MSRI 2007 Parallel Computation Problem List

SAGE-related 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]

General Computer Algebra Problems

• {part}{I Algebra} {chapter}{ Arithmetic in Global Commutative Rings}

  {section}{ The ring \@mathbb {Z} of Integers} {section}{ The ring \@mathbb {Q} of Rational Numbers} {section}{ Arbitrary Precision Real (and Complex) Numbers} {section}{ Univariate Polynomial Rings} {section}{ Number Fields} {section}{ Multivariate Polynomial Rings} {chapter}{ Arithmetic in Local Commutative Rings} {section}{ Univariate Power series rings} {section}{ p-adic numbers} {chapter}{ Linear Algebra} {section}{ Arithmetic of Vectors} {subsection}{ Addition} {subsection}{ Scalar Multiplication} {subsection}{ Vector times Matrix} {section}{ Rational reconstruction of a matrix} {section}{ Echelon form} {subsection}{ Echelon form over Finite Field} {subsection}{ Echelon form over \@mathbb {Q}} {subsection}{ Echelon form over Cyclotomic Fields} {subsection}{ Echelon form (Hermite form) over \@mathbb {Z}} {section}{Kernel} {subsection}{ Kernel over Finite Field} {subsection}{ Kernel over \@mathbb {Q}} {subsection}{ Kernel over \@mathbb {Z}} {section}{ Matrix multiplication} {subsection}{ Matrix multiplication over Finite Fields} {subsection}{ Matrix multiplication over \@mathbb {Z}} {subsection}{ Matrix multiplication over Extensions of \@mathbb {Z}} {chapter}{ Noncommutative Rings} {chapter}{ Group Theory} {part}{II Arithmetic Geometry} {chapter}{ Groebner Basis Computation} {chapter}{ Elliptic Curves} {section}{ Generic elliptic curve operations} {subsection}{ Group Law} {subsection}{ Invariants} {subsection}{ Division Polynomials} {section}{ Elliptic curves over finite fields} {subsection}{ Order of the group E({\@mathbb {F}}_{p})} {subsection}{ Order of the group E({\@mathbb {F}}_{q})} {subsection}{ Order of a point} {section}{ Elliptic curves over {\@mathbb {Q}} - part I} {subsection}{ Birch and Swinnerton-Dyer Conjecture} {subsection}{ Fourier coefficients} {subsection}{ Canonical height of a point} {subsection}{ Order of a point} {subsection}{ Periods} {subsection}{ Tate's algorithm} {subsection}{ Conductor and Globally minimal model} {subsection}{ CPS height bound} {subsection}{ Torsion subgroup} {subsubsection}{Nagell-Lutz} {subsubsection}{An l-adic algorithm} {subsubsection}{Another l-adic algorithm} {subsection}{ {7.3.10}Mordell-Weil via 2-descent} {subsection}{ {7.3.11}Saturation} {subsection}{ {7.3.12}Heegner points} {subsubsection}{Heegner discriminants} {subsubsection}{Heegner Hypothesis} {subsubsection}{Heegner point index and height} {section}{ Elliptic curves over {\@mathbb {Q}} - part II} {subsection}{ Root number} {subsection}{ Special values of L-series} {subsection}{ \# {\unhbox \voidb@x \hbox {{\fontencoding {OT2}\fontfamily {wncyr}\fontseries {m}\fontshape {n}\selectfont Sh}}}(E) bound} {subsection}{ Isogenies} {subsection}{ Attributes of primes} {subsection}{ p-adic height} {subsection}{ Modular Degree} {subsection}{ Modular Parameterization} {chapter}{ Hyperelliptic Curves} {chapter}{ Modular Forms} {section}{ Presentation of spaces of modular symbols} {section}{ Hecke operators on modular symbols} {section}{ Decomposition of spaces under the Hecke operators} {section}{ Trace formulas} {part}{III Other Topics} {chapter}{ Computation of tables} {section}{ Elliptic curves} {section}{ Modular forms} {section}{ Number fields} {chapter}{ Cryptography} {chapter}{ Coding Theory} {chapter}{ Constants, functions and numerical computation}