add Matthias notes

.singularhistory

@@ -45,184 +45,398 @@ LIB"AeCodPruebas.lib";
 ring r = 0,(x,y),ds;
 ideal f = x,y2,y3+x2y;
 TargetIdeal(f, std(ideal(x,y)));
+ring r = 0,(x,y),ds;
+ideal f = x,y2,y3+x2y;
 LIB"AeCodPruebas.lib";
-ring r = 0,(x),ds;
+TargetIdeal(f, std(ideal(x,y)));
-ideal f = x2+x4,x3;
+LIB"AeCodPruebas.lib";
+TargetIdeal(f, std(ideal(x,y)));
+LIB"AeCodPruebas.lib";
+TargetIdeal(f, std(ideal(x,y)));
+LIB"AeCodPruebas.lib";
+TargetIdeal(f, std(ideal(x,y)));
+LIB"AeCodPruebas.lib";
+TargetIdeal(f, std(ideal(x,y)));
+TargetIdeal(f, std(maxideal(3)));
+TargetIdeal(f, std(maxideal(5)));
+LIB"AeCodPruebas.lib";
+basering;
 AeNormal(f);
-AeNormal(f,maxideal(5));
+LIB"AeCodPruebas.lib";
+AeNormal(f);
+;
+LIB"AeCodPruebas.lib";
+AeNormal(f);
+LIB"AeCodPruebas.lib";
+AeNormal(f);
+;
+LIB"AeCodPruebas.lib";
+AeNormal(f);
+ideal f = x+x4,y2,y3+x2y;
+LIB"AeCodPruebas.lib";
+ideal f = x+x4,y2,y3+x2y;
+AeNormal(f,maxideal(3));
 AeNormal(f,maxideal(4));
-AeNormal(f,maxideal(10));
+AeNormal(f);
-AeNormal(f,maxideal(6));
+LIB"AeCodPruebas.lib";
-def Q = MalgrRing(ideal(0),1,f);
+AeNormal(f);
-GF;
+AeNormal(f,maxideal(1));
+AeNormal(f,maxideal(2));
+AeNormal(f,maxideal(3));
+AeNormal(f,maxideal(4));
+AeNormal(f,maxideal(7));
+AeNormal(f,maxideal(4));
+AeNormal(f,maxideal(5));
+f;
+def Q = MalgrRing(ideal(0),2,f);
 setring Q;
 GF;
 Gens;
 setring r;
-TargetIdeal(f,std(maxideal(10)));
+ideal w = x+x4,y2;
-int k = 5;
+kbase(std(w));
-matrix jf[2][1] = jacob(f);
-print(jf);
 setring Q;
-def f = imap(r,f);
+GF;
-def jf = imap(r,jf);
+basering;
-ideal J = x10;
+GF;
-setring r;
+reduce(x2, GF);
-def Q = MalgrRing(ideal(0),1,f);
+MalgrFormPoly(x2);
-setring Q;
+MalgrFormPoly(x2, maxideal(4));
-def f = imap(r,f);
+MalgrFormPoly(x2, maxideal(2));
-setring r;
+MalgrFormPoly(x2, maxideal(5));
-quit;
+MalgrFormPoly(x2, maxideal(6));
-quit;
+GF;
-quit;
+reduce(x2,GF);
-c
+x2;
-?
+X(3) - f[3];
-n;
+X(3) - mappingf[3];
-n
+MalgrFormPoly(x2, maxideal(6));
-n
-n
-p f
-?
-b
-n
-n
-n
-n
-p s
-n
-p k
-n
-n
-n
-n
-p f
-n
-p f
-n
-n
-p f
-n
-n
-p wf
-n
-p h
-n
-p m
-n
-n
-n
-n
-n
-n
-n
-n
-n
-p wf
-n
-n
-n
-p wf;
-p s
-n
-n
-n
-p jf
-p wf
-p jf
-n
-n
-n
-n
-n
-n
-n
-n
-p NAef
-p mk
-n
-n
-n
-p mk
-p jf
-p wf
-p GOX
-p G0X
-p GOX
-n
-p GOX
-p GOY
-p print(GOY)
-?
-p GOY
-n
-n
-n
-n
-n
-nn
-n
-n
-n
-n
-n
-n
-n
-n
-p T
-n
-n
-n
-n
-n
-n
-n
-n
-n
-n
-n
-n
-n
-n
-n
-p T
-p VAX
-p R1
-?
-p basering
-p Raux
-n
-n
-n
-n
-n
-n
-p T
-n
-n
-ring r = 0,(x),ds;
-ideal f = x2+x4,x3;
-def Q = MalgrRing(ideal(0),1,f);
 LIB"AeCodPruebas.lib";
