gulliet

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19 years, 29 days

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You are right in assuming that the warning messages you reported are not related to and do not prevent Maple to launch Having said that, I am clueless at what could be the issue. Not really helpful... [Updated] Yet, I am still convince that the issue is related to file authorization. Here is what I get on my system when using Maple in command line mode: 97_MapleCmdLine.jpg --Jean-Marc
I have copied and pasted the code you provided on my system --Maple 12.02 64-bit Intel Mac OS X Leopard 10.5.6--, evaluated it, then I have successfully inverted the resulting matrix thanks to the command MatrixInverse from the LinearAlgebra package.
> LinearAlgebra[MatrixInverse](C);

                          [ 36 x 36 Matrix       ]
                          [ Data Type: anything  ]
                          [ Storage: rectangular ]
                          [ Order: Fortran_order ]

97_MatrixInverse 36 by 36.png Therefore, the questions are: what platform are you working on and what command did you try to inverse the matrix? (And in addition, what is the result of LinearAlgebra[MatrixInverse]?) Regards, --Jean-Marc
I believe that the OP is looking for some kind of postfix operator that would allow to write at the end of an expression one or more commands rather than adding them at the beginning. (Of course, my interpretation might be totally wrong.) I am not aware of any such mechanism in Maple, so I will take an example form Mathematica. The equivalent function to evalf() is N[]. In prefix notation one would write N[Pi] to get an numerical approximation of Pi. In postfix notation, one would write Pi//N to get the same approximation (so // is the postfix operator). I think that the OP is looking for something like some_maple_expression//evalf. Best regards, --Jean-Marc
I believe that the OP is looking for some kind of postfix operator that would allow to write at the end of an expression one or more commands rather than adding them at the beginning. (Of course, my interpretation might be totally wrong.) I am not aware of any such mechanism in Maple, so I will take an example form Mathematica. The equivalent function to evalf() is N[]. In prefix notation one would write N[Pi] to get an numerical approximation of Pi. In postfix notation, one would write Pi//N to get the same approximation (so // is the postfix operator). I think that the OP is looking for something like some_maple_expression//evalf. Best regards, --Jean-Marc
Hum, the code works as expected ---i.e. yields random values rather than zeros--- with Maple 12.02 on 64-bit Intel Mac OS X Leopard 10.5.6. So could the weird behavior be platform dependent?
> with(LinearAlgebra[Modular]); A1 := Random(31, 5, 4, integer[]);

                                 [25  23  23   2]
                                 [              ]
                                 [21  22  15  20]
                                 [              ]
                           A1 := [ 2  28  12  19]
                                 [              ]
                                 [20   4  22   4]
                                 [              ]
                                 [26  24  12   7]
> A2 := Random(31, 20, 30, float[8], Fortran_order);
> A2[1 .. 10, 1 .. 10];

             [ 4.   4.  15.   6.  29.  14.   3.   8.   9.   6.]
             [                                                ]
             [ 6.   9.  23.  11.  14.  18.  13.  14.   7.  28.]
             [                                                ]
             [ 3.  30.  25.  25.  14.  12.   5.  21.   7.  11.]
             [                                                ]
             [27.  25.  23.  24.  19.   7.  11.  23.   6.  26.]
             [                                                ]
             [11.  25.  26.  20.  15.   9.   2.  10.   8.  25.]
             [                                                ]
             [28.  10.   8.  14.  25.  24.  14.  15.  27.  18.]
             [                                                ]
             [ 5.  16.  21.  15.   3.  16.  23.  24.   9.  24.]
             [                                                ]
             [ 7.  19.  28.  25.  17.  20.  16.  15.  15.   9.]
             [                                                ]
             [14.   1.  20.   5.   9.   6.  12.   4.  21.   0.]
             [                                                ]
             [22.  20.  29.  16.   6.  22.  15.   3.   0.  29.]
> A3 := Random(31, 3, 0, integer[]);

                                       [16]
                                       [  ]
                                 A3 := [27]
                                       [  ]
                                       [ 9]
> A4 := Random(31, 0, 5, float[8]);

                       A4 := [8., 12., 16., 10., 25.]


