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 1. [:msri07/threadsafety: Thread Safety of the SAGE Libraries]
 * [:msri07/pthread_sagex: Add Pthread support to SageX]
 * [:msri07/anlist: Implementation in SAGE parallel computation of elliptic curve a_p for all p up to some bound]
 * [:msri07/matrixadd: Implementation in SAGE matrix ADDITION over the rational numbers (say) using a multithreaded approach.]
 * [:msri07/pointcount: Brute force count points on a variety over a finite field in parallel.]		  1. [[msri07/threadsafety| Thread Safety of the SAGE Libraries]]
 * [[msri07/pthread_sagex| Add Pthread support to SageX]]
 * [[msri07/anlist| Implementation in SAGE parallel computation of elliptic curve a_p for all p up to some bound]]
 * [[msri07/matrixadd| Implementation in SAGE matrix ADDITION over the rational numbers (say) using a multithreaded approach.]]
 * [[msri07/pointcount| Brute force count points on a variety over a finite field in parallel.]]

MSRI 2007 Parallel Computation Problem List

  1. Thread Safety of the SAGE Libraries

  2. Add Pthread support to SageX

  3. Implementation in SAGE parallel computation of elliptic curve a_p for all p up to some bound

  4. Implementation in SAGE matrix ADDITION over the rational numbers (say) using a multithreaded approach.

  5. Brute force count points on a variety over a finite field in parallel.

Parallel Implementations

For each of the following, make remarks about how specific practical implementable parallel algorithms could be used to enhance mathematics software libraries (e.g., SAGE).

  • Arithmetic in Global Commutative Rings

    • The ring Z of Integers

    • The ring Q of Rational Numbers

    • Arbitrary Precision Real (and Complex) Numbers
    • Univariate Polynomial Rings
    • Number Fields
    • Multivariate Polynomial Rings
  • Arithmetic in Local Commutative Rings
    • Univariate Power series rings

    • p-adic numbers

  • Linear Algebra
    • Arithmetic of Vectors
      • Addition
      • Scalar Multiplication
      • Vector times Matrix
    • Rational reconstruction of a matrix
    • Echelon form
      • Echelon form over Finite Field

      • Echelon form over Q

      • Echelon form over Cyclotomic Fields

      • Echelon form (Hermite form) over Z

    • Kernel
      • Kernel over Finite Field

      • Kernel over Q

      • Kernel over Z

    • Matrix multiplication
      • Matrix multiplication over Finite Fields

      • Matrix multiplication over Z

      • Matrix multiplication over Extensions of Z

  • Noncommutative Rings
  • Group Theory
  • Groebner Basis Computation
  • Elliptic Curves
    • Generic elliptic curve operations
      • Group Law
      • Invariants
      • Division Polynomials
    • Elliptic curves over finite fields

      • Order of the group E(Fp)

      • Order of the group E(Fq)

      • Order of a point

    • Elliptic curves over Q - part I

      • Birch and Swinnerton-Dyer Conjecture
      • Fourier coefficients
      • Canonical height of a point
      • Order of a point
      • Periods
      • Tate's algorithm
      • Conductor and Globally minimal model
      • CPS height bound
      • Torsion subgroup
      • Nagell-Lutz

      • An l-adic algorithm

      • Another l-adic algorithm

      • Mordell-Weil via 2-descent
      • Saturation
      • Heegner points
      • Heegner discriminants
      • Heegner Hypothesis
      • Heegner point index and height

    • Elliptic curves over Q - part II

      • Root number
      • Special values of L-series
      • Sha bound
      • Isogenies
      • Attributes of primes

      • p-adic height

      • Modular Degree
      • Modular Parameterization
  • Hyperelliptic Curves
  • Modular Forms
    • Presentation of spaces of modular symbols
    • Hecke operators on modular symbols
    • Decomposition of spaces under the Hecke operators
    • Trace formulas
  • Computation of tables
    • Elliptic curves
    • Modular forms
    • Number fields
  • Cryptography
  • Coding Theory
  • Constants, functions and numerical computation

John McKay CHALLENGE system of polynomial equations

http://www.cargo.wlu.ca/McKay/

msri07/problems (last edited 2008-11-14 13:42:04 by anonymous)