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Annotation of OpenXM/src/asir-doc/parts/asir.texi, Revision 1.4

1.4     ! noro        1: @comment $OpenXM: OpenXM/src/asir-doc/parts/asir.texi,v 1.3 1999/12/21 02:47:31 noro Exp $
1.3       noro        2: \BJP
1.1       noro        3: @node $B%f!<%68@8l(B Asir,,, Top
                      4: @chapter $B%f!<%68@8l(B Asir
1.3       noro        5: \E
                      6: \BEG
                      7: @node User language Asir,,, Top
                      8: @chapter User language @b{Asir}
                      9: \E
1.1       noro       10:
                     11: @noindent
1.3       noro       12: \BJP
1.1       noro       13: @b{Asir} $B$NAH$_9~$_H!?t$O(B, $B0x?tJ,2r(B, GCD $B$J$I$N7W;;$r9T$&$b$N(B, $B%U%!(B
                     14: $B%$%kF~=PNO$r9T$&$b$N(B, $B$"$k$$$O?t<0$N0lIt$r<h$j=P$9$b$N$J$I$5$^$6$^$J$b$N(B
                     15: $B$,MQ0U$5$l$F$$$k$,(B, $B%f!<%6$,<B:]$K9T$$$?$$$3$H$r<B9T$5$;$k$?$a$K$O0l(B
                     16: $BHL$K$O%f!<%68@8l$K$h$k%W%m%0%i%`$r=q$/I,MW$,$"$k(B. $B%f!<%68@8l$b(B
                     17: @b{Asir} $B$H8F$P$l$k(B. $B0J2<$G$O(B, $B%f!<%68@8l$NJ8K!5,B'$*$h$S<B:]$N%f!<(B
                     18: $B%68@8l%W%m%0%i%`$rNc$H$7$?%W%m%0%i%`$N=q$-J}$K$D$$$F=R$Y$k(B.
1.3       noro       19: \E
                     20: \BEG
                     21: @b{Asir} provides many built-in functions, which perform algebraic
                     22: computations, e.g., factorization and GCD computation, file I/O,
                     23: extract a part of an algebraic expression, etc.
                     24: In practice, you will often encounter a specific problem for which
                     25: @b{Asir} does not provide a direct solution.  For such cases, you have
                     26: to write a program in a certain user language.  The user language for
                     27: @b{Asir} is also called @b{Asir}.  In the following, we describe the
                     28: Syntax and then show how to write a user program by several examples.
                     29: \E
1.1       noro       30:
                     31: @menu
1.3       noro       32: \BJP
1.1       noro       33: * $BJ8K!(B (C $B8@8l$H$N0c$$(B)::
                     34: * $B%f!<%6Dj5AH!?t$N=q$-J}(B::
1.3       noro       35: \E
                     36: \BEG
                     37: * Syntax (Difference from C language)::
                     38: * Writing user defined functions::
                     39: \E
1.1       noro       40: @end menu
                     41:
                     42:
1.3       noro       43: \BJP
1.1       noro       44: @node $BJ8K!(B (C $B8@8l$H$N0c$$(B),,, $B%f!<%68@8l(B Asir
                     45: @section $BJ8K!(B (C $B8@8l$H$N0c$$(B)
1.3       noro       46: \E
                     47: \BEG
                     48: @node Syntax (Difference from C language),,, User language Asir
                     49: @section Syntax --- Difference from C language
                     50: \E
1.1       noro       51:
                     52: @noindent
1.3       noro       53: \BJP
1.1       noro       54: @b{Asir} $B$NJ8K!$O(B C $B8@8l$K=`5r$7$F$$$k(B.
                     55: $B$*$b$JAj0cE@$O<!$NDL$j$G$"$k(B. $B0J2<$G(B, $BJQ?t$H$O(B @b{Asir} $B$K$*$1$k(B
                     56: $B%W%m%0%i%`MQ$NJQ?t(B, $B$9$J$o$ABgJ8;z$G;O$^$kJ8;zNs$r0UL#$9$k$3$H$H$9$k(B.
1.3       noro       57: \E
                     58: \BEG
                     59: The syntax of @b{Asir} is based on C language.
                     60: Main differences are as follows.
                     61: In this section, a variable does not mean an indeterminate, but
                     62: a program variable which is written by a string which begins with a
                     63: capital alphabetical letter in @b{Asir}.
                     64: \E
1.1       noro       65:
                     66: @itemize @bullet
                     67: @item
1.3       noro       68: \JP $BJQ?t$N7?$,$J$$(B.
                     69: \EG No types for variables.
1.4     ! noro       70: @*
1.3       noro       71: \BJP
1.1       noro       72: $B4{$K@bL@$7$?$H$*$j(B, @b{Asir} $B$G07$o$l$kBP>]<+?H$OA4$F2?$i$+$N7?(B
                     73: $B$r;}$C$F$$$k(B. $B$7$+$7(B, $B%W%m%0%i%`JQ?t<+BN$O(B, $B$I$N$h$&$JBP>]$G$b(B
                     74: $BBeF~$G$-$k$H$$$&0UL#$G7?$,$J$$$N$G$"$k(B.
1.3       noro       75: \E
                     76: \BEG
                     77: As is already mentioned, any object in @b{Asir} has their respective
                     78: types.  A program variable, however, is type-less, that is, any typed
                     79: object can be assigned to it.
                     80: \E
1.1       noro       81:
                     82: @example
                     83: [0] A = 1;
                     84: 1
                     85: [1] type(A);
                     86: 1
                     87: [2] A = [1,2,3];
                     88: [1,2,3]
                     89: [3] type(A);
                     90: 4
                     91: @end example
                     92:
                     93: @item
1.3       noro       94: \BJP
1.1       noro       95: $BH!?tFb$NJQ?t$O(B, $B%G%U%)%k%H$G$O2>0z?t$r$3$a$F$9$Y$F6I=jJQ?t(B.
1.4     ! noro       96: @*
1.1       noro       97: $B$?$@$7(B, @code{extern} $B@k8@$5$l$?JQ?t$O(B, $B%H%C%W%l%Y%k$K$*$1$kBg0hJQ?t$H$J$k(B.
                     98: $B$9$J$o$A(B, $BJQ?t$N%9%3!<%W$OBg0hJQ?t$H6I=jJQ?t$N(B 2 $B<oN`$KC1=c2=$5$l$F$$$k(B.
                     99: $B%H%C%W%l%Y%k(B, $B$9$J$o$A%W%m%s%W%H$KBP$7$FF~NO$5$l$?JQ?t$OA4$FBg0hJQ?t(B
                    100: $B$H$7$FEPO?$5$l$k(B. $B$^$?H!?tFb$G$O<!$N$$$:$l$+$H$J$k(B.
1.3       noro      101: \E
                    102: \BEG
                    103: Variables, together with formal parameters, in a function (procedure)
                    104: are all local to the function by default.
1.4     ! noro      105: @*
1.3       noro      106: Variables can be global at the top level,
                    107: if they are declared with the key word @code{extern}.
                    108: Thus, the scope rule of @b{Asir} is very simple.
                    109: There are only two types of variables: global variables and local
                    110: variables.
                    111: A name that is input to the @b{Asir}'s prompt at the top level
                    112: is denotes a global variable commonly accessed at the top level.
                    113: In a function (procedure) the following rules are applied.
                    114: \E
1.1       noro      115:
                    116: @enumerate
                    117: @item
1.3       noro      118: \BJP
1.1       noro      119: $BH!?t$,Dj5A$5$l$k%U%!%$%k$K$*$$$F(B, $B$=$NH!?tDj5A0JA0$K(B, $B$"$k(B
                    120: $BJQ?t$,(B @code{extern} $B@k8@$5$l$F$$$k>l9g(B, $BH!?tFb$N$=$NJQ?t$bBg0hJQ?t(B
                    121: $B$H$7$F07$o$l$k(B.
1.3       noro      122: \E
                    123: \BEG
                    124: If a variable is declared as global by an @code{extern} statement in
                    125: a function, the variable used in that function denotes a global variable
                    126: at the top level.
                    127: Furthermore, if a variable in a function is preceded by an @code{extern}
                    128: declaration outside the function but in a file where the function is
                    129: defined, all the appearance of that variable in the same file denote
                    130: commonly a global variable at the top level.
                    131: \E
                    132:
                    133: @item
                    134: \JP @code{extern} $B@k8@$5$l$F$$$J$$JQ?t$O$=$NH!?t$K6I=jE*$H$J$k(B.
                    135: \BEG
                    136: A variable in a function is local to that function, if it is not declared
                    137: as global by an @code{extern} declaration.
                    138: \E
1.1       noro      139: @end enumerate
                    140:
                    141: @example
                    142: % cat afo
                    143: def afo() @{ return A;@}
                    144: extern A$
                    145: def bfo() @{ return A;@}
                    146: end$
                    147: % asir
                    148: [0] load("afo")$
                    149: [5] A = 1;
                    150: 1
                    151: [6] afo();
                    152: 0
                    153: [7] bfo();
                    154: 1
                    155: @end example
                    156:
                    157: @item
1.3       noro      158: \JP $B%W%m%0%i%`JQ?t$OBgJ8;z$G;O$^$j(B, $BITDj85(B, $BH!?t$O>.J8;z$G;O$^$k(B.
