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Table of Contents
- 1. Preface
- 2. Introduction
- 3. General concepts
- 4. Data types
- 5. Functions and system variables
- 5.1 Functions
- 5.1.1 attrib
- 5.1.2 bareiss
- 5.1.3 betti
- 5.1.4 char
- 5.1.5 char_series
- 5.1.6 charstr
- 5.1.7 cleardenom
- 5.1.8 close
- 5.1.9 coef
- 5.1.10 coeffs
- 5.1.11 contract
- 5.1.12 dbprint
- 5.1.13 defined
- 5.1.14 deg
- 5.1.15 degree
- 5.1.16 delete
- 5.1.17 det
- 5.1.18 diff
- 5.1.19 dim
- 5.1.20 division
- 5.1.21 dump
- 5.1.22 eliminate
- 5.1.23 eval
- 5.1.24 ERROR
- 5.1.25 example
- 5.1.26 execute
- 5.1.27 exit
- 5.1.28 extgcd
- 5.1.29 facstd
- 5.1.30 factorize
- 5.1.31 fetch
- 5.1.32 fglm
- 5.1.33 fglmquot
- 5.1.34 files, input from
- 5.1.35 find
- 5.1.36 finduni
- 5.1.37 fprintf
- 5.1.38 freemodule
- 5.1.39 gcd
- 5.1.40 gen
- 5.1.41 getdump
- 5.1.42 groebner
- 5.1.43 help
- 5.1.44 highcorner
- 5.1.45 hilb
- 5.1.46 homog
- 5.1.47 hres
- 5.1.48 imap
- 5.1.49 impart
- 5.1.50 indepSet
- 5.1.51 insert
- 5.1.52 interred
- 5.1.53 intersect
- 5.1.54 jacob
- 5.1.55 jet
- 5.1.56 kbase
- 5.1.57 kill
- 5.1.58 killattrib
- 5.1.59 koszul
- 5.1.60 laguerre
- 5.1.61 lead
- 5.1.62 leadcoef
- 5.1.63 leadexp
- 5.1.64 leadmonom
- 5.1.65 LIB
- 5.1.66 lift
- 5.1.67 liftstd
- 5.1.68 listvar
- 5.1.69 lres
- 5.1.70 maxideal
- 5.1.71 memory
- 5.1.72 minbase
- 5.1.73 minor
- 5.1.74 minres
- 5.1.75 modulo
- 5.1.76 monitor
- 5.1.77 mpresmat
- 5.1.78 mres
- 5.1.79 mstd
- 5.1.80 mult
- 5.1.81 nameof
- 5.1.82 names
- 5.1.83 ncols
- 5.1.84 npars
- 5.1.85 nres
- 5.1.86 nrows
- 5.1.87 nvars
- 5.1.88 open
- 5.1.89 option
- 5.1.90 ord
- 5.1.91 ordstr
- 5.1.92 par
- 5.1.93 pardeg
- 5.1.94 parstr
- 5.1.95 preimage
- 5.1.96 prime
- 5.1.97 print
- 5.1.98 printf
- 5.1.99 prune
- 5.1.100 qhweight
- 5.1.101 quot
- 5.1.102 quote
- 5.1.103 quotient
- 5.1.104 random
- 5.1.105 read
- 5.1.106 reduce
- 5.1.107 regularity
- 5.1.108 repart
- 5.1.109 res
- 5.1.110 reservedName
- 5.1.111 resultant
- 5.1.112 rvar
- 5.1.113 setring
- 5.1.114 simplex
- 5.1.115 simplify
- 5.1.116 size
- 5.1.117 sortvec
- 5.1.118 sprintf
- 5.1.119 sres
- 5.1.120 status
- 5.1.121 std
- 5.1.122 stdfglm
- 5.1.123 stdhilb
- 5.1.124 subst
- 5.1.125 system
- 5.1.126 syz
- 5.1.127 trace
- 5.1.128 transpose
- 5.1.129 type
- 5.1.130 typeof
- 5.1.131 uressolve
- 5.1.132 vandermonde
- 5.1.133 var
- 5.1.134 varstr
- 5.1.135 vdim
- 5.1.136 wedge
- 5.1.137 weight
