Changes between Initial Version and Version 2 of Ticket #16742

08/19/14 11:29:42 (8 years ago)


  • Ticket #16742

    • Property Keywords matrix weak-popov-form added
    • Property Priority changed from major to minor
    • Property Component changed from PLEASE CHANGE to performance
    • Property Milestone changed from sage-6.3 to sage-6.4
  • Ticket #16742 – Description

    initial v2  
     1The target of this ticket is to enhance the function weak_popov of the matrix interface.
     2The 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.
     4Short 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).
     6The function will implement this only for polynomial rings, the order function is the degree of the polynomial. Example:
     8[x2+1, x]
     10[x, x+1]
     12is 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.
     14[x2+1, x]
     18is NOT in weak popov form, row 1 has now degrees 1 and -1, so the leading position is i=0 as in row 1.