-def Q = MalgrRing(ideal(0),1,f);
+MalgrFormPoly(x2, maxideal(6));
-ring r = 0,(x,y),(dp,c);
+LIB"AeCodPruebas.lib";
-ring r = 0,(x,y),dp;
+MalgrFormPoly(x2, maxideal(6));
-ring R0 = changeord(list(list("(dp,c)",nvars(basering))));
+MalgrFormPoly(x2, ideal(x,y)^4);
-ring R0 = changeord(list(list("dp,c",nvars(basering))));
+LIB"AeCodPruebas.lib";
-ring R0 = changeord(list("(dp,c)",nvars(basering)));
+MalgrFormPoly(x2, ideal(x,y)^4);
-n
+print(_);
-n
+MalgrFormPoly(x3, ideal(x,y)^4);
-p T
+MalgrFormPoly(x3, ideal(x,y)^6);
-n
+MalgrFormPoly(x3, ideal(x,y)^7);
-p T
-n
-p T
-n
-p T
-ring r = 0,(x),ds;
-LIB"ring.lib";
-changeordTo(r,"(dp,c)");
-changeordTo(r,"dp");
-changeordTo(r,r"dp");
-ring r = 0,(x),(dp,c);
-basering
 ;
+GF;
+LIB"AeCodPruebas.lib";
+ring r = 0,(x,y),ds;
+ideal f = x,y2,y7+x2y;
+AeNormal(f);
+ideal f = x,y2,y5+x2y;
+AeNormal(f);
+ring r = 0,(t,x,y),ds;
+ideal f = t,x,y3+t2y,(x+y)^4+t3y;
+AeNormal(f);
+ideal f = t,x,y4+t3y,(x+y)^3+t3y;
+AeNormal(f);
+ideal f = t,x,y5+t4y,(x+y)^4+t3y;
+ideal f = t,x,y4+t3y,(x+y)^3+t2y;
+AeNormal(f);
+ideal f = t,x,y4+t3y,(x+y)^3+t2y;
+AeNormal(f);
+ideal f = t,x,y5+t4y,(x+y)^4+t3y;
+AeNormal(f);
+ideal f = t,x,y4+t3y,(x+y)^5+t4y;
+AeNormal(f);
+quit;
+ring r = 0,(x,y),ds;
+ideal f = x,y2,y3+x2y;
+AeNormal(f);
+LIB"AeCodPruebas.lib";
+AeNormal(f);
+LIB"AeCodPruebas.lib";
+AeNormal(f);
+ideal f = x+x4,y2,y3+x2y;
+AeNormal(f);
+AeNormal(f,maxideal(4));
+ideal f = x+x4,y2,y3+x2y;
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(4));
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(4));
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(4));
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(4));
+LIB"AeCodPruebas.lib";
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(4));
+f;
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(4));
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(4));
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(4));
+f;
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(4));
+AeNormal(f,maxideal(6));
+AeNormal(f,maxideal(10));
+AeNormal(f,maxideal(20));
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(10));
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(10));
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(10));
+dimX
+;
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(10));
+AeNormal(f,maxideal(10));
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(10));
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(10));
+AeNormal(f,maxideal(20));
+LIB"AeCodPruebas.lib";
+AeNormal(f,maxideal(20));
