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3 Watch and Influence the Communication
 3.1 Functions
 3.2 The Pictograms

3 Watch and Influence the Communication

3.1 Functions

3.1-1 homalgIOMode
‣ homalgIOMode( str[, str2[, str3]] )( function )

This function sets different modes which influence how much of the communication becomes visible. Handling the string str is not case-sensitive. homalgIOMode invokes the global function homalgMode defined in the homalg package with an "appropriate" argument (see code below). Alternatively, if a second or more strings are given, then homalgMode is invoked with the remaining strings str2, str3, ... at the end. In particular, you can use homalgIOMode( str, "" ) to reset the effect of invoking homalgMode.

str str (long form) mode description
"" "" the default mode, i.e. the communication protocol won't be visible
(homalgIOMode( ) is a short form for homalgIOMode( "" ))
"a" "all" combine the modes "debug" and "file"
"b" "basic" the same as "picto" + homalgMode( "basic" )
"d" "debug" view the complete communication protocol
"f" "file" dump the communication protocol into a file with the name
Concatenation( "commands_file_of_", CAS, "_with_PID_", PID )
"p" "picto" view the abbreviated communication protocol
using the preassigned pictograms

 


All modes other than the "default"-mode only set their specific values and leave the other values untouched, which allows combining them to some extent. This also means that in order to get from one mode to a new mode (without the aim to combine them) one needs to reset to the "default"-mode first.

Caution:

InstallGlobalFunction( homalgIOMode,
  function( arg )
    local nargs, mode, s;
    
    nargs := Length( arg );
    
    if nargs = 0 or ( IsString( arg[1] ) and arg[1] = "" ) then
        mode := "default";
    elif IsString( arg[1] ) then	## now we know, the string is not empty
        s := arg[1];
        if LowercaseString( s{[1]} ) = "a" then
            mode := "all";
        elif LowercaseString( s{[1]} ) = "b" then
            mode := "basic";
        elif LowercaseString( s{[1]} ) = "d" then
            mode := "debug";
        elif LowercaseString( s{[1]} ) = "f" then
            mode := "file";
        elif LowercaseString( s{[1]} ) = "p" then
            mode := "picto";
        else
            mode := "";
        fi;
    else
        Error( "the first argument must be a string\n" );
    fi;
    
    if mode = "default" then
        ## reset to the default values
        HOMALG_IO.color_display := false;
        HOMALG_IO.show_banners := true;
        HOMALG_IO.save_CAS_commands_to_file := false;
        HOMALG_IO.DoNotDeleteTemporaryFiles := false;
        HOMALG_IO.SaveHomalgMaximumBackStream := false;
        HOMALG_IO.InformAboutCASystemsWithoutActiveRings := true;
        SetInfoLevel( InfoHomalgToCAS, 1 );
        homalgMode( );
    elif mode = "all" then
        homalgIOMode( "debug" );
        homalgIOMode( "file" );
    elif mode = "basic" then
        HOMALG_IO.color_display := true;
        HOMALG_IO.show_banners := true;
        SetInfoLevel( InfoHomalgToCAS, 4 );
        homalgMode( "basic" );	## use homalgIOMode( "basic", "" ) to reset
    elif mode = "debug" then
        HOMALG_IO.color_display := true;
        HOMALG_IO.show_banners := true;
        SetInfoLevel( InfoHomalgToCAS, 8 );
        homalgMode( "debug" );	## use homalgIOMode( "debug", "" ) to reset
    elif mode = "file" then
        HOMALG_IO.save_CAS_commands_to_file := true;
    elif mode = "picto" then
        HOMALG_IO.color_display := true;
        HOMALG_IO.show_banners := true;
        SetInfoLevel( InfoHomalgToCAS, 4 );
        homalgMode( "logic" );	## use homalgIOMode( "picto", "" ) to reset
    fi;
    
    if nargs > 1 and IsString( arg[2] ) then
        CallFuncList( homalgMode, arg{[ 2 .. nargs ]} );
    fi;
    
end );

