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# NCPolynomialRing -- exported from the NCAlgebra package, used to encode tensor algebras

## Methods that use an object of class NCPolynomialRing:

- `adjointWord(NCRingElement,NCPolynomialRing,List)` -- see adjointWord -- image of a word through the shuffle algebra homomorphism induced by a polynomial map
- `ambient(NCPolynomialRing)` -- see ambient -- exported from the NCALgebra package.
- Array _ NCPolynomialRing -- create a word from an array
- `CAxisTensor(ZZ,NCPolynomialRing)` -- see CAxisTensor -- the signature tensor of the canonical axis path at a given level
- `CMonTensor(ZZ,NCPolynomialRing)` -- see CMonTensor -- the signature tensor of the canonical monomial path at a given level
- `gbFromOutputFile(NCPolynomialRing,String)` -- see gbFromOutputFile -- Read in a NCGroebnerBasis from a Bergman output file.
- ideal(NCPolynomialRing) -- The defining ideal of an NCPolynomialRing
- `lieBasis(Array,NCPolynomialRing)` -- see lieBasis -- basis element corresponding to a Lyndon word in a Lie algebra
- `lieBasis(List,NCPolynomialRing)` -- see lieBasis -- basis element corresponding to a Lyndon word in a Lie algebra
- NCPolynomialRing / NCIdeal -- Construct a NCQuotientRing
- `sgnVolTensor(NCPolynomialRing)` -- see sgnVolTensor -- The signed volume tensor in a free associative algebra.

## For the programmer

The object NCPolynomialRing is a type, with ancestor classes NCRing < Ring < Type < MutableHashTable < HashTable < Thing.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PathSignatures/documentation.m2:159:0.