sursumCorda

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2 years, 41 days

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These are questions asked by sursumCorda

One may easily spot that the symbols “” and “” are missing here and here

These two PDF files were printed officially, so I think they can be considered examples of best practice for the export functionality. Does this mean that this functionality is still defective in the most recent release?

Currently, a stand-alone or embeddable Python is by default bundled with Maple and is installed silently (namely, without notification) when installing Maple, but why is there no prompt panel asking for Python configuration (just like Why does Maple ask for a Matlab installation when I install it? and Configuring the Maple Kernel for Jupyter)? 
Actually, I am wondering why I am not capable of installing Maple without bundling Python (even if I am able to clear those files in $MAPLE/Python.$SYS later). In my opinion, a bundling Python suite is more or less unnecessary; wouldn't it be better to provide a tooltip asking for approval? If one really need to interact with Python, one may instruct Maple to make use of some available local version of Python from the outset (rather than having to install an additional Python interpreter with numerous extra packages that occupy almost 2 GB!), and if one does not require such a functionality, one can simply skip the Python installation and free up 2GB immediately. So, will installing Python (or another popular external program, if it is going to be integrated or connected with Maple in future releases) be optional during the Maple installation process? 

I would like to get a (necessary and sufficient) condition on real parameters a, b, and c for which there exists (at least) one non-negative solution to 9*x**4 + c < 9*a*(x - 1) + 3*b*(x**2 - 1) + c*x**3
A convenient way to formulate this is using quantifiers. Unfortunately, if I run 

QuantifierElimination:-QuantifierEliminate(:-exists([x],:-And(x>=0,9*x^4+c<9*a*(x-1)+3*b*(x^2-1)+c*x^3)));

Maple will simply output 

Error, (in RootFinding:-RSGateway:-refine_uni_tri) invalid input: RootFinding:-RSGateway:-try_refine_iso_tri expects its 1st argument, box, to be of type nonemptylist([rational, rational]), but received [8019*x^2+(-9*v__2^2-96552*v__2-279834912)*x+49*v__2^3+78318*v__2^2-387436932*v__2+121801800168, v__2^4+2052*v__2^3-5536296*v__2^2+3575222064*v__2-710903793888]

As an alternative method, one can execute 

RealDomain:-solve([x >= 0, 9*x**4 + c < 9*a*(x - 1) + 3*b*(x**2 - 1) + c*x**3], 'parameters' = {a, b, c});
Warning,  computation interrupted

Regretfully, this time the computation is not done in several minutes (so one may have to abort it manually). 

So, what is the proper approach to the above problem in Maple (without any a priori knowledge, if possible)?

For instance, considering the expression  ≔ exp(1+LambertW(0,x))*(exp(1)*x+log[exp(1)](sqrt(2*Pi))-lnGAMMA(1/2+exp(1+LambertW(0,x))))

restart;
expr := exp(1+LambertW(x))*(exp(1)*x+ln(sqrt(2*Pi))-lnGAMMA(1/2+exp(1+LambertW(x)))) assuming x >= -1/exp(1):

The following limit can be calculated directly: 

1/:-limit(expr, x = +infinity, 'left');
                               24

We can also evaluate , 

:-limit(1/expr, x = +infinity, 'left'); # MultiSeries:-limit also returns wrong result. 
                               0

However, according to plot([1/(exp(1+LambertW(x))*(exp(1)*x+ln(sqrt(2*Pi))-lnGAMMA(1/2+exp(1+LambertW(x))))), 24], x = -1/exp(1) .. +exp(Pi), 'legend' = [1/expr, 24]), the limit value 0 cannot be correct. 
So is this a bug? (And has this been fixed in the forthcoming version?)

GraphTheory:-IsReachable can be used to "determine if there is a path between two vertices", and GraphTheory:-ShortestPath can be used to "find a path between two vertices with minimum distance", but which command can be used to "enumerate all (simple) paths from one node to another" like MatLab's allpaths in Maple? 

For instance, I would like to enumerate (not simply count) at most 3483192 paths with total weights at least 45 in the graph constructed from  that begin at node 30 and end at node 29
There exists a practically ready-made procedure  (where only a limited subset of its local variable  is needed) in a previous question. Nevertheless, after waiting for a quarter of an hour, the evaluation still did not terminate and I had to abort it manually. Meanwhile, MatLab completed the same computation within one minutes: 

So, how to list those 1008252 paths (without knowing the actual total number beforehand) faster in Maple?

Note. MatLab also has a built-in function allcycles, whose efficient Maple equivalent has been proposed in How to obtain all cycles in a graph from its cycle basis - MaplePrimes, yet I cannot find an analogue to MatLab's allpaths

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