### Abstract

We formalize the theory of subresultants and the subresultant polynomial remainder sequence as described by Brown and Traub. As a result, we obtain efficient certified algorithms for computing the resultant and the greatest common divisor of polynomials.

### License

BSD License

### Topics

- Mathematics/Algebra

### Session Subresultants

- Resultant_Prelim
- Dichotomous_Lazard
- Binary_Exponentiation
- More_Homomorphisms
- Coeff_Int
- Subresultant
- Subresultant_Gcd

### Depends on

- Matrices, Jordan Normal Forms, and Spectral Radius Theory
- Polynomial Factorization

### Used by

- The Factorization Algorithm of Berlekamp and Zassenhaus

## Cite

×

Subresultants-AFP

    @article{Subresultants-AFP,
      author  = {Sebastiaan J. C. Joosten and René Thiemann and Akihisa Yamada},
      title   = {Subresultants},
      journal = {Archive of Formal Proofs},
      month   = {April},
      year    = {2017},
      note    = {\url{https://isa-afp.org/entries/Subresultants.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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Older releases:

- Sep 13, 2023 : Isabelle2023
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