5.1.138 ring_list

Syntax:

ring_list ( ring_expression )
ring_list ( cring_expression )

Type:

list

Purpose:

decomposes a ring/qring/coefficient 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