This is the part of the global function homalgSendBlocking that controls the visibility of the communication.

io_info_level := InfoLevel( InfoHomalgToCAS );

if not IsBound( pictogram ) then
    pictogram := HOMALG_IO.Pictograms.unknown;
    picto := pictogram;
elif io_info_level >= 3 then
    picto := pictogram;
    ## add colors to the pictograms
    if pictogram = HOMALG_IO.Pictograms.ReducedEchelonForm and
       IsBound( HOMALG_MATRICES.color_BOE ) then
        pictogram := Concatenation( HOMALG_MATRICES.color_BOE, pictogram, "\033[0m" );
    elif pictogram = HOMALG_IO.Pictograms.BasisOfModule and
      IsBound( HOMALG_MATRICES.color_BOB ) then
        pictogram := Concatenation( HOMALG_MATRICES.color_BOB, pictogram, "\033[0m" );
    elif pictogram = HOMALG_IO.Pictograms.DecideZero and
      IsBound( HOMALG_MATRICES.color_BOD ) then
        pictogram := Concatenation( HOMALG_MATRICES.color_BOD, pictogram, "\033[0m" );
    elif pictogram = HOMALG_IO.Pictograms.SyzygiesGenerators and
      IsBound( HOMALG_MATRICES.color_BOH ) then
        pictogram := Concatenation( HOMALG_MATRICES.color_BOH, pictogram, "\033[0m" );
    elif pictogram = HOMALG_IO.Pictograms.BasisCoeff and
      IsBound( HOMALG_MATRICES.color_BOC ) then
        pictogram := Concatenation( HOMALG_MATRICES.color_BOC, pictogram, "\033[0m" );
    elif pictogram = HOMALG_IO.Pictograms.DecideZeroEffectively and
      IsBound( HOMALG_MATRICES.color_BOP ) then
        pictogram := Concatenation( HOMALG_MATRICES.color_BOP, pictogram, "\033[0m" );
    elif need_output or need_display then
        pictogram := Concatenation( HOMALG_IO.Pictograms.color_need_output,
                             pictogram, "\033[0m" );
    else
        pictogram := Concatenation( HOMALG_IO.Pictograms.color_need_command,
                             pictogram, "\033[0m" );
    fi;
else
    picto := pictogram;
fi;

if io_info_level >= 3 then
    if ( io_info_level >= 7 and not need_display ) or io_info_level >= 8 then
        ## print the pictogram, the prompt of the external system,
        ## and the sent command
        Info( InfoHomalgToCAS, 7, pictogram, " ", stream.prompt,
              L{[ 1 .. Length( L ) - 1 ]} );
    elif io_info_level >= 4 then
        ## print the pictogram and the prompt of the external system
        Info( InfoHomalgToCAS, 4, pictogram, " ", stream.prompt, "..." );
    else
        ## print the pictogram only
        Info( InfoHomalgToCAS, 3, pictogram );
    fi;
    
fi;

3.2 The Pictograms

3.2-1 HOMALG_IO.Pictograms
‣ HOMALG_IO.Pictograms( global variable )

The record of pictograms is a component of the record HOMALG_IO.

Pictograms := rec(
  
  ##
  ## colors:
  ##
  
  ## pictogram color of a "need_command" or assignment operation:
  color_need_command                      := "\033[1;33;44m",
  
  ## pictogram color of a "need_output" or "need_display" operation:
  color_need_output                       := "\033[1;34;43m",
  
