@comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/type.texi,v 1.4 2003/12/21 17:36:29 ohara Exp $
\BJP
@node 型を求める函数,,, 組み込み函数
@section 型を求める函数
\E
\BEG
@node Types,,, Built-in Function
@section Types
\E

@menu
* type::
* ntype::
* vtype::
@end menu

\JP @node type,,, 型を求める函数
\EG @node type,,, Types
@subsection @code{type}
@findex type

@table @t
@item type(@var{obj})
\JP :: @var{obj} の 型 (整数) を返す. 
\EG :: Returns an integer which identifies the type of the object @var{obj} in question.
@end table

@table @var 
@item return
\JP 整数
\EG integer
@item obj
\JP 任意
\EG arbitrary
@end table

@itemize @bullet
\BJP
@item
@var{obj} の 型の値は次の通り. 
@table @t
@item 0
0
@item 1
数
@item 2
多項式 (数でない)
@item 3
有理式 (多項式でない)
@item 4
リスト
@item 5
ベクトル
@item 6
行列
@item 7
文字列
@item 8
構造体
@item 9
分散表現多項式
@item 10
32bit 符号なし整数
@item 11
エラーオブジェクト
@item 12
GF(2) 上の行列
@item 13
MATHCAP オブジェクト
@item 14
一階述語論理式
@item -1
VOID オブジェクト
@end table
@item
数の型を求めるには, @code{ntype} を用いる. 
不定元の型を求めるには, @code{vtype} を用いる. 
\E
\BEG
@item
Current assignment of integers for object types is listed below.
@table @t
@item 0
0 
@item 1
number
@item 2
polynomial (not number)
@item 3
rational expression (not polynomial)
@item 4
list
@item 5
vector
@item 6
matrix
@item 7
string
@item 8
structure
@item 9
distributed polynomial
@item 10
32bit unsigned integer
@item 11
error object
@item 12
matrix over GF(2)
@item 13
MATHCAP object
@item 14
first order formula
@item -1
VOID object
@end table
@item
For further classification of @var{number}, use @code{ntype()}.
For further classification of @var{variable}, use @code{vtype()}.
\E
@end itemize

@table @t
\JP @item 参照
\EG @item References
@fref{ntype}, @fref{vtype}.
@end table

\JP @node ntype,,, 型を求める函数
\EG @node ntype,,, Types
@subsection @code{ntype}
@findex ntype

@table @t
@item ntype(@var{num})
\JP :: @var{num} (数) の 型 (整数) を返す. 
\EG :: Classifier of type @var{num}.  Returns a sub-type number, an integer, for @var{obj}.
@end table

@table @var
@item return
\JP 自然数
\EG integer  
@item obj
\JP 数
\EG number
@end table

@itemize @bullet
\BJP
@item
数の型の値は次の通り. 
@table @t
@item 0
有理数
@item 1
倍精度浮動小数
@item 2
代数的数
@item 3
任意精度浮動小数 (@b{bigfloat})
@item 4
複素数
@item 5
有限体の元
@item 6
大標数素体の元
@item 7
標数 2 の有限体の元
@end table
@item
@code{newalg(x^2+1)} で生成した数と, 虚数単位 @code{@@i} は, 
異なるものとして扱われる. 
@item
代数的数に関しては, @xref{代数的数に関する演算}. 
\E
\BEG
@item
Sub-types for type number are listed below.
@table @t
@item 0
rational number
@item 1
floating double (double precision floating point number)
@item 2
algebraic number over rational number field
@item 3
arbitrary precision floating point number (@b{bigfloat})
@item 4
complex number
@item 5
element of a finite field
@item 6
element of a large finite prime field
@item 7
element of a finite field of characteristic 2
@end table
@item
When arithmetic operations for numbers are performed,
type coercion will be taken if their number sub-types are different
so that the object having smaller sub-type number will be transformed
to match the other object, except for algebraic numbers.
@item
A number object created by @code{newalg(x^2+1)} and the unit of
imaginary number @code{@@i} have different number sub-types, and
it is treated independently.
@item
See @ref{Algebraic numbers} for algebraic numbers.
\E
@end itemize

@example
[0] [10/37,ntype(10/37)];
[10/37,0]
[1] [10.0/37.0,ntype(10.0/37.0)];
[0.27027,1]
[2] [newalg(x^2+1)+1,ntype(newalg(x^2+1)+1)];
[(#0+1),2]
[3] [eval(sin(@@pi/6)),ntype(eval(sin(@@pi/6)))];
[0.49999999999999999991,3]
[4] [@@i+1,ntype(@@i+1)];
[(1+1*@@i),4]
@end example

@table @t
\JP @item 参照
\EG @item References
@fref{type}.
@end table

\JP @node vtype,,, 型を求める函数
\EG @node vtype,,, Types   
@subsection @code{vtype}
@findex vtype

@table @t
@item vtype(@var{var})
\JP :: @var{var} (不定元) の 型 (整数) を返す. 
\EG :: Type of indetarminates @var{var}.
@end table

@table @var
@item return
\JP 整数
\EG integer
@item var
\JP 不定元
\EG indeterminate
@end table

@itemize @bullet
\BJP
@item
@var{var} (不定元) の型の値は次の通り. 詳細は @xref{不定元の型}.
@table @t
@item 0
一般不定元  (a,b,x,afo,bfo,...,etc)
@item 1
@code{uc()} で生成された不定元 (@code{_0}, @code{_1}, @code{_2}, ... etc)
@item 2
函数形式 (@code{sin(x)}, @code{log(a+1)}, @code{acosh(1)}, @code{@@pi}, @code{@@e}, ... etc)
@item 3
函数子 (組み込み函数子, ユーザ定義函数子, 初等函数子 : @code{sin}, @code{log}, ... etc)
@end table
@item
@code{a();} を実行(通常ではエラー)しただけでも @code{ntype(a)} は 3 となる. 
すなわち @code{a} はユーザ定義函数子とみなされる.
@item
ユーザが函数形式を定義するためにはキーワード @code{function} を用いる.
@item
@code{@@pi}, @code{@@e} は不定元として扱われるが, @code{eval()}, @code{pari()}
においては数として扱われる. 
\E
\BEG
@item
Classify indeterminates into sub-types by giving an integer value as follows.
For details  @xref{Types of indeterminates}.
@table @t
@item 0
ordinary indeterminate, which can be directly typed in on a keyboard
(a,b,x,afo,bfo,...,etc.)
@item 1
Special indeterminate, created by @code{uc()}
(@code{_0}, @code{_1}, @code{_2}, ... etc.)
@item 2
function form (@code{sin(x)}, @code{log(a+1)}, @code{acosh(1)}, @code{@@pi}, @code{@@e}, ... etc.)
@item 3
functor (built-in functor name, user defined functor, functor for
the elementary functions)
 : @code{sin}, @code{log}, ... etc)
@end table
@item
Note: An input `@code{a();}' will cause an error, but it changes
the system database for identifiers.  After this error, you will find
`@code{vtype(a)}' will result 3. (Identifier @code{a} is registered as
a user defined functor).
@item
Usually @code{@@pi} and @code{@@e} are treated as indeterminates,
whereas they are treated as numbers within functions @code{eval()} and
 @code{pari()}.
\E
@end itemize

@table @t
\JP @item 参照
\EG @item References
@fref{type}, @fref{ntype}, @fref{uc}.
@end table