Annotation of OpenXM/doc/ascm2001/openxm-servers.tex, Revision 1.1
1.1 ! takayama 1: %% $OpenXM$
! 2: \section{ 1077 functions are available on our servers and libraries}
! 3:
! 4: This is a list of examples and functions which our
! 5: servers provide.
! 6: For details, see manuals of each system.
! 7:
! 8: \noindent
! 9: \fbox{\large {Operations on Integers}}
! 10:
! 11: \noindent
! 12: {idiv},{irem} (division with remainder),
! 13: {ishift} (bit shifting),
! 14: {iand},{ior},{ixor} (logical operations),
! 15: {igcd},(GCD by various methods such as Euclid's algorithm and
! 16: the accelerated GCD algorithm),
! 17: {fac} (factorial),
! 18: {inv} (inverse modulo an integer),
! 19: {random} (random number generator by the Mersenne twister algorithm).
! 20:
! 21: \medbreak
! 22: \noindent
! 23: \fbox{\large {Ground Fields}}
! 24:
! 25: \noindent
! 26: Arithmetics on various fields: the rationals,
! 27: ${\bf Q}(\alpha_1,\alpha_2,\ldots,\alpha_n)$
! 28: ($\alpha_i$ is algebraic over ${\bf Q}(\alpha_1,\ldots,\alpha_{i-1})$),
! 29: $GF(p)$ ($p$ is a prime of arbitrary size), $GF(2^n)$.
! 30:
! 31: \medbreak
! 32: \noindent
! 33: \fbox{\large {Operations on Polynomials}}
! 34:
! 35: \noindent
! 36: {sdiv }, {srem } (division with remainder),
! 37: {ptozp } (removal of the integer content),
! 38: {diff } (differentiation),
! 39: {gcd } (GCD over the rationals),
! 40: {res } (resultant),
! 41: {subst } (substitution),
! 42: {umul} (fast multiplication of dense univariate polynomials
! 43: by a hybrid method with Karatsuba and FFT+Chinese remainder),
! 44: {urembymul\_precomp} (fast dense univariate polynomial
! 45: division with remainder by the fast multiplication and
! 46: the precomputed inverse of a divisor),
! 47:
! 48: \noindent
! 49: \fbox{\large {Polynomial Factorization}}
! 50: {fctr } (factorization over the rationals),
! 51: {fctr\_ff } (univariate factorization over finite fields),
! 52: {af } (univariate factorization over algebraic number fields),
! 53: {sp} (splitting field computation).
! 54:
! 55: \medbreak
! 56: \noindent
! 57: \fbox{\large {Groebner basis}}
! 58:
! 59: \noindent
! 60: {dp\_gr\_main } (Groebner basis computation of a polynomial ideal
! 61: over the rationals by the trace lifting),
! 62: {dp\_gr\_mod\_main } (Groebner basis over small finite fields),
! 63: {tolex } (Modular change of ordering for a zero-dimensional ideal),
! 64: {tolex\_gsl } (Modular rational univariate representation
! 65: for a zero-dimensional ideal),
! 66: {dp\_f4\_main } ($F_4$ over the rationals),
! 67: {dp\_f4\_mod\_main } ($F_4$ over small finite fields).
! 68:
! 69: \medbreak
! 70: \noindent
! 71: \fbox{\large {Ideal Decomposition}}
! 72:
! 73: \noindent
! 74: {primedec} (Prime decomposition of the radical),
! 75: {primadec} (Primary decomposition of ideals by Shimoyama/Yokoyama algorithm).
! 76:
! 77: \medbreak
! 78: \noindent
! 79: \fbox{\large {Quantifier Elimination}}
! 80:
! 81: \noindent
! 82: {qe} (real quantifier elimination in a linear and
! 83: quadratic first-order formula),
! 84: {simpl} (heuristic simplification of a first-order formula).
! 85:
! 86: %%$
! 87: {\scriptsize
! 88: \begin{verbatim}
! 89: [0] MTP2 = ex([x11,x12,x13,x21,x22,x23,x31,x32,x33],
! 90: x11+x12+x13 @== a1 @&& x21+x22+x23 @== a2 @&& x31+x32+x33 @== a3
! 91: @&& x11+x21+x31 @== b1 @&& x12+x22+x32 @== b2 @&& x13+x23+x33 @== b3
! 92: @&& 0 @<= x11 @&& 0 @<= x12 @&& 0 @<= x13 @&& 0 @<= x21
! 93: @&& 0 @<= x22 @&& 0 @<= x23 @&& 0 @<= x31 @&& 0 @<= x32 @&& 0 @<= x33)$
! 94: [1] TSOL= a1+a2+a3@=b1+b2+b3 @&& a1@>=0 @&& a2@>=0 @&& a3@>=0
! 95: @&& b1@>=0 @&& b2@>=0 @&& b3@>=0$
! 96: [2] QE_MTP2 = qe(MTP2)$
! 97: [3] qe(all([a1,a2,a3,b1,b2,b3],QE_MTP2 @equiv TSOL));
! 98: @true
! 99: \end{verbatim}}
! 100:
! 101: \medbreak
! 102: \noindent
! 103: \fbox{\large {Visualization of curves}}
! 104:
! 105: \noindent
! 106: {plot} (plotting of a univariate function),
! 107: {ifplot} (plotting zeros of a bivariate polynomial),
! 108: {conplot} (contour plotting of a bivariate polynomial function).
