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5.1.130 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:
-
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)
-
the names of the variables (a list L of strings: L[i] is the name of the i-th
variable)
-
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] )
-
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 contructed fron 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));
def ra = ring(l); //creates the newring
ra; setring ra;
==> // characteristic : 0
==> // 1 parameter : a
==> // minpoly : 0
==> // 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
list lra = ringlist(ra);
lra[1][4]=ideal(a2+1);
def Ra = ring(lra);
setring Ra; Ra;
==> // characteristic : 0
==> // 1 parameter : a
==> // minpoly : (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
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See
qring;
ring.
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