- 5.1.138 write
- 5.2 Control structures
- 5.3 System variables
- 5.1 Functions
- 6. Tricks and pitfalls
- A. Examples
- A.1 Milnor and Tjurina
- A.2 Procedures and LIB
- A.3 Critical points
- A.4 Saturation
- A.5 Long coefficients
- A.6 Parameters
- A.7 T1 and T2
- A.8 Deformations
- A.9 Finite fields
- A.10 Elimination
- A.11 Free resolution
- A.12 Computation of Ext
- A.13 Polar curves
- A.14 Depth
- A.15 Formatting output
- A.16 Cyclic roots
- A.17 G_a -Invariants
- A.18 Invariants of a finite group
- A.19 Factorization
- A.20 Puiseux pairs
- A.21 Primary decomposition
- A.22 Normalization
- A.23 Branches of an Isolated Space Curve Singularity
- A.24 Kernel of module homomorphisms
- A.25 Algebraic dependence
- A.26 Classification
- A.27 Fast lexicographical GB
- A.28 Parallelization with MPtcp links
- B. Polynomial data
- C. Mathematical background
- C.1 Standard bases
- C.2 Hilbert function
- C.3 Syzygies and resolutions
- C.4 Characteristic sets
- C.5 Gauss-Manin connection
- C.6 Toric ideals and integer programming
- C.7 References
- D. SINGULAR libraries
- D.1 standard_lib
- D.2 General purpose
- D.2.1 all_lib
- D.2.2 general_lib
- D.2.2.1 A_Z
- D.2.2.2 ASCII
- D.2.2.3 absValue
- D.2.2.4 binomial
- D.2.2.5 deleteSublist
- D.2.2.6 factorial
- D.2.2.7 fibonacci
- D.2.2.8 kmemory
- D.2.2.9 killall
- D.2.2.10 number_e
- D.2.2.11 number_pi
- D.2.2.12 primes
- D.2.2.13 product
- D.2.2.14 sort
- D.2.2.15 sum
- D.2.2.16 watchdog
- D.2.2.17 which
- D.2.2.18 primecoeffs
- D.2.2.19 primefactors
- D.2.2.20 timeStd
- D.2.2.21 timeFactorize
- D.2.2.22 factorH
- D.2.3 inout_lib
- D.2.4 poly_lib
- D.2.4.1 cyclic
- D.2.4.2 katsura
- D.2.4.3 freerank
- D.2.4.4 is_homog
- D.2.4.5 is_zero
- D.2.4.6 lcm
- D.2.4.7 maxcoef
- D.2.4.8 maxdeg
- D.2.4.9 maxdeg1
- D.2.4.10 mindeg
- D.2.4.11 mindeg1
- D.2.4.12 normalize
- D.2.4.13 rad_con
- D.2.4.14 content
- D.2.4.15 numerator
- D.2.4.16 denominator
- D.2.4.17 mod2id
- D.2.4.18 id2mod
- D.2.4.19 substitute
- D.2.4.20 subrInterred
- D.2.4.21 hilbPoly
- D.2.5 random_lib
- D.2.6 ring_lib
- D.3 Linear algebra
- D.3.1 matrix_lib
- D.3.1.1 compress
- D.3.1.2 concat
- D.3.1.3 diag
- D.3.1.4 dsum
- D.3.1.5 flatten
- D.3.1.6 genericmat
- D.3.1.7 is_complex
- D.3.1.8 outer
- D.3.1.9 power
- D.3.1.10 skewmat
- D.3.1.11 submat
- D.3.1.12 symmat
- D.3.1.13 tensor
- D.3.1.14 unitmat
- D.3.1.15 gauss_col
- D.3.1.16 gauss_row
- D.3.1.17 addcol
- D.3.1.18 addrow
