Weby shortcut 1a5a9004da81162f034eff2fc7a06c396dfddb022021fd13958735cc25a4882f
teste

Notícias

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PRINTPOL_strg
Em 20/07/2014 às 19:06
  • This function  prints a non-commutative polynomial as an input to a tex file.

ORDERING
Em 19/02/2014 às 15:56
  • This file provides a non-standard ordering for the monomials in the cubic algebra. The order is
  1. U < V < U^2 < V^2;
  2. syllable length of monomials;
  3. total length;
  4. reverse lexicographical ordering.

readall
Em 18/02/2014 às 18:13
  • This file is provided to call the others functions and set some parameters.

rel
Em 18/02/2014 às 17:07
  • This  routine produces a PDF file of relations from readrel.
  • This function calls another function: MULTREL, PRINTPOL;
  • This function calls external function: pdflatex, rm.

mrep
Em 18/02/2014 às 17:06
  • This file provides a matricial representations of the cubic algebra, here we use the GAP packge GBNP.

POL2REL
Em 18/02/2014 às 16:58
  • This function transforms a relation of type [pol, 0] in [mon, pol_1], where mon is a summand of largest order, where pol = mon  - pol_1, for example,

gap>POL2REL(U*V^2*U - V*U^2*V);

[V*U^2*V, U*V^2*U]

gap>

  • This function calls other functions: ORDERING.

TR
Em 18/02/2014 às 16:16
  • Give a non-commutative polynomial in the variables U and V, this function exchanges U and V by  other polynomials, for example

gap>TR(U*V, [V,U]);

gap>(1)*V*U;

  • That is TR(pol, [X,Y]) have the same effect of the endomorphism U --> X and V --> Y applied to pol;
  • This functions calls other functions: SUBS.

SUBSC
Em 18/02/2014 às 16:15
  • This routine substitutes one of the sub-summands of a given polynomial, produced in the list by the  function SEARCHC.

STRETCH
Em 18/02/2014 às 16:14
  • Given a non-commutative monomial written as a string, this function returns a non-commutative monomial, but this is represented without powers, for example

gap>STRETCH("V^3*U^2");

"V*V*V*U*U"

gap>

SEARCHC
Em 18/02/2014 às 16:13
  • Given a polynomial this routine produces a list of  summands which are substitutable from a list of relations.

SEARCH
Em 18/02/2014 às 16:12
  • Given a polynomial this routine produces a list of  sub-summands which are substitutable from a list of relations.

PRINTPOL
Em 18/02/2014 às 16:11
  • This function  prints a non-commutative polynomial as an input to a tex file.

MULTREL
Em 18/02/2014 às 16:11
  •  This function multiplies a given relation by a polynomial and  applies the trivial relations U^3=0 and V^3=0, for example

gap>M(U^2, [V*U^2*V, U*V^2*U]);M([V*U^2*V, U*V^2*U], V^2);

[(1)*U^2*VU^2*V, zero of ...]

[(1)*U*V^2*U*V^2, zero of ...]

  • This function calls others functions: POL2REL.

MON_STRG
Em 18/02/2014 às 16:10
  • Given a summand written as a string, this function returns the monomial written as a string, for example

gap>MON_STRG("(-10)*U*V");

"U*V"

gap>

COEF_STRG
Em 18/02/2014 às 16:10
  • A non-commutative polynomial is sum of summands where each summand is a multiple of a monomial by a rational number. This  routine produces the coeffient of a summand written as a string.

 

gap>COEF_STRG("(2)*U*V");
(2)
gap>

POTENBASIS
Em 18/02/2014 às 16:09
  • Give a list of relations [ [m_1, p_1], [m_2, p_2], ...], this function check if a relation of this list is independent of its predecessors, for this its uses a matricial representation provided by file matrep.
  • This function calls an external funtion, sed.

CHECKBYMAT
Em 18/02/2014 às 16:08
  • This function substitutes the generators in an equation [monomial, polynomial] by matrices from a file matrep, and returns true or false.  For example

gap>CHECKBYMAT([U,U]);CHECKBYMAT([U,V]);#A list of type [monomial, polynomial] means monomial = polynomial.

true

false

  • This fucntion calls a external function: sed.

SUBS
Em 17/02/2014 às 17:52
  • This routine substitutes one of the sub-summands of a given polynomial, produced in the list by the  function SEARCH.
  • This function calls other functions: COEF_STRG, MON_STRG and STRETCH.

 

GAP routines - Cubic polynomial conditions.
Em 17/02/2014 às 15:30

These routines are written in GAP language. They were used to  generate relations in a group algebra of a group generated by a,b modulo a finite number of cubic relations (x-1)^3=0, in a joint work with Alexandre Griskov - IME/USP and Said Sidki - MAT/UnB, On groups with cubic polynomial conditions( ref. arxiv ).

2013.2
Em 30/08/2013 às 14:23

Material de apoio aos estudantes.

 

Conference 2011
Em 23/12/2011 às 00:02

2009.2
Em 23/12/2011 às 00:02

Disciplinas
Em 23/12/2011 às 00:02

2010.1
Em 23/12/2011 às 00:02