For questions regarding the underlying implementation of built-in functions.

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Apparent issue with derivative of FractionalPart [duplicate]

This issue came to my attention from Math.SE: http://math.stackexchange.com/questions/1015325/is-the-derivative-of-x-on-0-1-always-equal-to-1/1015342#1015342 To summarize, it appears that ...
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102 views

How to find matrix exponential using RootSum? [duplicate]

From what I've been able to deduce, Mathematica uses a root sum scheme to determine the exponential of a matrix. Can someone please explain to me the theory behind this? I've searched, but have had no ...
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146 views

How to write my own interpolation method [duplicate]

I was comparing results of spline interpolation in Mathematica and C++/gsl-library Results of interpolation are different if I use ...
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0answers
36 views

Internals of Prime function [duplicate]

Does anyone knows how exactly Prime works ? For example how Prime[1000000000] is calculated ? The only information I found was ...
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1k views

How to Output Chi-Squared Statistics when using NonLinearModelFit

I am using NonLinearModelFit for some curve fitting and I was wondering if NLM is able to output chi-squared/leastsquared statistics from the best-fit parameters and confidence intervals. From my ...
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84 views

What algorithm is Mathematica using for FirstPassageTimeDistribution[]?

What algorithm is Mathematica 9 using for FirstPassageTimeDistribution[]? Is it attempting to use PseudoInverse[] on the ...
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1answer
91 views

Mathematica Lattice Reduce Command

I'm going through a very old copy of "Mathematica: A System for Doing Mathematics by Computer" for self practice. I'm on chapter 3, and ran into the LatticeReduce ...
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52 views

How to make work Plus function? [duplicate]

I have a little problem. I have k = 1.56343*10^9; r = 9.10492*10^18. And I should receive a (2*r*r-k*k)/2*r*r, it equals to ...
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68 views

Plot function failure, and understanding how mathematica selects recursion points for correction

I think it is best to start out by directing everyone to this link. The discussion concerns why the Plot function fails to accurately generate a simple sine wave for given parameters. The answer given ...
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61 views

Birch clustering in Mathematica

I want to implement birch clustering in Mathematica. MAthematica only has 4 methods of clustering, is there any implementation for Birch clustering? Birch clustering is much faster than K means ...
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133 views

How does Mathematica solve eigenvalues?

I believe mathematica uses some techniques beyond our book. According to the text book it is not possible to solve eigenvalues of which the matrix has not completely eigenvectors, or of those matrix ...
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130 views

Mathematica's steps towards the result of a definite integral

I am interested in this definite integral: $$ \eqalign{\int_0^\infty {x^2 \log(1-e^{-x})}\; dx\cr } $$ That is: ...
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1answer
70 views

Miller-Rabin algorithm [closed]

I want to implement the Miller-Rabin algorithm in Mathematica to check if a number is prime with at least 99.99% probability. I used this: ...