- D.3.1.19 multcol
- D.3.1.20 multrow
- D.3.1.21 permcol
- D.3.1.22 permrow
- D.3.1.23 rowred
- D.3.1.24 colred
- D.3.1.25 rm_unitrow
- D.3.1.26 rm_unitcol
- D.3.1.27 headStand
- D.3.2 linalg_lib
- D.3.2.1 inverse
- D.3.2.2 inverse_B
- D.3.2.3 inverse_L
- D.3.2.4 sym_gauss
- D.3.2.5 orthogonalize
- D.3.2.6 diag_test
- D.3.2.7 busadj
- D.3.2.8 charpoly
- D.3.2.9 adjoint
- D.3.2.10 det_B
- D.3.2.11 gaussred
- D.3.2.12 gaussred_pivot
- D.3.2.13 gauss_nf
- D.3.2.14 mat_rk
- D.3.2.15 U_D_O
- D.3.2.16 pos_def
- D.3.2.17 hessenberg
- D.3.2.18 evnf
- D.3.2.19 eigenvals
- D.3.2.20 minipoly
- D.3.2.21 jordan
- D.3.2.22 jordanbasis
- D.3.2.23 jordanmatrix
- D.3.2.24 jordannf
- D.3.1 matrix_lib
- D.4 Commutative algebra
- D.4.1 algebra_lib
- D.4.2 elim_lib
- D.4.3 homolog_lib
- D.4.3.1 cup
- D.4.3.2 cupproduct
- D.4.3.3 depth
- D.4.3.4 Ext_R
- D.4.3.5 Ext
- D.4.3.6 fitting
- D.4.3.7 flatteningStrat
- D.4.3.8 Hom
- D.4.3.9 homology
- D.4.3.10 isCM
- D.4.3.11 isFlat
- D.4.3.12 isLocallyFree
- D.4.3.13 isReg
- D.4.3.14 kernel
- D.4.3.15 kohom
- D.4.3.16 kontrahom
- D.4.3.17 KoszulHomology
- D.4.3.18 tensorMod
- D.4.3.19 Tor
- D.4.4 mprimdec_lib
- D.4.4.1 separator
- D.4.4.2 PrimdecA
- D.4.4.3 PrimdecB
- D.4.4.4 modDec
- D.4.4.5 zeroMod
- D.4.4.6 GTZmod
- D.4.4.7 dec1var
- D.4.4.8 annil
- D.4.4.9 splitting
- D.4.4.10 primTest
- D.4.4.11 preComp
- D.4.4.12 indSet
- D.4.4.13 GTZopt
- D.4.4.14 zeroOpt
- D.4.4.15 clrSBmod
- D.4.4.16 minSatMod
- D.4.4.17 specialModulesEqual
- D.4.4.18 stdModulesEqual
- D.4.4.19 modulesEqual
- D.4.4.20 getData
- D.4.5 mregular_lib
- D.4.6 normal_lib
- D.4.7 primdec_lib
- D.4.8 primitiv_lib
- D.4.9 reesclos_lib
- D.4.10 intprog_lib
- D.4.11 toric_lib
- D.5 Singularities
- D.5.1 classify_lib
- D.5.2 deform_lib
- D.5.3 equising_lib
- D.5.4 gaussman_lib
- D.5.4.1 gmsring
- D.5.4.2 gmsnf
- D.5.4.3 gmscoeffs
- D.5.4.4 bernstein
- D.5.4.5 monodromy
- D.5.4.6 spectrum
- D.5.4.7 sppairs
- D.5.4.8 spnf
- D.5.4.9 sppnf
- D.5.4.10 vfilt
- D.5.4.11 vwfilt
- D.5.4.12 tmatrix
- D.5.4.13 endvfilt
- D.5.4.14 spprint
- D.5.4.15 sppprint
- D.5.4.16 spadd
- D.5.4.17 spsub
- D.5.4.18 spmul
- D.5.4.19 spissemicont
- D.5.4.20 spsemicont
- D.5.4.21 spmilnor
- D.5.4.22 spgeomgenus
- D.5.4.23 spgamma
- D.5.5 hnoether_lib
- D.5.5.1 hnexpansion
- D.5.5.2 sethnering
- D.5.5.3 develop
- D.5.5.4 extdevelop
- D.5.5.5 parametrisation
- D.5.5.6 displayHNE
- D.5.5.7 invariants
- D.5.5.8 displayInvariants