                    159: \EG Program variables and algebraic indeterminates are distinguished in @b{Asir}.
1.4     ! noro      160: @*
1.3       noro      161: \BJP
1.1       noro      162: $B$3$NE@$O(B, $B4{B8$N?t<0=hM}%7%9%F%`$N$[$H$s$I$H0[$J$kE@$G$"$k(B. @b{Asir}
                    163: $B$,$3$N;EMM$r:NMQ$7$?$N$O(B, $B%f!<%6$,ITDj85$N$D$b$j$G;HMQ$7$?JQ?t$K(B
                    164: $B$J$s$i$+$NCM$,BeF~$5$l$F$$$?>l9g$K:.Mp$r>7$/(B, $B$H$$$&(B, $B4{B8$N(B
                    165: $B%7%9%F%`$K$"$j$,$A$J>u67$rHr$1$k$?$a$G$"$k(B.
1.3       noro      166: \E
                    167: \BEG
                    168: The names of program variables must begin with a capital letter;
                    169: while the names of indeterminates and functions must begin with
                    170: a small letter.
                    171:
                    172: This is an unique point that differs from almost all other existing
                    173: computer algebra systems.  The distinction between program variables
                    174: and indeterminates is adopted to avoid the possible and usual confusion
                    175: that may arise in a situation where a name is used as an indeterminate
                    176: but, as it was, the name has been already assigned some value.
                    177: To use different type of letters, capital and small, was a matter of
                    178: syntactical convention like Prolog, but it is convenient to distinguish
                    179: variables and indeterminates in a program.
                    180: \E
                    181:
                    182: @item
                    183: \JP @code{switch} $BJ8(B, @code{goto} $B$,$J$$(B.
                    184: \EG No @code{switch} statements, and @code{goto} statements.
1.4     ! noro      185: @*
1.3       noro      186: \JP @code{goto} $B$,$J$$$?$a(B, $BB?=E%k!<%W$r0lEY$KH4$1$k$N$,$d$dJ#;($K$J$k>l9g$,$"$k(B.
                    187: \EG Lack of @code{goto} statement makes it rather bothering to exit from within multiple loops.
                    188:
                    189: @item
                    190: \BJP
                    191: $B%3%s%^<0$O(B, @code{for (A;B;C)} $B$^$?$O(B, @code{while(A)} $B$N(B @code{A},
                    192: @code{B}, @code{C} $B$K$N$_;H$&$3$H$,$G$-$k(B.
                    193: \E
                    194: \BEG
                    195: Comma expressions are allowed only in @code{A}, @code{B} and @code{C}
                    196: of the constructs @code{for (A;B;C)} or @code{while(A)}.
                    197: \E
1.4     ! noro      198: @*
1.3       noro      199: \JP $B$3$l$O(B, $B%j%9%H$r@5<0$J%*%V%8%'%/%H$H$7$F2C$($?$3$H$K$h$k(B.
                    200: \EG This limitation came from adopting lists as legal data objects for @b{Asir}.
1.1       noro      201:
                    202: @end itemize
                    203:
                    204: @noindent
1.3       noro      205: \JP $B0J>e$O@)8B$G$"$k$,(B, $B3HD%$H$7$F$O<!$NE@$,5s$2$i$l$k(B.
                    206: \EG The above are limitations; extensions are listed as follows.
1.1       noro      207:
                    208: @itemize @bullet
                    209: @item
1.3       noro      210: \JP $BM-M}<0$KBP$9$k7W;;$r(B, $BDL>o$N(B C $B$K$*$1$k7W;;$HF1MM$K$G$-$k(B.
                    211: \BEG
                    212: Arithmetic for rational expressions can be done in the
                    213: same manner as is done for numbers in C language.
                    214: \E
1.1       noro      215:
                    216: @item
1.3       noro      217: \JP $B%j%9%H$,07$($k(B.
                    218: \EG Lists are available for data objects.
1.1       noro      219:
1.3       noro      220: \BJP
1.1       noro      221: $B9=B$BN$rMQ$$$k$^$G$b$J$$MWAG$N=89gBN$r(B, $B%j%9%H$GI=$9$3$H$,$G$-(B,
                    222: C $B$GD>@\=q$/>l9g$KHf3S$7$F%W%m%0%i%`$,C;$/(B, $BFI$_$d$9$/=q$1$k(B.
1.3       noro      223: \E
                    224: \BEG
                    225: Lists are conveniently used to represent a certain collection of objects.
                    226: Use of lists enables to write programs more easily, shorter and more
                    227: comprehensible than use of structure like C programs.
                    228: \E
1.2       noro      229:
                    230: @item
1.3       noro      231: \JP $B%f!<%6Dj5AH!?t$K$*$1$k%*%W%7%g%s;XDj(B.
                    232: \EG Options can be specified in calling user defined functions.
1.2       noro      233:
1.3       noro      234: \JP $B$3$l$K4X$7$F$O(B, @xref{$B%*%W%7%g%s;XDj(B}.
                    235: \EG @xref{option}.
1.1       noro      236: @end itemize
                    237:
1.3       noro      238: \BJP
1.1       noro      239: @node $B%f!<%6Dj5AH!?t$N=q$-J}(B,,, $B%f!<%68@8l(B Asir
                    240: @section $B%f!<%6Dj5AH!?t$N=q$-J}(B
1.3       noro      241: \E
                    242: \BEG
                    243: @node Writing user defined functions,,, User language Asir
                    244: @section Writing user defined functions
                    245: \E
1.1       noro      246:
                    247: @menu
1.3       noro      248: \BJP
1.1       noro      249: * $B%f!<%6Dj5AH!?t(B::
                    250: * $BJQ?t$*$h$SITDj85(B::
                    251: * $B0z?t(B::
                    252: * $B%3%a%s%H(B::
                    253: * $BJ8(B::
                    254: * return $BJ8(B::
                    255: * if $BJ8(B::
                    256: * $B%k!<%W(B break return continue::
                    257: * $B$5$^$6$^$J<0(B::
                    258: * $B%W%j%W%m%;%C%5(B::
1.2       noro      259: * $B%*%W%7%g%s;XDj(B::
1.3       noro      260: \E
                    261: \BEG
                    262: * User defined functions::
                    263: * variables and indeterminates::
                    264: * parameters and arguments::
                    265: * comments::
                    266: * statements::
                    267: * return statement::
                    268: * if statement::
                    269: * loop break return continue::
                    270: * various expressions::
                    271: * preprocessor::
                    272: * option::
                    273: \E
1.1       noro      274: @end menu
                    275:
1.3       noro      276: \BJP
1.1       noro      277: @node $B%f!<%6Dj5AH!?t(B,,, $B%f!<%6Dj5AH!?t$N=q$-J}(B
                    278: @subsection $B%f!<%6Dj5AH!?t(B
1.3       noro      279: \E
                    280: \BEG
                    281: @node User defined functions,,, Writing user defined functions
                    282: @subsection User defined functions
                    283: \E
1.1       noro      284:
                    285: @noindent
1.3       noro      286: \BJP
1.1       noro      287: $B%f!<%6$K$h$kH!?t$NDj5A$O(B @samp{def} $BJ8$G9T$&(B. $BJ8K!%(%i!<$OFI$_9~$_;~$K(B
                    288: $B$"$kDxEY%A%'%C%/$5$l(B, $B$*$*$h$=$N>l=j$,I=<($5$l$k(B.
                    289: $B4{$K(B($B0z?t$N8D?t$K4X78$J$/(B)$BF1L>$NH!?t$,Dj5A$5$l$F$$$k>l9g$K$O(B,
                    290: $B$=$NH!?t$O:FDj5A$5$l$k(B. @code{ctrl()} $BH!?t$K$h$j(B @code{verbose} $B%U%i%0(B
                    291: $B$,(B on $B$K$J$C$F$$$k>l9g(B,
1.3       noro      292: \E
                    293: \BEG
                    294: To define functions by an user himself, @samp{def} statement must be used.
                    295: Syntactical errors are detected in the parsing phase
                    296: of @b{Asir}, and notified with an indication of where @b{Asir} found the error.
                    297: If a function with the same name is already defined (regardless to
                    298: its arity,) the new definition will override the old one, and the user
                    299: will be told by a message,
                    300: \E
1.1       noro      301:
                    302: @example
                    303: afo() redefined.
                    304: @end example
                    305:
                    306: @noindent
1.3       noro      307: \BJP
1.1       noro      308: $B$H$$$&%a%C%;!<%8$,I=<($5$l$k(B. $B$"$kH!?t$NDj5A$K$*$$$F(B, $B$^$@L$Dj5A$NH!?t(B
                    309: $B$r8F$S=P$7$F$$$F$b(B, $BDj5A;~$K$O%(%i!<$K$J$i$J$$(B. $B<B9T;~$KL$Dj5A$NH!?t(B
                    310: $B$r8F$S=P$=$&$H$7$?>l9g$K%(%i!<$H$J$k(B.
1.3       noro      311: \E
                    312: \BEG
                    313: on the screen when a flag @code{verbose} is set to a non-zero value by
                    314: @code{ctrl()}.
