## 432 Reputation

15 years, 113 days

## closed form of sum...

I tried looking the series up in Hansen's Table, but no luck. Given how simple the definition, this seems like evidence that no one knows a closed form. Another approach, admittedly unlikely, is to use `identify(evalf(sum(...)))`. But this too gave no answer.

## Minimizing the maximum...

If the ranges for `r` and `zeta` are, for example, -2..3 and -6..7, then how about something like this? `with(Optimization):` `g:= zeta -> Maximize(a(r, zeta), r = -2 .. 3, method = 'branchandbound');` `Minimize(g, -6 .. 7, method='branchandbound');` Note that `method` is used to get a global solution.

## Monty Hall Problem...

For some general background, it is worth noting that this is the “Monty Hall Problem”.

## Optimization call...

How about this? ``` Optimization[Maximize](objective(x1, x2, x3, x4, x5, x6, x7, x8, x9), seq(x || i = 0 .. 7, i = 1 .. 9), initialpoint = [seq(x || i = some_point[i], i = 1 .. 9)]);``` [0.99999999999979594, [x1 = 0.249910963699999988, x2 = 2.07892373100000016, x3 = 2.25241025000000006, x4 = 5.71395350600000018, x7 = 3.14159233835433582, x8 = 3.14159233239993796, x9 = 3.14159261604398532, x5 = 0.347503411099999992, x6 = 1.57079632730711150 ]]

## Real fixed points...

To add to Robert Israel's answer, if you want only solutions in R4, try `RealDomain`. `use RealDomain in solve(F - [x1,x2,x3,x4]) end use;`           {x3 = 0, x1 = 0, x2 = 0, x4 = 0}

## changecoords...

Does `changecoords` help? This can do conversion to cartesian, from just about anything. changecoords([r, theta], [r, theta], 'polar')           [r*cos(theta), r*sin(theta)] changecoords([r, phi, theta], [r, phi, theta], 'spherical')           [r*sin(theta)*cos(`ϕ`), r*sin(theta)*sin(`ϕ`), r*cos(theta)]

## hah!...

… but about exp(Pi), this is transcendental, by the the Gelfond–Schneider theorem (which solved the seventh of Hilbert's problems). Gelfond also had a separate proof for exp(Pi), a few years earlier (cited here).

## Point-and-click methods...

A good general guideline for GUIs is that (almost) anything that can be done via point-and-click should also be doable via some sequence of keystrokes.

## Statistics:-PointPlot...

Have you looked at Statistics:-PointPlot? If `x` and `y` are lists, then `Statistics:-PointPlot(y,xcoords=x)` should work well. I just tried it with 5000 points (in Maple 11), and it worked fine; response time was <2 seconds.

## fsolve with Int...

Here is a simpler example that illustrates the issue. `fsolve(Int(t, t = 0 .. x) = 1);` `Error, (in fsolve) number of equations, 1, does not match number of variables, 2` But there is an easy solution: `fsolve(x->Int(t, t = 0 .. x) = 1);`

## Homework?...

Is this a homework assignment? (If so, does your teacher approve of asking on MaplePrimes?)

## Re: Is Maple 11 the answer?...

Brian, for some thoughts about using documents and the Standard Interface in Maple 11, see my blog entry related to this.

## collapsible section...

Another approach to the problem is to put the computation into its own section (or subsection). Then collapse the section.

## minimum vs. minimal...

There seems to be some terminological confusion. Yath is asking for all minimal cuts, whereas `mincut` finds a minimum cut. Maple does not have a built-in function for the "minimal cuts" problem. I googled a little and found some papers that have algorithms; here are two doi: 10.1007/BF01074775 10.1109/LCN.2000.891015 There might be others; I only spent a few minutes googling. Too, there might be different approaches that take advantage of some other functions in Maple.
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