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Annotation of OpenXM/doc/calc2000p/func1.tex, Revision 1.2

1.2     ! noro        1: % $OpenXM: OpenXM/doc/calc2000p/func1.tex,v 1.1 2000/07/21 07:11:52 noro Exp $
1.1       noro        2: \documentclass[twocolumn]{article}
                      3: \pagestyle{empty}
                      4: %\markright{ {\tt http://www.openxm.org} }
                      5: \usepackage{color}
                      6: \usepackage{epsfig}
                      7: \title{\huge \color{blue} 4252 functions are available
                      8: on our servers and libraries}
                      9: \author{} \date{}
                     10: \begin{document}
                     11: \maketitle
                     12:
                     13: \noindent
                     14: \fbox{\huge {\color{green}Operations on Integers}}
                     15:
                     16: \noindent
                     17: {\color{red} idiv},{\color{red} irem} (division with remainder),
                     18: {\color{red} ishift} (bit shifting),
                     19: {\color{red} iand},{\color{red} ior},{\color{red} ixor} (logical operations),
                     20: {\color{red} igcd},(GCD by various methods such as Euclid's algorithm and
                     21: the accelerated GCD algorithm),
                     22: {\color{red} fac} (factorial),
                     23: {\color{red} inv} (inverse modulo an integer),
                     24: {\color{red} random} (random number generator by the Mersenne twister algorithm),
                     25:
                     26:
                     27:
                     28: \medbreak
                     29:
                     30: \noindent
                     31: \fbox{\huge {\color{green}Ground Fields}}
                     32:
                     33: \noindent
                     34: Arithmetics on various fields: the rationals,
1.2     ! noro       35: ${\bf Q}(\alpha_1,\alpha_2,\ldots,\alpha_n)$
        !            36: ($\alpha_i$ is algebraic over ${\bf Q}(\alpha_1,\ldots,\alpha_{i-1})$),
1.1       noro       37: $GF(p)$ ($p$ is a prime of arbitrary size), $GF(2^n)$.
                     38:
                     39: \medbreak
                     40:
                     41: \noindent
                     42: \fbox{\huge {\color{green}Operations on Polynomials}}
                     43:
                     44: \noindent
                     45: {\color{red} sdiv }, {\color{red} srem } (division with remainder),
                     46: {\color{red} ptozp } (removal of the integer content),
                     47: {\color{red} diff } (differentiation),
                     48: {\color{red} gcd } (GCD over the rationals),
                     49: {\color{red} res } (resultant),
                     50: {\color{red} subst } (substitution),
                     51: {\color{red} umul} (fast multiplication of dense univariate polynomials
                     52: by a hybrid method with Karatsuba and FFT+Chinese remainder),
                     53: {\color{red} urembymul\_precomp} (fast dense univariate polynomial
                     54: division with remainder by the fast multiplication and
                     55: the precomputed inverse of a divisor),
                     56:
                     57: \noindent
                     58: \fbox{\huge {\color{green}Polynomial Factorization}}
                     59: {\color{red} fctr } (factorization over the rationals),
                     60: {\color{red} fctr\_ff } (univariate factorization over finite fields),
                     61: {\color{red} af } (univariate factorization over algebraic number fields),
                     62: {\color{red} sp} (splitting field computation).
                     63:
                     64: \medbreak
                     65:
                     66: \noindent
                     67: \fbox{\huge {\color{green} Groebner basis}}
                     68:
                     69: \noindent
                     70: {\color{red} dp\_gr\_main } (Groebner basis computation of a polynomial ideal
                     71: over the rationals by the trace lifting),
                     72: {\color{red} dp\_gr\_mod\_main } (Groebner basis over small finite fields),
                     73: {\color{red} tolex } (Modular change of ordering for a zero-dimensional ideal),
                     74: {\color{red} tolex\_gsl } (Modular rational univariate representation
                     75: for a zero-dimensional ideal),
                     76: {\color{red} dp\_f4\_main } ($F_4$ over the rationals),
                     77: {\color{red} dp\_f4\_mod\_main } ($F_4$ over small finite fields).
                     78:
                     79: \medbreak
                     80: \noindent
                     81: \fbox{\huge {\color{green} Ideal Decomposition}}
                     82:
                     83: \noindent
                     84: {\color{red} primedec} (Prime decomposition of the radical),
                     85: {\color{red} primadec} (Primary decomposition of ideals by Shimoyama/Yokoyama algorithm).
                     86:
                     87: \medbreak
                     88:
                     89: \noindent
                     90: \fbox{\huge {\color{green} Quantifier Elimination}}
                     91:
                     92: \noindent
                     93: {\color{red} qe} (real quantifier elimination in a linear and
                     94: quadratic first-order formula),
                     95: {\color{red} simpl} (heuristic simplification of a first-order formula).
                     96:
                     97: \medbreak
                     98:
                     99: \noindent
                    100: \fbox{\huge {\color{green} Visualization of curves}}
                    101:
                    102: \noindent
                    103: {\color{red} plot} (plotting of a univariate function),
                    104: {\color{red} ifplot} (plotting zeros of a bivariate polynomial),
                    105: {\color{red} conplot} (contour plotting of a bivariate polynomial function).
                    106:
                    107: \medbreak
                    108:
                    109: \noindent
                    110: \fbox{\huge {\color{green} Miscellaneous functions}}
                    111:
                    112: \noindent
                    113: {\color{red} det} (determinant),
                    114: {\color{red} qsort} (sorting of an array by the quick sort algorithm),
1.2     ! noro      115: {\color{red} eval} (evaluation of a formula containing transcendental functions
        !           116: such as
        !           117: {\color{red} sin}, {\color{red} cos}, {\color{red} tan}, {\color{red} exp},
        !           118: {\color{red} log})
1.1       noro      119: {\color{red} roots} (finding all roots of a univariate polynomial),
                    120: {\color{red} lll} (computation of an LLL-reduced basis of a lattice).
                    121:
                    122: \medbreak
                    123: \vfill
                    124: \noindent
                    125: \rightline{ {\color{red} {\tt http://www.openxm.org} }}
                    126:
                    127: \end{document}