#16888: weak popov form does not compute weak popov form
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Reporter: ketzu | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: linear algebra | Resolution:
Keywords: weak-popov-form matrix | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by ketzu:
Old description:
> While working on the sage.matrix.matrix2.weak_popov_form method for
> performance issues I noticed something.
>
> The 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.
>
> While renaming I see this as a chance to correct some (in my opinion)
> strange behavior of the method:
>
> 1. It takes a parameter ascend but does not relay it to the function (it
> is entirely ignored)
> 1. It takes a parameter ascend which is not related to either weak Popov
> form or row reduced form
> 1. It returns a 3-touple even though it is only expected to compute the
> wpf/rrf
> 1. d of the 3-touple and the sorting is unnecessary computation and
> should probably not be part of the method.
> 1. while N is nice to check some things, in my opinion it should only be
> given if asked for
>
> [MS] T. Mulders, A. Storjohann, "On lattice reduction for
> polynomial[[BR]] matrices," J. Symbolic Comput. 35 (2003), no.
> 4, 377--401
>
> Comment of weak_popov_form:
>
> 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
New description:
While working on the sage.matrix.matrix2.weak_popov_form method for
performance issues I noticed something.
The 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.
While renaming I see this as a chance to correct some (in my opinion)
strange behavior of the method:
1. It takes a parameter ascend but does not relay it to the function (it
is entirely ignored)
1. It takes a parameter ascend which is not related to either weak Popov
form or row reduced form
1. It returns a 3-touple even though it is only expected to compute the
wpf/rrf
1. d of the 3-touple and the sorting is unnecessary computation and
should probably not be part of the method.
1. while N is nice to check some things, in my opinion it should only be
given if asked for
Followup ticket for reimplementation of wpf: [ticket:16742 #16742.]
[MS] T. Mulders, A. Storjohann, "On lattice reduction for polynomial[[BR]]
matrices," J. Symbolic Comput. 35 (2003), no. 4, 377--401
Comment of weak_popov_form:
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
--
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Ticket URL: <http://trac.sagemath.org/ticket/16888#comment:2>
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