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5.1.135 ringlist

Syntax:
ringlist ( ring_expression )
Type:
list
Purpose:
decomposes a ring/qring into a list of 4 (or 6 in the non-commutative case, see ringlist (plural)) components. It is identical to ring_list with the exception of the first list entry.
  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 ). If the attribute "maxExp" of the ring is different from the default 32767, it is also set for the list.
Note: All data which depends on a ring belong to the current ring,
not to a ring which can be constructed from a modified list. These data will be mapped via fetch to the ring to be constructed.
Example:
 
 ring r = 0,(x(1..3)),dp;
 list l = ringlist(r);
 l;
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       x(1)
==>    [2]:
==>       x(2)
==>    [3]:
==>       x(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          dp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
 //  Now change l and create a new ring, by
 //- changing the base field to the function field with parameter a,
 //- introducing one extra variable y,
 //- defining the block ordering (dp(2),wp(3,4)).
 //- define the minpoly after creating the function field
 l[1]=list(0,list("a"),list(list("lp",1)),ideal(0));
 l[2][size(l[2])+1]="y";
 l[3][3]=l[3][2]; // save the module ordering
 l[3][1]=list("dp",intvec(1,1));
 l[3][2]=list("wp",intvec(3,4));
 attrib(l,"maxExp",100); // and lower the limit for exponents to 100
 def ra = ring(l);     //creates the newring
 ra; setring ra;
==> // coefficients: QQ(a)
==> // number of vars : 4
==> //        block   1 : ordering dp
==> //                  : names    x(1) x(2)
==> //        block   2 : ordering wp
==> //                  : names    x(3) y
==> //                  : weights  3 4
==> //        block   3 : ordering C
 attrib(ra,"maxExp");
==> 65535
 list lra = ringlist(ra);
 lra[1][4]=ideal(a2+1);
 def Ra = ring(lra);
 setring Ra; Ra;
==> // coefficients: QQ[a]/(a^2+1)
==> // number of vars : 4
==> //        block   1 : ordering dp
==> //                  : names    x(1) x(2)
==> //        block   2 : ordering wp
==> //                  : names    x(3) y
==> //                  : weights  3 4
==> //        block   3 : ordering C
See qring; ring; ring_list.

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