@article{10.1145_3614408.3614415,
    author = {Tabuguia, Bertrand Teguia},
    title = {Operations for D-Algebraic Functions},
    year = {2023},
    issue_date = {June 2023},
    publisher = {Association for Computing Machinery},
    address = {New York, NY, USA},
    volume = {57},
    number = {2},
    issn = {1932-2240},
    url = {https://doi.org/10.1145/3614408.3614415},
    doi = {10.1145/3614408.3614415},
    abstract = {A function is differentially algebraic (or simply D-algebraic) if there is a polynomial relationship between some of its derivatives and the indeterminate variable. Many functions in the sciences, such as Mathieu functions, the Weierstrass elliptic functions, and holonomic or D-finite functions are D-algebraic. These functions form a field, and are closed under composition, taking functional inverse, and derivation. We present implementation for each underlying operation. We also give a systematic way for computing an algebraic differential equation from a linear differential equation with D-finite function coefficients.Each command is a feature of our Maple package NLDE available at https://mathrepo.mis.mpg.de/DAlgebraicFunctions/NLDEpackage.},
    journal = {ACM Commun. Comput. Algebra},
    month = {aug},
    pages = {51–56},
    numpages = {6},
    keywords = {differential algebra, gr\"{o}bner basis, mathieu functions, triangular set, weirstrass elliptic functions},
    date-added = {2024-8-21 12:47:26 +0100}
}

@article{10.1145_3614408.3614415, author = {Tabuguia, Bertrand Teguia}, title = {Operations for D-Algebraic Functions}, year = {2023}, issue_date = {June 2023}, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, volume = {57}, number = {2}, issn = {1932-2240}, url = {https://doi.org/10.1145/3614408.3614415}, doi = {10.1145/3614408.3614415}, abstract = {A function is differentially algebraic (or simply D-algebraic) if there is a polynomial relationship between some of its derivatives and the indeterminate variable. Many functions in the sciences, such as Mathieu functions, the Weierstrass elliptic functions, and holonomic or D-finite functions are D-algebraic. These functions form a field, and are closed under composition, taking functional inverse, and derivation. We present implementation for each underlying operation. We also give a systematic way for computing an algebraic differential equation from a linear differential equation with D-finite function coefficients.Each command is a feature of our Maple package NLDE available at https://mathrepo.mis.mpg.de/DAlgebraicFunctions/NLDEpackage.}, journal = {ACM Commun. Comput. Algebra}, month = {aug}, pages = {51–56}, numpages = {6}, keywords = {differential algebra, gr\"{o}bner basis, mathieu functions, triangular set, weirstrass elliptic functions}, date-added = {2024-8-21 12:47:26 +0100} }