////////example of the qth power algorithm///////////////////////////////////////////////////////////////////////////////////
////////This is a variant of example 5.1 from the joint paper with Ruud Pellikaan////////////////////////////////////////////
////////To run this, open MAGMA, load the file qthpower.txt gotten from this sight, load this, and run///////////////////////



F:=FiniteField(2);
WT_MATRIX_S:=[[31,12]];
S:=PolynomialRing(F,2,"weight",
[31,12,1,0]);

AssignNames(~S,
["x" cat &cat
[ "_" cat IntegerToString(WT_MATRIX_S[i,j]) 
: i in [1..#WT_MATRIX_S]]
: j in [1..#WT_MATRIX_S[1]]]);

WT_MATRIX_icS,integral_closure_S,I,delta,phi,psi:=
integral_closure(F,S,
2,
[[31,12]],
[S|],
S.1^12+S.1^11+S.1^10*S.2^2+S.1^8*S.2^9+S.2^31);

AssignNames(~integral_closure_S,
["y" cat &cat
[ "_" cat IntegerToString(WT_MATRIX_icS[i,j]) 
: i in [1..#WT_MATRIX_icS]]
: j in [1..#WT_MATRIX_icS[1]]]);


"I=";
for i in [1..#Basis(I)] do
   i,Basis(I)[i];
end for;

"delta=",delta;

"phi=";
for i in [1..#WT_MATRIX_icS[1]] do
i,integral_closure_S.i@phi;
end for;

"psi=";
for i in [1..Rank(S)] do
i,S.i@psi;
end for;



///////To compare this to output from the Integral Closure function in MAGMA, uncomment the following MAGMA code and run it////////

//F:=FiniteField(2);
//FF<x>:=FunctionField(F);
//P<y>:=PolynomialRing(FF);
//f:=y^12+y^11+y^10*x^2+y^8*x^9+x^31;
//Ff<Y>:=FunctionField(f);
//C<X>:=CoefficientRing(Ff);
//INT:=Integers(C);
//IC:=IntegralClosure(INT,Ff);
//B:=Basis(IC);B;

//To compare this to the normal function in SINGULAR's normal.lib, uncomment the following input and run it in a SINGULAR session///

//LIB "normal.lib";
//ring r=2,(y,x),wp(31,12);
//ideal i=y12+y11+y10x2+y8x9+x31;
//list nor=normal(i);
//def R=nor[1];
//setring R;
//normap;
//norid;