## 90 Reputation

11 years, 104 days

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

Maple

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.

## converting list to table fails...

Maple 2022

I have a list as follows:
lst := [`A=70`, `B=17`, `C=27`, `D=37`, `E=74`, `F=57`, `G=67`, `H=08`, `I=81`, `J=28`, `K=38`, `L=48`, `M=58`, `N=68`, `O=90`, `P=19`, `Q=29`, `R=39`, `S=49`, `T=59`, `U=96`, `V=010`, `W=110`, `X=210`, `Y=310`, `Z=410`, "SPACE=105", "DOT=106"]

however using tt:=convert(lst, table) gives

tt:=table([1 = `A=70`, 2 = `B=17`, 3 = `C=27`, 4 = `D=37`, 5 = `E=74`, 6 = `F=57`, 7 = `G=67`, 9 = `I=81`, 8 = `H=08`, 11 = `K=38`, 10 = `J=28`, 13 = `M=58`, 12 = `L=48`, 15 = `O=90`, 14 = `N=68`, 18 = `R=39`, 19 = `S=49`, 16 = `P=19`, 17 = `Q=29`, 22 = `V=010`, 23 = `W=110`, 20 = `T=59`, 21 = `U=96`, 27 = "SPACE=105", 26 = `Z=410`, 25 = `Y=310`, 24 = `X=210`, 28 = "DOT=106"])

I want this to be such that I can retrieve the numerical value assigned to each alphabet e.g.
tt[A] should produce 70.

## Finite Topology of a Dynamical System...

Maple

Help, have no idea what to do.

Obtain a finite topological space from a dynamical system specified as a system of ODEs, by writing Maple code for following steps (use Maple packages DynamicSytems and GraphTheory, preferablly):

1. Visualize the phase space of the system by plotting solution curves for different initial conditions.

2. Consider a finite region of the phase space.

3. Define a finite grid of points in the region.

4. Define a topology on the grid points based on their connectivity.

5. Give some useful information regarding the dynamical system in terms of topological properties.

## Burger's PDE Solution...

Maple 2022

My following code:

restart;
PDE := diff(u(x, t), t) + u(x, t)*diff(u(x, t), x) - 0.1*diff(diff(u(x, t), x), x) = 0;
IC := u(x, 0) = sin(x);
BC := [u(0, t) = u(2*Pi, t)];
pds := {BC, IC, PDE};
ds := {pds, t = 0 .. 10, x = 0 .. 2*Pi};
p := pdsolve(ds, numeric);
u := rhs(p[1]);
u(x, t);

producing following 2 errors, don't know how to handle?

Error, (in anonymous procedure called from pdsolve/numeric) invalid terms in sum: 0 .. 10
Error, invalid input: rhs received p[1], which is not valid for its 1st argument, expr

## Questions about a Family of Subsets...

Maple

Hi, someone help please. How I can fix the following problem (preferably avoiding for-loops as they are too slow):

From a family of subsets (say) S={{a,b},{a,b,c},{b,c},{c}} of the set X={a,b,c}
1). Extract all the subsets i.e. members of S, which have 'a' as their member?
2). For any (a,b) in X x X, check if 'a' is member of all those subsets which have 'b' also as their member or not?

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