sursumCorda

How to efficiently find the length of so...

Asked: sursumCorda 1279 Product: Maple 2023

July 28 2023

1 2

The old question "Longest distance in a graph via Maple code" offers some general methods to find longest paths in a given graph, while for directed acyclic graphs, the longest paths can be found much more directly via built-in functions. However, it apprears that even for small dags, Maple cannot solve this in an acceptable time. In the following example, I'd like to count the number of nodes that on longest paths for certain source and target vertexes.

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restart;

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Warning, the use of _seed is deprecated. Please consider using one of the alternatives listed on the _seed help page.

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(1)

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t, s := combinat:-randcomb(GraphTheory:-Vertices(G__0), 5^2), combinat:-randcomb(GraphTheory:-Vertices(G__0), integermul2exp(5, 2))

(2)

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"DataFrame((`M__1`:=CodeTools:-Usage(Matrix(numelems(s),numelems(t),(i,j)->numelems((GraphTheory:-BellmanFordAlgorithm(`G__0`,s[i],t[j]))[1]),datatype=integer[2]))),'columns'=t,'rows'=s)"

memory used=7.99GiB, alloc change=0 bytes, cpu time=5.74m, real time=5.63m, gc time=22.55s

module DataFrame () description "two-dimensional rich data container"; local columns, rows, data, binder; option object(BaseDataObject); end module

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memory used=4.34GiB, alloc change=32.00MiB, cpu time=3.26m, real time=3.19m, gc time=14.34s

module DataFrame () description "two-dimensional rich data container"; local columns, rows, data, binder; option object(BaseDataObject); end module

(4)

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(5)

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Download longest_paths_in_a_DAG.mw

Unfortunately, I have to wait for almost four minutes in the above instance. Can this task be done in 0.4s?

GraphTheory['AllPairsDistance']: Which o...

Asked: sursumCorda 1279 Product: Maple 2023

July 25 2023

0 5

GraphTheory:-GraphEqual says that G₁ and G₂ are equal, but GraphTheory:-AllPairsDistance gives different results instead:

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restart;

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(1)

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Matrix(%id = 36893491227039185244)

Error, (in GraphTheory:-AllPairsDistanceExt) negative cycle detected

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Download allpairs.mw

So, which one is incorrect? Any reasons?

Limitations of `sum`?...

Asked: sursumCorda 1279 Product: Maple

July 23 2023

3 1

Some work, while others don't work.

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restart;

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(1)

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sum(1/sqrt(n)-1/sqrt(n+1), n = 1 .. infinity)

(2)

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sum(1/(sqrt(n*(n+1))*(sqrt(n)+sqrt(n+1))), n = 1 .. infinity)

sum(1/((n*(n+1))^(1/2)*(n^(1/2)+(n+1)^(1/2))), n = 1 .. infinity)

(3)

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`assuming`([sum(binomial(3*n, n)*x^n/(2*n+1), n = 0 .. infinity)], [abs(x) <= 4/27])

(2/3)*3^(1/2)*sin((1/3)*arcsin((3/2)*3^(1/2)*x^(1/2)))/x^(1/2)

(4)

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`assuming`([eval(binomial(3*n, n)*x^n/(2*n+1), n = 0)+sum(binomial(3*n, n)*x^n/(2*n+1), n = 1 .. infinity, parametric)], [abs(x) <= 4/27])

(5)

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(1/3)*(3*x^(1/2)+3*x^(3/2)*hypergeom([1, 4/3, 5/3], [2, 5/2], (27/4)*x)-2*3^(1/2)*sin((1/3)*arcsin((3/2)*3^(1/2)*x^(1/2))))/x^(1/2)

(6)

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(7)

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Download unable_to_sum.mw

How to explain this behavior?
I have read the help page, but I can not get the point.

Unable to find appropriate parameters su...