+f;
+ideal g = x,xy+y^6+y^9;
+AeNormal(g,maxideal(20));
+AeNormal(g,maxideal(10));
+AeNormal(g,maxideal(12));
+AeNormal(f,maxideal(12));
+AeNormal(f);
+AeNormal(g);
+AeNormal(g,maxideal(12));
+AeNormal(g,maxideal(20));
+AeNormal(g);
+AeNormal(g,maxideal(50));
+ring r = 0,(x,y),ds;
+ring R = 0,(X,Y),ds;
+setring r;
+map Rr = R,x2,y3;
+ideal J = maxideal(20);
+setring R;
+preimage(r,Rr,J);
+setring r;
+ideal J = maxideal(50);
+setring R;
+ideal J = maxideal(50);
+preimage(r,Rr,J);
+setring r;
+ideal J = maxideal(100);
+setring R;
+preimage(r,Rr,J);
+setring r;
+map f = R,x2+y3,y5+x7;
+J = maxideal(20);
+setring R;
+preimage(r,f,J);
+LIB"AeCodPruebas.lib";
+ring r = 0,(t,x,y),ds;
+ideal f = t,x,y3+t2y,(x+y)^4+t3y;
+AeNormal(f);
+ideal f = t,x,y3+t2y,(x+y)^4+t3y;
+f[4];
+LIB"AeCodPruebas.lib";
+ring r = 0,(t,x,y),ds;
+ideal f = t,x,y3+t2y,y4+(t3+x3)*y;
+AeNormal(f);
+ideal f = t,x,y3+t2y,(x+y)^4+t3y;
+f[4];
+f[4] = f[4] -x4;
+f;
+AeNormal(f);
+f[4]
+;
+f[4] = y3+(t3+x3)*y+xy3;
+AeNormal(f);
+f[4] = y3+(t3+x3)*y+xy3+x2y2;
+AeNormal(f);
+f[4] = y3+(t3+4x3)*y+4xy3+6x2y2;
+AeNormal(f);
+f;
+f[4] = y4+(t3+4x3)*y+4xy3+6x2y2;
+AeNormal(f);
+f[4] = y4+(t3+x3)*y+xy3+x2y2;
+AeNormal(f);
+f[4] = y4+t3y+x3y+xy3+x2y2;
+AeNormal(f);
+f[4] = y4+t3y+xy3+x2y2;
+AeNormal(f);f
+;
+f[4] = y4+t3y+xy3+x2y2+x3y;
+AeNormal(f);f
+;
+AeNormal(f);
+f[4] = y4+t3y+xy3+x2y2+x3y;
+AeNormal(f);
+f[4] = y4+t3y+xy3+x3y;
+AeNormal(f);
+f[4] = y4+t3y+xy3+x2y2+x3y;
+AeNormal(f);
+f[4] = y4+xy3+x2y2+x3y;
+AeNormal(f);
+f;
+AeNormal(f);
+f;
+f[4] = y4+x3y;
+AeNormal(f);
+f[4] = y4+x3y+xy3;
+AeNormal(f);
+f[4] = y4+x2y2+xy3;
+AeNormal(f);
+f[4] = y4+x3y+x2y2;
+AeNormal(f);f
+f;
+f = t,x,y4+t3y,y5+xy3+x2y3+x3y2+xy4;
+size(AeNormal(f));
+f = t,x,y4+t3y,y5+xy3+x2y3+x3y2+xy4+t4y;
+size(AeNormal(f));
+f = t,x,y4+t3y,(x+y)^5;
+size(AeNormal(f));
+f = t,x,y4+t3y,(x+y)^5+t4y;
+size(AeNormal(f));
+f[4];
+f[4]=x5+t4y+x4y+x3y2+x2y3+xy4+y5;
+size(AeNormal(f));
+f[4]=t4y+x4y+x3y2+x2y3+xy4+y5;
+size(AeNormal(f));
+f[4]=t4y+x3y2+x2y3+xy4+y5;
+size(AeNormal(f));
+f[4]=t4y+x4y+x3y2+x2y3+xy4+y5;
+size(AeNormal(f));
+f[4]=t4y+x4y+x3y2+x2y3+y5;
+size(AeNormal(f));
+f[4]=x4y+x3y2+x2y3+y5;
+size(AeNormal(f));
+f = t,x,y4+t3y,(x+y)^3,t2y;
+size(AeNormal(f));
+f = t,x,y4+t3y,(x+y)^3+t2y;
+size(AeNormal(f));
+f[4];
+f[4] = t2y+x2t+xy2+y3;
+size(AeNormal(f));
+f[4] = t2y+x2y+xy2+y3;
+size(AeNormal(f));
+f[4] = t2y+3x2y+3xy2+y3;
+size(AeNormal(f));
+f[4] =3x2y+3xy2+y3;
+size(AeNormal(f));
+f[4] = t3y + 3x2y+3xy2+y3;
+size(AeNormal(f));
+f[4] = t5y + 3x2y+3xy2+y3;
