Maple 2022.1 on windows 10

restart;
w:=y-x/(c-x):
p1:=plots:-implicitplot(eval(w,c=2),x=-6..9,y=-3..3):
p2:=plots:-implicitplot(eval(w,c=2),x=-6..10,y=-3..3):
p3:=plots:-implicitplot(eval(w,c=2),x=-6..11,y=-3..3):
[p1,p2,p3]

Gives

Notice p2. The vertical line is gone. This happens when the range x=-6..10 and it shows back again when x=-6..11 or x=-6..9

Why does this happen? It is the same equation.

I tried different things but can't figure how to make Maple give a simplified result from int command without these RootOf with sums in them. Here is an example.

restart;
anti:=int(1/(a+x^(1/5)),x);

The strange thing is that doing

eval(anti,a=1)

Keeps these rootsOf and Sums there. But doing

anti:=int(1/(1+x^(1/5)),x);

Gives simplified result without RootOf

I tried DEtools:-remove_RootOf and assumptions and value() but nothing worked. I tried assumptions on a, such as assuming a::integer,a>0 and other things. 

I need similar result as Mathematica:

ClearAll[x, a];
Integrate[1/(a + x^(1/5)), x]

I am sure there is an option in Maple to do that, i.e. give result without these RootOf and Sums. But so far, I could not find it. I looked at options to int() command also. 

Any one know what option to use or how to simplifies it the the above result by Mathematica? 

Maple 2022.1 on windows 10

Is it considered OK to give singular solution to an ode which does not satisfy the ode?

I thought may be because it is singular solution and not general solution, then that is allowed sometimes. But it seems strange to me to give a solution which cleary do not satisfy the ode, even if it is singular.  But may be because it is singular, it is not required to satisfy the ode? Here is an example

restart;
ode_1:=diff(y(x),x)=sqrt(1+x+y(x)) ;
sol_1:=DEtools:-dalembertsol(ode_1);

Gives

But the first given "solution" (singular) does not satisfy the ode. Plugging it into the ode gives  -1=1.  Also odetest(y(x)=-x,ode_1) agrees it does not satisfy the ode. It gives -2 and not zero.

What do others think about this?  

This works

restart;
ode := diff(y(x),x)=a0+a1*y(x)+a2*y(x)^2+a3*y(x)^3;
DEtools:-abelsol(ode);

But this does not

restart;
ode := diff(y(x),x)=a0+a1*y(x)+a2*y(x)^2+a3*y(x)^3;
name_of_solver:=abelsol;
DEtools:-name_of_solver(ode);

Then I found this made it work

eval(DEtools:-name_of_solver)(ode);

So I am guessing what happens is this: doing DEtools:-name_of_solver Maple first searched for a proc called name_of_solver inside DEtools package, and found none. So it does not work.

But adding eval first, then name_of_solver is evaluated and replaced by abelsol and after that the call is made, and it then finds this proc inside the DEtools package.

But my question is, why is eval needed here?

Is it not automatically happens that a variable is replaced by its value? So I expected DEtools:-name_of_solver to automatically become DEtools:-abelsol and only then the call is made.

Why the rule of evaluation is different in this case?

Formatting_exponents_in_typesetting_situations.mw
How do I format express an exponent in standard notation when typesetting a caption?  10^2 displays as 100 when I want it to display as 10^2 but without the caret.

Download Formatting_exponents_in_typesetting_situations.mw

Any one knows of a way to have Maple verify that this solution of the ODE is correct?

restart;
ode:=diff(y(x),x)=x*(y(x)^2-1)^(2/3);
sol:=dsolve(ode);
odetest(sol,ode);

gives

-4*x*y(x)^2*hypergeom([3/2, 5/3], [5/2], y(x)^2)*(y(x)^2 - 1)^(2/3)*signum(y(x)^2 - 1)^(1/3) - 9*x*hypergeom([1/2, 2/3], [3/2], y(x)^2)*(y(x)^2 - 1)^(2/3)*signum(y(x)^2 - 1)^(1/3) - 9*x*(-signum(y(x)^2 - 1))^(1/3)

Tried different simplications, but can't get zero.

For reference, this is Mathematica's solution and it verifies it:

Using Maple 2022.1 on windows 10.

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 D^k to be simplified to the form

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

How can I get it?

TKS in advance!

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

• 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.

• https://mathematica.stackexchange.com/questions/173124/lexicographic-product-of-graphs

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 k_th power G^k 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.

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?

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

Download implicitplot_error.mw

I do not remember now if this was asked before. Doing search here is hard. 

But I am trying this now on 2022.1 and this gives FAIL.

What is the correct syntax to use odetest to verify solution to ode using series method with expansion around infinity? Why do I get FAIL here?
 

Download odetest_series.mw

Update

I've testsed methods given below on 6 random ode's using Maple odetest, VV method and Axel method. THis is the result obtained using Maple 2022.1 

odetest was able to verify the solution zero out of 6 times.
VV method was able to verify the solution 3 out of 6 times.
Axel method was able to verify the solution 5 out of 6 times.

So based on this small test, Axel method seems to do the best. Attached worksheet. I will use this method to verify my series solution to ode's instead of Maple's odetest but will use Maple's odetest for non-series method solutions.

Download test_new_odetest.mw

The solution from LPSolve shown in the worksheet below is displayed very weirdly:

1. The first element is rounded to 3 significant digits.
2. The variable indices have decimal points.
3. Zeros are displayed as just decimal points with no digit 0.

Closer inspection (with, say, lprint) will reveal that the weirdness is only with the prettyprinting; the actual entries are as expected.
 

Download BadLPSolveDisp.mw

I am reading some expressions from file.

In the file, it is written as GAMMA(-1,x). When read into Maple using the read file command, it shows as  1/x*Ei(2,x)

I know these are the same mathematically. But I am translating these expressions to sagemath. in sagemath, Ei only accepts one argument.

Now the translator sees Ei in the input, then it keeps it as Ei as it does not know it was the GAMMA with two arguments,  which gives an error when used by sagemath since sagemath only has the one argument version of Ei.

If Maple would keep GAMMA(-1,x) as is, then the translator will just translate it to gamma(-1,x) which works in sage.

To keep things simple, I was wondering if there an option to tell Maple to keep the input as GAMMA(-1,x) and not rewrite to Ei?

Otherwise I would have to now parse each Ei to see if it is the two argument version or the one argument version, and use gamma  for the 2 argument version to keep sage happy which will complicate things for me. 

expr:=GAMMA(-1,x)

               Ei(2, x)/x

Maple 2022.1

I am trying to rotate a region about the y-axis. However, entering axis=vertical rotates it about the z-axis. I have also tried interchanging the x and y values. However, it produces the same output. The left image is what I'd like to rotate about the y-axis. The code below is for the right image. How would I revolve this region about the y-axis? Please help.

VolumeOfRevolution(2*x^2 + 1, x = 0 .. 1, labels = [x, y, z], output = plot, axis = vertical, orientation = [270, 0, 90])

I am transitioning from Mathcad to Maple, and I am currently working on some code to do a Gage R&R study using ANOVA. The attached math is from the 4th edition of the MSA manual. I got it to work in Mathcad, although I had to adjust things since Mathcad does not support 3D matrices.

My input matrix is a 2D matrix in which each cell contains a vector of measurements. In Maple, I seem to be able to make a 3D array with my data (if it is easier).

I have searched for a couple days for the right syntax. I am able to get the "right" number for SSA using my 2D Mathcad matrix--at least it is really close--but the other varibles are woefully off.

I would appreciate it if someone could at least point me in the right direction. Thanks.

Jno.