                    315: Recursive definition, and of course, recursive use of functions are
                    316: available.
                    317: A call for an yet undefined function in a function definition is not
                    318: detected as an error.  An error will be detected at execution of the
                    319: call of that yet undefined function.
                    320: \E
1.1       noro      321: @example
                    322: @tex
                    323: /* $X!$ */
                    324: @end tex
                    325:
                    326: def f(X) @{
                    327:     if ( !X )
                    328:         return 1;
                    329:     else
                    330:         return X * f(X-1);
                    331: @}
                    332:
                    333: @tex
1.3       noro      334: \JP /* ${_i}C_j ( 0 \le i \le N, 0 \le j \le i )$ */
                    335: \EG /* ${_i}C_j ( 0 \le i \le N, 0 \le j \le i )$ */
1.1       noro      336: @end tex
                    337:
                    338: def c(N)
                    339: @{
                    340:     A = newvect(N+1); A[0] = B = newvect(1); B[0] = 1;
                    341:     for ( K = 1; K <= N; K++ ) @{
                    342:         A[K] = B = newvect(K+1); B[0] = B[K] = 1;
                    343:         for ( P = A[K-1], J = 1; J < K; J++ )
                    344:             B[J] = P[J-1]+P[J];
                    345:         @}
                    346:     return A;
                    347: @}
                    348: @end example
                    349:
                    350: @noindent
1.3       noro      351: \BJP
1.1       noro      352: 2 $B$DL\$NNc$G$O(B, $BD9$5(B @code{N+1} $B$N%Y%/%H%k(B (@code{A}$B$H$9$k(B) $B$,JV$5$l$k(B.
                    353: @code{A[I]} $B$OD9$5(B @code{I+1} $B$NG[Ns$G$"$j(B, $B$=$N$=$l$>$l$NMWAG$,(B
1.3       noro      354: \E
                    355: \BEG
                    356: In the second example, @code{c(N)} returns a vector, say @code{A}, of length
                    357: @code{N+1}.  @code{A[I]} is a vector of length @code{I+1}, and
                    358: each element is again a vector which contains
                    359: \E
1.1       noro      360: @iftex
                    361: @tex
                    362: ${_I}C_J$
                    363: @end tex
                    364: @end iftex
                    365: @ifinfo
                    366: ICJ
                    367: @end ifinfo
1.3       noro      368: \JP $B$rMWAG$H$9$kG[Ns$G$"$k(B.
                    369: \EG as its elements.
1.1       noro      370:
                    371: @noindent
1.3       noro      372: \BJP
1.1       noro      373: $B0J2<$G$O(B, C $B$K$h$k%W%m%0%i%_%s%0$N7P83$,$J$$?M$N$?$a$K(B, @b{Asir} $B8@8l(B
                    374: $B$K$h$k%W%m%0%i%`$N=q$-J}$r2r@b$9$k(B.
1.3       noro      375: \E
                    376: \BEG
                    377: In the following, the manner of writing @b{Asir} programs is exhibited
                    378: for those who have no experience in writing C programs.
                    379: \E
1.1       noro      380:
1.3       noro      381: \BJP
1.1       noro      382: @node $BJQ?t$*$h$SITDj85(B,,, $B%f!<%6Dj5AH!?t$N=q$-J}(B
                    383: @subsection $BJQ?t$*$h$SITDj85(B
1.3       noro      384: \E
1.1       noro      385:
                    386: @noindent
1.3       noro      387: \BJP
1.1       noro      388: $B4{$K=R$Y$?DL$j(B, @b{Asir} $B$K$*$$$F$O%W%m%0%i%`JQ?t$HITDj85$rL@3N$K(B
                    389: $B6hJL$7$F$$$k(B.
1.3       noro      390: \E
                    391: \BEG
                    392: @node variables and indeterminates,,, Writing user defined functions
                    393: @subsection variables and indeterminates
                    394: \E
1.1       noro      395:
                    396: @table @b
1.3       noro      397: \BJP
1.1       noro      398: @item $BJQ?t(B
                    399: $BBgJ8;z$G;O$^$j(B, $B%"%k%U%!%Y%C%H(B, $B?t;z(B, @samp{_} $B$+$i$J$kJ8;zNs(B
1.3       noro      400: \E
                    401: \BEG
                    402: @item variables (program variables)
                    403: A program variable is a string that begins with a capital
                    404: alphabetical letter followed by any numbers of alphabetical letters,
                    405: digits and @samp{_}.
                    406: \E
1.1       noro      407:
1.3       noro      408: \BJP
1.1       noro      409: $BJQ?t$"$k$$$O%W%m%0%i%`JQ?t$H$O(B, @b{Asir} $B$N$5$^$6$^$J7?$NFbIt7A<0$r(B
                    410: $B3JG<$9$k$?$a$NH"$G$"$j(B, $B3JG<$5$l$?FbIt7A<0$,(B, $B$3$NJQ?t$NCM$G$"$k(B.  $BJQ(B
                    411: $B?t$,<0$NMWAG$H$7$FI>2A$5$l$k;~$O(B, $B$=$3$K<}$a$i$l$?CM$KCV$-49$($i$l$k(B.
                    412: $B$9$J$o$A(B, $BFbIt7A<0$NCf$K$O%W%m%0%i%`JQ?t$O8=$l$J$$(B. $BJQ?t$OA4$F(B 0 $B$G(B
                    413: $B=i4|2=$5$l$F$$$k(B.
1.3       noro      414: \E
                    415: \BEG
                    416: A program variable is thought of a box (a carrier) which can contain
                    417: @b{Asir} objects of various types.  The content is called the `value'
                    418: of that variable.  When an expression in a program is to be evaluated,
                    419: the variable appearing in the expression is first replaced by its value
                    420: and then the expression is evaluated to some value and stored in
                    421: the memory.  Thus, no program variable appears in objects in the
                    422: internal form.
                    423: All the program variables are initialized to the value 0.
                    424: \E
1.1       noro      425:
                    426: @example
                    427: [0] X^2+X+1;
                    428: 1
                    429: [1] X=2;
                    430: 2
                    431: [2] X^2+X+1;
                    432: 7
                    433: @end example
                    434:
1.3       noro      435: \BJP
1.1       noro      436: @item $BITDj85(B
                    437: $B>.J8;z$G;O$^$j(B, $B%"%k%U%!%Y%C%H(B, $B?t;z(B, @samp{_} $B$+$i$J$kJ8;zNs(B
                    438:
                    439: $BITDj85$H$O(B, $BB?9`<04D$r9=@.$9$k:]$KE:2C$5$l$kJQ?t$r$$$&(B. @b{Asir} $B$K(B
                    440: $B$*$$$F$O(B, $BITDj85$OCM$r$b$?$J$$D61[E*$J85$G$"$j(B, $BITDj85$X$NCM$NBeF~$O(B
                    441: $B5v$5$l$J$$(B.
1.3       noro      442: \E
                    443: \BEG
                    444: @item indeterminates
                    445: An indeterminate is a string that begins with a small alphabetical letter
                    446: followed by any numbers of alphabetical letters, digits and @samp{_}.
                    447:
                    448: An indeterminate is a transcendental element, so-called variable,
                    449: which is used to construct polynomial rings.
                    450: An indeterminate cannot have any value.  No assignment is allowed to it.
                    451: \E
1.1       noro      452:
                    453: @example
                    454: [3] X=x;
                    455: x
                    456: [4] X^2+X+1;
                    457: x^2+x+1
                    458: @end example
                    459: @end table
                    460:
1.3       noro      461: \BJP
1.1       noro      462: @node $B0z?t(B,,, $B%f!<%6Dj5AH!?t$N=q$-J}(B
                    463: @subsection $B0z?t(B
1.3       noro      464: \E
                    465: \BEG
                    466: @node parameters and arguments,,, Writing user defined functions
                    467: @subsection parameters and arguments
                    468: \E
1.1       noro      469:
                    470: @example
                    471: def sum(N) @{
                    472:     for ( I = 1, S = 0; I <= N; I++ )
                    473:         S += I;
                    474:     return S;
                    475: @}
                    476: @end example
                    477:
                    478: @noindent
1.3       noro      479: \BJP
1.1       noro      480: $B$3$l$O(B, 1 $B$+$i(B @code{N} $B$^$G$N<+A3?t$NOB$r5a$a$kH!?t(B @code{sum()} $B$N(B
                    481: $BDj5A$G$"$k(B. $B$3$NNc$K$*$1$k(B @code{sum(N)} $B$N(B @code{N} $B$,0z?t$G$"$k(B.