- D.5.5.9 multsequence
- D.5.5.10 displayMultsequence
- D.5.5.11 intersection
- D.5.5.12 stripHNE
- D.5.5.13 is_irred
- D.5.5.14 delta
- D.5.5.15 newtonpoly
- D.5.5.16 is_NND
- D.5.5.17 puiseux2generators
- D.5.5.18 separateHNE
- D.5.5.19 squarefree
- D.5.5.20 allsquarefree
- D.5.5.21 further_hn_proc
- D.5.6 mondromy_lib
- D.5.7 qhmoduli_lib
- D.5.8 sing_lib
- D.5.9 spcurve_lib
- D.5.10 spectrum_lib
- D.6 Invariant theory
- D.6.1 finvar_lib
- D.6.1.1 invariant_ring
- D.6.1.2 invariant_ring_random
- D.6.1.3 primary_invariants
- D.6.1.4 primary_invariants_random
- D.6.1.5 cyclotomic
- D.6.1.6 group_reynolds
- D.6.1.7 molien
- D.6.1.8 reynolds_molien
- D.6.1.9 partial_molien
- D.6.1.10 evaluate_reynolds
- D.6.1.11 invariant_basis
- D.6.1.12 invariant_basis_reynolds
- D.6.1.13 primary_char0
- D.6.1.14 primary_charp
- D.6.1.15 primary_char0_no_molien
- D.6.1.16 primary_charp_no_molien
- D.6.1.17 primary_charp_without
- D.6.1.18 primary_char0_random
- D.6.1.19 primary_charp_random
- D.6.1.20 primary_char0_no_molien_random
- D.6.1.21 primary_charp_no_molien_random
- D.6.1.22 primary_charp_without_random
- D.6.1.23 power_products
- D.6.1.24 secondary_char0
- D.6.1.25 secondary_charp
- D.6.1.26 secondary_no_molien
- D.6.1.27 secondary_and_irreducibles_no_molien
- D.6.1.28 secondary_not_cohen_macaulay
- D.6.1.29 orbit_variety
- D.6.1.30 relative_orbit_variety
- D.6.1.31 image_of_variety
- D.6.2 ainvar_lib
- D.6.3 rinvar_lib
- D.6.3.1 HilbertSeries
- D.6.3.2 HilbertWeights
- D.6.3.3 ImageVariety
- D.6.3.4 ImageGroup
- D.6.3.5 InvariantRing
- D.6.3.6 InvariantQ
- D.6.3.7 LinearizeAction
- D.6.3.8 LinearActionQ
- D.6.3.9 LinearCombinationQ
- D.6.3.10 MinimalDecomposition
- D.6.3.11 NullCone
- D.6.3.12 ReynoldsImage
- D.6.3.13 ReynoldsOperator
- D.6.3.14 SimplifyIdeal
- D.6.3.15 TransferIdeal
- D.6.4 stratify_lib
- D.6.1 finvar_lib
- D.7 Symbolic-numerical solving
- D.7.1 presolve_lib
- D.7.1.1 degreepart
- D.7.1.2 elimlinearpart
- D.7.1.3 elimpart
- D.7.1.4 elimpartanyr
- D.7.1.5 fastelim
- D.7.1.6 findvars
- D.7.1.7 hilbvec
- D.7.1.8 linearpart
- D.7.1.9 tolessvars
- D.7.1.10 solvelinearpart
- D.7.1.11 sortandmap
- D.7.1.12 sortvars
- D.7.1.13 shortid
- D.7.1.14 valvars
- D.7.1.15 idealSimplify
- D.7.1.16 idealSplit
- D.7.2 solve_lib
- D.7.3 triang_lib
- D.7.4 ntsolve_lib
- D.7.5 zeroset_lib
- D.7.1 presolve_lib
- D.8 Visualization
- D.9 Coding theory
- E. Release Notes
- F. Index