Changes between Version 24 and Version 25 of Ticket #10720


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Timestamp:
Dec 18, 2017, 11:23:37 AM (5 years ago)
Author:
Vincent Delecroix
Comment:

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  • Ticket #10720 – Description

    v24 v25  
    1 There is a nth_root method defined on univariate and multivariate polynomials.
     1There is a nth_root method defined on univariate polynomial (via Newton method)
    22{{{
    3 sage: R.<x,y,z> = QQ[]
    4 sage: (32 * (x*y + 1)^5 * (x+y+z)^5).nth_root(5)
     3sage: R.<x> = QQ[]
     4sage: ((1 + x - x^2)**5).nth_root(5)
    552*x^2*y + 2*x*y^2 + 2*x*y*z + 2*x + 2*y + 2*z
    66}}}
    7 We provide a more general implementation in a new method `nth_root_series_trunc` that compute the series expansion (there might not be a n-th root that is a polynomial). Using it we implement straightforward `nth_root` for
     7On multi-variate polynomials there is another `nth_root` method implemented via factorization (sic)!!
     8
     9We provide a more general implementation in a new method `nth_root_series_trunc` that compute the series expansion of the n-th root for both univariate and multivariate polynomials (there might not be a n-th root that is a polynomial). Using it we implement straightforward `nth_root` for
    810
    911- univariate and multivariate Laurent polynomials