Annotation of OpenXM/doc/OpenXM-specs/appendix.tex, Revision 1.1.1.1
1.1 noro 1: %% $OpenXM$
2: //&C \section{Appendix: English translation}
3:
4: /*&C
5: \noindent
6: (This section has not been updated.)
7:
8: \subsection{Common Mathematical Object format}
9:
10: \begin{verbatim}
11: #define LARGEID 0x7f000000
12: #define CMO_ERROR2 (LARGEID+2)
13: #define CMO_NULL 1
14: #define CMO_INT32 2
15: #define CMO_DATUM 3
16: #define CMO_STRING 4
17: #define CMO_LIST 17
18: \end{verbatim}
19:
20: \bigbreak
21: \noindent
22: Group CMObject/Basic0 requires nothing. \\
23: Error2, Null, Integer32, Datum, Cstring, List $\in$ CMObject/Basic0. \\
24: Document of CMObject/Basic0 is at {\tt http://www.math.kobe-u.ac.jp/openxxx}
25: (in Japanese) \\
26: \begin{eqnarray*}
27: \mbox{Error2}&:& ({\tt CMO\_ERROR2}, {\sl CMObject}\, \mbox{ob}) \\
28: \mbox{Null} &:& ({\tt CMO\_NULL}) \\
29: \mbox{Integer32}
30: &:& ({\tt CMO\_INT32}, {\sl int32}\ \mbox{n}) \\
31: \mbox{Datum} &:& ({\tt CMO\_DATUM}, {\sl int32}\, \mbox{n}, {\sl byte}\,
32: \mbox{data[0]},
33: \ldots , {\sl byte}\, \mbox{data[n-1]}) \\
34: \mbox{Cstring}&:& ({\tt CMO\_STRING},{\sl int32}\, \mbox{n},
35: {\sl string}\, \mbox{s}) \\
36: \mbox{List} &:&
37: \mbox{({\tt CMO\_LIST}, {\sl int32}\, m, {\sl CMObject}\, ob[1], $\ldots$,
38: {\sl CMObject}\, ob[m])} \\
39: & & \mbox{--- m is the length of the list.} \\
40: \end{eqnarray*}
41:
42: In the definition of ``Cstring'', if we decompose ``{\sl string} s'' into
43: bytes, then ``Cstring'' should be defined as
44: \begin{eqnarray*}
45: \mbox{Cstring}&:& ({\tt CMO\_STRING},{\sl int32}\, n,
46: {\sl byte}\, \mbox{s[0]},
47: \ldots, {\sl byte}\ \mbox{s[n-1]})
48: \end{eqnarray*}
49:
50: \noindent
51: Example:
52: \begin{center}
53: ({\tt CMO\_INT32}, 1234)
54: \end{center}
55: Example:
56: \begin{center}
57: ({\tt CMO\_STRING}, 5, "Hello")
58: \end{center}
59:
60: \begin{verbatim}
61: #define CMO_MONOMIAL32 19
62: #define CMO_ZZ 20
63: #define CMO_QQ 21
64: #define CMO_ZERO 22
65: #define CMO_DMS 23 /* Distributed monomial system */
66: #define CMO_DMS_GENERIC 24
67: #define CMO_DMS_OF_N_VARIABLES 25
68: #define CMO_RING_BY_NAME 26
69: \end{verbatim}
70: \bigbreak
71: \noindent
72: Group CMObject/Basic1 requires CMObject/Basic0. \\
73: ZZ, QQ, Zero $\in$ CMObject/Basic1. \\
74: \begin{eqnarray*}
75: \mbox{Zero} &:& ({\tt CMO\_ZERO}) \\
76: & & \mbox{ --- universal zero } \\
77: \mbox{ZZ} &:& ({\tt CMO\_ZZ},{\sl int32}\, f, {\sl byte}\, \mbox{a[1]}, \ldots
78: {\sl byte}\, \mbox{a[m]} ) \\
79: &:& \mbox{ --- bignum }\\
80: \mbox{QQ} &:& ({\tt CMO\_QQ}, {\sl ZZ}\, a, {\sl ZZ}\, b) \\
81: & & \mbox{ --- rational number $a/b$. } \\
82: \end{eqnarray*}
83:
84: \bigbreak
85: Let us define a group for distributed polynomials.
