@article{BorealeCollodiGorla:ACMTCL:2024,
    author = {Boreale, Michele and Collodi, Luisa and Gorla, Daniele},
    title = {Products, Polynomials and Differential Equations in the Stream Calculus},
    year = {2024},
    issue_date = {January 2024},
    publisher = {Association for Computing Machinery},
    address = {New York, NY, USA},
    volume = {25},
    number = {1},
    issn = {1529-3785},
    url = {https://doi.org/10.1145/3632747},
    doi = {10.1145/3632747},
    abstract = {We study connections among polynomials, differential equations, and streams over a field 𝕂, in terms of algebra and coalgebra. We first introduce the class of (F,G)-products on streams, those where the stream derivative of a product can be expressed as a polynomial function of the streams and their derivatives. Our first result is that, for every (F,G)-product, there is a canonical way to construct a transition function on polynomials such that the resulting unique final coalgebra morphism from polynomials into streams is the (unique) commutative 𝕂-algebra homomorphism—and vice versa. This implies that one can algebraically reason on streams via their polynomial representation. We apply this result to obtain an algebraic-geometric decision algorithm for polynomial stream equivalence, for an underlying generic (F,G)-product. Finally, we extend this algorithm to solve a more general problem: finding all valid polynomial equalities that fit in a user specified polynomial template.},
    journal = {ACM Trans. Comput. Logic},
    month = {jan},
    articleno = {7},
    numpages = {26},
    keywords = {Streams, polynomials, differential equations, coalgebra, algebraic geometry},
    date-added = {2024-4-19 6:46:4 +0100}
}

@article{BorealeCollodiGorla:ACMTCL:2024, author = {Boreale, Michele and Collodi, Luisa and Gorla, Daniele}, title = {Products, Polynomials and Differential Equations in the Stream Calculus}, year = {2024}, issue_date = {January 2024}, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, volume = {25}, number = {1}, issn = {1529-3785}, url = {https://doi.org/10.1145/3632747}, doi = {10.1145/3632747}, abstract = {We study connections among polynomials, differential equations, and streams over a field 𝕂, in terms of algebra and coalgebra. We first introduce the class of (F,G)-products on streams, those where the stream derivative of a product can be expressed as a polynomial function of the streams and their derivatives. Our first result is that, for every (F,G)-product, there is a canonical way to construct a transition function on polynomials such that the resulting unique final coalgebra morphism from polynomials into streams is the (unique) commutative 𝕂-algebra homomorphism—and vice versa. This implies that one can algebraically reason on streams via their polynomial representation. We apply this result to obtain an algebraic-geometric decision algorithm for polynomial stream equivalence, for an underlying generic (F,G)-product. Finally, we extend this algorithm to solve a more general problem: finding all valid polynomial equalities that fit in a user specified polynomial template.}, journal = {ACM Trans. Comput. Logic}, month = {jan}, articleno = {7}, numpages = {26}, keywords = {Streams, polynomials, differential equations, coalgebra, algebraic geometry}, date-added = {2024-4-19 6:46:4 +0100} }