int iszero ( int n, dcmplx a[] )
{
int i;
for ( i=0; i<=n; i++ )
if (! equal_dcmplx(a[i], create1(0), tol) )
return 0;
return 1;
}
int degree ( dcmplx *a, int d )
{
int i;
for ( i=d; i>0; i-- )
if ( !equal_dcmplx( a[i], create1(0), tol ))
break;
return i;
}
void manual_test ( int n, int m, int l )
{
double eps = 1.0e-12;
double tol = 1.0e-8;
double mul_tol = 1.0e-3;
dcmplx aa[n+1], bb[m+1], c[l+1], a[n+l+1], *dcmplx_a, b[m+l+1], *dcmplx_b, ra[n+l], rb[m+l], rc[l];
int i, j, c_num, bug, dk, dl, dgcd, k1, k2, dc_gcd;
dcmplx **gcd_coeff;
dcmplx *t1, *t2, *c_gcd;
int dbd, dad, mult[l];
printf("please input the polynomial aa\n");
for(i=0; i<=n; i++)
read_dcmplx( &(aa[i]));
printf("please input the polynomial bb\n");
for(i=0; i<=m; i++)
read_dcmplx(&(bb[i]));
printf("please input the polynomial c, (the leading coefficient must be one!)\n");
for(i=0; i<=l; i++)
read_dcmplx(&(c[i]));
for(i=0; i<=n+l; i++)
a[i]=create1(0.0);
for(i=0; i<=n; i++)
for(j=0; j<=l; j++)
a[i+j]=add_dcmplx(a[i+j], mul_dcmplx(aa[i], c[j]));
for(i=0; i<=m+l; i++)
b[i]=create1(0.0);
for(i=0; i<=m; i++)
for(j=0; j<=l; j++)
b[i+j]=add_dcmplx(b[i+j], mul_dcmplx(bb[i], c[j]));
gcd( n+l+1, a, m+l+1, b, &c_num, ra, rb );
printf("the roots number of the given common diviser is: %d \n", l);
multiple_roots(l+1, c, eps, 10*l, rc, mul_tol, mult);
printf("the root of the gcd is:\n");
for(i=0; i<l; i++)
writeln_dcmplx(rc[i]);
printf("the roots number of the calculated common diviser is: %d \n", c_num);
if(l!= c_num)
{
printf("Bug!!\n");
exit(1);
}
for(i=0; i<l; i++)
{
bug=1;
for(j=0; j<l; j++)
{
if(equal_dcmplx(rc[i], ra[j], tol))
bug=0;
}
if( bug==1 )
{
printf(" Bug!!\n");
exit(1);
}
}
printf("the gcd is correct !\n");
/* now begin to test extended gcd method */
gcd_coeff=ExtPolyGcd( n+l+1, a, m+l+1, b, &dgcd, &dk, &dl, &dbd, &dad);
Print_Poly(dl, gcd_coeff[1]);
printf("a is:\n");
Print_Poly(n+l, a);
dcmplx_a=(dcmplx*) calloc(n+l+1, sizeof(dcmplx));
/* for(i=0; i<=n+l; i++)
dcmplx_a[i]=a[i]; */
t1=mul_poly( dk, gcd_coeff[0], n+l, a, &k1 );
t2=mul_poly( dl, gcd_coeff[1], m+l, b, &k2 );
/*
printf("t1 is:\n");
for(i=0; i<=k1; i++)
writeln_dcmplx(t1[i]);
printf("t2 is:\n");
printf("dl=%d\n", dl);
printf("m+l=%d\n", m+l);
for(i=0; i<=k2; i++)
writeln_dcmplx(t2[i]);
*/
printf("\n");
printf("k is:\n");
for(i=0; i<=dk; i++)
writeln_dcmplx(gcd_coeff[0][i]);
printf("l is:\n");
for(i=0; i<=dl; i++)
writeln_dcmplx(gcd_coeff[1][i]);
printf("\n");
