sursumCorda

Is there any bugs in GraphTheory['Transi...

Asked: sursumCorda 1284 Product: Maple 2023

April 16 2023

0 7

the transitive reduction of graph G, is the graph with the fewest edges that still shares the same reachability as G (but might contain new edges not present in G).

However, in Maple 2023, things become strange; different branches return distinct numbers of edges:
(33 arcs or 40 arcs?)

>

restart;

>	with(GraphTheory):

>

GraphTheory:-TransitiveReduction := proc(G::GRAPHLN, $)
local D, V, T, i, j, k, A, M, n, flags, B;
       ...
   4   if _EnvDisableExt <> true then
           ...
       elif D <> (':-directed') then
           ...
       else
           ...
       end if;
       ...
end proc

>

$G__0 := Digraph({[2, 8], [3, 1], [4, 9], [5, 10], [6, 19], [7, 12], [8, 13], [9, 3], [10, 4], [10, 14], [11, 5], [11, 15], [12, 6], [12, 16], [13, 7], [13, 17], [14, 9], [15, 10], [15, 18], [16, 19], [17, 12], [17, 20], [18, 14], [19, 11], [19, 21], [20, 22], [21, 18], [22, 16], [22, 23], [23, 19]})$

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Download TransReduction.mw

Any bugs?

G__0 := GraphTheory:-Digraph({[3, 1], [9, 3], [4, 9], [14, 9], [10, 4], [5, 10], [15, 10], [11, 5], [19, 11], [12, 6], [7, 12], [17, 12], [13, 7], [8, 13], [2, 8], [10, 14], [18, 14], [11, 15], [6, 19], [16, 19], [23, 19], [13, 17], [15, 18], [21, 18], [12, 16], [22, 16], [22, 23], [20, 22], [19, 21], [17, 20]}):

How to use any number of expressions or ...

Asked: sursumCorda 1284 Product: Maple 2023

April 15 2023

1 2

For example, I'd like to do something like this (and then plot the graph):

 # display LaTeX markup
label__1 := '"\[\cfrac{\biguplus_\LaTeX}{{\color{red}\leadsto}^\unicode{2254}}\]"':
 # display non-executable notation
label__2 := '(Product(Int(i, j), Sum(k, l)) %assuming convert(log2(1 - 'x'), confrac, subdiagonal))':
 # display graphical object
label__3 := 'plots:-display(plottools:-stellate(plottools:-icosahedron()))':
 # note that the desired one is  instead of 
GraphTheory:-RelabelVertices(`some graph with 3 nodes`, [label__1, label__2, label__3]):

But unfortunately, the second argument of GraphTheory:-RelabelVertices must be of type list({indexed, integer, string, symbol}), and the GraphTheory:-SetVertexAttribute command doesn't work here. Is it possible to do so in Maple^® (rather than in other mathematical softwares)?

Why can't the Maple simplifier combine t...

Asked: sursumCorda 1284 Product: Maple 2023

April 14 2023

1 2

The result of is said to be the Catalan constant, but unfortunately, Maple^® only returns a lengthy output, so I have to apply the simplify command to get a shorter (and equivalent) form of it. However, I find that these do not work here:

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restart;

>

((1/2)*I)*dilog(1-(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))+((1/2)*I)*dilog(1-(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2+Catalan

(1)

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simplify(expr__1, size = false)-Catalan; Physics:-Simplify(expr__1)-Catalan; simplify(expr__1-Catalan, size = false); Physics:-Simplify(expr__1-Catalan); verify(expr__1, Catalan, equal); is(expr__1 = Catalan); verify(expr__1-Catalan, 0, equal); is(expr__1-Catalan, 0)

((1/2)*I)*dilog(1-(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))+((1/2)*I)*dilog(1-(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2

((1/8)*I)*(-Pi^2+4*dilog(1-(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))+4*dilog(1-(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-4*dilog(1+(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-4*dilog(1+(1/2)*2^(1/2)-((1/2)*I)*2^(1/2)))

(2)

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((1/2)*I)*polylog(2, (1/2)*2^(1/2)-((1/2)*I)*2^(1/2))+((1/2)*I)*polylog(2, (1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/2)*I)*polylog(2, -((1/2)*I)*2^(1/2)-(1/2)*2^(1/2))-((1/2)*I)*polylog(2, -(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2+Catalan

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simplify(expr__2, size = false)-Catalan; Physics:-Simplify(expr__2)-Catalan; simplify(expr__2-Catalan, size = false); Physics:-Simplify(expr__2-Catalan); verify(expr__2, Catalan, equal); is(expr__2 = Catalan); verify(expr__2-Catalan, 0, equal); is(expr__2-Catalan, 0)

((1/2)*I)*polylog(2, (1/2-(1/2)*I)*2^(1/2))+((1/2)*I)*polylog(2, (1/2+(1/2)*I)*2^(1/2))-((1/2)*I)*polylog(2, (-1/2-(1/2)*I)*2^(1/2))-((1/2)*I)*polylog(2, (-1/2+(1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2

-((1/8)*I)*(Pi^2+4*polylog(2, (-1/2+(1/2)*I)*2^(1/2))+4*polylog(2, (-1/2-(1/2)*I)*2^(1/2))-4*polylog(2, (1/2+(1/2)*I)*2^(1/2))-4*polylog(2, (1/2-(1/2)*I)*2^(1/2)))

(4)

>

Download Unable_to_simplify_expressions_containing_dilog.mw

(By the way, Mathematica's Integrate cannot compute this double integral explicitly.)

Is the use of `solvefor` less reliable?...

Asked: sursumCorda 1284 Product: Maple 2023

April 08 2023

1 3

Certainly, ½ cannot be a root of the following equations:

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restart;

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solvefor[x]((x-RealDomain:-`^`(2, -1))*RealDomain:-`^`(x-2*RealDomain:-`^`(3, -1), -1)*(1-sqrt(1-x*(x-2*RealDomain:-`^`(3, -1))*RealDomain:-`^`(RealDomain:-`^`(x-RealDomain:-`^`(2, -1), 2), -1))) = 0)

Warning, solvefor is deprecated. Please use solve command.

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`~`[limit]((x-1/2)*(1-sqrt(1-x*(x-2/3)/(x-1/2)^2))/(x-2/3), [x = 0, x = 1/2])

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solvefor[x]((x-RealDomain:-`^`(2, -1))*RealDomain:-`^`(x-2*RealDomain:-`^`(3, -1), -1)*(1-sqrt(1+3*x*(x-2*RealDomain:-`^`(3, -1))*RealDomain:-`^`(5*RealDomain:-`^`(x-RealDomain:-`^`(2, -1), 2), -1))) = 0)

Warning, solvefor is deprecated. Please use solve command.

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`~`[limit]((x-1/2)*(1-sqrt(1+3*x*(x-2/3)/(5*(x-1/2)^2)))/(x-2/3), [x = 0, x = 1/2])

(5)

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Download solvefor_BUG.mw

But why can't Maple's solvefor rigorously verify (or at least try to check) the solution by itself?
Please note that this issue is irrelevant to the alleged deprecated command. You may reproduce these via :-solve, Degrees:-solve, RealDomain:-solve, PDEtools:-Solve, etc.