| 1 | While working on the sage.matrix.matrix2.weak_popov_form method for performance issues I noticed something. |

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| 3 | 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. |

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| 5 | While renaming I see this as a chance to correct some (in my opinion) strange behavior of the method: |

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| 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 |

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| 13 | [MS] T. Mulders, A. Storjohann, "On lattice reduction for polynomial[[BR]] matrices," J. Symbolic Comput. 35 (2003), no. 4, 377--401 |

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| 15 | Comment 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 |