Z3_ast Z3_API Z3_algebraic_root(Z3_context c, Z3_ast a, unsigned k) {
Z3_TRY;
LOG_Z3_algebraic_root(c, a, k);
RESET_ERROR_CODE();
CHECK_IS_ALGEBRAIC_X(a, 0);
if (k % 2 == 0) {
if ((is_rational(c, a) && get_rational(c, a).is_neg()) ||
(!is_rational(c, a) && am(c).is_neg(get_irrational(c, a)))) {
SET_ERROR_CODE(Z3_INVALID_ARG);
RETURN_Z3(0);
}
}
algebraic_numbers::manager & _am = am(c);
scoped_anum _r(_am);
if (is_rational(c, a)) {
scoped_anum av(_am);
_am.set(av, get_rational(c, a).to_mpq());
_am.root(av, k, _r);
}
else {
algebraic_numbers::anum const & av = get_irrational(c, a);
_am.root(av, k, _r);
}
expr * r = au(c).mk_numeral(_r, false);
mk_c(c)->save_ast_trail(r);
RETURN_Z3(of_ast(r));
Z3_CATCH_RETURN(0);
}
Z3_ast Z3_API Z3_algebraic_div(Z3_context c, Z3_ast a, Z3_ast b) {
Z3_TRY;
LOG_Z3_algebraic_div(c, a, b);
RESET_ERROR_CODE();
CHECK_IS_ALGEBRAIC_X(a, 0);
CHECK_IS_ALGEBRAIC_X(b, 0);
if ((is_rational(c, b) && get_rational(c, b).is_zero()) ||
(!is_rational(c, b) && am(c).is_zero(get_irrational(c, b)))) {
SET_ERROR_CODE(Z3_INVALID_ARG);
RETURN_Z3(0);
}
BIN_OP(/,div);
Z3_CATCH_RETURN(0);
}
static bool to_anum_vector(Z3_context c, unsigned n, Z3_ast a[], scoped_anum_vector & as) {
algebraic_numbers::manager & _am = am(c);
scoped_anum tmp(_am);
for (unsigned i = 0; i < n; i++) {
if (is_rational(c, a[i])) {
_am.set(tmp, get_rational(c, a[i]).to_mpq());
as.push_back(tmp);
}
else if (is_irrational(c, a[i])) {
as.push_back(get_irrational(c, a[i]));
}
else {
return false;
}
}
return true;
}
int Z3_API Z3_algebraic_sign(Z3_context c, Z3_ast a) {
Z3_TRY;
LOG_Z3_algebraic_sign(c, a);
RESET_ERROR_CODE();
CHECK_IS_ALGEBRAIC(a, 0);
if (is_rational(c, a)) {
rational v = get_rational(c, a);
if (v.is_pos()) return 1;
else if (v.is_neg()) return -1;
else return 0;
}
else {
algebraic_numbers::anum const & v = get_irrational(c, a);
if (am(c).is_pos(v)) return 1;
else if (am(c).is_neg(v)) return -1;
else return 0;
}
Z3_CATCH_RETURN(0);
}
matrix3_p
koeffizienten_gamma_1dim(int grad) {
int a, b, k, n, q;
fepc_real_t ***g;
matrix3_p back, matrix;
fepc_real_t temp, wurzel, rat, reell;
fepc_real_t *A, *B;
ASSERT(grad >= 0);
A = (fepc_real_t*) malloc(sizeof(fepc_real_t)*(3*grad+1));
ASSERT(A != NULL);
B = (fepc_real_t*) malloc(sizeof(fepc_real_t)*(3*grad+1));
ASSERT(B != NULL);
for (n=0;n<=3*grad;n++) {
A[n] = sqrt(2*n+3)*sqrt(2*n+1)/(fepc_real_t)(n+1);
}
B[0] = 0.0;
for (n=1;n<=3*grad;n++) {
B[n] = (sqrt(2*n+3)/sqrt(2*n-1)) * ( (fepc_real_t)n/(fepc_real_t)(n+1) );
}
