Table of Contents

1. PLURAL conventions
2. Data types

2.1 ideal

2.1.1 ideal declarations
2.1.2 ideal expressions
2.1.3 ideal operations
2.1.4 ideal related functions

2.2 map

2.2.1 map declarations
2.2.2 map expressions
2.2.3 map operations
2.2.4 map related functions

2.3 module

2.3.1 module declarations
2.3.2 module expressions
2.3.3 module operations
2.3.4 module related functions

2.4 poly

2.4.1 poly declarations
2.4.2 poly expressions
2.4.3 poly operations
2.4.4 poly related functions

2.5 qring

2.5.1 qring declaration

2.6 resolution

2.6.1 resolution declarations
2.6.2 resolution expressions
2.6.3 resolution related functions

2.7 ring

2.7.1 ring declarations
2.7.2 ring operations
2.7.3 ring related functions

3. Functions

3.1 betti
3.2 bracket
3.3 eliminate
3.4 fetch
3.5 imap
3.6 intersect
3.7 kbase
3.8 memory
3.9 minres
3.10 mres
3.11 ncalgebra
3.12 nres
3.13 option
3.14 preimage
3.15 quotient
3.16 reduce
3.17 std
3.18 subst
3.19 syz
3.20 twostd
3.21 vdim

A. Mathematical background

A.1 G-algebras
A.2 Groebner bases
A.3 Syzygies and resolutions
A.4 References

B. PLURAL libraries

B.1 ncalg_lib

B.1.0.1 sl
B.1.0.2 sl2
B.1.0.3 g2
B.1.0.4 gl
B.1.0.5 Qso3
B.1.0.6 Qso3Casimir
B.1.0.7 Qsl2
B.1.0.8 Qsl3

B.2 ncdecomp_lib

B.2.0.1 CentralQuot
B.2.0.2 CentralSaturation
B.2.0.3 CenCharDec

B.3 nctools_lib

B.3.0.1 Gweights
B.3.0.2 weightedRing
B.3.0.3 ndc
B.3.0.4 RootOfUnity
B.3.0.5 Weyl
B.3.0.6 CreateWeyl
B.3.0.7 Heisenberg
B.3.0.8 Exterior
B.3.0.9 Fin_dim_algebra
B.3.0.10 Newton
B.3.0.11 NCRelations
B.3.0.12 IsCentral
B.3.0.13 UpOneMatrix
B.3.0.14 wRing

B.4 gkdim_lib

B.4.0.1 GKdim

B.5 qmatrix_lib

B.5.0.1 quant
B.5.0.2 qminor
B.5.0.3 SymGroup
B.5.0.4 LengthSymElement
B.5.0.5 LengthSym

C. Release Notes

C.1 News and changes
C.2 Downloading instructions
C.3 Unix installation instructions
C.4 Windows installation instructions
C.5 Macintosh installation instructions

D. Index