Changeset dfa15b in git


Ignore:
Timestamp:
Feb 11, 2019, 1:47:34 PM (5 years ago)
Author:
Hans Schoenemann <hannes@…>
Branches:
(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
Children:
5bccbab76d678f9334a22ed665fd3dab33eb614ba9cc0df15d51a9d109f5ce94030146c1f9168173
Parents:
c012cdb589e1d8374fa0ae69e9dc817138933b2b
Message:
fix doc in LP-libs
Location:
Singular/LIB
Files:
5 edited

Legend:

Unmodified
Added
Removed

  • Singular/LIB/fpadim.lib

    rc012cdb rdfa15b  
    1515
    1616KEYWORDS: finitely presented algebra; Letterplace Groebner basis; K-basis; K-dimension; Hilbert series
    17 
    18 PROCEDURES:
    19 lpKDimCheck(G);            checks whether the K-dimension of A/<G> is finite
    20 lpKDim(G[,d,n]);           computes the K-dimension of A/<G>
    21 lpMonomialBasis(d, donly, J); computes a list of monomials not contained in J
    22 lpHilbert(G[,d,n]);        computes the truncated Hilbert series of A/<G>
    23 lpSickleDim(G[,d,n]);      computes the mistletoes and the K-dimension of A/<G>
    2417
    2518NOTE:
    … …  
    7366[Stu] G. Studzinski: Dimension computations in non-commutative,
    7467associative algebras, Diploma thesis, RWTH Aachen, 2010.
     68
     69PROCEDURES:
     70lpKDimCheck(G);            checks whether the K-dimension of A/<G> is finite
     71lpKDim(G[,d,n]);           computes the K-dimension of A/<G>
     72lpMonomialBasis(d, donly, J); computes a list of monomials not contained in J
     73lpHilbert(G[,d,n]);        computes the truncated Hilbert series of A/<G>
     74lpSickleDim(G[,d,n]);      computes the mistletoes and the K-dimension of A/<G>
    7575
    7676SEE ALSO: freegb_lib, fpaprops_lib, ncHilb_lib

  • Singular/LIB/fpalgebras.lib

    rc012cdb rdfa15b  
    7878RETURN:  ideal
    7979ASSUME: basering has a letterplace ring structure and
    80 @*          A is a generalized Cartan matrix with integer entries
     80        A is a generalized Cartan matrix with integer entries
    8181PURPOSE: compute the ideal of Serre's relations associated to A
    8282EXAMPLE: example serreRelations; shows examples
    … …  
    145145RETURN:  ring (and ideal)
    146146PURPOSE: compute the inhomogeneous Serre's relations associated to A in given
    147 @*       variable names
     147         variable names
    148148ASSUME: three ideals in the input are of the same sizes and contain merely
    149 @* variables which are interpreted as follows: N resp. P stand for negative
    150 @* resp. positive roots, C stand for Cartan elements. d is the degree bound for
    151 @* letterplace ring, which will be returned.
    152 @* The matrix A is a generalized Cartan matrix with integer entries
    153 @* The result is the ideal called 'fsRel' in the returned ring.
     149  variables which are interpreted as follows: N resp. P stand for negative
     150  resp. positive roots, C stand for Cartan elements. d is the degree bound for
     151  letterplace ring, which will be returned.
     152  The matrix A is a generalized Cartan matrix with integer entries
     153  The result is the ideal called 'fsRel' in the returned ring.
    154154EXAMPLE: example fullSerreRelations; shows examples
    155155"
    … …  
    363363RETURN:  ring (and exports ideal)
    364364PURPOSE: compute the ideal of Adem relations for i<2j in characteristic 0
    365 @*  the ideal is exported under the name AdemRel in the output ring
     365    the ideal is exported under the name AdemRel in the output ring
    366366EXAMPLE: example ademRelations; shows examples
    367367"

  • Singular/LIB/fpaprops.lib

    rc012cdb rdfa15b  
    5555"USAGE: lpNoetherian(G); G an ideal in a Letterplace ring
    5656RETURN: int
    57 @*      0 not Noetherian
    58 @*      1 left Noetherian
    59 @*      2 right Noetherian
    60 @*      3 Noetherian
    61 @*      4 weak Noetherian
     57      0 not Noetherian
     58      1 left Noetherian
     59      2 right Noetherian
     60      3 Noetherian
     61      4 weak Noetherian
    6262PURPOSE: Check whether the monomial algebra A/<LM(G)> is (left/right) noetherian
    6363ASSUME: - basering is a Letterplace ring
    64 @*      - G is a Groebner basis
     64      - G is a Groebner basis
    6565THEORY: lpNoetherian works with the monomial algebra A/<LM(G)>.
    6666If it gives an affirmative answer for one of the properties, then it
    … …  
    644644start. The parameter visited, cyclic and path should be 0.
    645645RETURN: int
    646 @*:     Maximal number of distinct cycles
     646     Maximal number of distinct cycles
    647647PURPOSE: Calculate the maximal number of distinct cycles in a single path starting at v
    648648ASSUME: Basering is a Letterplace ring
    … …  
    730730proc lpUfGraph(ideal G, list #)
    731731"USAGE: lpUfGraph(G); G a set of monomials in a letterplace ring.
    732 @*      lpUfGraph(G,1); G a set of monomials in a letterplace ring.
    733732RETURN: intmat or list
    734733NOTE: lpUfGraph(G); returns intmat. lpUfGraph(G,1); returns list L with L[1] an intmat and L[2] an ideal.
    … …  
    882881RETURN: int
    883882PURPOSE: Determines the Gelfand Kirillov dimension of A/<G>
    884 @*       -1 means positive infinite
     883       -1 means positive infinite
    885884ASSUME: - basering is a Letterplace ring
    886 @*      - G is a Groebner basis
     885      - G is a Groebner basis
    887886"
    888887{