matrix = matrix3_new(3*grad+1,3*grad+1,3*grad+1);
g = matrix->a;
for(b=0;b<=3*grad;b++) {
for(k=0;k<=3*grad;k++) {
g[0][b][k] = 0.0;
}
}
for (k=1;k<=3*grad;k++) {
temp = 2.0*sqrt( (2.0*k-1)*(2.0*k+1) );
g[0][k-1][k] = pow(-1,k)/temp;
}
for (k=1;k<=3*grad;k++) {
g[0][k][k-1] = g[0][k-1][k];
}
g[0][0][0] = 1.0/2.0;
for(q=1;q<=3*grad;q++) {
for(a=1;a<=q;a++) {
for(b=0;b<=(q-a);b++) {
k = q-a-b;
if ( (a>b+k+1)||(b>a+k+1)||(k>a+b+1) ) {
g[a][b][k] = 0.0;
}
if (b==0) {
g[a][0][k] = pow(-1,a) * g[0][a][k];
}
if (k==0) {
g[a][b][0] = pow(-1,a) * g[0][b][a];
}
if ( ((a>b+k+1)||(b>a+k+1)||(k>a+b+1)||(b==0)||(k==0)) == 0) {
temp = A[a-1]*(g[a-1][b][k+1]/A[k] + g[a-1][b+1][k]/A[b] + g[a-1][b][k]);
if (k>0)
temp = temp + A[a-1]*B[k]*g[a-1][b][k-1]/A[k];
if (b>0)
temp = temp + A[a-1]*B[b]*g[a-1][b-1][k]/A[b];
if (a>1)
temp = temp - B[a-1]*g[a-2][b][k];
g[a][b][k] = temp;
/*Korrektur der Werte (siehe Dokumentation)*/
wurzel = sqrt( (2*a+1)*(2*b+1)*(2*k+1) );
reell = temp;
rat = reell*wurzel;
rat = get_rational(rat,1e-14,10000);
reell = rat/wurzel;
g[a][b][k] = reell;
}
}
}
}
back = matrix3_new(grad+1,grad+1,grad+1);
for(a=0;a<=grad;a++) {
for(b=0;b<=grad;b++) {
for(k=0;k<=grad;k++) {
back->a[a][b][k] = matrix->a[a][b][k];
}
}
}
free(A);
free(B);
matrix3_del(matrix);
return back;
}
matrix_p
koeffizienten_xi_1dim(int grad) {
matrix_p back, matrix;
int q, m, n;
fepc_real_t **x;
fepc_real_t *a, *b;
fepc_real_t rat, reell, faktor, temp;
ASSERT(grad >= 0);
a = (fepc_real_t*) malloc(sizeof(fepc_real_t) * (2*grad + 1) );
ASSERT(a != NULL);
b = (fepc_real_t*) malloc(sizeof(fepc_real_t) * (2*grad + 1) );
ASSERT(b != NULL);
matrix = matrix_new( 2*grad+1, 2*grad+1 );
x = matrix->a;
for (n=0;n<=2*grad;n++) {
a[n] = sqrt(2*n+3)*sqrt(2*n+1)/(fepc_real_t)(n+1);
}
b[0] = 0.0;
for (n=1;n<=2*grad;n++) {
b[n] = (sqrt(2*n+3)/sqrt(2*n-1)) * ( (fepc_real_t)n/(fepc_real_t)(n+1) );
}
x[0][0] = 1./sqrt(2);
for (q=1;q<=2*grad;q++) {
for (n=0;n<=q;n++) {
m = q-n;
if (n<m) {
x[n][m] = 0.0;
}
else {
temp = a[n-1]/2.0*(x[n-1][m+1]/a[m]+x[n-1][m]);
if (m>0) {
temp = temp + a[n-1]/2.0*b[m]/a[m]*x[n-1][m-1];
}
if (n>=2) {
temp = temp - b[n-1]*x[n-2][m];
}
/*Korrektur der Werte (siehe Dokumentation)*/
faktor = pow(2,((fepc_real_t)n+0.5))/sqrt( (2*n+1)*(2*m+1) );
reell = temp;
rat = reell*faktor;
rat = get_rational(rat,1e-14,10000);
reell = rat/faktor;
x[n][m] = reell;
}
}
}
back = matrix_new(grad+1,grad+1);
for (m=0;m<=grad;m++) {
for (n=0;n<=grad;n++) {
back->a[m][n] = matrix->a[m][n];
}
}
free(a);
free(b);
matrix_del(matrix);
return back;
}
