### D.2.12 ring_lib

Library:
  ring.lib
Purpose:
  Manipulating Rings and Maps
Authors:
  Singular team

Procedures:

> D.2.12.1 changechar |  | make a copy of basering [ring r] with new char c
> D.2.12.2 changeord |  | make a copy of basering [ring r] with new ord o
> D.2.12.3 changevar |  | make a copy of basering [ring r] with new vars v
> D.2.12.4 defring |  | define a ring R in specified char c, n vars v, ord o
> D.2.12.5 defrings |  | define ring Sn in n vars, char 32003 [p], ord ds
> D.2.12.6 defringp |  | define ring Pn in n vars, char 32003 [p], ord dp
> D.2.12.7 extendring |  | extend given ring by n vars v, ord o and name it R
> D.2.12.8 fetchall |  | fetch all objects of ring R to basering
> D.2.12.9 imapall |  | imap all objects of ring R to basering
> D.2.12.10 mapall |  | map all objects of ring R via ideal i to basering
> D.2.12.11 ord_test |  | test whether ordering of R is global, local or mixed
> D.2.12.12 ringtensor |  | create ring, tensor product of rings s,t,...
> D.2.12.13 ringweights |  | intvec of weights of ring variables of ring r
> D.2.12.14 preimageLoc |  | computes preimage for non-global orderings
> D.2.12.15 rootofUnity |  | the minimal polynomial for the n-th primitive root of unity (parameters in square brackets [] are optional)
> D.2.12.16 optionIsSet |  | check if as a string given option is set or not. hasFieldCoefficient check if the coefficient ring is considered a field hasGFCoefficient check if the coefficient ring is GF(p,k) hasZpCoefficient check if the coefficient ring is ZZ/p hasZp_aCoefficient check if the coefficient ring is an elag. ext. of ZZ/p hasQQCoefficient check if the coefficient ring is QQ
> D.2.12.17 hasNumericCoeffs |  | check for use of floating point numbers
> D.2.12.18 hasCommutativeVars |  | non-commutative or commutative polynomial ring
> D.2.12.19 hasGlobalOrdering |  | global versus mixed/local monomial ordering
> D.2.12.20 hasMixedOrdering |  | mixed versus global/local ordering
> D.2.12.21 hasAlgExtensionCoefficient |  | coefficients are an algebraic extension
> D.2.12.22 hasTransExtensionCoefficient |  | coefficients are rational functions
> D.2.12.23 isQuotientRing |  | ring is a qotient ring
> D.2.12.24 isSubModule |  | check if I is in J as submodule
> D.2.12.25 changeordTo |  | change the ordering of a ring to a simple one
> D.2.12.26 addvarsTo |  | add variables to a ring
> D.2.12.27 addNvarsTo |  | add N variables to a ring

User manual for Singular version 4.4.1, 2025, generated by texi2html.