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Annotation of OpenXM/doc/calc2000p/func1.tex, Revision 1.1

1.1     ! noro        1: % $OpenXM$
        !             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,
        !            35: $Q(\alpha_1,\alpha_2,\ldots,\alpha_n)$
        !            36: ($\alpha_i$ is algebraic over $Q(\alpha_1,\ldots,\alpha_{i-1})$),
        !            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),
        !           115: {\color{red} eval} (evaluation of a formula containing transcendental functions),
        !           116: {\color{red} roots} (finding all roots of a univariate polynomial),
        !           117: {\color{red} lll} (computation of an LLL-reduced basis of a lattice).
        !           118:
        !           119: \medbreak
        !           120: \vfill
        !           121: \noindent
        !           122: \rightline{ {\color{red} {\tt http://www.openxm.org} }}
        !           123:
        !           124: \end{document}