c_gcd=add_poly( k1, t1, k2, t2, &dc_gcd);
printf("the given polynomial a is:\n");
for(i=0; i<=n+l; i++)
writeln_dcmplx(a[i]);
printf("a's roots are:\n");
for(i=0; i<n+l; i++)
writeln_dcmplx(ra[i]);
printf("\n");
printf("the given polynomial b is:\n");
for(i=0; i<=m+l; i++)
writeln_dcmplx(b[i]);
printf("b's roots are:\n");
for(i=0; i<m+l; i++)
writeln_dcmplx(rb[i]);
printf("\n");
printf("the given gcd polynomial is:\n");
for(i=0; i<=l; i++)
writeln_dcmplx(c[i]);
printf("\n");
if(l!= dc_gcd)
{
printf("Bug!! the given gcd is different with the gcd method result.(0 is special case).\n");
}
printf("the calculated gcd polynomial is:\n");
for(i=0; i<=dc_gcd; i++)
writeln_dcmplx(c_gcd[i]);
printf("\n");
printf("the gcd from common roots method is:\n");
for(i=0; i<=dgcd; i++)
writeln_dcmplx(gcd_coeff[2][i]);
printf("\n");
free(t1); free(t2);
free(c_gcd);
free(gcd_coeff[0]);
free(gcd_coeff[1]);
free(gcd_coeff[2]);
free(gcd_coeff[3]);
free(gcd_coeff[4]);
free(gcd_coeff);
}
void random_test ( int n, int m, int l )
{
double eps = 1.0e-12;
double tol = 1.0e-8;
double mul_tol = 1.0e-3;
dcmplx aa[n+1], bb[m+1], c[l+1], a[n+l+1], b[m+l+1], ra[n+l], rb[m+l], rc[l];
int i, j, c_num, bug, dk, dl, dgcd, k1, k2, dc_gcd;
dcmplx **gcd_coeff;
dcmplx *t1, *t2, *c_gcd;
dcmplx near;
double error=1.0;
int dbd, dad, mult[l];
srand(time(NULL));
for(i=0; i<=n; i++)
aa[i] = random_dcmplx1();
for(i=0; i<=m; i++)
bb[i] = random_dcmplx1();
c[l]=create1(1.0);
for(i=0; i<l; i++)
c[i] = random_dcmplx1();
for(i=0; i<=n+l; i++)
a[i]=create1(0.0);
for(i=0; i<=n; i++)
for(j=0; j<=l; j++)
a[i+j]=add_dcmplx(a[i+j], mul_dcmplx(aa[i], c[j]));
for(i=0; i<=m+l; i++)
b[i]=create1(0.0);
for(i=0; i<=m; i++)
for(j=0; j<=l; j++)
b[i+j]=add_dcmplx(b[i+j], mul_dcmplx(bb[i], c[j]));
gcd( n+l+1, a, m+l+1, b, &c_num, ra, rb );
printf("the roots number of the given common diviser is: %d \n", l);
multiple_roots(l+1, c, eps, 10*l, rc, mul_tol, mult);
/*
printf(" the root of the gcd is:\n");
for(i=0; i<l; i++)
writeln_dcmplx(rc[i]);
printf("\n");
*/
printf("the roots number of the calculated common diviser is: %d \n", c_num);
if(l!= c_num)
{
printf("Bug!!\n");
printf("a is:\n");
for(i=0; i<=n+l; i++)
writeln_dcmplx(a[i]);
printf("b is:\n");
for(i=0; i<=m+l; i++)
writeln_dcmplx(b[i]);
printf("a's roots are:\n");
for(i=0; i<n+l; i++)
writeln_dcmplx(ra[i]);
printf("b's roots are:\n");
for(i=0; i<m+l; i++)
writeln_dcmplx(rb[i]);
printf("fail reason: gcd roots number is not correct.\n");