                    482: $B$3$NNc$O(B, 1 $B0z?tH!?t$NNc$G$"$k$,(B, $B0lHL$K0z?t$N8D?t$OG$0U$G$"$j(B,
                    483: $BI,MW$J$@$1$N8D?t$r(B @samp{,} $B$G6h@Z$C$F;XDj$9$k$3$H$,$G$-$k(B. $B0z?t$O(B
                    484: $BCM$,EO$5$l$k(B. $B$9$J$o$A(B, $B0z?t$r<u$1$H$C$?B&$,(B, $B$=$N0z?t$NCM$rJQ99$7$F(B
                    485: $B$b(B, $BEO$7$?B&$NJQ?t$OJQ2=$7$J$$(B. $B$?$@$7(B, $BNc30$,$"$k(B. $B$=$l$O(B, $B%Y%/%H%k(B,
                    486: $B9TNs$r0z?t$KEO$7$?>l9g$G$"$k(B. $B$3$N>l9g$b(B, $BEO$5$l$?JQ?t$=$N$b$N$r=q$-(B
                    487: $BBX$($k$3$H$O(B, $B$=$NH!?t$K6I=jE*$JA`:n$G$"$k$,(B, $BMWAG$r=q$-49$($?>l9g(B,
                    488: $B$=$l$O(B, $B8F$S=P$7B&$N%Y%/%H%k(B, $B9TNs$NMWAG$r=q$-49$($k$3$H$K$J$k(B.
1.3       noro      489: \E
                    490: \BEG
                    491: This is an example definition of a function that sums up integers
                    492: from 1 to @code{N}.  The @code{N} in @code{sum(N)} is called the
                    493: (formal) parameter of @code{sum(N)}.
                    494: The example shows a function of the single argument.
                    495: In general, any number of parameters can be specified by separating
                    496: by commas (@samp{,}).
                    497: A (formal) parameter accepts a value given as an argument (or an actual
                    498: parameter) at a function call of the function.
                    499: Since the value of the argument is given to the formal parameter,
                    500: any modification to the parameter does not usually affect the argument
                    501: (or actual parameter).  However, there are a few exceptions: vector
                    502: arguments and matrix arguments.
                    503:
                    504: Let @code{A} be a program variable and assigned to a vector value
                    505: @code{[ a, b ]}.
                    506: If A is given as an actual parameter to a formal parameter, say @code{V},
                    507: of a function, then an assignment in the function to the vector element
                    508: designator @code{V[1]}, say @code{V[1]=c;}, causes modification of the
                    509: actual parameter @code{A} resulting @code{A} to have an altered value
                    510: @code{[ a c ]}.  Thus, if a vector is given to a formal parameter of
                    511: a function, then its element (and subsequently the vector itself) in
                    512: the calling side is modified through modification of the formal parameter
                    513: by a vector element designator in the called function.
                    514: The same applies to a matrix argument.
                    515: Note that, even in such case where a vector (or a matrix) is given to
                    516: a formal parameter, the assignment to the whole parameter itself has
                    517: only a local effect within the function.
                    518: \E
1.1       noro      519:
                    520: @example
                    521: def clear_vector(M) @{
                    522:     /* M is expected to be a vector */
                    523:     L = size(M)[0];
                    524:     for ( I = 0; I < L; I++ )
                    525:         M[I] = 0;
                    526: @}
                    527: @end example
                    528:
                    529: @noindent
1.3       noro      530: \BJP
1.1       noro      531: $B$3$NH!?t$O(B, $B0z?t$N%Y%/%H%k$r(B 0 $B%Y%/%H%k$K=i4|2=$9$k$?$a$NH!?t$G$"$k(B.
                    532: $B$^$?(B, $B%Y%/%H%k$r0z?t$KEO$9$3$H$K$h$j(B, $BJ#?t$N7k2L$r0z?t$N%Y%/%H%k$K(B
                    533: $B<}G<$7$FJV$9$3$H$,$G$-$k(B. $B<B:]$K$O(B, $B$3$N$h$&$J>l9g$K$O(B, $B7k2L$r%j%9%H(B
                    534: $B$K$7$FJV$9$3$H$b$G$-$k(B. $B>u67$K1~$8$F;H$$$o$1$9$k$3$H$,K>$^$7$$(B.
1.3       noro      535: \E
                    536: \BEG
                    537: This function will clear off the vector given as its argument to the
                    538: formal parameter @code{M} and return a 0 vector.
                    539:
                    540: Passing a vector as an argument to a function enables returning
                    541: multiple results by packing each result in a vector element.
                    542: Another alternative to return multiple results is to use a list.
                    543: Which to use depends on cases.
                    544: \E
1.1       noro      545:
1.3       noro      546: \BJP
1.1       noro      547: @node $B%3%a%s%H(B,,, $B%f!<%6Dj5AH!?t$N=q$-J}(B
                    548: @subsection $B%3%a%s%H(B
1.3       noro      549: \E
                    550: \BEG
                    551: @node comments,,, Writing user defined functions
                    552: @subsection comments
                    553: \E
1.1       noro      554:
                    555: @noindent
1.3       noro      556: \JP C $B$HF1MM(B @samp{/*} $B$H(B @samp{*/} $B$G0O$^$l$?ItJ,$O%3%a%s%H$H$7$F07$o$l$k(B.
                    557: \BEG
                    558: The text enclosed by @samp{/*} and @samp{*/} (containing @samp{/*} and
                    559: @samp{*/}) is treated as a comment and has no effect to the program
                    560: execution as in C programs.
                    561: \E
1.1       noro      562:
                    563: @example
                    564: /*
                    565:  * This is a comment.
                    566:  */
                    567:
                    568: def afo(X) @{
                    569: @end example
                    570:
                    571: @noindent
1.3       noro      572: \BJP
1.1       noro      573: $B%3%a%s%H$OJ#?t9T$KEO$C$F$b9=$o$J$$$,(B, $BF~$l;R$K$9$k$3$H$O$G$-$J$$(B.
                    574: @samp{/*} $B$,$$$/$D$"$C$F$b:G=i$N$b$N$N$_$,M-8z$H$J$j(B, $B:G=i$K8=$l$?(B
                    575: @samp{*/} $B$G%3%a%s%H$O=*N;$7$?$H8+$J$5$l$k(B. $B%W%m%0%i%`$J$I$G(B, $B%3%a%s%H(B
                    576: $B$r4^$`2DG=@-$,$"$kItJ,$r%3%a%s%H%"%&%H$7$?>l9g$K$O(B, @code{#if 0},
                    577: @code{#endif}$B$r;H$($P$h$$(B. (@xref{$B%W%j%W%m%;%C%5(B})
1.3       noro      578: \E
                    579: \BEG
                    580: A comment can span to several lines, but it cannot be nested.
                    581: Only the first @samp{/*} is effective no matter how many @samp{/*}'s
                    582: in the subsequent text exist, and the comment terminates at the first
                    583: @samp{*/}.
                    584:
                    585: In order to comment out a program part that may contain comments in it,
                    586: use the pair, @code{#if 0} and @code{#endif}. (@xref{preprocessor})
                    587: \E
1.1       noro      588:
                    589: @example
                    590: #if 0
                    591: def bfo(X) @{
                    592: /* empty */
                    593: @}
                    594: #endif
                    595: @end example
                    596:
1.3       noro      597: \BJP
1.1       noro      598: @node $BJ8(B,,, $B%f!<%6Dj5AH!?t$N=q$-J}(B
                    599: @subsection $BJ8(B
1.3       noro      600: \E
                    601: \BEG
                    602: @node statements,,, Writing user defined functions
                    603: @subsection statements
                    604: \E
1.1       noro      605:
                    606: @noindent
1.3       noro      607: \BJP
1.1       noro      608: @b{Asir} $B$N%f!<%6H!?t$O(B,
                    609:
                    610: @example
                    611: def $BL>A0(B($B0z?t(B,$B0z?t(B,...,$B0z?t(B) @{
                    612:     $BJ8(B
                    613:     $BJ8(B
                    614:     ...
                    615:     $BJ8(B
                    616: @}
1.3       noro      617: \E
                    618: \BEG
                    619: An user function of @b{Asir} is defined in the following form.
                    620:
                    621: @example
                    622: def name(parameter, parameter,...,parameter) @{
                    623:     statement
                    624:     statement
                    625:     ...
                    626:     statement
                    627: @}
                    628: \E
1.1       noro      629: @end example
                    630:
                    631: @noindent
1.3       noro      632: \BJP
1.1       noro      633: $B$H$$$&7A$GDj5A$5$l$k(B. $B$3$N$h$&$K(B, $BJ8$OH!?t$N4pK\E*9=@.MWAG$G$"$j(B, $B%W%m(B
                    634: $B%0%i%`$r=q$/$?$a$K$O(B, $BJ8$,$I$N$h$&$J$b$N$G$"$k$+CN$i$J$1$l$P$J$i$J$$(B.
                    635: $B:G$bC1=c$JJ8$H$7$F(B, $BC1J8$,$"$k(B. $B$3$l$O(B,
1.3       noro      636: \E
                    637: \BEG
                    638: As you can see, the statement is a fundamental element of the
                    639: function.
                    640: Therefore, in order to write a program, you have to learn what
                    641: the statement is.  The simplest statement is the simple statement.
                    642: One example is an expression with a terminator (@samp{;} or @samp{$}.)
                    643: \E
1.1       noro      644:
                    645: @example
                    646: S = sum(N);
                    647: @end example
                    648:
                    649: @noindent
1.3       noro      650: \BJP
1.1       noro      651: $B$N$h$&$K(B, $B<0$K=*C<5-9f(B (@samp{;} $B$^$?$O(B @samp{$}) $B$r$D$1$?$b$N$G$"$k(B.
