## effect of evala on expression when using integrate...

Could someone help me understand why Maple's int hangs when using int on an integrand if evala is not first applied to the integrand?

When I mean hangs, I mean really hangs. I have timelimit and maple server.exe runs at high CPU for hrs. When adding evala(), it completes instantly and returns unevaluated integral (which is just fine as I did not expect this to be evaluated) but it does not hang which is the main point.

Is this considered normal behaviour or a bug?  Should then one always add evala() on the integrand before using int?  As I get many hangs on int (even when using timelimit). I am not familiar with evala command as I have never had to use it before, but by chance I tried it and noticed this.

V 2023 on windows 10. Worksheet attached.

 > restart;

 > expr:=-1/3*2^(2/3)/((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)*((-1/2*a^2*p-1/2*p^2*a+1/2*p*((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)*a-3)*(-p^2*(-((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)+a+p))^(2/3)+2^(2/3)*p*(-(a+3/2*p)*p*((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)+a^2*p+5/2*p^2*a+3/2*p^3+3))/(-((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)+a+p)/(-1/2*2^(2/3)*(-p^2*(-((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)+a+p))^(2/3)+p*(p*(-p^2*(-((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)+a+p))^(1/3)+2^(1/3)))/p^2: try     anti := timelimit(30,int(evala(expr),p)); catch:     print("timed out OK"); end try: print("done");

 > restart;
 > expr:=-1/3*2^(2/3)/((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)*((-1/2*a^2*p-1/2*p^2*a+1/2*p*((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)*a-3)*(-p^2*(-((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)+a+p))^(2/3)+2^(2/3)*p*(-(a+3/2*p)*p*((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)+a^2*p+5/2*p^2*a+3/2*p^3+3))/(-((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)+a+p)/(-1/2*2^(2/3)*(-p^2*(-((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)+a+p))^(2/3)+p*(p*(-p^2*(-((a^2*p+2*a*p^2+p^3+4)/p)^(1/2)+a+p))^(1/3)+2^(1/3)))/p^2: try     anti := timelimit(30,int(expr,p)); catch:     print("timed out"); end try; print("done");

The second case above just hangs. Make sure to save all your work. I found I have to terminate all of Maple sometimes as killing server.exe seems to make the frontend hangs and not respond, ending up losing work in other worksheets which I did not save.

## Re: Substituting an expression...

Hello there,

Is there any chance to ask for your expertise in this issue of substitution?

I tried to make the expression 'eq_m1' to 'eq_m1_desired' by substituting 'L__ads*L__fd/(L__fd + L__ads)' as 'L__ads_p', but did not succeeded, after a series of different attempts. Would you show me how to achive the desired expression?

 > restart;
 > with(LinearAlgebra):
 > with(DynamicSystems):
 > interface(imaginaryunit=j):
 > eq_m1 := m1 = (X__Tq*E__B*sin(delta) - R__T*E__B*cos(delta))/(R__E^2 + 2*R__a*R__E + R__a^2 + X__E^2 + X__E*L__ads*L__fd/(L__fd + L__ads) + 2*X__E*L__l + L__aqs*X__E + L__aqs*L__ads*L__fd/(L__fd + L__ads) + L__aqs*L__l + L__l*L__ads*L__fd/(L__fd + L__ads) + L__l^2);
 (1)
 > eq_m1_desired := m1 = (X__Tq*E__B*sin(delta) - R__T*E__B*cos(delta))/(R__E^2 + 2*R__a*R__E + R__a^2 + X__E^2 + X__E*L__ads_p + 2*X__E*L__l + L__aqs*X__E + L__aqs*L__ads_p + L__aqs*L__l + L__l*L__ads_p + L__l^2);
 (2)
 > ######
 >

## On the bondage number of a graph....

• A set D of vertices in a graph G is a dominating set if each vertex of G that is not in D is adjacent to at least one vertex of D.
• The minimum cardinality among all dominating sets in G is called the domination number of G and denoted σ(G).
• We define the bondage number b(G) of a graph G to be the cardinality of a smallest set E of edges for which σ(GE)>σ(G).

In the previous post, Carl Love provided a code for calculating domination number, so we could use it to calculate bondage number. I wrote a piece of code using a relatively basic approach. I feel like there is room for improvement.  I still can't determine the bondage number of the following graph so far.