  • Singular/LIB/freegb.lib

    rc012cdb rdfa15b  
    2626lpDegBound(R);                   returns the degree bound of a letterplace ring
    2727lpVarBlockSize(R);               returns the size of the letterplace blocks
    28 
    29 letplaceGBasis(I);               (deprecated, use twostd) two-sided Groebner basis of a letterplace ideal I
    30 
     28letplaceGBasis(I);               (deprecated) two-sided Groebner basis of a letterplace ideal I
    3129lpDivision(f,I);                 two-sided division with remainder
    3230lpGBPres2Poly(L,I);              reconstructs a polynomial from the output of lpDivision
    33 
    3431lieBracket(a,b[, N]);            Lie bracket ab-ba of two letterplace polynomials
    3532isOrderingShiftInvariant(i);     tests shift-invariance of the monomial ordering
    3633isVar(p);                        check whether p is a power of a single variable
    37 
    38 makeLetterplaceRing(d);          (deprecated, use freeAlgebra) creates a Letterplace ring out of given data
     34makeLetterplaceRing(d);          (deprecated) creates a Letterplace ring out of given data
    3935setLetterplaceAttributes(R,d,b); (for testing purposes) supplies ring R with the letterplace structure
    4036
    … …  
    9187RETURN: ring with special attributes set
    9288PURPOSE: sets attributes for a letterplace ring:
    93 @*      'isLetterplaceRing' = true, 'uptodeg' = d, 'lV' = b, where
    94 @*      'uptodeg' stands for the degree bound,
    95 @*      'lV' for the number of variables in the block 0.
     89  'isLetterplaceRing' = true, 'uptodeg' = d, 'lV' = b, where
     90  'uptodeg' stands for the degree bound,
     91  'lV' for the number of variables in the block 0.
    9692NOTE: Activate the resulting ring by using @code{setring}
    9793"
    … …  
    331327RETURN:  int
    332328PURPOSE: check, whether leading monomial of p is a power of a single variable
    333 @* from the basering. Returns the exponent or 0 if p is multivariate.
     329  from the basering. Returns the exponent or 0 if p is multivariate.
    334330EXAMPLE: example isVar; shows examples
    335331"
    … …  
    374370"USAGE: letplaceGBasis(I);  I an ideal/module
    375371RETURN: ideal/module
    376 ASSUME: basering is a Letterplace ring, input consists of Letterplace
    377 @*      polynomials
    378 PURPOSE: compute the two-sided Groebner basis of I via Letterplace
    379 @*       algorithm (legacy routine)
     372ASSUME: basering is a Letterplace ring, input consists of Letterplace polynomials
     373PURPOSE: compute the two-sided Groebner basis of I via Letterplace algorithm (legacy routine)
    380374NOTE: the degree bound for this computation is read off the letterplace
    381 @*    structure of basering
     375      structure of basering
    382376EXAMPLE: example letplaceGBasis; shows examples
    383377"
    … …  
    418412PURPOSE:compute the Lie bracket [a,b] = ab - ba between letterplace polynomials
    419413NOTE: if N>1 is specified, then the left normed bracket [a,[...[a,b]]]] is
    420 @*    computed.
     414computed.
    421415EXAMPLE: example lieBracket; shows examples
    422416"
    … …  
    515509RETURN:  ring
    516510ASSUME: L has a special form. Namely, it is a list of modules, where
    517 
    518511 - each generator of every module stands for a monomial times coefficient in
    519 @* free algebra,
    520 
     512   free algebra,
    521513 - in such a vector generator, the 1st entry is a nonzero coefficient from the
    522 @* ground field
    523 
     514   ground field
    524515 - and each next entry hosts a variable from the basering.
    525516PURPOSE: compute the two-sided Groebner basis of an ideal, encoded by L
    526 @* in the free associative algebra, up to degree d
     517  in the free associative algebra, up to degree d
    527518NOTE: Apply @code{lst2str} to the output in order to obtain a better readable
    528 @*    presentation
     519   presentation
    529520EXAMPLE: example freeGBasis; shows examples
    530521"
    … …  
    31603151RETURN: int
    31613152NOTE: Tests whether the ordering of the current ring is shift invariant, which is the case, when LM(p) > LM(p') for all p and p' where p' is p shifted by any number of places.
    3162 @*      If withHoles != 0 even Letterplace polynomials with holes (eg. x(1)*y(4)) are considered.
     3153
     3154If withHoles != 0 even Letterplace polynomials with holes (eg. x(1)*y(4)) are considered.
    31633155ASSUME: - basering is a Letterplace ring.
    31643156"

  • Singular/LIB/nctools.lib

    rc012cdb rdfa15b  
    17641764RETURN:  ring
    17651765PURPOSE: create a copy of a given ring equipped with the
    1766 @* elimination ordering for module components @code{(c,<)}
     1766  elimination ordering for module components @code{(c,<)}
    17671767NOTE: usually the list argument contains a ring to work with
    17681768EXAMPLE: example makeModElimRing; shows an example
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