                    652: $B$3$NC1J85Z$SN`;w$N(B @code{return} $BJ8(B, @code{break} $BJ8$J$I$,J8$N:G>.9=@.(B
                    653: $BC10L$H$J$k(B. @code{if} $BJ8$d(B @code{for} $BJ8$NDj5A(B (@xref{$BJ8K!$N>\:Y(B}) $B$r8+$l(B
                    654: $B$P$o$+$kDL$j(B, $B$=$l$i$NK\BN$O(B, $BC1$J$k0l$D$NJ8$H$7$FDj5A$5$l$F$$$k(B. $BDL>o(B
                    655: $B$O(B, $BK\BN$K$OJ#?t$NJ8$,=q$1$k$3$H$,I,MW$H$J$k(B.  $B$3$N$h$&$J>l9g(B,
                    656: @samp{@{} $B$H(B @samp{@}} $B$GJ8$NJB$S$r3g$C$F(B, $B0l$D$NJ8$H$7$F07$&$3$H$,$G(B
                    657: $B$-$k(B. $B$3$l$rJ#J8$H8F$V(B.
1.3       noro      658: \E
                    659: \BEG
                    660: A `@code{return} statement' and `@code{break} statement' are also
                    661: primitives to construct `statements.'
                    662: As you can see the syntactic definition of `@code{if} statement' and
                    663: `@code{for} statement', each of their bodies consists of a single
                    664: `statement.'  Usually, you need several statements in such a body.
                    665: To solve this contradictory requirement, you may use the `compound
                    666: statement.'  A `compound statement' is a sequence of `statement's
                    667: enclosed by a left brace @samp{@{} and a right brace @samp{@}}.
                    668: Thus, you can use multiple statement as if it were a single statement.
                    669: \E
1.1       noro      670:
                    671: @example
                    672: if ( I == 0 ) @{
                    673:     J = 1;
                    674:     K = 2;
                    675:     L = 3;
                    676: @}
                    677: @end example
                    678:
                    679: @noindent
1.3       noro      680: \BJP
1.1       noro      681: @samp{@}} $B$N8e$m$K$O=*C<5-9f$OI,MW$J$$(B. $B$J$<$J$i(B, @samp{@{} $BJ8JB$S(B
                    682: @samp{@}}$B$,4{$KJ8$H$J$C$F$$$F(B, @code{if} $BJ8$NMW@A$rK~$?$7$F$$$k$+$i$G(B
                    683: $B$"$k(B.
1.3       noro      684: \E
                    685: \BEG
                    686: No terminator symbol is necessary after @samp{@}},
                    687: because @samp{@{} statement sequence @samp{@}} already forms a statement,
                    688: and it satisfies the syntactical requirement of the
                    689: `@code{if} statement.'
                    690: \E
1.1       noro      691:
1.3       noro      692: \BJP
1.1       noro      693: @node return $BJ8(B,,, $B%f!<%6Dj5AH!?t$N=q$-J}(B
                    694: @subsection @code{return} $BJ8(B
1.3       noro      695: \E
                    696: \BEG
                    697: @node return statement,,, Writing user defined functions
                    698: @subsection @code{return} statement
                    699: \E
1.1       noro      700:
                    701: @noindent
1.3       noro      702: \JP @code{return} $BJ8$O(B,
                    703: \EG There are two forms of @code{return} statement.
1.1       noro      704:
                    705: @example
1.3       noro      706: \JP return $B<0(B;
                    707: \EG return expression;
1.1       noro      708:
                    709: return;
                    710: @end example
                    711:
                    712: @noindent
1.3       noro      713: \BJP
1.1       noro      714: $B$N(B 2 $B$D$N7A<0$,$"$k(B. $B$$$:$l$bH!?t$+$iH4$1$k$?$a$NJ8$G$"$k(B. $BA0<T$O(B
                    715: $BH!?t$NCM$H$7$F(B $B<0(B $B$rJV$9(B. $B8e<T$G$O(B, $BH!?t$NCM$H$7$F2?$,JV$5$l$k$+(B
                    716: $B$O$o$+$i$J$$(B.
1.3       noro      717: \E
                    718: \BEG
                    719: Both forms are used for exiting from a function.
                    720: The former returns the value of the expression as a function value.
                    721: The function value of the latter is not defined.
                    722: \E
1.1       noro      723:
1.3       noro      724: \BJP
1.1       noro      725: @node if $BJ8(B,,, $B%f!<%6Dj5AH!?t$N=q$-J}(B
                    726: @subsection @code{if} $BJ8(B
1.3       noro      727: \E
                    728: \BEG
                    729: @node if statement,,, Writing user defined functions
                    730: @subsection @code{if} statement
                    731: \E
1.1       noro      732:
                    733: @noindent
1.3       noro      734: \JP @code{if} $BJ8$K$O(B
                    735: \EG There are two forms of @code{if} statement.
1.1       noro      736:
                    737: @example
1.3       noro      738: \BJP
1.1       noro      739: if ( $B<0(B )             if ( $B<0(B )
                    740:     $BJ8(B       $B5Z$S(B         $BJ8(B
                    741: else
                    742:     $BJ8(B
1.3       noro      743: \E
                    744: \BEG
                    745: if ( expression )             if ( expression )
                    746:      statement       and           statement
                    747: else
                    748:      statement
                    749: \E
1.1       noro      750: @end example
                    751:
                    752: @noindent
1.3       noro      753: \BJP
1.1       noro      754: $B$N(B 2 $B<oN`$,$"$k(B. $B$3$l$i$NF0:n$OL@$i$+$G$"$k$,(B, $BJ8$N0LCV$K(B @code{if} $BJ8(B
                    755: $B$,Mh$?>l9g$KCm0U$rMW$9$k(B. $B<!$NNc$r9M$($F$_$h$&(B.
1.3       noro      756: \E
                    757: \BEG
                    758: The interpretation of these forms are obvious.  However, be careful
                    759: when another @code{if} statement comes at the place for `statement'.
                    760: Let us examine the following example.
                    761: \E
1.1       noro      762:
                    763: @example
1.3       noro      764: \BJP
1.1       noro      765: if ( $B<0(B )
                    766:     if ( $B<0(B ) $BJ8(B
                    767: else
                    768:     $BJ8(B
1.3       noro      769: \E
                    770: \BEG
                    771: if ( expression1 )
                    772:     if ( expression2 ) statement1
                    773: else
                    774:     statement2
                    775: \E
1.1       noro      776: @end example
                    777:
                    778: @noindent
1.3       noro      779: \BJP
1.1       noro      780: $B$3$N>l9g(B, $B;z2<$2$+$i$O(B, @code{else} $B0J2<$O(B, $B:G=i$N(B @code{if} $B$KBP1~$9$k(B
                    781: $B$h$&$K8+$($k$,(B, $B%Q!<%6$O(B, $B<+F0E*$K(B 2 $BHVL\$N(B @code{if} $B$KBP1~$9$k$HH=CG$9$k(B.
                    782: $B$9$J$o$A(B, 2 $B<oN`$N(B @code{if} $BJ8$r5v$7$?$?$a$K(B, $BJ8K!$K[#Kf@-$,8=$l(B, $B$=$l$r(B
                    783: $B2r>C$9$k$?$a$K(B, @code{else} $B0J2<$O(B, $B:G$b6a$$(B @code{if} $B$KBP1~$9$k$H(B
                    784: $B$$$&5,B'$,E,MQ$5$l$k$N$G$"$k(B. $B=>$C$F(B, $B$3$NNc$O(B,
1.3       noro      785: \E
                    786: \BEG
                    787: One might guess @code{statement2} after @code{else} corresponds with the
                    788: first @code{if ( expression1 )} by its appearance of indentation.
                    789: But, as a matter of fact, the @code{Asir} parser decides that it
                    790: correspond with the second @code{if ( expression2 )}.
                    791: Ambiguity due to such two kinds of forms of @code{if} statement is
                    792: thus solved by introducing a rule that a statement preceded by an
                    793: @code{else} matches to the nearest preceding @code{if}.
                    794:
                    795: Therefore, rearrangement of the above example for improving readability
                    796: according to the actual interpretation gives the following.
                    797: \E
1.1       noro      798:
                    799: @example
1.3       noro      800: \BJP
1.1       noro      801: if ( $B<0(B ) @{
                    802:     if ( $B<0(B ) $BJ8(B else $BJ8(B
                    803: @}
1.3       noro      804: \E
                    805: \BEG
                    806: if ( expression1 ) @{
                    807:     if ( expression2 ) statement1 else statement2
                    808: @}
                    809: \E
1.1       noro      810: @end example
                    811:
                    812: @noindent
1.3       noro      813: \JP $B$H$$$&0UL#$H$J$k(B. $B;z2<$2$KBP1~$5$;$k$?$a$K$O(B,
                    814: \BEG
                    815: On the other hand, in order to reflect the indentation, it must be
                    816: written as the following.
                    817: \E
1.1       noro      818:
                    819: @example
1.3       noro      820: \BJP
1.1       noro      821: if ( $B<0(B ) @{
                    822:     if ( $B<0(B ) $BJ8(B
                    823: @} else
                    824:     $BJ8(B
1.3       noro      825: \E
                    826: \BEG
                    827: if ( expression1 ) @{
                    828:     if ( expression2 ) statement1
                    829: @} else
                    830:     statement2
                    831: \E
1.1       noro      832: @end example
                    833:
                    834: @noindent
1.3       noro      835: \JP $B$H$7$J$1$l$P$J$i$J$$(B.
