Differences between revisions 9 and 10
Revision 9 as of 2007-01-22 13:12:47
Size: 3970
Revision 10 as of 2007-01-22 13:22:31
Size: 3949
Deletions are marked like this. Additions are marked like this.
Line 9: Line 9:
== General Computer Algebra Problems == == Computer Algebra Problems ==
Line 13: Line 13:
 {part}{I Algebra}
Line 45: Line 44:
 {part}{II Arithmetic Geometry} }}}

Arithmetic Geometry Problems ==
Line 69: Line 71:
 {subsection}{ {7.3.10}Mordell-Weil via 2-descent}
 {subsection}{ {7.3.11}Saturation}
 {subsection}{ {7.3.12}Heegner points}
 {subsection}{ Mordell-Weil via 2-descent}
 {subsection}{ Saturation}
 {subsection}{ Heegner points}
Line 90: Line 92:
 {part}{III Other Topics} }}}

== Other Topics Problems ==


MSRI 2007 Parallel Computation Problem List

  • [: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]

Computer Algebra Problems

 {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 $\@mathbb {Z}$}
 {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}

Arithmetic Geometry Problems

 {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}{An $l$-adic algorithm}
 {subsubsection}{Another $l$-adic algorithm}
 {subsection}{ Mordell-Weil via 2-descent}
 {subsection}{ Saturation}
 {subsection}{ 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 \[email protected] \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}


Other Topics Problems

 {chapter}{ Computation of tables}
 {section}{ Elliptic curves}
 {section}{ Modular forms}
 {section}{ Number fields}
 {chapter}{ Cryptography}
 {chapter}{ Coding Theory}
 {chapter}{ Constants, functions and numerical computation}

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