It may be

sum(ln(1+1/n)/n,n=1..infinity);

                         infinity
                          -----
                           \      ln(1 + 1/n)
                            )     -----------
                           /           n
                          -----
                          n = 1

evalf(%);

                             1.257746887

Alec

Everybody's pictures have disappeared.

Alec

I just thought that I might submit a rpoof,

Rpoof.

eq:=(pi-(pi-1)/2)^2=((pi-1)/2-pi)^2:
verify(op(eq),expand);

                                 true

evalb(expand(eq));

                                 true

solve(map2(op,1,eq),{pi});

                              {pi = -1}

Alec

Is it a therom that Pi is -1?

Alec

Also, to make it looking like a circle, one would have to add an additional specification - something like a vector normal to the plane containing it. Possibly depending on the point coordinates.

Something like 'filled' option also might be useful.

Alec

Also, to make it looking like a circle, one would have to add an additional specification - something like a vector normal to the plane containing it. Possibly depending on the point coordinates.

Something like 'filled' option also might be useful.

Alec

It would be nice to be able to do that with other plot elements as well - axes, tickmarks, the legend box shape and placement etc.

Alec

It would be nice to be able to do that with other plot elements as well - axes, tickmarks, the legend box shape and placement etc.

Alec

With new badges on the new MaplePrimes site, a similar system could be introduced in beta testing. Say, people contributing the most, could be renamed to alpha-testers, and people not contributing at all - to gamma-testers. Then it would be clear that alpha-testers will get a box, beta-testers - a download, and gamma-testers - nothing.

Unfortunately, I am not a beta tester (and neither alpha- or gamma- one.)

Alec

Statistics:-Shuffle seems to be twice as fast as combinat:-randperm in few examples that I tried, and it can be applied to Arrays. I'm not sure about the garbage it produces though.

A simple and obvious speed improvement could be achieved in combinat:-randperm by replacing [seq](...) with [seq(...)]. and N[[seq(...)]] should be better than [seq](N[...],..) and would work for rtables as well, permutting the rows in this example, after changing the n assignment at the very beginning.

A corresponding NAG library procedure (one that is used in LU-decomposition, for instance), for applying a permutation to a matrix (or another kind of rtable) should work fine.

Alec

Statistics:-Shuffle seems to be twice as fast as combinat:-randperm in few examples that I tried, and it can be applied to Arrays. I'm not sure about the garbage it produces though.

A simple and obvious speed improvement could be achieved in combinat:-randperm by replacing [seq](...) with [seq(...)]. and N[[seq(...)]] should be better than [seq](N[...],..) and would work for rtables as well, permutting the rows in this example, after changing the n assignment at the very beginning.

A corresponding NAG library procedure (one that is used in LU-decomposition, for instance), for applying a permutation to a matrix (or another kind of rtable) should work fine.

Alec

Other arithmetic operations seem to have the same problem,

zip(`+`,Array([3],datatype=integer[4]),Array([9],datatype=integer[4]));
                           
                                [12.]

op([4,1],%);

                         datatype = float[8]

Also,

zip(`<>`,Array([3],datatype=integer[4]),Array([9],datatype=integer[4]));
                           
                                 [1.]

zip(`=`,Array([3],datatype=integer[4]),Array([9],datatype=integer[4]));
                            
                                 [0.]

Strangely enough, integer[8] seem to be OK (but integer[1] - not.)

Alec

Other arithmetic operations seem to have the same problem,

zip(`+`,Array([3],datatype=integer[4]),Array([9],datatype=integer[4]));
                           
                                [12.]

op([4,1],%);

                         datatype = float[8]

Also,

zip(`<>`,Array([3],datatype=integer[4]),Array([9],datatype=integer[4]));
                           
                                 [1.]

zip(`=`,Array([3],datatype=integer[4]),Array([9],datatype=integer[4]));
                            
                                 [0.]

Strangely enough, integer[8] seem to be OK (but integer[1] - not.)

Alec

Still, am wondering...

Alec

Not anymore. And neither am Maple's one. I'm still a Mathematica's fan there though.

Alec