  ##
  ## good morning computer algebra system:
  ##
  
  ## initialize:
  initialize                              := "ini",
  
  ## define macros:
  define                                  := "def",
  
  ## get time:
  time                                    := ":ms",
  
  ## memory usage:
  memory                                  := "mem",
  
  ## unknown:
  unknown                                 := "???",
  
  ##
  ## external garbage collection:
  ##
  
  ## delete a variable:
  delete                                  := "xxx",
  
  ## delete serveral variables:
  multiple_delete                         := "XXX",
  
  ## trigger the garbage collector:
  garbage_collector                       := "grb",
  
  ##
  ## create lists:
  ##
  
  ## define a list:
  CreateList                              := "lst",
  
  ##
  ## create rings:
  ##
  
  ## define a ring:
  CreateHomalgRing                        := "R:=",
  
  ## get the names of the "variables" defining the ring:
  variables                               := "var",
  
  ## define zero:
  Zero                                    := "0:=",
  
  ## define one:
  One                                     := "1:=",
  
  ## define minus one:
  MinusOne                                := "-:=",
  
  ##
  ## mandatory ring operations:
  ##
  
  ## get the name of an element:
  ## (important if the CAS pretty-prints ring elements,
  ##  we need names that can be used as input!)
  ## (install a method instead of a homalgTable entry)
  homalgSetName                           := "\"a\"",
  
  ## a = 0 ?
  IsZero                                  := "a=0",
  
  ## a = 1 ?
  IsOne                                   := "a=1",
  
  ## substract two ring elements
  ## (needed by SimplerEquivalentMatrix in case
  ##  CopyRow/ColumnToIdentityMatrix are not defined):
  Minus                                   := "a-b",
  
  ## divide the element a by the unit u
  ## (needed by SimplerEquivalentMatrix in case
  ##  DivideEntryByUnit is not defined):
  DivideByUnit                            := "a/u",
  
  ## important ring operations:
  ## (important for performance since existing
  ##  fallback methods cause a lot of traffic):
  
  ## is u a unit?
  ## (mainly needed by the fallback methods for matrices, see below):
  IsUnit                                  := "?/u",
  
  ##
  ## optional ring operations:
  ##
  
  ## copy an element:
  CopyElement                             := "a>a",
  
  ## add two ring elements:
  Sum                                     := "a+b",
  
  ## multiply two ring elements:
  Product                                 := "a*b",
  
  ## the (greatest) common divisor:
  Gcd                                     := "gcd",
  
  ## cancel the (greatest) common divisor:
  CancelGcd                               := "ccd",
  
  ## random polynomial:
  RandomPol                               := "rpl",
  
  ## numerator:
  Numerator                               := "num",
  
  ## denominator:
  Denominator                             := "den",
  
  ## evaluate polynomial:
  Evaluate                                := "evl",
  
  ## degree of a multivariate polynomial
  DegreeOfRingElement                     := "deg",
  
  ## is irreducible:
  IsIrreducible                           := "irr",
  
  ##
  ## create matrices:
  ##
  
  ## define a matrix:
  HomalgMatrix                            := "A:=",
  
  ## copy a matrix:
  CopyMatrix                              := "A>A",
  
  ## load a matrix from file:
  LoadHomalgMatrixFromFile                := "A<<",
  
  ## save a matrix to file:
  SaveHomalgMatrixToFile                  := "A>>",
  
  ## get a matrix entry as a string:
  MatElm                  := "<ij",
  
  ## set a matrix entry from a string:
  SetMatElm                  := ">ij",
  
  ## add to a matrix entry from a string:
  AddToMatElm                := "+ij",
  
  ## get a list of the matrix entries as a string:
  GetListOfHomalgMatrixAsString           := "\"A\"",
  
  ## get a listlist of the matrix entries as a string:
  GetListListOfHomalgMatrixAsString       := "\"A\"",
  
  ## get a "sparse" list of the matrix entries as a string:
  GetSparseListOfHomalgMatrixAsString     := ".A.",
  
  ## assign a "sparse" list of matrix entries to a variable:
  sparse                                  := "spr",
  
  ## list of assumed inequalities:
  Inequalities                            := "<>0",
  
  ## list of assumed inequalities:
  MaximalIndependentSet                   := "idp",
  
  ##
  ## mandatory matrix operations:
  ##
  
  ## test if a matrix is the zero matrix:
  ## CAUTION: the external system must be able to check
  ##          if the matrix is zero modulo possible ring relations
  ##          only known to the external system!
  IsZeroMatrix                            := "A=0",
  
