList[g2]}], (* also allow setting graph options *) opt ] lexicographicProduct[CycleGraph[5], CycleGraph[3]] It utilizes the function RelationGraph in Mathematica. I feel that this function is generic in nature. So here I would ask maple if they had a similar function. Function RelationGraph is to generate a graph based on data and a binary relation. For example, using RelationGraph I can get easily the kth power Gk of an graph G which is another graph that has the same set of vertices, but in which two vertices are adjacent when their distance in G is at most k. Dis[g1_?UndirectedGraphQ, k_] := RelationGraph[ GraphDistance[g1, #1, #2] <= k && GraphDistance[g1, #1, #2] != 0 &, VertexList[g1]] Dis[PathGraph[Range[10]], 2]  If I use maple and do not use the built-in function GraphPower, I might deal with the following. with(GraphTheory): with(SpecialGraphs): graphpower:=proc(G,k): local choo,edge,vex,g; vex:=convert(Vertices(G),list); choo:= choose(vex, 2): g:= Graph(Vertices(G)): for edge in choo do if Distance(G, edge[1], edge[2])<=k then AddEdge(g, convert(edge,set)) fi; end do: return g; end proc: s:=graphpower(PathGraph(10),2);DrawGraph(s)  I believe if the RelationGraph function can be implemented in maple, the function lexicographicProduct would be easier to obtain. ## plot of function... Asked by: Hey, guys! My Maple 2020 program does not build a plot. that is, it cuts it off. everything is correct in maple 2015. plot(140^t*exp(-140)/t!, t = 0 .. 300) Maple 2015 My maple 2020 creates Why??????????? ## How do we plot the least integer function [x]?... Asked by: How do we plot the least integer function [x]? I am referring to a function with the following graph ## What is the best way to have a type declaration fo... Asked by: Declaring types of arguments of a procedure or checking type of something when working with lists or Arrays is easy. For example one can easily use A :: list( posint ) or type( B :: 'Array'( polynom ) ), but with MutableSet, the same approach ends with an error; Error, module does not have a ModuleType member to accept structured type arguments. I guess it is the same for other objects defined as a module with option object. Is there a recommended way to have type declaration for such objects or MutableSet in specific? ## coefficient of nonlinear terms... Asked by: Dear Mapler I have an expression that consist of power of main variable x. I aim to fetch the coefficient of square root of x for example. I get an error when I am using COEFF(esp, sqrt(x)) Is there any solution? ## Maple to Latex - empty page pdf only... Asked by: When I export a very simple Maple 2018 (MaxOS) document to Latex, this tex file results: %% Created by Maple 2018.2, Mac OS X %% Source Worksheet: untitled 3 %% Generated: Sun Jul 03 16:34:49 CEST 2022 \documentclass{article} \usepackage{maplestd2e} \def\emptyline{\vspace{12pt}} \begin{document} \pagestyle{empty} \DefineParaStyle{Maple Bullet Item} \DefineParaStyle{Maple Heading 1} \DefineParaStyle{Maple Warning} \DefineParaStyle{Maple Heading 4} \DefineParaStyle{Maple Heading 2} \DefineParaStyle{Maple Heading 3} \DefineParaStyle{Maple Dash Item} \DefineParaStyle{Maple Error} \DefineParaStyle{Maple Title} \DefineParaStyle{Maple Text Output} \DefineParaStyle{Maple Normal} \DefineCharStyle{Maple 2D Output} \DefineCharStyle{Maple 2D Input} \DefineCharStyle{Maple Maple Input} \DefineCharStyle{Maple 2D Math} \DefineCharStyle{Maple Hyperlink} \begin{Maple Normal}{ \begin{Maple Normal}{ \mapleinline{inert}{2d}{restart; 1}{\[\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\begin{Maple Normal}{

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\begin{maplegroup}

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

\mapleresult

\begin{maplelatex}

\mapleinline{inert}{2d}{a := b^2-2; "_noterminate"}{$\displaystyle$}

\end{maplelatex}

\end{maplegroup}

\begin{Maple Normal}{

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\begin{maplegroup}

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

\mapleresult

\begin{maplelatex}

\mapleinline{inert}{2d}{a := b^2-2; "_noterminate"}{$\displaystyle$}

\end{maplelatex}

\end{maplegroup}

\begin{Maple Normal}{

\begin{Maple Normal}{

\mapleinline{inert}{2d}{}{$\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\end{document}

However, when trying to process the tex file in both Overleaf and TexShop the pdf output is only an empty page. No error occurs, i.e. the maplestd2e.sty file is recognised by both Overleaf and TexShop.

What is going wrong here?

## resolution of the equation of degree 3...

restart:
eq := a*x^3 + b*x^2 + c*x + d;
s := x1 + x2 + x3 = -b/a;
sp := x1*x2 + x1*x3 + x2*x3 = c/a;
p := x1*x2*x3 = -d/a;
sol:=solve({eq, p, s, sp}, {x1, x2, x3},explicit);
a := 1;
b := -5;
c := 6;
d := -1;
sol;

why is not successfull ?   Thank you.

## unable to implicit plot a procedure...

I have a problem in plotting bellow function. actually because my main program is not working so I decided to do it in simple way. I found that my program in maple can't plot the function I introduced it as a procudure and is an implicit function. can you help me please?

>EQ := proc(x, t) local y, m, func;
m := 3;
func := m*x^2 + t*y^2 = 4;
end proc;

>eq := EQ(x, 10);
eq := 3*x^2  + 10*y^2  = 4

>implicitplot(eq, x = -1 .. 1, y = 0 .. 2)
Error, (in plots/implicitplot) invalid input: the following extra unknowns were found in the input expression: {y}

## How to construct a multiple layered arrow procedur...

Given this "pattern" to transfporm an expression into an arrow procedure

e := 1/b:
f := unapply(e, b):
f(3)
1
-
3


I would like now to use this same "pattern" to transform an expression e which depends on 2 indeterminates a and b into a "double layered arrow procedure" f.
Here is a notional example

e := a/b:
f := unapply(unapply(e, b), a);
a
a -> b -> -
b

f(A)(B)
a
-
B


How can I proceed in order that f(A)(B) gives A/B ?

TIA

## implicitplot doesn't recognize the constant Pi...

I was surprised to learn that implicitplot doesn't recognize the constant Pi.  I attach a simple example to illustrate.

 (1)

 (2)

 (3)

## how to make a new function from a derivative?...

dgdx := (x, T) -> diff(g(x, T), x);

g := (x, T) -> T*x + x^2;#just an example

dgdx(1, 2);
Error, (in dgdx) invalid input: diff received 1, which is not valid for its 2nd argument

So, I like to introduce a new function dgdx(x,T) from the x-derivative of g(x,T) but if I insert a value for x I get an error message. It would be great if you can help me out!

## Is it possible to stack to dataframe columns?...

Perhaps a silly question but is it possible to stack two dataframe columns? When I use the Vector command the columns are stacked but nested.

Thank you for your help