Regards, --Jean-Marc
I totally agree; however this article ---from my point of view and my understanding of the OP's request(s)--- has some advantages for the OP: 1. It is available online 2. It is not wikipedia like 3. It should be understandable by the OP 4. The algorithms described should fit more of less the intuitive yet fuzzy definition of widely use Of course, a modern treatment of the subject as of today would inevitably describe parallel algorithms. Now, are they widely used? That is the question :-)] Best regards, --Jean-Marc
I totally agree; however this article ---from my point of view and my understanding of the OP's request(s)--- has some advantages for the OP: 1. It is available online 2. It is not wikipedia like 3. It should be understandable by the OP 4. The algorithms described should fit more of less the intuitive yet fuzzy definition of widely use Of course, a modern treatment of the subject as of today would inevitably describe parallel algorithms. Now, are they widely used? That is the question :-)] Best regards, --Jean-Marc
"A Survey of Modern Integer Factorization Algorithms" by Peter Montgomery [1] should be an academic article of utmost interest. You should find it at your institution's library and/or also online. Abstract Every positive integer is expressible as a product of prime numbers, in a unique way. Although it is easy toprove that this factorization exists, it is believed very hard to factor an arbitrary integer. We survey the bestknown algorithms for this problem, and give some factorizations found at CWI. Hope this helps, --Jean-Marc [1] A survey of modern integer factorization algorithms. Montgomery, Peter L.. CWI Quarterly 01/01/1994.Vol.7,Iss.4;p.337-366
"A Survey of Modern Integer Factorization Algorithms" by Peter Montgomery [1] should be an academic article of utmost interest. You should find it at your institution's library and/or also online. Abstract Every positive integer is expressible as a product of prime numbers, in a unique way. Although it is easy toprove that this factorization exists, it is believed very hard to factor an arbitrary integer. We survey the bestknown algorithms for this problem, and give some factorizations found at CWI. Hope this helps, --Jean-Marc [1] A survey of modern integer factorization algorithms. Montgomery, Peter L.. CWI Quarterly 01/01/1994.Vol.7,Iss.4;p.337-366
Certainly the best website dedicated to the history of mathematics. Check The MacTutor History of Mathematics archive Regards, --Jean-Marc
Certainly the best website dedicated to the history of mathematics. Check The MacTutor History of Mathematics archive Regards, --Jean-Marc
Could you post a simplified version of the procedure(s) just long and complicated enough to exhibit the same behavior as the real one(s)? Doing so would greatly help readers of this forum giving you specific and accurate advices about the issues(s), suggestions that would also be easily applicable to the real procedure(s). Regards, --Jean-Marc
You are right, indeed: the error is generated by the Sample command.
> restart; with(Statistics); 
ZetaII := proc (g, a) local i; sum(1/(i+a)^g, i = 0 .. infinity) end proc; 
f := simplify(piecewise(`and`(k >= kmin, k::integer), 
k^(-lambda)/ZetaII(lambda, kmin), 0), piecewise);

      f :=  /          (-lambda)                                       
            |         k                                                
            | ---------------------------      kmin <= k and k::integer
            | infinity                                                 
            |  -----                                                   
            |   \                                                      
           <     )              (-lambda)                              
            |   /     (i + kmin)                                       
            |  -----                                                   
            |  i = 0                                                   
            |                                                          
            |              0                          otherwise        
            \                                                          

> ND := Distribution(PDF = unapply(f, k));

ND := module () export PDF, Type; option Distribution, Continuous; end module

> X := RandomVariable(ND);

                                   X := _R

> Sample(X, 5);
%;
Error, (in simplify) too many levels of recursion
Regards, --Jean-Marc
You are right, indeed: the error is generated by the Sample command.
> restart; with(Statistics); 
ZetaII := proc (g, a) local i; sum(1/(i+a)^g, i = 0 .. infinity) end proc; 
f := simplify(piecewise(`and`(k >= kmin, k::integer), 
k^(-lambda)/ZetaII(lambda, kmin), 0), piecewise);

      f :=  /          (-lambda)                                       
            |         k                                                
            | ---------------------------      kmin <= k and k::integer
            | infinity                                                 
            |  -----                                                   
            |   \                                                      
           <     )              (-lambda)                              
            |   /     (i + kmin)                                       
            |  -----                                                   
            |  i = 0                                                   
            |                                                          
            |              0                          otherwise        
            \                                                          

> ND := Distribution(PDF = unapply(f, k));

ND := module () export PDF, Type; option Distribution, Continuous; end module

> X := RandomVariable(ND);

                                   X := _R

> Sample(X, 5);
%;
Error, (in simplify) too many levels of recursion
Regards, --Jean-Marc
As you can see, running your code on my system ---Maple 12.02 64-bit Intel Mac OS X 10.5.6--- I have got the error message "too many recursions" from the command simplify. I suspect this is due to the absence of definition for the function Zetall.
restart;
with(Statistics); 
f := simplify(piecewise(`and`(k >= kmin, k::integer),
k^(lambda)/ZetaII(lambda, kmin), 0)); 
ND := Distribution(PDF = unapply(f, k)); 
X := RandomVariable(ND); Sample(X, 5);
%;
         f :=  /       (-lambda)                                   
               |      k                                            
               | --------------------      kmin <= k and k::integer
              <  ZetaII(lambda, kmin)                              
               |                                                   
               |          0                       otherwise        
               \                                                   
ND := module () export PDF, Type; option Distribution, Continuous; end module
Error, (in simplify) too many levels of recursion
> help("ZetaII");

Regards, --Jean-Marc
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