wolfram-mathematica

This is a design issue I came across while working on implementation of Generalized Distributive Law . Suppose you need to automatically generate expressions of the following form (source: yaroslavvb.com ) Terms inside the sum, fixed variables and "summed over" variables are automatically generated for each such expression, and "f" functions are defined separately. To generate expression above, I may need to call sumProduct(factors,fixedVariables,fixedValues,freeVariables,freeRanges) where factors={{1,4},{3,4},{3,4,5}} fixedVariables={1,3} fixedValues={-1,9} freeVariables={4,5} freeRanges=

Similar questions have been asked previously here but none seem to answer my example. I compute the eigenvalues and eigenvectors of a matrix A using Mathematica and SciPy; the eigenvalues agree but this is not the case for the eigenvectors: (1) the lowest (eigenvalued) eigenvector agrees (2) the remaining corresponding eigenvectors of Mathematica and SciPy are not related by a multiplicative factor (3) I can compute the transformation matrix T sending SciPy's eigenvector to Mathematica's corresponding eigenvector using the outer product T = numpy.outer(MathematicaEigenvector, SciPyEigenvector)

I have a list of pairs of values in mathematica, for example List= {{3,1},{5,4}} . How do I change the first element (3 & 5) if the second element does not reach a threshold. For example, if the second parts are below 2 then i wish the first parts to go to zero. so that list then = {{0,1},{5,4}} . Some of these lists are extremely long so manually doing it is not an option, unfortunately. Conceptually, the general way is to use Map . In your case, the code would be In[13]:= lst = {{3, 1}, {5, 4}} Out[13]= {{3, 1}, {5, 4}} In[14]:= thr = 2 Out[14]= 2 In[15]:= Map[{If[#[[2]] < thr, 0, #[[1]]], #

I am looking to make a nice demo of the problem I mentioned in Integration in Mathematica but it is very slow yet and the Manipulate is not smooth at all. Considering the below, is there means by which I could improve the situation. That is see a more continuous dynamic. Also I can't get to have the Manipulator open using Control->Manipulator[Appearance->Open] arrows = ParallelTable[{ RandomVariate[NormalDistribution[0, Sqrt[1]]], RandomVariate[NormalDistribution[0, Sqrt[1]]]}, {20000}]; Manipulate[ Graphics[{ White, Rectangle[{-5, -5}, {5, 5}], Red, Disk[{0, 0}, 1], Black, Point /@ (arrows[[;