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5.1.125 ringlist

Syntax:
ringlist ( ring_expression )
ringlist ( qring_expression )
Type:
list
Purpose:
decomposes a ring/qring into a list of 4 (or 6 in the non-commutative case, see ringlist (plural)) components:
  1. the field description in the following format:
    • for Q, Z/p: the characteristic, type int (0 or prime number)
    • for real, complex: a list of:
      the characteristic, type int (always 0)
      the precision, type list (2 integers: external, internal precision)
      the name of the imaginary unit, type string
    • for transcendental or algebraic extensions: described as a ringlist (that is, as list L with 4 entries: L[1] the characteristic, L[2] the names of the parameters, L[3] the monomial ordering for the ring of parameters (default: lp), L[4] the minimal polynomial (as ideal))
    • for Z, Z/n, Z/n^m a list ["integer", [n, m]] with:
      the base n is of type int or bigint (if not given n = 0, Z/0 = Z)
      the exponent m is of type int (if not given m = 1)
  2. the names of the variables (a list L of strings: L[i] is the name of the i-th variable)
  3. the monomial ordering (a list L of lists): each block L[i] consists of
    • the name of the ordering ( string )
    • parameters specifying the ordering and the size of the block ( intvec : typically the weights for the variables [default: 1] )
  4. the quotient ideal.
From a list of such structure, a new ring may be defined by the command ring ( see the following example ).
Example:
 
See qring; ring.

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