MaelstromYamato's profile - activity

Thanks. This does help!

1. Matrix -> type 'sage.matrix.matrix_integer_dense.Matrix_integer_dense'

   from sage.matrix.all import Matrix

   or

   from sage.matrix.constructor import Matrix

2. vector -> type 'sage.modules.vector_integer_dense.Vector_integer_dense'

   from sage.modules.free_module_element import vector

3. ZZ -> type 'sage.rings.integer_ring.IntegerRing_class'

   from sage.rings.integer_ring import ZZ

4. MixedIntegerLinearProgram -> type 'sage.numerical.mip.MixedIntegerLinearProgram'

   from sage.numerical.mip import MixedIntegerLinearProgram

Once you know roughly where the class is defined, for example Matrix is defined somewhere in SAGE_ROOT/devel/sage/sage/matrix/, take a look at the file all.py in that directory. In this case you'll find a line

from constructor import matrix, Matrix, column_matrix, random_matrix, diagonal_matrix, identity_matrix, block_matrix, block_diagonal_matrix, jordan_block, zero_matrix, ones_matrix, elementary_matrix, companion_matrix

So that tells you that you can import Matrix from sage.matrix.all or from sage.matrix.constructor. Your other examples can be dealt with similarly.

Try the following in a notebook:

from sage.misc.latex import latex_extra_preamble
latex.add_to_preamble('\\usepackage{amsmath}')
latex.add_to_preamble('\\usepackage{amsthm}')
latex.add_to_preamble('\\usepackage{amssymb}')

you can use show(), save('/my/favorite/folder/for/graphs/graph1.png'), return graph object from the function and have another function show it.

An easy way to use sage in python files is demonstrated in the Sage Tutorial.

#!/usr/bin/env sage -python

import sys
from sage.all import *

if len(sys.argv) != 2:
    print "Usage: %s <n>"%sys.argv[0]
    print "Outputs the prime factorization of n."
    sys.exit(1)

print factor(sage_eval(sys.argv[1]))

Well, what if I don't want to import all of sage as shown above using:

from sage.all import *

Instead of this command above, I just want to import the following:

1. Matrix -> type 'sage.matrix.matrix_integer_dense.Matrix_integer_dense'
2. vector -> type 'sage.modules.vector_integer_dense.Vector_integer_dense'
3. ZZ -> type 'sage.rings.integer_ring.IntegerRing_class'
4. MixedIntegerLinearProgram -> type 'sage.numerical.mip.MixedIntegerLinearProgram'

So I should be able to write something like this in python

from sage.library.package.for.Matrix import *
from sage.library.package.for.vector import *
from sage.library.package.for.ZZ import *
from sage.library.package.for.MixedIntegerLinearProgram import *

I just don't know what they are. Any help is appreciated.

Thanks.

Oh boy... I feel silly how that stumped me all day long. Thank you!

The problem is in the line

dict = {j:Set(int(Vec[i]))}

The Set constructor takes an iterable object and the python int type is not iterable. If you change the line to:

dict = {j:Set( [int(Vec[i])] )}

that problem should go away.

Hello,

For a given matrix M (m by n) and vector V of size n, my goal is to do the following:

1. Take the $\text{i}^{\text{th}}$ column of M and convert them as keywords for a dictionary and associate the keywords to the $\text{i}^{\text{th}}$ value of the vector V.
   1. I do (1) in MatVec(M,V) in the code below by creating a dictionary for each keyword and value. Finally I try to merge all the dictionaries.

Here is my code:

def DictionaryMerge(*args):
    import collections
    super_dict = collections.defaultdict(set)
    for d in args:
        for k, v in d.iteritmes():
            super_dict[k].add(v)
    return super_dict

def MatVec(M,V):
    from sets import Set
    Vec = V.list()
    MatCols = M.ncols()
    D2 = {}
    for i in range(MatCols):
        ColumnVec = M.column(i).list()
        CVec = list()
        for k in range(len(ColumnVec)):
            CVec.append(int(ColumnVec[k]))
        for j in CVec:
            dict = {j:Set(int(Vec[i]))}
            D2 = DictionaryMerge(dict,D2)
     return dict

M = matrix([[(i+1)*(j+2) for i in range(5)] for j in range(6)])
V = vector([int(i+100) for i in range(5)])
MatVec(M,V)

The error I get is:

Traceback (most recent call last):        return super_dict
  File "", line 1, in <module>

  File "/tmp/tmp4m6HiR/___code___.py", line 29, in <module>
     exec compile(u'MatVec(M,V)
  File "", line 1, in <module>

  File "/tmp/tmp4m6HiR/___code___.py", line 22, in MatVec
     dict = {j:Set(int(Vec[i]))}
  File "/home/usr111/sage/local/lib/python/sets.py", line 414, in __init__
     self._update(iterable)
  File "/home/usr111/sage/local/lib/python/sets.py", line 368, in _update
     for element in iterable:
 TypeError: 'int' object is not iterable

I am not so sure why I am getting this error.

perhaps someone can forward this to the sage trac or provide it a tracking number (if the idea has not been considered already).

That was a wonderful explanation of the solution. Thank you!!!

One way to do the general case uses the all_paths method:

sage: [path for path in g.all_paths(0,1) if len(path) == 5]
[[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]]
sage: [path for path in g.all_paths(0,1) if len(path) == 4]
[[0, 2, 3, 1], [0, 2, 4, 1], [0, 3, 2, 1], [0, 3, 4, 1], [0, 4, 2, 1], [0, 4, 3, 1]]
sage: [path for path in g.all_paths(0,1) if len(path) == 3]
[[0, 2, 1], [0, 3, 1], [0, 4, 1]]
sage: [path for path in g.all_paths(0,1) if len(path) == 2]
[[0, 1]]

There is also a longest_path method that takes source and destination as input parameters, but there seems to be a bug with directed graphs. I've made this #13019.

At the theoretical level, the problem is really easy for this specific graph since there are edges between all the vertices. Thus, you can just pick the endpoints and take any permutation of the remaining vertices (or subset of them) to get a path of a fixed length.

In general, I would also like to find if the complete digraph has n vertices, how can I find the path(s) from any two vertices of distance (n-1), (n-2), ..., 2?

Have you tried building from source?

If you need help installing the necessary packages to make sage, review the packages you'll need in SUSE from the debian repositories for build-essential, m4, and gfortran

I was wondering how can I find the path of the maximal distance between two vertices on a complete digraph. Suppose the digraph has 5 vertices:

sage: g = graphs.CompleteGraph(5).to_directed()

I have seen a maximal flow example which is nice but it is not the same type of problem. How can I use sage to find the longest path?

did you mean this link: "http://localhost:8000 "?

At which step are you stuck on in the "http://www.sagemath.org/mirror/win/README.txt"?