 > restart: with(GraphTheory): with(Iterator): #Author: Carl Love , the Glorious 1st of June, 2023 # Domination_number:= (G::Graph)-> local V:= {\$nops(op(3,G))}, A:= op(4,G) union~ `{}`~(V), s, v, U:= table([{}= {}]), Us;     in V do         for s in {indices}(U, 'nolist') do             Us:= U[s]; U[s]:= evaln(U[s]);             for v in V minus s do                 if (U[s union {v}]:= Us union A[v]) = V then return nops({s[], v}) fi             od         od     od :
 > Bondage_number:=proc(g::Graph) local dom,vn,edge_ofg,t,M,removeedge,H,i,hasNext, getNext,result; dom:=Domination_number(g); vn:=nops(op(3,g)); edge_ofg:=convert(Edges(g),list); result:="Null"; for t from 1 to vn do     M := Combination(vn, t);     hasNext, getNext := ModuleIterator(M);       while hasNext() do         removeedge:= {seq(edge_ofg[i], i in getNext()+~1)};         H := DeleteEdge(g, removeedge,inplace = false);         if Domination_number(H)> dom then                 result:=nops(removeedge);          break t;         end if;         end do; end do: return result; end proc:
 > ed:={{1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 7}, {1, 9}, {1, 11}, {2, 3}, {2, 5},  {2, 6}, {2, 7}, {2, 12}, {2, 14}, {3, 4}, {3, 7}, {3, 8}, {3, 9}, {3, 16}, {4, 5},  {4, 9}, {4, 10}, {4, 11}, {4, 17}, {5, 6}, {5, 11}, {5, 12}, {5, 19}, {6, 7}, {6, 12},{6, 13}, {6, 14}, {6, 21}, {7, 8}, {7, 14}, {7, 15}, {8, 9}, {8, 14}, {8, 15}, {8, 16}, {8, 22}, {9, 10}, {9, 16}, {9, 17}, {10, 11}, {10, 17}, {10, 18}, {10, 19}, {10, 23}, {11, 12},{11, 18}, {11, 19}, {12, 13}, {12, 19}, {12, 20}, {13, 14}, {13, 19}, {13, 20}, {13, 21}, {13, 24},{14, 15}, {14, 21}, {15, 16}, {15, 21}, {15, 22}, {15, 24}, {16, 17}, {16, 22}, {16, 23}, {17, 18}, {17, 22}, {17, 23}, {18, 19}, {18, 20}, {18, 23}, {18, 24}, {19, 20}, {20, 21}, {20, 23}, {20, 24},{21, 22}, {21, 24}, {22, 23}, {22, 24}, {23, 24}}: g:=Graph(ed);
 (1)
 > Domination_number(g)
 (2)
 > Bondage_number(g);#Long time..

Bondage_number.mw

For arbitrarily given graph, it has been proved that determining its bondage number is NP-hard.

I always have a feeling that when removing subsets of edges, the symmetry of these edge subsets can be utilized. Above, we blindly traverse k-subsets of edges. If the graph is symmetric enough, perhaps we can reduce the amount of traversal. However, I have been struggling to understand how to express the symmetry of these edge subsets. Recently, I raised a similar question.

## does mserver.exe use threads? How to turn that off...

In trying to find why my Maple program encouter long delays when using timelimit and hangs, I found from windows 10 task manager that it uses thread and the thread can hang on network IO. I have no idea why mserver.exe is doing network IO for in the middle of timelimit().

But I think this has something to do with the problems I am seeing (reference).

The first thing I noticed is the network panel has check for update ON. So I turned that off.

I do not know if this was causing the problem, where Maple in middle of computation was trying to check for an update over the network or not.

But my question here is this: Does mserver.exe uses threads under the cover? If so, is there an option to turn this off? I.e tell Maple server.exe not to use threads at all?

I was to see if this is the cause or not. I see on the help on kernel options it says

And when I do   kernelopts(multithreaded)  it says  true

But how to turn this off? When I type

Error, kernelopts cannot set multithreaded value

Is it enough to tell it to use ONE thread only then? Like this

numcpus

1

If one is not able turn multhreading off, will setting gcmaxthreads=1 have same effect or is there a better way to do these things?

My code does not do any mutlithreading. So I do not need it.

Maple 2023 on windows 10

Is it possible to permanently turn off threading? I looked at options and see no such option.

## How can I calculate the domination number of a gra...

In graph theory, a dominating set for a graph G is a subset D of its vertices, such that any vertex of G is either in D, or has a neighbor in D. The domination number γ(G) is the number of vertices in a smallest dominating set for G. The domination number is a well-known parameter in graph theory. But I am unable to find a built-in function in Maple to calculate the domination number of a graph. Did I miss something?

For example, I would like to calculate the domination number of the following graph.

```ed:={{1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 7}, {1, 9},
{1, 11}, {2, 3}, {2, 5}, {2, 6}, {2, 7}, {2, 12}, {2, 14},
{3, 4}, {3, 7}, {3, 8}, {3, 9}, {3, 16}, {4, 5}, {4, 9},
{4, 10}, {4, 11}, {4, 17}, {5, 6}, {5, 11}, {5, 12}, {5, 19},
{6, 7}, {6, 12}, {6, 13}, {6, 14}, {6, 21}, {7, 8}, {7, 14},
{7, 15}, {8, 9}, {8, 14}, {8, 15}, {8, 16}, {8, 22}, {9, 10},
{9, 16}, {9, 17}, {10, 11}, {10, 17}, {10, 18}, {10, 19},
{10, 23}, {11, 12}, {11, 18}, {11, 19}, {12, 13}, {12, 19},
{12, 20}, {13, 14}, {13, 19}, {13, 20}, {13, 21}, {13, 24},
{14, 15}, {14, 21}, {15, 16}, {15, 21}, {15, 22}, {15, 24},
{16, 17}, {16, 22}, {16, 23}, {17, 18}, {17, 22}, {17, 23},
{18, 19}, {18, 20}, {18, 23}, {18, 24}, {19, 20}, {20, 21},
{20, 23}, {20, 24}, {21, 22}, {21, 24}, {22, 23}, {22, 24}, {23, 24}};
g:=Graph(ed);
```