86:
87: \medbreak
88: \noindent
89: Group CMObject/DistributedPolynomials requires CMObject/Basic0,
90: CMObject/Basic1. \\
91: Monomial, Monomial32, Coefficient, Dpolynomial, DringDefinition,
92: Generic DMS ring, RingByName, DMS of N variables $\in$
93: CMObject/DistributedPolynomials. \\
94: \begin{eqnarray*}
95: \mbox{Monomial} &:& \mbox{Monomial32}\, |\, \mbox{Zero} \\
96: \mbox{Monomial32}&:& ({\tt CMO\_MONOMIAL32}, {\sl int32}\, n,
97: {\sl int32}\, \mbox{e[1]}, \ldots,
98: {\sl int32}\, \mbox{e[n]}, \\
99: & & \ \mbox{Coefficient}) \\
100: & & \mbox{ --- e[i] is the exponent $e_i$ of the monomial
101: $x^e = x_1^{e_1} \cdots x_n^{e_n}$. } \\
102: \mbox{Coefficient}&:& \mbox{ZZ} | \mbox{Integer32} \\
103: \mbox{Dpolynomial}&:& \mbox{Zero} \\
104: & & |\ ({\tt CMO\_LIST},{\sl int32} m, \\
105: & & \ \ {\tt CMO\_DMS}, \mbox{DringDefinition},
106: [\mbox{Monomial32}|\mbox{Zero}], \\
107: & &\ \
108: \{\mbox{Monomial32}\}) \\
109: & &\mbox{--- Distributed polynomial is a sum of monomials}\\
110: & &\mbox{--- m is equal to the number of monomials $+2$.}\\
111: \mbox{DringDefinition}
112: &:& \mbox{DMS of N variables} \\
113: & & |\ \mbox{RingByName} \\
114: & & |\ \mbox{Generic DMS ring} \\
115: & & \mbox{ --- definition of the ring of distributed polynomials. } \\
116: \mbox{Generic DMS ring}
117: &:& ({\tt CMO\_INT32, CMO\_DMS\_GENERIC}) \\
118: \mbox{RingByName}&:& ({\tt CMO\_RING\_BY\_NAME}, {\sl Cstring} s) \\
119: & & \mbox{ --- The ring definition refered by the name ``s''.} \\
120: \mbox{DMS of N variables}
121: &:& ({\tt CMO\_DMS\_OF\_N\_VARIABLES}, \\
122: & & \ ({\tt CMO\_LIST}, {\sl int32}\, \mbox{m},
123: {\sl Integer32}\, \mbox{n}, {\sl Integer32}\,\mbox{p} \\
124: & & \ \ [,{\sl Cstring}\,\mbox{s}, {\sl List}\, \mbox{vlist},
125: {\sl List}\, \mbox{wvec}, {\sl List}\, \mbox{outord}]) \\
126: & & \mbox{ --- m is the number of elements.} \\
127: & & \mbox{ --- n is the number of variables, p is the characteristic} \\
128: & & \mbox{ --- s is the name of the ring, vlist is the list of variables.} \\
129: & & \mbox{ --- wvec is the weight vector.} \\
130: & & \mbox{ --- outord is the order of variables to output.} \\
131: \end{eqnarray*}
132:
133:
134: \subsection{ Stackmachine commands}
135:
136: \begin{verbatim}
137: #define SM_popSerializedLocalObject 258
138: #define SM_popCMO 262
139: #define SM_popString 263
140:
141: #define SM_mathcap 264
142: #define SM_pops 265
143: #define SM_setName 266
144: #define SM_evalName 267
145: #define SM_executeStringByLocalParser 268
146: #define SM_executeFunction 269
147: #define SM_beginBlock 270
148: #define SM_endBlock 271
149: #define SM_shutdown 272
150:
151:
152: #define SM_control_kill 1024
153: #define SM_control_reset_connection 1030
154: \end{verbatim}
155:
156:
157: \subsection{OX messages}
158:
159: Top level messages are OX messages.
160: These messages start with one of the following tags.
161:
162: \begin{verbatim}
163: #define OX_COMMAND 513 // for stackmachine commands
164: #define OX_DATA 514 // for CMO
165: #define OX_SECURED_DATA 521
166:
167: #define OX_SYNC_BALL 515
168: \end{verbatim}
169:
170: \noindent
171: Example:
172: \begin{center}
173: (OX\_COMMAND, SM\_popCMO)
174: \end{center}
175:
176: \noindent
177: Example:
178: \begin{center}
179: (OX\_DATA, ({\tt CMO\_STRING}, 5, "Hello"))
180: \end{center}
181:
182: */
183:
184:
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