+size(AeNormal(f));
+f[4] = t10y + 3x2y+3xy2+y3;
+size(AeNormal(f));
+f[4] = 3y + 3x2y+3xy2+y3;
+size(AeNormal(f));
+f;
+size(AeNormal(f));
+f[4] =  + 3x2y+3xy2+y3;
+size(AeNormal(f));
+f[4] = y;
+size(AeNormal(f));
+size(AeNormal(f));
+f = t,x,y3+t2y,(x+y)^4;
+AeNormal(f);
+f = t,x,y3+t2y,(x+y)^4+t3y;
+AeNormal(f);
+f[4];
+f[4] = x4+t3y+4x3y+6x2y2+4xy3+y4
+;
+AeNormal(f);
+size(AeNormal(f));
+f[4] = x4+t3y+4x3y+6x2y2+4xy3+y4;
+size(AeNormal(f));
+f[4] = t3y+4x3y+6x2y2+4xy3+y4;
+size(AeNormal(f));
+f[4] = t3y+x3y+x2y2+xy3+y4;
+size(AeNormal(f));
+f[4] = x3y+x2y2+xy3+y4;
+size(AeNormal(f));
+f[4] = t3y+4x3y+6x2y2+4xy3+y4;
+size(AeNormal(f));
+f[4] = 4x3y+6x2y2+4xy3+y4;
+size(AeNormal(f));
+f[4] = x3y+x2y2+xy3+y4;
+size(AeNormal(f));
+f[4] = x2y2+xy3+y4;
+size(AeNormal(f));
+f[4] = x3y+x2y2+y4;
+size(AeNormal(f));
+f[3] = y4+t3y;
+size(AeNormal(f));
+f[4] = (x+y)^5+t4y;
+size(AeNormal(f));
+f[4];
+f[4] = x4y+x3y2+x2y3+y5;
+size(AeNormal(f));
+f[4]^2;
+f[4] = x4y+x3y2+x2y3+y5;
+size(AeNormal(f));
+f[4] = x4y+x3y2+y5;
+size(AeNormal(f));
+f[4] = x4y+2x3y2+y5;
+size(AeNormal(f));
+f[4] = x4y+3x3y2+y5;
+size(AeNormal(f));
+f[4] = 5x4y+3x3y2+y5;
+size(AeNormal(f));
+f;
+f = t,x,(x+y)^4+t2y,y3+t2y;
+AeNormal(f);
+f:
+;
+f = t,x,(x+y)^4+t3y,y3+t2y;
+AeNormal(f);
+f = t,x,(x+y)^4+t2y,y3+t2y;
+AeNormal(f);
+f = t,x,(x+y)^5+t2y,y3+t2y;
+AeNormal(f);
+f = t,x,(x+y)^5+t2y,y4+t2y;
+AeNormal(f);
+f;
+f = t,x,(x+y)^4+t3y,y3+t2y;
+AeNormal(f);
+f = t,x,(x+y)^4+t3y,y3;
+AeNormal(f);
+f = t,x,(x+y)^4+t3y,y3+t2y;
+f = t,x,(x+y)^4+t3y,y3+t2y;
+AeNormal(f);
+f[3];
+f = t,x,(x+y)^4+t3y,y3+t2y;
+f[3];
+f[3] = x4+x3y+x2y2+xy3+y4;
+AeNormal(f);
+f;
+LIB"AeCodPruebas.lib";
+ring r = 0,(t,x,y),ds;
+map f = t,x,y3+t2y,y4+x3y;
+ideal f = t,x,y3+t2y,y4+x3y;
+size(AeNormal(f));
+ideal f = t,x,y5+t4y,y6+x5y;
+size(AeNormal(f));
+ideal f = t,x,y5+t4y,y6+(x5+t4)*y;
+size(AeNormal(f));
+ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
+size(AeNormal(f));
+ideal f = t,x,y3+t2y,xy3+x2y2+x3y;
+size(AeNormal(f));
+ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
+size(AeNormal(f));
+ideal f = t,x,y3+t2y,y4+xy3+x3y;
+size(AeNormal(f));
+ideal f = t,x,y3+t2y,y4+xy3-x3y;
+size(AeNormal(f));
+ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
+ideal f = t,x,y3+t2y,y4+x2y2+x3y;
+ideal f = t,x,y3+t2y,y4+xy3+x2y2+x3y;
+ideal f = t,x,y3+t2y,y4+x2y2+x3y;
+size(AeNormal(f));
+ideal f = t,x,y4+t2y,y5+x2y2+x3y;
+size(AeNormal(f));
+ideal f = t,x,y4+t3y,y5+x4y+x3y2;
+size(AeNormal(f));
+ideal f = t,x,y4+t3y,y5+x4y+x3y2+x2y3;
+size(AeNormal(f));
+quit;