1.1       noro      836:
1.3       noro      837: \BJP
1.1       noro      838: @node $B%k!<%W(B break return continue,,, $B%f!<%6Dj5AH!?t$N=q$-J}(B
                    839: @subsection $B%k!<%W(B, @code{break}, @code{return}, @code{continue}
1.3       noro      840: \E
                    841: \BEG
                    842: @node loop break return continue,,, Writing user defined functions
                    843: @subsection @code{loop}, @code{break}, @code{return}, @code{continue}
                    844: \E
1.1       noro      845:
                    846: @noindent
1.3       noro      847: \BJP
1.1       noro      848: $B%k!<%W$r9=@.$9$kJ8$O(B, @code{while} $BJ8(B, @code{for} $BJ8(B, @code{do} $BJ8(B
                    849: $B$N(B 3 $B<oN`$,$"$k(B.
1.3       noro      850: \E
                    851: \BEG
                    852: There are three kinds of statements for loops (repetitions):
                    853: the @code{while} statement, the @code{for} statement, and  the
                    854: @code{do} statement.
                    855: \E
1.1       noro      856:
                    857: @itemize @bullet
                    858: @item
1.3       noro      859: \JP @code{while} $BJ8(B
                    860: \EG @code{while} statement
1.4     ! noro      861: @*
1.3       noro      862: \JP $B7A<0$O(B,
                    863: \EG It has the following form.
1.1       noro      864:
                    865: @example
1.3       noro      866: \JP while ( $B<0(B ) $BJ8(B
                    867: \EG while ( expression ) statement
1.1       noro      868: @end example
                    869:
                    870: @noindent
1.3       noro      871: \BJP
1.1       noro      872: $B$G(B, $B$3$l$O(B, $B<0(B $B$rI>2A$7$F(B, $B$=$NCM$,(B 0 $B$G$J$$8B$j(B $BJ8(B $B$r<B9T$9$k$H$$$&(B
                    873: $B0UL#$H$J$k(B. $B$?$H$($P(B $B<0(B $B$,(B 1 $B$J$i$P(B, $BC1=c$JL58B%k!<%W$H$J$k(B.
1.3       noro      874: \E
                    875: \BEG
                    876: This statement specifies that @code{statement} is repeatedly evaluated
                    877: as far as the @code{expression} evaluates to a non-zero value.
                    878: If the expression 1 is given to the @code{expression}, it forms an
                    879: infinite loop.
                    880: \E
1.1       noro      881:
                    882: @item
1.3       noro      883: \JP @code{for} $BJ8(B
                    884: \EG @code{for} statement
1.4     ! noro      885: @*
1.3       noro      886: \JP $B7A<0$O(B,
                    887: \EG It has the following form.
1.1       noro      888:
                    889: @example
1.3       noro      890: \JP for ( $B<0JB$S(B-1; $B<0(B; $B<0JB$S(B-2 ) $BJ8(B
                    891: \EG for ( expression list-1; expression; expression list-2 ) statement
1.1       noro      892: @end example
                    893:
1.3       noro      894: \JP $B$G(B, $B$3$l$O(B
                    895: \EG This is equivalent to the program
1.1       noro      896:
                    897: @example
1.3       noro      898: \BJP
1.1       noro      899: $B<0JB$S(B-1 ($B$rC1J8JB$S$K$7$?$b$N(B)
                    900: while ( $B<0(B ) @{
                    901:     $BJ8(B
                    902:     $B<0JB$S(B-2 ($B$rC1J8JB$S$K$7$?$b$N(B)
                    903: @}
1.3       noro      904: \E
                    905: \BEG
                    906: expression list-1 (transformed into a sequence of simple statement)
                    907: while ( expression ) @{
                    908:     statement
                    909:     expression list-2 (transformed into a sequence of simple statement)
                    910: @}
                    911: \E
1.1       noro      912: @end example
                    913:
1.3       noro      914: \JP $B$HEy2A$G$"$k(B.
1.1       noro      915:
                    916: @item
1.3       noro      917: \JP @code{do} $BJ8(B
                    918: \EG @code{do} statement
1.4     ! noro      919: @*
1.1       noro      920: @example
1.3       noro      921: \BJP
1.1       noro      922: do @{
                    923:     $BJ8(B
                    924: @} while ( $B<0(B )
1.3       noro      925: \E
                    926: \BEG
                    927: do @{
                    928:     statement
                    929: @} while ( expression )
                    930: \E
1.1       noro      931: @end example
                    932:
1.3       noro      933: \BJP
1.1       noro      934: $B$O(B, $B@h$K(B $BJ8$r<B9T$7$F$+$i>r7o<0$K$h$kH=Dj$r9T$&=j$,(B @code{while} $BJ8(B
                    935: $B$H0[$J$C$F$$$k(B.
1.3       noro      936: \E
                    937: \BEG
                    938: This statement differs from @code{while} statement by the location of
                    939: the termination condition: This statement first execute the
                    940: @code{statement} and then check the condition, whereas @code{while}
                    941: statement does it in the reverse order.
                    942: \E
1.1       noro      943: @end itemize
                    944:
                    945: @noindent
1.3       noro      946: \BJP
1.1       noro      947: $B%k!<%W$rH4$1=P$9<jCJ$H$7$F(B,
                    948: @code{break} $BJ85Z$S(B @code{return} $BJ8$,$"$k(B. $B$^$?(B, $B%k!<%W$N@)8f$r(B
                    949: $B$"$k0LCV$K0\$9<jCJ$H$7$F(B @code{continue} $BJ8$,$"$k(B.
1.3       noro      950: \E
                    951: \BEG
                    952: As means for exiting from loops, there are @code{break} statement and
                    953: @code{return} statement.  The @code{continue} statement allows to move
                    954: the control to a certain point of the loop.
                    955: \E
1.1       noro      956: @itemize @bullet
                    957:
                    958: @item
                    959: @code{break}
1.4     ! noro      960: @*
1.3       noro      961: \JP @code{break} $BJ8$O(B, $B$=$l$r0O$`%k!<%W$r0l$D$@$1H4$1$k(B.
                    962: \EG The @code{break} statement is used to exit the inner most loop.
1.1       noro      963: @item
                    964: @code{return}
1.4     ! noro      965: @*
1.3       noro      966: \BJP
1.1       noro      967: @code{return} $BJ8$O(B, $B0lHL$KH!?t$+$iH4$1$k$?$a$NJ8$G$"$j(B,
                    968: $B%k!<%W$NCf$+$i$G$bM-8z$G$"$k(B.
1.3       noro      969: \E
                    970: \BEG
                    971: The @code{return} statement is usually used to exit from a function call
                    972: and it is also effective in a loop.
                    973: \E
1.1       noro      974:
                    975: @item
                    976: @code{continue}
1.4     ! noro      977: @*
1.3       noro      978: \BJP
1.1       noro      979: @code{continue} $BJ8$O(B, $B%k!<%W$NK\BN$NJ8$NKvC<$K@)8f$r0\$9(B.
                    980: $BNc$($P(B @code{for} $BJ8$G$O(B, $B:G8e$N<0JB$S$N<B9T$r9T$$(B, @code{while}
                    981: $BJ8$G$O>r7o<0$NH=Dj$K0\$k(B.
1.3       noro      982: \E
                    983: \BEG
                    984: The @code{continue} statement is used to move the control to the end
                    985: point of the loop body.
                    986: For example, the last expression list will be evaluated in a @code{for}
                    987: statement, and the termination condition will be evaluated in a
                    988: @code{while} statement.
                    989: \E
1.1       noro      990: @end itemize
                    991:
1.3       noro      992: \BJP
1.1       noro      993: @node $B$5$^$6$^$J<0(B,,, $B%f!<%6Dj5AH!?t$N=q$-J}(B
                    994: @subsection $B$5$^$6$^$J<0(B
1.3       noro      995: \E
                    996: \BEG
                    997: @node various expressions,,, Writing user defined functions
                    998: @subsection various expressions
                    999: \E
1.1       noro     1000:
                   1001: @noindent
1.3       noro     1002: \JP $B<g$J<0$N9=@.MWAG$H$7$F$O(B, $B<!$N$h$&$J$b$N$,$"$k(B.
                   1003: \EG Major elements to construct expressions are the following:
1.1       noro     1004:
                   1005: @itemize @bullet
                   1006: @item
1.3       noro     1007: \JP $B2C8:>h=|(B, $BQQ(B
                   1008: \EG addition, subtraction, multiplication, division, exponentiation
1.4     ! noro     1009: @*
1.3       noro     1010: \BJP
1.1       noro     1011: $BQQ$O(B, @samp{^} $B$K$h$jI=$9(B. $B=|;;(B @samp{/} $B$O(B, $BBN$H$7$F$N1i;;$KMQ$$$k(B.
                   1012: $BNc$($P(B, @code{2/3} $B$OM-M}?t$N(B @code{2/3} $B$rI=$9(B.
