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== SAGErelated Problems ==  == Specific SAGErelated Problems == 
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== Computer Algebra Problems ==  == SAGE: General Problems == 
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For each of the following, make remarks about how '''specific practical implementable''' parallel algorithms could be used to enhance SAGE. 
MSRI 2007 Parallel Computation Problem List
Specific SAGErelated Problems
 [: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]
SAGE: General Problems
For each of the following, make remarks about how specific practical implementable parallel algorithms could be used to enhance 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
padic 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}
 Arithmetic of Vectors
 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({{F}}_{p})
Order of the group E({{F}}_{q})
 Order of a point
Elliptic curves over {{Q}}  part I
 Birch and SwinnertonDyer 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
 NagellLutz
An ladic algorithm
Another ladic algorithm
 MordellWeil via 2descent
 Saturation
 Heegner points
 Heegner discriminants
 Heegner Hypothesis
 Heegner point index and height
Elliptic curves over {{Q}}  part II
 Root number
 Special values of Lseries
 Sha bound
 Isogenies
 Attributes of primes
padic height
 Modular Degree
 Modular Parameterization
 Generic elliptic curve operations
 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