Asked: sursumCorda 1279 Product: Maple 2023

July 19 2023

2 2

Here is a symmetric matrix with three real parameters (`k__1`, `k__2`, and `k__3`).

mm:=<0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\
,0,0,0,0,0,0,0,0,0|0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0|0,0,1,0,0,0,0,0,0,0,0,0,0\
,k__3-1/2,0,k__3-1/2,0,0,0,0,0,0,0,0,-1/2,0,1-2*k__3,0,-1/\
2,0,0,0,0,0,0,0|0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,\
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0|0,0,0,0,0,0,0,0,0,0,0,0,0,0,\
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0|0,0,0,0,0,1,0,\
k__3,0,-1/2,0,0,0,0,0,0,0,0,0,k__3,0,-2*k__3,0,0,0,0,0,0,0\
,0,-1/2,0,0,0,0,0|0,0,0,0,0,0,-2*k__3,0,k__3-1,0,-1/2,0,0,\
0,0,0,0,0,0,0,k__3,0,1-2*k__3,0,0,0,0,0,0,0,0,k__1,0,0,0,0\
|0,0,0,0,0,k__3,0,1-4*k__3,0,k__3-1,0,0,0,0,0,0,0,0,0,(1-k\
__2)/2,0,k__3-1/2,0,0,0,0,0,0,0,0,1-2*k__3,0,0,0,0,0|0,0,0\
,0,0,0,k__3-1,0,1-4*k__3,0,k__3,0,0,0,0,0,0,0,0,0,k__3-1/2\
,0,(1-k__2)/2,0,0,0,0,0,0,0,0,1-2*k__3,0,0,0,0|0,0,0,0,0,-\
1/2,0,k__3-1,0,-2*k__3,0,0,0,0,0,0,0,0,0,1-2*k__3,0,k__3,0\
,0,0,0,0,0,0,0,k__1,0,0,0,0,0|0,0,0,0,0,0,-1/2,0,k__3,0,1,\
0,0,0,0,0,0,0,0,0,-2*k__3,0,k__3,0,0,0,0,0,0,0,0,-1/2,0,0,\
0,0|0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,\
0,0,0,0,0,0,0,0,0|0,0,0,0,0,0,0,0,0,0,0,0,-2*k__3,0,k__3,0\
,k__1,0,0,0,0,0,0,0,0,k__3-1,0,1-2*k__3,0,0,0,0,0,0,-1/2,0\
|0,0,k__3-1/2,0,0,0,0,0,0,0,0,0,0,k__2,0,-k__1+5*k__3-1/2,\
0,0,0,0,0,0,0,0,k__3-1/2,0,-k__1+5*k__3-1/2,0,1-2*k__3,0,0\
,0,0,0,0,0|0,0,0,0,0,0,0,0,0,0,0,0,k__3,0,1-2*k__3,0,k__3,\
0,0,0,0,0,0,0,0,k__3-1/2,0,k__3-1/2,0,0,0,0,0,0,-2*k__3,0|\
0,0,k__3-1/2,0,0,0,0,0,0,0,0,0,0,-k__1+5*k__3-1/2,0,k__2,0\
,0,0,0,0,0,0,0,1-2*k__3,0,-k__1+5*k__3-1/2,0,k__3-1/2,0,0,\
0,0,0,0,0|0,0,0,0,0,0,0,0,0,0,0,0,k__1,0,k__3,0,-2*k__3,0,\
0,0,0,0,0,0,0,1-2*k__3,0,k__3-1,0,0,0,0,0,0,-1/2,0|0,0,0,0\
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\
,0,0,0|0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\
,0,0,0,0,0,0,0,0,0,0|0,0,0,0,0,k__3,0,(1-k__2)/2,0,1-2*k__\
3,0,0,0,0,0,0,0,0,0,1-4*k__3,0,k__3-1/2,0,0,0,0,0,0,0,0,k_\
_3-1,0,0,0,0,0|0,0,0,0,0,0,k__3,0,k__3-1/2,0,-2*k__3,0,0,0\
,0,0,0,0,0,0,1-2*k__3,0,k__3-1/2,0,0,0,0,0,0,0,0,k__3,0,0,\
0,0|0,0,0,0,0,-2*k__3,0,k__3-1/2,0,k__3,0,0,0,0,0,0,0,0,0,\
k__3-1/2,0,1-2*k__3,0,0,0,0,0,0,0,0,k__3,0,0,0,0,0|0,0,0,0\
,0,0,1-2*k__3,0,(1-k__2)/2,0,k__3,0,0,0,0,0,0,0,0,0,k__3-1\
/2,0,1-4*k__3,0,0,0,0,0,0,0,0,k__3-1,0,0,0,0|0,0,0,0,0,0,0\
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\
|0,0,-1/2,0,0,0,0,0,0,0,0,0,0,k__3-1/2,0,1-2*k__3,0,0,0,0,\
0,0,0,0,1,0,k__3-1/2,0,-1/2,0,0,0,0,0,0,0|0,0,0,0,0,0,0,0,\
0,0,0,0,k__3-1,0,k__3-1/2,0,1-2*k__3,0,0,0,0,0,0,0,0,1-4*k\
__3,0,(1-k__2)/2,0,0,0,0,0,0,k__3,0|0,0,1-2*k__3,0,0,0,0,0\
,0,0,0,0,0,-k__1+5*k__3-1/2,0,-k__1+5*k__3-1/2,0,0,0,0,0,0\
,0,0,k__3-1/2,0,k__2,0,k__3-1/2,0,0,0,0,0,0,0|0,0,0,0,0,0,\
0,0,0,0,0,0,1-2*k__3,0,k__3-1/2,0,k__3-1,0,0,0,0,0,0,0,0,(\
1-k__2)/2,0,1-4*k__3,0,0,0,0,0,0,k__3,0|0,0,-1/2,0,0,0,0,0\
,0,0,0,0,0,1-2*k__3,0,k__3-1/2,0,0,0,0,0,0,0,0,-1/2,0,k__3\
-1/2,0,1,0,0,0,0,0,0,0|0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0|0,0,0,0,0,-1/2,0,1-2*\
k__3,0,k__1,0,0,0,0,0,0,0,0,0,k__3-1,0,k__3,0,0,0,0,0,0,0,\
0,-2*k__3,0,0,0,0,0|0,0,0,0,0,0,k__1,0,1-2*k__3,0,-1/2,0,0\
,0,0,0,0,0,0,0,k__3,0,k__3-1,0,0,0,0,0,0,0,0,-2*k__3,0,0,0\
,0|0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\
,0,0,0,0,0,0,0,0|0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0|0,0,0,0,0,0,0,0,0,0,0,0,-1/\
2,0,-2*k__3,0,-1/2,0,0,0,0,0,0,0,0,k__3,0,k__3,0,0,0,0,0,0\
,1,0|0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0>#assuming'real':
cc:={evalindets}(LinearAlgebra:-IsDefinite(mm,query='positive_semidefinite'),`and`,op):

