phoenix's profile - activity

Some basic things about matrices don't seem to work, like, Z = matrix([[1,0],[2,3]]) Z.charpoly(y)

Thats a very generic description. Is there something specific which helps?

Like say I want to create a $4k \times 4k$ size matrix by putting together certain $4\times 4$ matrices into a $k \times k$ array.

• Can the "block_matrix" command help me create such a $4k \times 4k$ array of 0s called $A$ ? (such later I can say something like $A[a,b] = X$ where $0 \leq a,b \leq k$ and $X$ is some $4\times 4$ matrix and that will assign the matrix $X$ at the $(a,b)$ array position)

(3) And why is "d={}" different from starting as "d=[]" ?

(2) Can you explain this " m = [[matrix(2, 2, 0)]*4 for _ in range(4)]" ? What exactly is this doing? Is m not defined as a matrix at this step?

(1) Why does $d[0,2]$ make sense? $d$ is not a matrix but just an empty list. If assigning matrices to $d$'s tuple coordinates make sense then why not just read the data and list and assign the appropriate matrices to d's corresponding positions?

Say I am given a data set which looks like $[ (0,2,A), (0,3,B), (1,2,C), (1,4,D) ]$ where $A,B,C,D$ are matrices all of the same dimension say $k$. (the data set will always have unique pairs of integers - as in if (1,2,) tuple occurs then (2,1,) tuple will not occur)

Now I want to create a 4x4 matrix say X of dimension $4k$ thought of as a 4x4 array of k-dimensional matrices. The arrays in $X$ are to be defined as $X(0,2) = A, X(2,0) = A^{-1}, X(0,3) = B, X(3,0) = B^{-1}, X(1,2) = C, X(2,1) = C^{-1}, X(1,4) = D, X(4,1) = D^{-1}$ and all other array positions in $X$ are to be filled in with $0$ matrices of dimension $k$.

• How can one create such a X on SAGE?

  X is a matrix of matrices and I am not sure how one can define this on SAGE. Like saying "X(0,3) = B" is not going to make any obvious sense to SAGE. I necessarily need X to be a matrix so that i can later say calculate its characteristic polynomial.

[I showed this above example with just $4$ tuples. I want to eventually do it with much larger data sets]

Can someone help me with the process?

I downloaded a .ova and a .vmdk file from the mirror

Now what?

Why is this slightly modified thing not working? def All_Maps(A,B): from itertools import product k = len (A) return product(B,repeat = k)

for f in All_Maps ([a,b],[0,1]): print f

Is that "repeat" a command?

What I want to do is this : Say I take a graph $K_{n,n}$ and choose an ordering for each edge arbitrarily - say denote each edge as $(i,j)$ where $i$ is in the left partition and $j$ is in the right partition. I have a set of matrices $A = { A_1, A_2,...,A_k }$. I want to iterate over all possible ways in which one could have assigned an A matrix to an edge of this graph.

• How does one do that? (..apart from writing a massive sequence of nested loops!..)

Thanks! Somehow I got confused!

@tmonteil I don't know in what kind of a course can this be a homework :D I am a researcher who recently started using Python and Sage for my research! Back to the question : I don't understand what you are saying. Roughly I would think that one needs to simulate a coin toss where heads come with probability $f(x)$. How is that equivalent to comparing $f(x)$ to a randomly generated number in the interval $[0,1]$ ? (If the two options are $a$ and $b$ then say I want to choose $a$ with a probability $f(x)$ and $b$ with a probability $1-f(x)$ and then I guess you mean that this is equivalent to choosing $a$ if the random number is (greater? or lesser?) then $f(x)$ or else otherwise?) I am not getting you.

Like say in the middle of a code I compute a function value $f(x)$ and I knwo that $0 \leq f(x) \leq 1$. Now I want to write an if-then-else which will do one option with probability $f(x)$ and the other otion with probability $1-f(x)$. How does one make Sage do this?

Can somoen kindly show a template example to simulate this?

Why is Sage hanging up trying to find roots of this equation?

0 = (x^2 - 6.00000000000000)*x^2 - 4*x*(e^(2/5*I*pi) + e^(-2/5*I*pi)) - e^(4/5*I*pi) - e^(-4/5*I*pi) - 1

If some of the roots turned out to be complex then would "max" throw up some kind of an error message which as an user I can catch ?