#16742: overload for faster weak_popov_form
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Reporter: ketzu | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.4
Component: performance | Resolution:
Keywords: matrix weak-popov-form #16739 | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by ketzu:
Old description:
> The target of this ticket is to enhance the function weak_popov of the
> matrix interface. The function should transform the matrix in weak popov
> form, it will use mulders-storjohann algorithm and should be much faster
> than the current implementation but will not work for polynomials over a
> fraction field only for polynomial rings over finite fields.
>
> This ticket is independent from but connected to !#16739.
>
> Short description of weak popov form: Let R be an ordered Ring and Amxn a
> matrix over R. The leading position of a row is called the position i in
> [1,m) such that the order of A[i,_] is maximal within the row. If there
> are multiple entries with the maximum order, the highest i is the leading
> position (the furthest to the right in the matrix). A is in weak popov
> form if all leading positions are different (zero lines ignored).
>
> The function will implement this only for polynomial rings, the order
> function is the degree of the polynomial. Example:
>
> [x2+1, x]
>
> [x, x+1]
>
> is in weak popov form: Row 1 has the degrees 2 and 1, the leading
> position is for i=0, row 2 has two times degree 1 so the higher i is
> chosen with i=1.
>
> [x2+1, x]
>
> [x,0]
>
> is NOT in weak popov form, row 1 has now degrees 1 and -1, so the leading
> position is i=0 as in row 1.
New description:
The target of this ticket is to enhance the function weak_popov of the
matrix interface. The function should transform the matrix in weak popov
form, it will use mulders-storjohann algorithm and should be much faster
than the current implementation but will not work for polynomials over a
fraction field only for polynomial rings over finite fields.
This ticket is independent from but connected to
[wiki:trac.sagemath.org/ticket/16739 #16739].
Short description of weak popov form: Let R be an ordered Ring and Amxn a
matrix over R. The leading position of a row is called the position i in
[1,m) such that the order of A[i,_] is maximal within the row. If there
are multiple entries with the maximum order, the highest i is the leading
position (the furthest to the right in the matrix). A is in weak popov
form if all leading positions are different (zero lines ignored).
The function will implement this only for polynomial rings, the order
function is the degree of the polynomial. Example:
[x2+1, x]
[x, x+1]
is in weak popov form: Row 1 has the degrees 2 and 1, the leading position
is for i=0, row 2 has two times degree 1 so the higher i is chosen with
i=1.
[x2+1, x]
[x,0]
is NOT in weak popov form, row 1 has now degrees 1 and -1, so the leading
position is i=0 as in row 1.
--
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Ticket URL: <http://trac.sagemath.org/ticket/16742#comment:7>
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