                   1013: $B@0?t=|;;(B, $BB?9`<0=|;;(B ($B>jM>$r4^$`1i;;(B) $B$K$OJLESAH$_9~$_H!?t$,MQ0U$5$l$F$$$k(B.
1.3       noro     1014: \E
                   1015: \BEG
                   1016: The exponentiation is denoted by @samp{^}. (This differs from C language.)
                   1017: Division denoted by @samp{/} is used to operate in a field, for example,
                   1018: @code{2/3} results in a rational number @code{2/3}.
                   1019: For integer division and polynomial division, both including remainder
                   1020: operation, built-in functions are provided.
                   1021: \E
1.1       noro     1022:
                   1023: @example
                   1024: x+1  A^2*B*afo X/3
                   1025: @end example
                   1026:
                   1027: @item
1.3       noro     1028: \JP $B%$%s%G%C%/%9$D$-$NJQ?t(B
                   1029: \EG programming variables with indices
1.4     ! noro     1030: @*
1.3       noro     1031: \BJP
1.1       noro     1032: $B%Y%/%H%k(B, $B9TNs(B, $B%j%9%H$NMWAG$O%$%s%G%C%/%9$rMQ$$$k$3$H$K$h$j<h$j=P$;$k(B.
                   1033: $B%$%s%G%C%/%9$O(B 0 $B$+$i;O$^$k$3$H$KCm0U$9$k(B. $B<h$j=P$7$?MWAG$,%Y%/%H%k(B,
                   1034: $B9TNs(B, $B%j%9%H$J$i(B, $B$5$i$K%$%s%G%C%/%9$r$D$1$k$3$H$bM-8z$G$"$k(B.
1.3       noro     1035: \E
                   1036: \BEG
                   1037: An element of a vector, a matrix or a list can be referred to by
                   1038: indexing.
                   1039: Note that the indices begin with number 0.  When the referred element
                   1040: is again a vector, a matrix or a list, repeated indexing is also
                   1041: effective.
                   1042: \E
1.1       noro     1043:
                   1044: @example
                   1045: V[0] M[1][2]
                   1046: @end example
                   1047:
                   1048: @item
1.3       noro     1049: \JP $BHf3S1i;;(B
                   1050: \EG comparison operation
1.4     ! noro     1051: @*
1.3       noro     1052: \BJP
1.1       noro     1053: $BEy$7$$(B (@samp{==}), $BEy$7$/$J$$(B (@samp{!=}), $BBg>.(B (@samp{>}, @samp{<},
                   1054: @samp{>=}, @samp{<=}) $B$N(B 2 $B9`1i;;$,$"$k(B. $B??$J$i$PM-M}?t$N(B 1, $B56$J$i$P(B
                   1055: 0 $B$rCM$K;}$D(B.
1.3       noro     1056: \E
                   1057: \BEG
                   1058: There are comparison operations
                   1059: @samp{==} for equivalence, @samp{!=} for non-equivalence,
                   1060: @samp{>}, @samp{<},@samp{>=}, and @samp{<=} for larger or smaller.
                   1061: The results of these operations are either value 1 for the truth,
                   1062: or 0 for the false.
                   1063: \E
1.1       noro     1064:
                   1065: @item
1.3       noro     1066: \JP $BO@M}<0(B
                   1067: \EG logical expression
1.4     ! noro     1068: @*
1.3       noro     1069: \BJP
1.1       noro     1070: $BO@M}@Q(B (@samp{&&}), $BO@M}OB(B (@samp{||}) $B$N(B 2 $B9`1i;;$H(B, $BH]Dj(B (@samp{!})
                   1071: $B$,MQ0U$5$l$F$$$k(B. $BCM$O$d$O$j(B 1, 0 $B$G$"$k(B.
1.3       noro     1072: \E
                   1073: \BEG
                   1074: There are two binary logical operations
                   1075: @samp{&&} for logical @samp{conjunction}(and),
                   1076: @samp{||} for logical @samp{disjunction}(or),
                   1077: and one unary logical operation @samp{!} for logical @samp{negation}(not).
                   1078: The results of these operations are either value 1 for the truth,
                   1079: and 0 for the false.
                   1080: \E
1.1       noro     1081:
                   1082: @item
1.3       noro     1083: \JP $BBeF~(B
                   1084: \EG assignment
1.4     ! noro     1085: @*
1.3       noro     1086: \BJP
1.1       noro     1087: $BDL>o$NBeF~$O(B @samp{=} $B$G9T$&(B. $B$3$N$[$+(B, $B;;=Q1i;;;R$HAH$_9g$o$;$F(B
                   1088: $BFC<l$JBeF~$r9T$&$3$H$b$G$-$k(B.
1.3       noro     1089: \E
                   1090: \BEG
                   1091: Value assignment of a program variable is usually done by @samp{=}.
                   1092: There are special assignments combined with arithmetic operations.
                   1093: \E
1.1       noro     1094: (@samp{+=}, @samp{-=}, @samp{*=}, @samp{/=}, @samp{^=})
                   1095:
                   1096: @example
1.3       noro     1097: \JP A = 2  A *= 3 ($B$3$l$O(B A = A*3 $B$HF1$8(B; $B$=$NB>$N1i;;;R$bF1MM(B)
                   1098: \EG A = 2  A *= 3 (the same as A = A*3; The other combination are alike.)
1.1       noro     1099: @end example
                   1100: @item
1.3       noro     1101: \JP $BH!?t8F$S=P$7(B
                   1102: \EG function call
1.4     ! noro     1103: @*
1.3       noro     1104: \JP $BH!?t8F$S=P$7$b<0$N0l<o$G$"$k(B.
                   1105: \EG A function call is also an expression.
1.1       noro     1106: @item
                   1107: @samp{++}, @samp{--}
1.4     ! noro     1108: @*
1.3       noro     1109: \JP $B$3$l$i$O(B, $BJQ?t$NA08e$K$D$$$F(B, $B$=$l$>$l<!$N$h$&$JA`:n(B, $BCM$rI=$9(B.
                   1110: \BEG
                   1111: These operators are attached to or before a program variable,
                   1112: and denote special operations and values.
                   1113: \E
1.1       noro     1114: @example
1.3       noro     1115: \BJP
1.1       noro     1116: A++  $BCM$O85$N(B A $B$NCM(B, A = A+1
                   1117: A--  $BCM$O85$N(B A $B$NCM(B, A = A-1
                   1118: ++A  A = A+1, $BCM$OJQ2=8e$NCM(B
                   1119: --A  A = A-1, $BCM$OJQ2=8e$NCM(B
1.3       noro     1120: \E
                   1121: \BEG
                   1122: A++  the expression value is the previous value of A, and A = A+1
                   1123: A--  the expression value is the previous value of A, and A = A-1
                   1124: ++A  A = A+1, and the expression value is the value after increment of A
                   1125: --A  A = A-1, and the expression value is the value after decrement of A
                   1126: \E
1.1       noro     1127: @end example
                   1128:
                   1129: @end itemize
                   1130:
1.3       noro     1131: \BJP
1.1       noro     1132: @node $B%W%j%W%m%;%C%5(B,,, $B%f!<%6Dj5AH!?t$N=q$-J}(B
                   1133: @subsection $B%W%j%W%m%;%C%5(B
1.3       noro     1134: \E
                   1135: \BEG
                   1136: @node preprocessor,,, Writing user defined functions
                   1137: @subsection preprocessor
                   1138: \E
1.1       noro     1139:
                   1140: @noindent
1.3       noro     1141: \BJP
1.1       noro     1142: @b{Asir} $B$N%f!<%68@8l$O(B C $B8@8l$rLO$7$?$b$N$G$"$k(B. C $B$NFCD'$H$7$F(B,
                   1143: $B%W%j%W%m%;%C%5(B @code{cpp} $B$K$h$k%^%/%mE83+(B, $B%U%!%$%k$N%$%s%/%k!<%I(B
                   1144: $B$,$"$k$,(B, @b{Asir} $B$K$*$$$F$b%f!<%68@8l%U%!%$%k$NFI$_9~$_$N:](B
                   1145: @code{cpp} $B$rDL$7$F$+$iFI$_9~$`$3$H$H$7$?(B. $B$3$l$K$h$j%f!<%68@8l(B
                   1146: $B%U%!%$%kCf$G(B @code{#include}, @code{#define}, @code{#if} $B$J$I$,;H$($k(B.
1.3       noro     1147: \E
                   1148: \BEG
                   1149: he @b{Asir} user language imitates C language.  A typical features of
                   1150: C language include macro expansion and file inclusion by the
                   1151: preprocessor @code{cpp}.  Also, @b{Asir} read in user program files
                   1152: through @code{cpp}.  This enables @b{Asir} user to use
                   1153: @code{#include}, @code{#define}, @code{#if} etc. in his programs.
                   1154: \E
1.1       noro     1155:
                   1156: @itemize @bullet
                   1157: @item
                   1158: @code{#include}
1.4     ! noro     1159: @*
1.3       noro     1160: \BJP
1.1       noro     1161: @code{cpp} $B$KFC$K0z?t$rEO$5$J$$$?$a(B, $B%$%s%/%k!<%I%U%!%$%k$O(B,
                   1162: @code{#include} $B$,=q$+$l$F$$$k%U%!%$%k$HF1$8%G%#%l%/%H%j$G%5!<%A$5$l$k(B.