  ## number of rows:
  NrRows                                  := "#==",
  
  ## number of columns:
  NrColumns                               := "#||",
  
  ## determinant of a matrix over a (commutative) ring:
  Determinant                             := "det",
  
  ## create a zero matrix:
  ZeroMatrix                              := "(0)",
  
  ## create a initial zero matrix:
  InitialMatrix                           := "[0]",
  
  ## create an identity matrix:
  IdentityMatrix                          := "(1)",
  
  ## create an initial identity matrix:
  InitialIdentityMatrix                   := "[1]",
  
  ## "transpose" a matrix (with "the" involution of the ring):
  Involution                              := "A^*",
  
  ## get certain rows of a matrix:
  CertainRows                             := "===",
  
  ## get certain columns of a matrix:
  CertainColumns                          := "|||",
  
  ## stack to matrices vertically:
  UnionOfRows                             := "A_B",
  
  ## glue to matrices horizontally:
  UnionOfColumns                          := "A|B",
  
  ## create a block diagonal matrix:
  DiagMat                                 := "A\\B",
  
  ## the Kronecker (tensor) product of two matrices:
  KroneckerMat                            := "AoB",
  
  ## multiply a ring element with a matrix:
  MulMat                                  := "a*A",
  
  ## multiply a matrix with a ring element:
  MulMatRight                             := "A*a",
  
  ## add two matrices:
  AddMat                                  := "A+B",
  
  ## substract two matrices:
  SubMat                                  := "A-B",
  
  ## multiply two matrices:
  Compose                                 := "A*B",
  
  ## pullback a matrix by a ring map:
  Pullback                                := "pbk",
  
  ##
  ## important matrix operations:
  ## (important for performance since existing
  ##  fallback methods cause a lot of traffic):
  ##
  
  ## test if two matrices are equal:
  ## CAUTION: the external system must be able to check
  ##          equality of the two matrices modulo possible ring relations
  ##          only known to the external system!
  AreEqualMatrices                        := "A=B",
  
  ## test if a matrix is the identity matrix:
  IsIdentityMatrix                        := "A=1",
  
  ## test if a matrix is diagonal (needed by the display method):
  IsDiagonalMatrix                        := "A=\\",
  
  ## get the positions of the zero rows:
  ZeroRows                                := "0==",
  
  ## get the positions of the zero columns:
  ZeroColumns                             := "0||",
  
  ## get "column-independent" unit positions
  ## (needed by ReducedBasisOfModule):
  GetColumnIndependentUnitPositions       := "ciu",
  
  ## get "row-independent" unit positions
  ## (needed by ReducedBasisOfModule):
  GetRowIndependentUnitPositions          := "riu",
  
  ## get the position of the "first" unit in the matrix
  ## (needed by SimplerEquivalentMatrix):
  GetUnitPosition                         := "gup",
  
  ## position of the first non-zero entry per row
  PositionOfFirstNonZeroEntryPerRow       := "fnr",
  
  ## position of the first non-zero entry per column
  PositionOfFirstNonZeroEntryPerColumn    := "fnc",
  
  ## indicator matrix of non-zero entries
  IndicatorMatrixOfNonZeroEntries         := "<>0",
  
  ## transposed matrix:
  TransposedMatrix                        := "^tr",
  
  ## divide an entry of a matrix by a unit
  ## (needed by SimplerEquivalentMatrix in case
  ##  DivideRow/ColumnByUnit are not defined):
  DivideEntryByUnit                       := "ij/",
  
  ## divide a row by a unit
  ## (needed by SimplerEquivalentMatrix):
  DivideRowByUnit                         := "-/u",
  
  ## divide a column by a unit
  ## (needed by SimplerEquivalentMatrix):
  DivideColumnByUnit                      := "|/u",
  
