Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
Note that the __init__ function must construct the all zero matrix if ‘‘entries == None‘‘.
*********** LEVEL 2 **********
IMPORTANT (and *highly* recommended):
After getting the special class with all level 1 functionality to
work, implement all of the following (they should not change
functionality, except speed (always faster!) in any way):
* def _pickle(self):
return data, version
* def _unpickle(self, data, int version)
reconstruct matrix from given data and version; may assume _parent, _nrows, and _ncols are
Use version numbers >= 0 so if you change the pickle strategy then
old objects still unpickle.
* cdef _list -- list of underlying elements (need not be a copy)
* cdef _dict -- sparse dictionary of underlying elements
* cdef _add_ -- add two matrices with identical parents
* _matrix_times_matrix_c_impl -- multiply two matrices with compatible dimensions and
identical base rings (both sparse or both dense)
* cdef _cmp_c_impl -- compare two matrices with identical parents
* cdef _lmul_c_impl -- multiply this matrix on the right by a scalar, i.e., self * scalar
* cdef _rmul_c_impl -- multiply this matrix on the left by a scalar, i.e., scalar * self
* __copy__
* __neg__
The list and dict returned by _list and _dict will *not* be changed
by any internal algorithms and are not accessible to the user.
*********** LEVEL 3 **********
OPTIONAL:
* cdef _sub_
* __invert__
* _multiply_classical
* __deepcopy__
Further special support:
* Matrix windows -- to support Strassen multiplication for a given base ring.
* Other functions, e.g., transpose, for which knowing the
specific representation can be helpful.
.. note::
- For caching, use self.fetch and self.cache.
- Any method that can change the matrix should call
‘‘check_mutability()‘‘ first. There are also many fast cdef’d bounds checking methods.
- Kernels of matrices
Implement only a left_kernel() or right_kernel() method, whichever requires
the least overhead (usually meaning little or no transposing). Let the
methods in the matrix2 class handle left, right, generic kernel distinctions.
3.1. Indexing 65