6.8 Types

6.8.1 type

type(obj)

:: Returns an integer which identifies the type of the object obj in question.

return

integer

obj

arbitrary

• Current assignment of integers for object types is listed below.

  0

  0

  1

  number

  2

  polynomial (not number)

  3

  rational expression (not polynomial)

  4

  list

  5

  vector

  6

  matrix

  7

  string

  8

  structure

  9

  distributed polynomial

  10

  32bit unsigned integer

  11

  error object

  12

  matrix over GF(2)

  13

  MATHCAP object

  14

  first order formula

  -1

  VOID object

• For further classification of number, use ntype(). For further classification of variable, use vtype().

References

ntype, vtype.

6.8.2 ntype

ntype(num)

:: Classifier of type num. Returns a sub-type number, an integer, for obj.

return

integer

obj

number

• Sub-types for type number are listed below.

  0

  rational number

  1

  floating double (double precision floating point number)

  2

  algebraic number over rational number field

  3

  arbitrary precision floating point number (bigfloat)

  4

  complex number

  5

  element of a finite field

  6

  element of a large finite prime field

  7

  element of a finite field of characteristic 2

• 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.
• A number object created by newalg(x^2+1) and the unit of imaginary number @i have different number sub-types, and it is treated independently.
• See Algebraic numbers for algebraic numbers.

[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]

References

type.

6.8.3 vtype

vtype(var)

:: Type of indetarminates var.

return

integer

var

indeterminate

• Classify indeterminates into sub-types by giving an integer value as follows. For details See section Types of indeterminates.

  0

  ordinary indeterminate, which can be directly typed in on a keyboard (a,b,x,afo,bfo,...,etc.)

  1

  Special indeterminate, created by uc() (_0, _1, _2, ... etc.)

  2

  function form (sin(x), log(a+1), acosh(1), @pi, @e, ... etc.)

  3

  functor (built-in functor name, user defined functor, functor for the elementary functions) : sin, log, ... etc)

• Note: An input ‘a();’ will cause an error, but it changes the system database for identifiers. After this error, you will find ‘vtype(a)’ will result 3. (Identifier a is registered as a user defined functor).
• Usually @pi and @e are treated as indeterminates, whereas they are treated as numbers within functions eval() and pari().

References

type, ntype, uc.

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