Hi everyone 

I solve several differential equations using dsolve. Now I want to change one initial condition a little bit: 

before: 

new: 

When solving the new system I am getting the error message: Error, (in dsolve/numeric/process_input) unknown piecewise(0 < 16-(xn(t)^2+(zn(t)-16)^2)^(1/2), 16-(xn(t)^2+(zn(t)-16)^2)^(1/2), 0) present in ODE system is not a specified dependent variable or evaluatable procedure

I am guessing this has to do with a function in an initial condition. 

Has anyone an idea how to solve this problem?

I added the maple file for the whole overview.

Thanks in advance!

Fractional part of a negative number is always positive. But maple command frac(-7.8) gives -0.8 instead of 0.2. Why is this? Though we can find it by using 1-frac(x), maple command may be there to give fractional part for all real numbers as per definition.

Like frac(9.8)=0.8 and frac(-9.8)=0.2.

Is there a command in maple?

Thanks. Ramakrishnan V

Dear all

I have the following code, that solves a linear system 
But I get the error 

Error, (in rtable/Sum) invalid arguments

code.mw

Thank you for any help 

Good day everyone,

I am trying to rotate the plots of pde solution using transplot, but it is giving me errors. Anyone with better suggestions should help. The code is attached below. Thanks

Transplot_not_working.mw

Let the square matrix A satisfy A^2023 = 0.

a. Prove: I-A is invertible.

b. If B is invertible, is B - A invertible?

This is not a Maple problem but it has something to do with math, specifically linear algebra, and I need help. Sorry if I bothered you. If possible please help me!

Dear all:

    I am trying to use the subs command to replace 5 varibles with other specific 5 varibles.

to be simple, here is issue.

Now I and using the stupid way(manually replace eachstep by my self) which did work but with some small issue such as  simplify or subs not work for replacements

all the steps I did are contained inside here:

ModelExtrinsicParasiticExtraction_QuestionsV2.mw

thanks for your help.

best regards

The following expression

returns undefined in Maple 2022.

I am not certain about if this limit exists, but shouldn't it be -infinity?

 For famous constants like pi and e, are the values stored or are they calculated?

Download Unit_of_t.mw

How to improve this program ? Thank you.

restart;
Equation de la conique
eqcon := (45 - 27*cos(alpha))*x^2 - 54*sin(alpha)*x*y + (45 + 27*cos(alpha))*y^2 - 8;
Delta := (-54*sin(alpha))^2 - 4*(45 - 27*cos(alpha))*(45 + 27*cos(alpha));
expand(%);
simplify(%);
Discriminant : Δ<0 ce qui correxpond à une ellipse
Eq := simplify(expand(subs(x = cos(alpha/2)*X - sin(alpha/2)*Y, y = sin(alpha/2)*X + cos(alpha/2)*Y, eqcon)));
kx := coeff(Eq, X, 2);
ky := coeff(Eq, Y, 2);
k := -tcoeff(Eq);

EQ := X^2/(sqrt(1/kx^2)*k) + Y^2/(sqrt(1/ky^2)*k) = 1;
Calcul du grand et du petit axe 
a := 1/sqrt(coeff(lhs(EQ), X, 2));
b := 1/sqrt(coeff(lhs(EQ), Y, 2));
print(X^2/('a^2') + Y^2/('b^2') = 1);
 

The edge connectivity of a connected graph G  is the minimum number of edges whose deletion from the graph G disconnects G. Below we are concerned with a particular kind of edge-cut.

• For a connected graph G=(V ,E), an edge set S ⊂ E is a restricted-edge-cut, if G−S is disconnected and every connected component of  G−S has at least 2 vertices. 

Clearly, a restricted-edge-cut is an edge cut with a special requirement.

• The restricted-edge-connectivity of G, denoted by κres(G), is defined as the cardinality of a minimum restricted-edge-cut.

For example, a graph g is as follows.