1.3       noro     1163: \E
                   1164: \BEG
                   1165: Include files are searched within the same directory as the file
                   1166: containing @code{#include} so that no arguments are passed to @code{cpp}.
                   1167: \E
1.1       noro     1168:
                   1169: @item
                   1170: @code{#define}
1.4     ! noro     1171: @*
1.3       noro     1172: \JP $B$3$l$O(B, C $B$K$*$1$k$N$HA4$/F1MM$KMQ$$$k$3$H$,$G$-$k(B.
                   1173: \EG This can be used just as in C language.
1.1       noro     1174:
                   1175: @item
                   1176: @code{#if}
1.4     ! noro     1177: @*
1.3       noro     1178: \BJP
1.1       noro     1179: @code{/*}, @code{*/} $B$K$h$k%3%a%s%H$OF~$l;R$K$G$-$J$$$N$G(B, $B%W%m%0%i%`(B
                   1180: $B$NBg$-$JItJ,$r%3%a%s%H%"%&%H$9$k:]$K(B, @code{#if 0}, @code{#endif}
                   1181: $B$r;H$&$HJXMx$G$"$k(B.
1.3       noro     1182: \E
                   1183: \BEG
                   1184: This is conveniently used to comment out a large part of a user program
                   1185: that may contain comments by @code{/*} and @code{*/},
                   1186: because such comments cannot be nested.
                   1187: \E
1.1       noro     1188: @end itemize
                   1189:
                   1190: @noindent
1.3       noro     1191: \JP $B<!$NNc$O(B, @samp{defs.h} $B$K$"$k%^%/%mDj5A$G$"$k(B.
                   1192: \EG the following are the macro definitions in @samp{defs.h}.
1.1       noro     1193:
                   1194: @example
                   1195: #define ZERO 0
                   1196: #define NUM 1
                   1197: #define POLY 2
                   1198: #define RAT 3
                   1199: #define LIST 4
                   1200: #define VECT 5
                   1201: #define MAT 6
                   1202: #define STR 7
                   1203: #define N_Q 0
                   1204: #define N_R 1
                   1205: #define N_A 2
                   1206: #define N_B 3
                   1207: #define N_C 4
                   1208: #define V_IND 0
                   1209: #define V_UC 1
                   1210: #define V_PF 2
                   1211: #define V_SR 3
                   1212: #define isnum(a) (type(a)==NUM)
                   1213: #define ispoly(a) (type(a)==POLY)
                   1214: #define israt(a) (type(a)==RAT)
                   1215: #define islist(a) (type(a)==LIST)
                   1216: #define isvect(a) (type(a)==VECT)
                   1217: #define ismat(a) (type(a)==MAT)
                   1218: #define isstr(a) (type(a)==STR)
                   1219: #define FIRST(L) (car(L))
                   1220: #define SECOND(L) (car(cdr(L)))
                   1221: #define THIRD(L) (car(cdr(cdr(L))))
                   1222: #define FOURTH(L) (car(cdr(cdr(cdr(L)))))
                   1223: #define DEG(a) deg(a,var(a))
                   1224: #define LCOEF(a) coef(a,deg(a,var(a)))
                   1225: #define LTERM(a) coef(a,deg(a,var(a)))*var(a)^deg(a,var(a))
                   1226: #define TT(a) car(car(a))
                   1227: #define TS(a) car(cdr(car(a)))
                   1228: #define MAX(a,b) ((a)>(b)?(a):(b))
                   1229: @end example
1.2       noro     1230:
                   1231:
1.3       noro     1232: \BJP
1.2       noro     1233: @node $B%*%W%7%g%s;XDj(B,,, $B%f!<%6Dj5AH!?t$N=q$-J}(B
                   1234: @subsection $B%*%W%7%g%s;XDj(B
1.3       noro     1235: \E
                   1236: \BEG
                   1237: @node option,,, Writing user defined functions
                   1238: @subsection option
                   1239: \E
1.2       noro     1240:
1.3       noro     1241: \BJP
1.2       noro     1242: $B%f!<%6Dj5A4X?t$,(B @var{N} $BJQ?t$G@k8@$5$l$?>l9g(B, $B$=$N4X?t$O(B, @var{N}
                   1243: $BJQ?t$G$N8F$S=P$7$N$_$,5v$5$l$k(B.
1.3       noro     1244: \E
                   1245: \BEG
                   1246: If a user defined function is declared with @var{N} arguments,
                   1247: then the function is callable with @var{N} arguments only.
                   1248: \E
1.2       noro     1249:
                   1250: @example
                   1251: [0] def factor(A) @{ return fctr(A); @}
                   1252: [1] factor(x^5-1,3);
                   1253: evalf : argument mismatch in factor()
                   1254: return to toplevel
                   1255: @end example
                   1256:
1.3       noro     1257: \BJP
1.2       noro     1258: $BITDj8D0z?t$N4X?t$r%f!<%68@8l$G5-=R$7$?$$>l9g(B, $B%j%9%H(B, $BG[Ns$rMQ$$$k$3$H$G(B
                   1259: $B2DG=$H$J$k$,(B, $B<!$N$h$&$J$h$jJ,$+$j$d$9$$J}K!$b2DG=$G$"$k(B.
1.3       noro     1260: \E
                   1261: \BEG
                   1262: A function with indefinite number of arguments can be realized by
                   1263: using a list or an array as its argument. Another method is available
                   1264: as follows:
                   1265: \E
1.2       noro     1266:
                   1267: @example
                   1268: % cat factor
                   1269: def factor(F)
                   1270: @{
                   1271:     Mod = getopt(mod);
                   1272:     ModType = type(Mod);
                   1273:     if ( ModType == 1 ) /* 'mod' is not specified. */
                   1274:         return fctr(F);
                   1275:     else if ( ModType == 0 ) /* 'mod' is a number */
                   1276:         return modfctr(F,Mod);
                   1277: @}
                   1278: @end example
                   1279:
                   1280: @example
                   1281: [0] load("factor")$
                   1282: [1] factor(x^5-1);
                   1283: [[1,1],[x-1,1],[x^4+x^3+x^2+x+1,1]]
                   1284: [2] factor(x^5-1|mod=11);
                   1285: [[1,1],[x+6,1],[x+2,1],[x+10,1],[x+7,1],[x+8,1]]
                   1286: @end example
                   1287:
1.3       noro     1288: \BJP
1.2       noro     1289: 2 $BHVL\$N(B @code{factor()} $B$N8F$S=P$7$K$*$$$F(B, $B4X?tDj5A$N:]$K@k8@$5$l$?0z(B
1.3       noro     1290: $B?t(B @code{x^5-1}$B$N8e$m$K(B @code{|mod=11} $B$,CV$+$l$F$$$k(B. $B$3$l$O(B, $B4X?t<B9T;~(B
                   1291: $B$K(B, @code{mod} $B$H$$$&(B keyword $B$KBP$7$F(B @code{11} $B$H$$$&CM$r3d$jEv$F$k$3$H(B
1.2       noro     1292: $B$r;XDj$7$F$$$k(B. $B$3$l$r%*%W%7%g%s;XDj$H8F$V$3$H$K$9$k(B. $B$3$NCM$O(B
                   1293: @code{getopt(mod)} $B$G<h$j=P$9$3$H$,$G$-$k(B. 1 $BHVL\$N8F$S=P$7$N$h$&$K(B
1.3       noro     1294: @code{mod} $B$KBP$9$k%*%W%7%g%s;XDj$,$J$$>l9g$K$O(B, @code{getopt(mod)} $B$O7?(B
1.2       noro     1295: $B<1JL;R(B -1 $B$N%*%V%8%'%/%H$rJV$9(B. $B$3$l$K$h$j(B, $B;XDj$,$J$$>l9g$NF0:n$r(B if $BJ8(B
                   1296: $B$K$h$j5-=R$G$-$k(B. @samp{|} $B$N8e$m$K$O(B, $BG$0U8D$N%*%W%7%g%s$r(B, @samp{,}
                   1297: $B$G6h@Z$C$F;XDj$9$k$3$H$,$G$-$k(B.
1.3       noro     1298: \E
                   1299: \BEG
                   1300: In the second call of @code{factor()}, @code{|mod=11} is placed
                   1301: after the argument @code{x^5-1}, which appears in the declaration of
                   1302: @code{factor()}. This means that the value @code{11} is assigned to
                   1303: the keyword @code{mod} when the function is executed. The value
                   1304: can be retrieved by @code{getopt(mod)}. We call such machinery
                   1305: @var{option}. If the option for @var{mod} is not specified,
                   1306: @code{getopt(mod)} returns an object whose type is -1. By this
                   1307: feature, one can describe the behaviour of the function when
                   1308: the option is not specified by @var{if} statements.
                   1309: After @samp{|} one can append any number of options seperated by @samp{,}.
                   1310: \E
1.2       noro     1311: @example
                   1312: [100] xxx(1,2,x^2-1,[1,2,3]|proc=1,index=5);
                   1313: @end example
                   1314:
1.1       noro     1315: