I understand how I overlooked the possibility of the distribution not remaining the same. Thanks! I've tried to look for applications of when people would want to randomly generate matrices in the echelon form (to make a reasonable default) but an unable to think of/ find any.
Why is taking maximal number of pivots a reasonable choice? If this is indeed the case, I will go ahead with maximal number of pivots. Otherwise, the second method you suggested seems like the more expected output for a user who doesn't specify num_pivots? Doing this + adding to the documentation should fix this? On Sunday, January 19, 2020 at 10:48:39 PM UTC+5:30, Nils Bruin wrote: > > The proposal in the ticket is not very desirable. If you're going to > generate a random matrix, you do that with a specific probability > distribution on the matrix space. The target distribution would generally > be one on an infinite space of matrices, but in those cases you usually > want to define a sequence of distributions on finite sets (usually > parametrized by "size of coefficients" somehow) that converges nicely to to > the target distribution. > > What distribution are you proposing on the number of pivots? Uniform? What > is the description of the distribution you are trying to model? > > I think you first want to write a reasonable specification > (mathematically) of what the routine should accomplish and then see what > the implementation should be. > > I suspect that this ticket should actually read "generate a better error > message if user does not supply`num_pivots` with > `algorithm='echelon_form'`". > > Alternatively, taking num_pivots to be maximal by default seems like a > reasonable choice. Or perhaps the pivots should first be generated > uniform-independent randomly from a (finite?) set and then if zeros are > found, build the echelon form with those pivots. It all depends on what the > routine is for. > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/26cc9b2b-f83e-4598-af90-a1899923831c%40googlegroups.com.