Clearly, its edge-connectivity is 1 since (0,3) or (0,4) is a edge cut of g. But we can find that  if we remove the edge (0,3), then "3" is a isolated vertex. Similarly, "4" is a isolated vertex if we remove  (0,4). It is not difficult to find g has exactly the two cut-edges (0,3) and (0,4).

Based on the definition of the restricted-edge-cuts, neither {(0,3)} nor  {(0,4)} are restricted-edge-cuts.  A minimum restricted-edge-cut is {(0,1),(0,2)} since every connected component of G-{(0,1),(0,2)} has  (at least) 2 vertices.

So  κres(g) is 2.  My problem is:

Given a graph G, how to calculate the restricted-edge-connectivity of  G?  Moreover, how to find a minimum restricted-edge-cut? 

A specific graph that I want to test is as follows. (it has 16 vertices and 56 edges.) I would like to calculate its restricted-edge-connectivity and find a minimum restricted-edge-cut. 

g:=ConvertGraph("O~tIID@wL~j`PbOqgLJ@p");
DrawGraph(g, stylesheet=[vertexborder=false,vertexpadding=15,edgecolor = "Black",
     vertexcolor="Black",edgethickness=2])

EdgeConnectivity(g) 

6

One option I came up with is to find all 6-edge subsets first. Test if they satisfy  the restricted condition (one by one). Then continue to increase to 7 or more. But this violent calculation may get stuck in the first step. That is, test all the minimum edge cut sets (Note that we will consider 32468436 edge-subsets!) I was referring to the efficiency aspect.  

with(Iterator):
C:=Combination(58,6):
K:=Edges(g):
#sub:=seq( K[[seq(c[]+1)]], c=C); # do not run this code since it has 32468436 members.

Any language is acceptable.( C or C++, Python. )

PS: Some time ago, I also asked a related question (but with some differences) on mathematica stack （Find all the minimum edge cuts of a graph）. Although Bob Hanlon  gave a reply, the actual result is not good.

Edits: The following literature gives a polynomial algorithm for computing the restricted-edge-connectivity of a given  graph. The heart of it is to computing the least cardinality of some  edge-pairs's edge separator. I'm stuck here.

• Esfahanian A H, Hakimi S L. On computing a conditional edge-connectivity of a graph[J]. Information processing letters, 1988, 27(4): 195-199.

How to implement this algorithm is my current concern.

Hi All,

I solved a high degree polynomial equation for two variables and obtained a list of solutions as under:

{s = 0.01291429045, t = 0.06099359500}, {s = -0.6944124361, t = 0.8895072341}, {s = 0.3000821715, t = -0.06855860577}, {s = 0.1246366197, t = -0.06899397557}, {s = 43.29465387, t = -10.98020355}, {s = 7.400522990*10^6, t = -1.879497900*10^6}, {s = 7.442623977*10^6, t = -1.890190214*10^6}

In the second stage, I have to plug these solutions into another expression andsolve for second stage decision variables. However, I am only interested in the solutions where both s and t are non negative. How can I reduce the set to have a smaller subset?

Thanks for help

I use to write modules with option package and store them in a .mla files.
Let's assume M is the name of the module and P1, P2, ..., PN are the procedures M contains.
Each time one of these procedures hass to call another one, I write 

Pm := proc(...)
 ...
 a := M:-Pn(...)
 ...
end proc:

instead of simply

Pm := proc(...)
 ...
 a := Pn(...)
 ...
end proc:

It seemed to me that the first method sometimes saved me a lot of trouble

Is it a common/necessary/safer/useless practice to write a:=M:Pn(...) instead of a:=Pn(...) ?

 {[[b/(sin(x-y-z))=a/(sin(z)),],[(a^(2)+b^(2)+2 abcos(x-y))cos(m(y+z)+n)=acos(mx+n)+bcos(my+n),]];

Why cannot this group of equations be solved in Maple software?