Changes between Initial Version and Version 1 of Ticket #16888


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Timestamp:
08/28/14 11:53:30 (7 years ago)
Author:
ketzu
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  • Ticket #16888

    • Property Cc jsrn added
    • Property Component changed from PLEASE CHANGE to linear algebra
    • Property Type changed from PLEASE CHANGE to defect
    • Property Keywords weak-popov-form matrix added
  • Ticket #16888 – Description

    initial v1  
     1While working on the sage.matrix.matrix2.weak_popov_form method for performance issues I noticed something.
     2
     3The weak Popov form as defined in [MS] is not computed by this method. The other references do not call this form weak Popov form, it is a les restrictive definition for a certain row reduced form of matrix.
     4
     5While renaming I see this as a chance to correct some (in my opinion) strange behavior of the method:
     6
     7 1. It takes a parameter ascend but does not relay it to the function (it is entirely ignored)
     8 1. It takes a parameter ascend which is not related to either weak Popov form or row reduced form
     9 1. It returns a 3-touple even though it is only expected to compute the wpf/rrf
     10 1. d of the 3-touple and the sorting is unnecessary computation and should probably not be part of the method.
     11 1. while N is nice to check some things, in my opinion it should only be given if asked for
     12
     13[MS] T. Mulders, A. Storjohann, "On lattice reduction for polynomial[[BR]]          matrices," J. Symbolic Comput. 35 (2003), no. 4, 377--401
     14
     15Comment of weak_popov_form:
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     17        OUTPUT:[[BR]][[BR]]        A 3-tuple !`(W,N,d)` consisting of:[[BR]][[BR]]        1. !`W` - a matrix over !`k(x)` giving a weak the Popov form of self[[BR]]        2. !`N` - a matrix over !`k[x]` representing row operations used to[[BR]]            transform !`self` to !`W`[[BR]]        3. !`d` - degree of respective columns of W; the degree of a column is[[BR]]           the maximum of the degree of its elements