exit(1);
}
for(i=0; i<l; i++)
{
bug=1;
for(j=0; j<l; j++)
{
if(equal_dcmplx(rc[i], ra[j], tol))
bug=0;
if(dcabs(sub_dcmplx(rc[i], ra[j]))<error)
{
error=dcabs(sub_dcmplx(rc[i], ra[j]));
near=ra[j];
}
}
if( bug==1 )
{
printf("a is:\n");
for(i=0; i<=n+l; i++)
writeln_dcmplx(a[i]);
printf("b is:\n");
for(i=0; i<=m+l; i++)
writeln_dcmplx(b[i]);
printf("a's roots are:\n");
for(i=0; i<n+l; i++)
writeln_dcmplx(ra[i]);
printf("b's roots are:\n");
for(i=0; i<m+l; i++)
writeln_dcmplx(rb[i]);
printf("the given common root is:");
writeln_dcmplx(rc[i]);
printf("the nearest one to the given common roots is:");
writeln_dcmplx(near);
printf("the difference is:%lf\n", error);
printf("fail reason: the common root is not the given gcd root\n");
printf(" Bug!!\n");
exit(1);
}
}
printf("the result is correct !\n");
/* now begin to test extended gcd method */
gcd_coeff=ExtPolyGcd( n+l+1, a, m+l+1, b, &dgcd, &dk, &dl, &dbd, &dad);
t1=mul_poly( dk, gcd_coeff[0], n+l, a, &k1 );
t2=mul_poly( dl, gcd_coeff[1], m+l, b, &k2 );
c_gcd=add_poly( k1, t1, k2, t2, &dc_gcd);
/*
printf("the given polynomial a is:\n");
for(i=0; i<=n+l; i++)
writeln_dcmplx(a[i]);
printf("\n");
printf("the given polynomial b is:\n");
for(i=0; i<=m+l; i++)
writeln_dcmplx(b[i]);
printf("\n");
*/
printf("the given gcd polynomial is:\n");
for(i=0; i<=l; i++)
writeln_dcmplx(c[i]);
printf("\n");
printf("the calculated gcd polynomial is:\n");
for(i=0; i<=dc_gcd; i++)
writeln_dcmplx(c_gcd[i]);
printf("\n");
printf("the gcd got from common roots is:\n");
for(i=0; i<=dgcd; i++)
writeln_dcmplx(gcd_coeff[2][i]);
printf("\n");
if(l!= dc_gcd)
{
printf("Bug!!\n");
printf("a is:\n");
for(i=0; i<=n+l; i++)
writeln_dcmplx(a[i]);
printf("b is:\n");
for(i=0; i<=m+l; i++)
writeln_dcmplx(b[i]);
printf("a's roots are:\n");
for(i=0; i<n+l; i++)
writeln_dcmplx(ra[i]);
printf("b's roots are:\n");
for(i=0; i<m+l; i++)
writeln_dcmplx(rb[i]);
exit(1);
}
if(l!=dgcd)
{
printf("Bug!! (get_poly)\n");
exit(1);
}
for(i=0; i<=l; i++)
{
bug=1;
for(j=0; j<=l; j++)
{
if(equal_dcmplx(c[i], c_gcd[j], tol))
bug=0;
}
if( bug==1 )
{
printf(" Bug!!\n");
exit(1);
}
}
for(i=0; i<=l; i++)
{
bug=1;
for(j=0; j<=l; j++)
{
if(equal_dcmplx(c[i], gcd_coeff[2][j], tol))
bug=0;
}
if( bug==1 )
{
printf(" Bug!!(get_poly)\n");
exit(1);
}
}
printf(" the extended gcd result is correct !\n");
free(t1); free(t2);
free(c_gcd);
free(gcd_coeff[0]);
free(gcd_coeff[1]);
free(gcd_coeff[2]);
free(gcd_coeff);
}