! 109:
! 110: \medbreak
! 111: \noindent
! 112: \fbox{\large {Miscellaneous functions}}
! 113:
! 114: \noindent
! 115: {det} (determinant),
! 116: {qsort} (sorting of an array by the quick sort algorithm),
! 117: {eval} (evaluation of a formula containing transcendental functions
! 118: such as
! 119: {sin}, {cos}, {tan}, {exp},
! 120: {log})
! 121: {roots} (finding all roots of a univariate polynomial),
! 122: {lll} (computation of an LLL-reduced basis of a lattice).
! 123:
! 124: \medbreak
! 125: \noindent
! 126: \fbox{\large {$D$-modules}} ($D$ is the Weyl algebra)
! 127:
! 128: \noindent
! 129: {gb } (Gr\"obner basis),
! 130: {syz} (syzygy),
! 131: {annfs} (Annhilating ideal of $f^s$),
! 132: {bfunction},
! 133: {schreyer} (free resolution by the Schreyer method),
! 134: {vMinRes} (V-minimal free resolution),
! 135: {characteristic} (Characteristic variety),
! 136: {restriction} in the derived category of $D$-modules,
! 137: {integration} in the derived category,
! 138: {tensor} in the derived category,
! 139: {dual} (Dual as a D-module),
! 140: {slope}.
! 141:
! 142: \medbreak
! 143: \noindent
! 144: \fbox{\large {Cohomology groups}}
! 145:
! 146: \noindent
! 147: {deRham} (The de Rham cohomology groups of
! 148: ${\bf C}^n \setminus V(f)$,
! 149: {ext} (Ext modules for a holonomic $D$-module $M$
! 150: and the ring of formal power series).
! 151:
! 152: \medbreak
! 153: \noindent
! 154: \fbox{\large {Differential equations}}
! 155:
! 156: \noindent
! 157: Helping to derive and prove {combinatorial} and
! 158: {special function identities},
! 159: {gkz} (GKZ hypergeometric differential equations),
! 160: {appell} (Appell's hypergeometric differential equations),
! 161: {indicial} (indicial equations),
! 162: {rank} (Holonomic rank),
! 163: {rrank} (Holonomic rank of regular holonomic systems),
! 164: {dsolv} (series solutions of holonomic systems).
! 165:
! 166: \medbreak
! 167: \noindent
! 168: \fbox{\large {OpenMATH support}}
! 169:
! 170: \noindent
! 171: {om\_xml} (CMO to OpenMATH XML),
! 172: {om\_xml\_to\_cmo} (OpenMATH XML to CMO).
! 173:
! 174: \medbreak
! 175: \noindent
! 176: \fbox{\large {Homotopy Method}}
! 177:
! 178: \noindent
! 179: {phc} (Solving systems of algebraic equations by
! 180: numerical and polyhedral homotopy methods).
! 181:
! 182: \medbreak
! 183: \noindent
! 184: \fbox{\large {Toric ideal}}
! 185:
! 186: \noindent
! 187: {tigers} (Enumerate all Gr\"obner basis of a toric ideal.
! 188: Finding test sets for integer program),
! 189: {arithDeg} (Arithmetic degree of a monomial ideal),
! 190: {stdPair} (Standard pair decomposition of a monomial ideal).
! 191:
! 192: \medbreak
! 193: \noindent
! 194: \fbox{\large {Communications}}
! 195:
! 196: \noindent
! 197: {ox\_launch} (starting a server),
! 198: {ox\_launch\_nox},
! 199: {ox\_shutdown},
! 200: {ox\_launch\_generic},
! 201: {generate\_port},
! 202: {try\_bind\_listen},
! 203: {try\_connect},
! 204: {try\_accept},
! 205: {register\_server},
! 206: {ox\_rpc},
! 207: {ox\_cmo\_rpc},
! 208: {ox\_execute\_string},
! 209: {ox\_reset} (reset the server),
! 210: {ox\_intr},
! 211: {register\_handler},
! 212: {ox\_push\_cmo},
! 213: {ox\_push\_local},
! 214: {ox\_pop\_cmo},
! 215: {ox\_pop\_local},
! 216: {ox\_push\_cmd},
! 217: {ox\_sync},
! 218: {ox\_get},
! 219: {ox\_pops},
! 220: {ox\_select},
! 221: {ox\_flush},
! 222: {ox\_get\_serverinfo}
! 223:
! 224: \medbreak
! 225: \noindent
! 226: In addition to these functions, {Mathematica functions}
! 227: can be called as server functions.
! 228:
! 229: \medbreak
! 230: \noindent
! 231: \fbox{\large {Examples}}
! 232: {\footnotesize
! 233: \begin{verbatim}
! 234: [345] sm1_deRham([x^3-y^2*z^2,[x,y,z]]);
! 235: [1,1,0,0]
! 236: /* dim H^i = 1 (i=0,1), =0 (i=2,3) */
! 237: \end{verbatim}}
! 238:
! 239: %%\noindent
! 240: %%{\footnotesize \begin{verbatim}
! 241: %%[287] phc(katsura(7)); B=map(first,Phc)$
! 242: %%[291] gnuplot_plotDots(B,0)$
! 243: %%\end{verbatim} }
! 244:
! 245: % \epsfxsize=3cm
! 246: % \begin{center}
! 247: % %\epsffile{../calc2000/katsura7.ps}
! 248: % \epsffile{katsura7.ps}
! 249: % \end{center}
! 250: %%The first components of the solutions to the system of algebraic equations Katsura 7.
! 251:
! 252: \medbreak
! 253: \noindent
! 254: \fbox{ {Authors}}
! 255: Castro-Jim\'enez, Dolzmann, Hubert, Murao, Noro, Oaku, Okutani,
! 256: Shimoyama, Sturm, Takayama, Tamura, Verschelde, Yokoyama.
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