As the title says, I hope to find some values satisfying andseq('cc') (so `mm` becomes positive semidefinite). Unfortunately, these don't work:

# SMTLIB:-Satisfy(cc);
Optimization:-Maximize(0, cc, initialpoint = eval({k__ || (1 .. 3)} =~ 'rand(-2e1 .. 2e1)'()));
Error, (in Optimization:-NLPSolve) no feasible point found for the nonlinear constraints
timelimit(1e2, RealDomain:-solve(cc, [k__ || (1 .. 3)](*, 'maxsols' = 1*)));
Error, (in RegularChains:-SemiAlgebraicSetTools:-CylindricalAlgebraicDecompose) time expired

Is there a way to do so as accurately (and precisely) as possible?

Error, (in interface) prettyprint must ...

Asked: sursumCorda 1279 Product: Maple 2023

July 15 2023

1 1

According to print - Maple Help (maplesoft.com),

calling print[N] instead of print where N is an integer between -2 and +3, temporarily overrides the prettyprint interface variable.

However, I find that

print[-2]();
Error, prettyprint must be an integer in the range 0..3
print[-1]();
Error, prettyprint must be an integer in the range 0..3

Also,

interface(prettyprint = -2);
Error, (in interface) prettyprint must be an integer in the range 0..3
interface(prettyprint = -1);
Error, (in interface) prettyprint must be an integer in the range 0..3

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How to efficiently find the length of so...

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Limitations of `sum`?...

Unable to find appropriate parameters su...

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