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#############################################################################
####
##
#W Maple.gi RADIROOT package Andreas Distler
##
## Installation file for the functions that generate Maple expressions
##
#Y 2006
##
#############################################################################
##
#F RR_M_Radikalbasis( <erw>, <elements>, <file> )
##
## Produces a basis for the matrixfield in the record <erw> from the
## generating matrices <elements> and returns Maple-readable strings
## for the basis as well
##
InstallGlobalFunction( RR_M_Radikalbasis, function( erw, elements, file )
local k, basis, elm, mat, i, ll, basstr, elmstr, m, coeffs, scale;
k := DegreeOverPrimeField(erw.K) / Product(erw.degs);
basis := Basis(erw.K){[ 1..k ]};
if k = 1 then
basstr := [""];
else
basstr := ["",Concatenation("E(",String(Order(erw.unity)),")")];
fi;
for i in [ 2..k-1 ] do
Add( basstr, Concatenation( basstr[2], "^", String(i) ) );
od;
for m in [ 1..Length(elements) ] do
mat := List( basis, Flat );;
elm := elements[m][1];
k := elements[m][2];
coeffs := SolutionMat(mat, Flat(elm^k));
scale := RR_Potfree(Concatenation(List(coeffs, ExtRepOfObj)), k);
elm := elm / scale; elements[m][1] := elm;
elmstr := RR_WurzelAlsString( k, coeffs / scale^k, basstr );
AppendTo( file, "w", String(m)," := ", elmstr, ";\n");
basis := Concatenation( List( [1..k], i -> elm^(i-1) * basis));;
ll := [ basstr, List( basstr, str ->
Concatenation( str,"*w",String(m) ) ) ];
for i in [ 3..k ] do
ll[i] := List( basstr, str -> Concatenation( str,
Concatenation( "*w", String(m), "^", String(i-1) ) ) );
od;
basstr := Concatenation( ll );
od;
AppendTo( file, "\n");
return [ basis, basstr ];
end );
#############################################################################
##
#F RR_M_KoeffizientAlsString( <coeff>, <anf> )
##
## Creates a Maple-readable String for the cyclotomic <coeff>; if <anf>
## is true, positive signs of rationals will be omitted; if <coeff> is a
## sum, it will be included in brackets; finitely an empty string
## will be returned, if <coeff> is equal to 1
##
InstallGlobalFunction( RR_M_KoeffizientAlsString, function( coeff, anf )
local cstr;
cstr := String( coeff );
if not IsInt( coeff ) then
cstr := Concatenation( "(",cstr,")" );
fi;
if not anf then
if IsPosInt( coeff ) then
cstr := Concatenation( " + ", cstr );
elif not IsInt( coeff ) then
cstr := Concatenation( " + ", cstr );
fi;
fi;
return cstr;
end );
#############################################################################
##
#F RR_M_WurzelAlsString( <k>, <coeffs>, <basstr> )
##
## Creates a Maple-readable String for the <k>-th root of the element
## described by <coeffs> and <basstr>
##
InstallGlobalFunction( RR_M_WurzelAlsString, function( k, coeffs, basstr )
local i, str, anf;
str := ""; anf := true;
for i in [ 1..Length(coeffs) ] do
if coeffs[i] in [ -1, 1 ] and basstr[i] = "" then
if not anf and coeffs[i] = 1 then
str := Concatenation( str, " + ", String( coeffs[i] ) );
else
str := Concatenation( str, String( coeffs[i] ) );
fi;
anf := false;
elif coeffs[i] <> 0 then
str := Concatenation( str,
RR_M_KoeffizientAlsString( coeffs[i], anf ),
basstr[i]);
anf := false;
fi;
od;
if k <> 1 then
str := Concatenation( "(", str, ")^(1/", String(k),")" );
fi;
return str;
end );
#############################################################################
##
#F RR_MapleFile( <f>, <erw>, <elements>, <file> )
##
## Creates a file for a radical expression of the roots of the polynomial
## <f> which can be read into Maple.
##
InstallGlobalFunction( RR_MapleFile, function( poly, erw, elements, file )
local i,cstr,bas,root,coeffs,B,k,offset,str,min;
Info( InfoRadiroot, 2, " creating maple file" );
# Create maple code and write to file
bas := RR_M_Radikalbasis( erw, elements, file );;
offset := CoefficientsOfUnivariatePolynomial(poly)[Degree(poly)] /
(Degree(poly) * LeadingCoefficient(poly));
k := Degree(poly) / Length(erw.roots);
AppendTo( file, "a := " );
if k <> 1 and offset <> 0 then
AppendTo( file, String(-offset), "+");
fi;
B := Basis( erw.K, bas[1] );
coeffs := List([1..Length(erw.roots)], i->Coefficients(B, erw.roots[i]));
str := List([ 1..Length(erw.roots) ],
i -> RR_M_WurzelAlsString(k, coeffs[i], bas[2]));
min := First( [ 1..Length(erw.roots) ],
i -> Length(str[i]) = Minimum( List( str, Length )));
if Length( str[min] ) < 1400 then
AppendTo( file, str[min] );
else
AppendTo( file, RR_M_NstInDatei( k, coeffs[min], bas[2] ));
fi;
AppendTo( file, ";\n" );
return file;
end );
#############################################################################
##
#F RR_M_NstInDatei( <k>, <coeffs>, <basstr> )
##
## Creates a Maple-output containing a string for the <k>-th root of the
## element described by <coeffs> and <basstr>
##
InstallGlobalFunction( RR_M_NstInDatei, function( k, coeffs, basstr )
local str, i, anf;
str := "";
if k <> 1 then
str := Concatenation( str, "(" );
fi;
repeat
i := 0;
while Length( coeffs ) >= i+1 and
Length(RR_M_WurzelAlsString(1,coeffs{[1..i+1]},basstr{[1..i+1]}))
< 1400 do
i := i+1;
od;
str := Concatenation(str, RR_M_WurzelAlsString(1, coeffs{[1..i]},
basstr{[1..i]}));
coeffs := coeffs{[i+1..Length(coeffs)]};
basstr := basstr{[i+1..Length(basstr)]};
until coeffs = [ ];
if k <> 1 then
str := Concatenation( str, ")^(1/",String(k),")");
fi;
return str;
end );
#############################################################################
##
#E
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