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5.1.136 ring_list

Syntax:
ring_list ( ring_expression )
ring_list ( cring_expression )
Type:
list
Purpose:
decomposes a ring/qring/coeffcient ring into a list of 4 (or 6 in the non-commutative case, see ringlist (plural)) or 1/4 (for cring) components. It is identical to ringlist with the exception of the first list entry.
  1. the field description as cring
  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 ).
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 = ring_list(r);
 ring_list(l[1]);
==> 0
 l;
==> [1]:
==> QQ
==> [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 ZZ/32003
 //- introducing one extra variable y,
 //- defining the block ordering (dp(2),wp(3,4)).
 //- define the minpoly after creating the function field
 l[1]=ZZ/32003;
 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));
 def ra = ring(l);     //creates the newring
 ra; setring ra;
==> // coefficients: ZZ/32003
==> // 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; ringlist.

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