  ## divide a row by a unit
  ## (needed by SimplerEquivalentMatrix):
  CopyRowToIdentityMatrix                 := "->-",
  
  ## divide a column by a unit
  ## (needed by SimplerEquivalentMatrix):
  CopyColumnToIdentityMatrix              := "|>|",
  
  ## set a column (except a certain row) to zero
  ## (needed by SimplerEquivalentMatrix):
  SetColumnToZero                         := "|=0",
  
  ## get the positions of the rows with a single one
  ## (needed by SimplerEquivalentMatrix):
  GetCleanRowsPositions                   := "crp",
  
  ## convert a single row matrix into a matrix
  ## with specified number of rows/columns
  ## (needed by the display methods for homomorphisms):
  ConvertRowToMatrix                      := "-%A",
  
  ## convert a single column matrix into a matrix
  ## with specified number of rows/columns
  ## (needed by the display methods for homomorphisms):
  ConvertColumnToMatrix                   := "|%A",
  
  ## convert a matrix into a single row matrix:
  ConvertMatrixToRow                      := "A%-",
  
  ## convert a matrix into a single column matrix:
  ConvertMatrixToColumn                   := "A%|",
  
  ##
  ## basic matrix operations:
  ##
  
  ## compute a (r)educed (e)chelon (f)orm:
  ReducedEchelonForm                      := "ref",
  
  ## compute a "(bas)is" of a given set of module elements:
  BasisOfModule                           := "bas",
  
  ## compute a reduced "(Bas)is" of a given set of module elements:
  ReducedBasisOfModule                    := "Bas",
  
  ## (d)e(c)ide the ideal/submodule membership problem,
  ## i.e. if an element is (0) modulo the ideal/submodule:
  DecideZero                              := "dc0",
  
  ## compute a generating set of (syz)ygies:
  SyzygiesGenerators                      := "syz",
  
  ## compute a generating set of reduced (Syz)ygies:
  ReducedSyzygiesGenerators               := "Syz",
  
  ## compute a (R)educed (E)chelon (F)orm
  ## together with the matrix of coefficients:
  ReducedEchelonFormC                     := "REF",
  
  ## compute a "(BAS)is" of a given set of module elements
  ## together with the matrix of coefficients:
  BasisCoeff                              := "BAS",
  
  ## (D)e(C)ide the ideal/submodule membership problem,
  ## i.e. write an element effectively as (0) modulo the ideal/submodule:
  DecideZeroEffectively                   := "DC0",
  
  ##
  ## optional matrix operations:
  ##
  
  ## Hilbert-Poincare series of a module:
  HilbertPoincareSeries                   := "HPs",
  
  ## Hilbert polynomial of a module:
  HilbertPolynomial                       := "Hil",
  
  ## affine dimension of a module:
  AffineDimension                         := "dim",
  
  ## affine degree of a module:
  AffineDegree                            := "adg",
  
  ## the constant term of the hilbert polynomial:
  ConstantTermOfHilbertPolynomial         := "P_0",
  
  ## primary decomposition:
  PrimaryDecomposition                    := "YxZ",
  
  ## eliminate variables:
  Eliminate                               := "eli",
  
  ## leading module:
  LeadingModule                           := "led",
  
  ## the i-th monomial matrix
  MonomialMatrix                          := "mon",
  
  ## matrix of symbols:
  MatrixOfSymbols                         := "smb",
  
  ## leading module:
  ## coefficients:
  Coefficients                            := "cfs",
  
  ##
  ## optional module operations:
  ##
  
  ## compute a better equivalent matrix
  ## (field -> row+col Gauss, PIR -> Smith, Dedekind domain -> Krull, etc ...):
  BestBasis                               := "(\\)",
  
  ## compute elementary divisors:
  ElementaryDivisors                      := "div",
  
  ##
  ## for the eye:
  ##
  
  ## display objects:
  Display                                 := "dsp",
  
  ## the LaTeX code of the mathematical entity:
  homalgLaTeX                             := "TeX",
  
)
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