Axel Vogt

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20 years, 226 days
Munich, Bavaria, Germany

MaplePrimes Activity


These are answers submitted by Axel Vogt

You should use UpperCase Int instead of lowercase int, if you want to evaluate numerical.
And here it is better to use 3/10 instead of 0.3:

  Int((diff(-ln(1-Fy), y))*fy, y = -infinity .. infinity):
  IntegrationTools:-Change(%, y-3/10 = t, t);
  #convert(%, erfc);
  evalf(%); # using Digits:=15

                   infinity
                  /
                 |                        2
                 |                  exp(-t )
                 |          - --------------------- dt
                 |               /            1/2 \
                 |               |         t 2    |
                /             Pi |-1 + erf(------)|
                  -infinity      \           2    /


                          0.903197285568625

You may write S1 := [allvalues(sol)]; to have a list of the 4 solutions (of a 
general polynomial of degree 4, so already this is quite lengthy):

map(length, S1);
                       [2698, 2698, 2698, 2698]

Now at least you can do it for each of them (if it makes sense):

S2 := eval(S1, PARAM): # now a list, output is suppressed using ":"

map(length, S2);
                   [116652, 116652, 116652, 116652]

If you assume, that 1 printed page has 80 columns and 60 lines, then each of the
entries (having 116652 characters) would need ~ 24 pages to be printed, and thus
about 100 pages overall.

It usually would not make much sense to show that on a screen (though the
classical interface could do it, I used it with M17 for your task).

- (1^r) vs. (-1)^r

I stick to the first notation of f. For me that is not a function, since RootOf stands
for the set of solutions (hence there is no unique number assigned to n).

One has to select for the roots. And I simplify the results. Then 2 cases remain:

[allvalues(f(n))]:
simplify(%): evala(%);

h:=unapply(%[1],n);
g:=unapply(%%[2],n);

   h := n -> -1/3*(6*n^2-(21*n^2-24*n+7)^(1/2)-6*n+2)/(2*n^2-3*n+1)

Considering the first gives

[solve(h(n), n)];

                               1/2          1/2
                             33           33
                      [1/4 - -----, 1/4 + -----]
                              12           12
map(h,%): simplify(%);

                                [0, 0]


The second possible selection is interesting, it has no solution.
I am using 32 Bit on Win 7
theDLL:="C:\\WINDOWS\\SYSTEM32\\urlmon.dll";

URLDownloadToFile := define_external(
  'URLDownloadToFileA',
  pCaller::integer[4],
  szURL::string,
  szFileName::string,
  dwReserved::integer[4],
  lpfnCB::integer[4],
  'RETURN'::integer[4] ,
  LIB=theDLL):

Url:= " ... "; # as string

myDirectory:= "d:\\temp";
myFile:=      "data.csv";
Destination := cat(myDirectory, "\\", myFile);

DL:= proc() URLDownloadToFile(0, Url, Destination, 0, 0) end proc;
DL(); # now download

-3*b*k*u^2-3*b*k^2*u^4-k^3*u^6*b+k*u+5*k^2*u^3-b;
subs(b=1, k=1, %);
[solve(%, u)]: evalf(%);


  [0.794972852988398 + 0.401160655470270 I,
        -0.102016745838554 + 0.541867900596280 I,
        -0.692956107149844 + 1.91520931667072 I,
        -0.692956107149844 - 1.91520931667072 I,
        -0.102016745838554 - 0.541867900596280 I,
        0.794972852988398 - 0.401160655470270 I]

In my second live I work as privacy officer. And as such I already would stop using
that service at registration: the most idiotic thing I can imagine, that already at
that stage Google analytics is present and tracking.

Similar thoughts for your other data source, which uses Amazon's cloud.

Due to politeness I do not want to comment on Maple :-)

I think it is possible to download such files without browser or Maple in anonymous
way (using WIN DLLs or wget) and that this is a better idea.

In your case actually Maple does it "only" numerically, try it with 32/10 instead of 3.2

Z / nZ = Z / (-n)Z, that's all ...

This is a polynomial of degree 6 and the command 'irreduc' returns true, so it is not likely to be solvable by radical expressions

Setting k=1, b=1 and using fsolve(%, complex) shows, that it may have only non-real roots

The answer is: yes, it has no roots.

That follows by looking at Eigenvalues and Eigenvectors, using linear Algebra only.
The appended sheet shows it and I hope it is correctly written down.

MP_primitive_matri.mws

MP_primitive_matri.pdf

edited: changed file names

You may use "signum".

eq := x = y*(25+2*x)^(2/3)/(25*(.566*(25*x)^(2/3))); 

[seq( eq, y in [1,2,5])];
map(fsolve, %);

    [.205293886670198, .312212133156964, .544930149205805]


Or if you have written it in rational notation you will end up with

RootOf(113325935*_Z^15-256*_Z^6*y^3-6400*_Z^3*y^3-40000*y^3, index=1)^3;
[seq(%, y in [1,2,5])];
evalf(%);

    [.205293886670197, .312212133156964, .544930149205804]

why do you expect that? how would you prove it?

sqrt(1+x^2+y^2);
int(%,z=-1..2);                       # does not depend on z, so kill it
Int(%, y=-sqrt(8-x^2)..sqrt(8-x^2));  # and the 2nd integral is 1-dim
Change(%, y=sqrt(8-x^2)*eta, eta);    # get rid of variable bounds
value(%);                             # solve it
Int(%, x=0..2*sqrt(2)); simplify(%);  # set up final task, keep it simple
value(%);                             # now finish it

                                26 Pi

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