AeCodPruebas.lib

@@ -123,12 +123,15 @@ proc AeNormal(ideal f, list #)
    int n = nvars(basering);
    int p = ncols(f);
 
+
    int s = size(#);
 
+   /*
    if (s > 0)
    {
       int k = TargetIdeal(f,std(#[1]));
    }
+   */
 
    def Raux = MalgrRing(ideal(0),n,ideal(f[1..n]));
 
@@ -141,6 +144,7 @@ proc AeNormal(ideal f, list #)
    execute("def f = imap("+RName+",f)");
    execute("def jf = imap("+RName+",jf)");
 
+   
    if (s > 0)
    {
       execute("def # = imap("+RName+",#)");
@@ -161,10 +165,12 @@ proc AeNormal(ideal f, list #)
       }
    }
 
+   /*
    if (s>0)
    {
       wf = wf + freemodule(p)*(f^k);
    }
+   */
 
    /*
    if (size(#)>0)
@@ -250,6 +256,8 @@ proc TargetIdeal(ideal f, ideal J)
 
    ideal auxf = 1;
    
+   J = std(J);
+
    while (done == 0)
    {
       auxf = auxf*f;
@@ -287,14 +295,19 @@ proc GenerateOYModule(matrix GOX, matrix GOY, list #)
    int i;
    int j;
 
+   int s = size(#);
+   int k = 0;
+   if (s > 0)
+   {
+      k = TargetIdeal(mappingf, #[1]);
+   }
+
    int m = ncols(Gens);
 
    int ny = ncols(GOY);
    int nx = ncols(GOX);
    int a = nrows(GOY);
 
-   
-
    module M = 0;           // This will be module with the same generators but over O_n
 
    matrix col[a][1] = 0;   // Auxiliar variable to store the particular vector to be transformed at each step
@@ -327,6 +340,11 @@ proc GenerateOYModule(matrix GOX, matrix GOY, list #)
       }
    }
 
+   if (s > 0)
+   {
+      M = M + (X(1..dimX)^k)*freemodule(m*a);
+   }
+
    return(M);
 }
 
@@ -403,8 +421,11 @@ proc MalgrRing(ideal J, int n, ideal f)
 
    ideal mappingf = f;
    export(mappingf);
+
    int dimX = n;
+   option(noredefine);
    export(dimX);
+   option(redefine);
    
    return(R2);
 }

checklist.md

@@ -66,3 +66,5 @@ If $f(x)=x + x^3$, there is no solution for (3) with polynomial unit.
 - In all rings generated: change ordering to (dp/ds,c/C)
 
 - Change the use of the maximal ideal so that it works modulo a power in the target already.
+
+- Do a baby example of why the implementation of the modulo power in the target is not working (try crosscap or Hiroshi example).