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Ben Petschel

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22 Jul 2011 wordhit determines probabilities and expected times to produce words in a random character stream Author: Ben Petschel probability, coin toss, random string, markov chain, transition matrix 4 0
16 Jun 2011 quantilese determines quantiles of data and their standard errors or confidence intervals Author: Ben Petschel quantile, standard error, confidence interval, percentile 2 0
15 Jun 2011 scatterquad2 calculates the volume under a surface defined by scattered points Author: Ben Petschel quad2, dblquad, delaunay 2 0
02 Nov 2010 groebner manipulate and solve systems of multivariate polynomial equations by computing the groebner basis Author: Ben Petschel groebner, polynomial equations 28 14
  • 4.66667
4.7 | 4 ratings
20 Aug 2010 election Implements many different methods for determining the winner of an election given voter preferences. Author: Ben Petschel election, voting 3 0
Comments and Ratings by Ben View all
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18 Aug 2011 fdep: a pedestrian function dependencies finder FDEP dissects ML files and iteratively looks for all user defined functions used during runtime Author: us

Excellent tool, much faster and more informative than DEPFUN.

An especially useful feature is detection of unresolved function calls, which DEPFUN doesn't seem to do. The synopses of each module have a list of unresolved names, though I couldn't see a way to get a single list of all unresolved names except by browsing.

Also you might want to switch off latex interpretation in the point labels in the dependency matrix (line 1921, I think).

Good work!
14 Aug 2011 Special Functions math library Collection of Special Functions programs. Author: Paul Godfrey

Nice work, these should be included in the core MATLAB.

Since erf rapidly goes to infinity along the i axis (e.g. erfz(1i*30) = 1i*Inf in floating point), it would be useful to have a function that calculates exp(z^2)*erf(z) or z*exp(z^2)*erfc(z).
14 Aug 2011 Dett Computes the determinant of non-square matrices. Author: Paul Godfrey

Interesting idea, it would be good to see references to the literature; for example does it relate to the one in
 http://www.emis.de/journals/BAG/vol.46/no.2/b46h2rad.pdf

which can be used to calculate the areas of polygons, for example.

Any definition for rectangular matrices, including the above, would be a major rewrite of the theory for square determinants which are defined as alternating multilinear forms; this would imply that det(A)=0 whenever m<n.
11 Aug 2011 Fractions Toolbox create and manipulate fractions (K+N/D) using exact arithmetic Author: Ben Petschel

Ok, to do that you'd need to define a total ordering on the polynomials by partitioning R[x] into P, -P and {0}, so p(x)>0 if p(x) is in P. See Lang's Algebra chapter 11 (real fields) for examples and details on the theory - e.g. the monomial orderings used for Groebner basis calculation are valid. This way you have sign(p)=1 if p is in P, etc, and similarly abs(p)=sign(p)*p.

Also I forgot to mention that MOD is required, but once this is defined then it's easy to write a GCD function. To define MOD you just need to define the representative elements of the cosets R[x]/p(x), such that MOD(q,p)>=0.

If you're willing to put in the effort implementing this, I'd be keen to see the results, but otherwise you're probably better off with a professional package such as Mathematica (which has an affordable home-use version) or the Symbolic Toolbox.
29 Jul 2011 Complex Function Grapher A tool to graph complex functions on the Argand plane (x + iy). Author: Jon Moller

Could be very useful if you turn the script into a function and allow command-line inputs (e.g. with function handles) to avoid having to retype the inputs interactively; also show which parameters and additional commands produced the example in the screenshot.
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16 Jan 2012 groebner manipulate and solve systems of multivariate polynomial equations by computing the groebner basis Author: Ben Petschel Tang, Rongfu

excellent work! thanks.
11 Aug 2011 Fractions Toolbox create and manipulate fractions (K+N/D) using exact arithmetic Author: Ben Petschel Petschel, Ben

Ok, to do that you'd need to define a total ordering on the polynomials by partitioning R[x] into P, -P and {0}, so p(x)>0 if p(x) is in P. See Lang's Algebra chapter 11 (real fields) for examples and details on the theory - e.g. the monomial orderings used for Groebner basis calculation are valid. This way you have sign(p)=1 if p is in P, etc, and similarly abs(p)=sign(p)*p.

Also I forgot to mention that MOD is required, but once this is defined then it's easy to write a GCD function. To define MOD you just need to define the representative elements of the cosets R[x]/p(x), such that MOD(q,p)>=0.

If you're willing to put in the effort implementing this, I'd be keen to see the results, but otherwise you're probably better off with a professional package such as Mathematica (which has an affordable home-use version) or the Symbolic Toolbox.
11 Aug 2011 Fractions Toolbox create and manipulate fractions (K+N/D) using exact arithmetic Author: Ben Petschel Lauwerys, Christophe

Great stuff, but I wonder how your two statements quoted below can be unified.

In other words: how can you define for instance SIGN and ABS for objects that represent polynomials? Not to mention GCD for multivariate polynomials ... Not an expert but do you need Groebner bases for this?

Thanks

Christophe

A)

% Non-standard objects must include 0, 1, -1 and require the following
% operations to be defined in order to create a fraction object:
% gcd
% rem
% sign
% abs
% +, - , .*, ./
% ==, <, <=, >, >=, ~=
%
% The following additional operation definitions are recommended:
% *, .^
% sort
% floor
% factor
% gcd (3-output form)
% rat (if floor(x) or mod(x,1) is not always equal to x)

B) If there exists a suitably defined polynomial object, this toolbox could be used to perform partial fractions.
23 Jun 2011 Fractions Toolbox create and manipulate fractions (K+N/D) using exact arithmetic Author: Ben Petschel McKeeman, Bill

I used this toolbox in the computation of pi (see FX 29504).
26 Jan 2011 golaycodec encode/decode a binary array using the Golay code with error correction Author: Ben Petschel Petschel, Ben

This is all described in the help text.
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sql, arithmetic, chebyshevmarkovstieltjes, coin toss, combination
Files Tagged by Ben View all
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Updated   File Tags Downloads
(last 30 days) 		Comments Rating
22 Jul 2011 wordhit determines probabilities and expected times to produce words in a random character stream Author: Ben Petschel probability, coin toss, random string, markov chain, transition matrix 4 0
16 Jun 2011 quantilese determines quantiles of data and their standard errors or confidence intervals Author: Ben Petschel quantile, standard error, confidence interval, percentile 2 0
15 Jun 2011 scatterquad2 calculates the volume under a surface defined by scattered points Author: Ben Petschel quad2, dblquad, delaunay 2 0
02 Nov 2010 groebner manipulate and solve systems of multivariate polynomial equations by computing the groebner basis Author: Ben Petschel groebner, polynomial equations 28 14
  • 4.66667
4.7 | 4 ratings
20 Aug 2010 election Implements many different methods for determining the winner of an election given voter preferences. Author: Ben Petschel election, voting 3 0

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