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}
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